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1MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
2 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
3MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
4 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
5MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Mathematics: Intermediate Phase
Preamble
The Multi-grade toolkit for Mathematics is designed to assist teachers in multi-grade schools to teach
effectively and cover the curriculum adequately. In the past, teachers in the multi-grade schools
were expected to use the mono-grade curriculum and adapt it to meet the needs and demands of
learners in a multi-grade class. Some teachers did not have the requisite skills to carry out this
demanding task and it resulted in content being either too scantly covered or completely ignored, thus
compromising the content knowledge and skills that learners needed to acquire at all levels of
schooling. To obviate such situations in our multi-grade schools and ensure that learners in the multi-
grade schools receive quality education, the Department of Basic Education developed a multi-grade
toolkit for teachers.
The toolkit compromises of the following documents:
A generic manual which provides literature about multi-grade teaching, methodologies,
management, etc.
A Multi-grade Annual Teaching Plan (MATP) informed by and aligned to the Curriculum and
Assessment Policy Statement (CAPS) to support teachers with lesson planning;
Exemplar lesson plans to assist teachers in developing, managing and adapting lessons to
suit their own individual context. The activities in the lesson plans were taken from the
o DBE workbooks for Grades 4 to 9 (the same worksheets numbers are used in the
lesson plans).
o Sasol-Inzalo workbooks for Grades 7 – 9 (chapters were cited).
More activities can be added by the individual teacher using a book of his or her own choice.
Exemplar Assessment tasks to assist teachers in designing their own individual tasks to suit
their own specific context.
The MATP was developed and designed according to topics that could lend themselves for robust
discussion in the Mathematics class without compromising the content thereof. Each topic was
carefully chosen and linked to each other in each grade. A common thread was carefully identified
across the topics before they were aligned together, for example the topic Numeric and Geometric Patterns cuts across all the grades in the Intermediate Phase. A teacher can introduce a concept to all the learners and then pitch to different levels as dictated to by CAPS. .
Through the “Whole Class” teaching methodology, the teacher can easily introduce each topic and
engage learners in discussion before embarking on teaching specific grades in a multi-grade class
through small group teaching.
6 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MU
LTI-G
RA
DE
AN
NU
AL
TEA
CH
ING
PLA
N
7MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
T ER
M 1
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
5
Who
le n
umbe
rs:
Cou
ntin
g
O
rder
, com
pare
and
repr
esen
t num
bers
;
O
dd a
nd e
ven
num
bers
;
Pl
ace
valu
e;
Mul
tiple
s ;
Rou
ndin
g of
f;
Who
le n
umbe
rs:
Cou
ntin
g
O
rder
, com
pare
and
repr
esen
t num
bers
;
O
dd a
nd e
ven
num
bers
;
Pl
ace
valu
e;
M
ultip
les;
Fact
ors;
Rou
ndin
g of
f;
Who
le n
umbe
rs:
Cou
ntin
g
O
rder
, com
pare
and
repr
esen
t num
bers
;
Pr
ime
num
bers
;
Pl
ace
valu
e;
M
ultip
les
;
Fact
ors;
Rou
ndin
g of
f 1
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
6 N
umbe
r sen
tenc
es
Num
ber s
ente
nces
N
umbe
r sen
tenc
es
7 Ad
ditio
n an
d su
btra
ctio
n of
who
le n
umbe
rs
Addi
tion
and
subt
ract
ion
of w
hole
num
bers
Ad
ditio
n an
d su
btra
ctio
n of
who
le n
umbe
rs
1 In
form
al a
sses
smen
t In
form
al a
sses
smen
t In
form
al a
sses
smen
t
3
Num
eric
and
geo
met
ric p
atte
rns
In
vest
igat
e an
d ex
tend
pat
tern
s
Inpu
t and
out
put v
alue
s
Equi
vale
nt fo
rms
Num
eric
and
geo
met
ric p
atte
rns
In
vest
igat
e an
d ex
tend
pat
tern
s
Inpu
t and
out
put v
alue
s
Equi
vale
nt fo
rms
Num
eric
and
geo
met
ric p
atte
rns
In
vest
igat
e an
d ex
tend
pat
tern
s
Inpu
t and
out
put v
alue
s
Equi
vale
nt fo
rms
9 M
ultip
licat
ion
and
divi
sion
of w
hole
nu
mbe
rs
Mul
tiplic
atio
n an
d di
visi
on o
f who
le
num
bers
M
ultip
licat
ion
and
divi
sion
of w
hole
nu
mbe
rs
6
Tim
e
M
easu
ring
inst
rum
ents
Rea
ding
tim
e
Cal
cula
tion
and
prob
lem
sol
ving
invo
lvin
g tim
e
His
tory
of t
ime
Tim
e an
d te
mpe
ratu
re
M
easu
ring
inst
rum
ents
Rea
ding
tim
e an
d te
mpe
ratu
re
C
alcu
latio
n an
d pr
oble
m s
olvi
ng in
volv
ing
time
and
tem
pera
ture
His
tory
of t
ime
Tim
e an
d te
mpe
ratu
re
M
easu
ring
inst
rum
ents
Rea
ding
tim
e an
d te
mpe
ratu
re
C
alcu
latio
n an
d pr
oble
m s
olvi
ng in
volv
ing
time
and
tem
pera
ture
His
tory
of t
ime
IMPO
RTAN
T NO
TE: A
lway
s co
nsul
t the
CAP
S to
est
ablis
h a
deta
iled
prog
ress
ion
acro
ss th
e gr
ades
and
the
dept
hs w
ithin
the
grad
e re
gard
ing
topi
cs, c
once
pts
and
skills
.
8 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
6
Dat
a ha
ndlin
g
Col
lect
ing
and
orga
nizi
ng d
ata
R
epre
sent
ing
data
Anal
ysin
g, in
terp
retin
g an
d re
porti
ng d
ata
Pr
obab
ility
Dat
a ha
ndlin
g
Col
lect
ing
and
orga
nizi
ng d
ata
R
epre
sent
ing
data
Anal
ysin
g, in
terp
retin
g an
d re
porti
ng d
ata
Pr
obab
ility
Dat
a ha
ndlin
g
Col
lect
ing
and
orga
nizi
ng d
ata
R
epre
sent
ing
data
Anal
ysin
g, in
terp
retin
g an
d re
porti
ng d
ata
Pr
obab
ility
1
Form
al S
BA
Task
: Ass
ignm
ent
Form
al S
BA
Task
: Ass
ignm
ent
Form
al S
BA
Task
: Ass
ignm
ent
6
2 - D
sha
pes,
R
ecog
nize
, vis
ualiz
e an
d na
me
2-D
sha
pes
in
re
gula
r and
irre
gula
r pol
ygon
s –
trian
gles
, sq
uare
s, re
ctan
gles
, oth
er q
uadr
ilate
rals
, pe
ntag
ons,
hex
agon
s an
d ci
rcle
s C
hara
cter
istic
s of
sha
pes
st
raig
ht s
ides
curv
ed s
ides
num
ber o
f sid
es
Dra
w 2
-D s
hape
s on
grid
pap
er
2 -
D s
hape
s,
Rec
ogni
ze, v
isua
lize
and
nam
e 2-
D s
hape
s in
regu
lar a
nd ir
regu
lar p
olyg
ons
– tri
angl
es,
squa
res,
rect
angl
es, o
ther
qua
drila
tera
ls,
pent
agon
s, h
exag
ons,
hep
tago
ns a
nd
circ
les
si
mila
ritie
s an
d di
ffere
nces
bet
wee
n sq
uare
s an
d re
ctan
gles
C
hara
cter
istic
s of
sha
pes
st
raig
ht s
ides
curv
ed s
ides
num
ber o
f sid
es
an
gles
in s
hape
D
raw
2-D
sha
pes
on g
rid p
aper
In
volv
ing
angl
es
• Rec
ogni
ze a
nd d
escr
ibe
angl
es in
2-D
sh
apes
2 - D
sha
pes,
R
ecog
nize
, vis
ualiz
e an
d na
me
2-D
sha
pes
in
re
gula
r and
irre
gula
r pol
ygon
s - t
riang
les,
sq
uare
s, re
ctan
gles
, par
alle
logr
ams,
oth
er
quad
rilat
eral
s, p
enta
gons
, hex
agon
s,
hept
agon
s, o
ctag
ons
si
mila
ritie
s an
d di
ffere
nces
bet
wee
n re
ctan
gles
and
par
alle
logr
ams
Cha
ract
eris
tics
of s
hape
s
num
ber o
f sid
es
le
ngth
s in
sid
es
si
zes
of a
ngle
s D
raw
2-D
sha
pes
on g
rid p
aper
In
volv
ing
angl
es
• Rec
ogni
ze a
nd d
escr
ibe
angl
es in
2-D
sh
apes
1
Form
al S
BA
Task
: Tes
t Fo
rmal
SB
A Ta
sk: T
est
Form
al S
BA
Task
: Tes
t 4
Rev
isio
n
Rev
isio
n
Rev
isio
n
56
IM
PORT
ANT
NOTE
: Alw
ays
cons
ult t
he C
APS
to e
stab
lish
a de
taile
d pr
ogre
ssio
n ac
ross
the
grad
es a
nd th
e de
pths
with
in th
e gr
ade
rega
rdin
g to
pics
, con
cept
s an
d sk
ills.
9MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
T ER
M 2
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
3
Who
le n
umbe
rs:
Cou
ntin
g
O
rder
, com
pare
and
repr
esen
t num
bers
;
O
dd a
nd e
ven
num
bers
;
Pl
ace
valu
e;
Mul
tiple
s ;
Rou
ndin
g of
f;
Who
le n
umbe
rs:
Cou
ntin
g
O
rder
, com
pare
and
repr
esen
t num
bers
;
O
dd a
nd e
ven
num
bers
;
Pl
ace
valu
e;
M
ultip
les;
Fact
ors;
Rou
ndin
g of
f;
Who
le n
umbe
rs:
Cou
ntin
g
O
rder
, com
pare
and
repr
esen
t num
bers
;
Pr
ime
num
bers
;
Pl
ace
valu
e;
M
ultip
les
;
Fact
ors;
Rou
ndin
g of
f 1
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
6 Ad
ditio
n an
d su
btra
ctio
n of
who
le n
umbe
rs
Addi
tion
and
subt
ract
ion
of w
hole
num
bers
Ad
ditio
n an
d su
btra
ctio
n of
who
le n
umbe
rs
3 M
ultip
licat
ion
of w
hole
num
bers
M
ultip
licat
ion
of w
hole
num
bers
M
ultip
licat
ion
of w
hole
num
bers
3
Div
isio
n of
who
le n
umbe
rs
Div
isio
n of
who
le n
umbe
rs
Div
isio
n of
who
le n
umbe
rs
1 Fo
rmal
SB
A Ta
sk: T
est
Form
al S
BA
Task
: Tes
t Fo
rmal
SB
A Ta
sk: T
est
9
Com
mon
frac
tions
Des
crib
ing
and
orde
ring
fract
ions
Cal
cula
tions
with
frac
tions
Solv
ing
prob
lem
s in
con
text
s
Equi
vale
nt fo
rms
Com
mon
frac
tions
Des
crib
ing
and
orde
ring
fract
ions
Cal
cula
tions
with
frac
tions
Solv
ing
prob
lem
s in
con
text
s
Equi
vale
nt fo
rms
Com
mon
frac
tions
Des
crib
ing
and
orde
ring
fract
ions
Cal
cula
tions
with
frac
tions
Solv
ing
prob
lem
s in
con
text
s
Perc
enta
ges
Eq
uiva
lent
form
s D
ecim
al fr
actio
ns
R
ecog
nisi
ng, o
rder
ing
and
plac
e va
lue
of d
ecim
al fr
actio
ns
C
alcu
latio
ns w
ith d
ecim
al fr
actio
ns
So
lvin
g pr
oble
ms
in c
onte
xts
Eq
uiva
lent
form
s
2 Sy
mm
etry
Rec
ogni
ze, d
raw
and
des
crib
e lin
e(s)
of
sym
met
ry in
2-D
sha
pes.
Sym
met
ry
R
ecog
nize
, dra
w a
nd d
escr
ibe
line(
s) o
f sy
mm
etry
in 2
-D s
hape
s.
Sym
met
ry
R
ecog
nize
, dra
w a
nd d
escr
ibe
line(
s) o
f sy
mm
etry
in 2
-D s
hape
s.
IMPO
RTAN
T NO
TE: A
lway
s co
nsul
t the
CAP
S to
est
ablis
h a
deta
iled
prog
ress
ion
acro
ss th
e gr
ades
and
the
dept
hs w
ithin
the
grad
e re
gard
ing
topi
cs, c
once
pts
and
skills
.
10 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
5
Leng
th
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
leng
th
Leng
th
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
leng
th
Leng
th
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
leng
th
5
Mas
s
Prac
tical
mea
surin
g of
2-D
sha
pes
and
3-D
ob
ject
s
Mea
surin
g in
stru
men
ts
U
nits
Cal
cula
tions
and
pro
blem
sol
ving
invo
lvin
g m
ass
Mas
s
Prac
tical
mea
surin
g of
2-D
sha
pes
and
3-D
ob
ject
s
Mea
surin
g in
stru
men
ts
U
nits
Cal
cula
tions
and
pro
blem
sol
ving
invo
lvin
g m
ass
Mas
s
Prac
tical
mea
surin
g of
2-D
sha
pes
and
3-D
ob
ject
s
Mea
surin
g in
stru
men
ts
U
nits
Cal
cula
tions
and
pro
blem
sol
ving
invo
lvin
g m
ass
1
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
5
Cap
acity
/Vol
ume
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
capa
city
/vol
ume
Cap
acity
/Vol
ume
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
capa
city
/vol
ume
Cap
acity
/Vol
ume
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
capa
city
/vol
ume
IM
PORT
ANT
NOTE
: Alw
ays
cons
ult t
he C
APS
to e
stab
lish
a de
taile
d pr
ogre
ssio
n ac
ross
the
grad
es a
nd th
e de
pths
with
in th
e gr
ade
rega
rdin
g to
pics
, con
cept
s an
d sk
ills.
11MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
5
3-D
obj
ects
R
ange
of O
bjec
ts:
re
ctan
gula
r pris
ms,
sphe
res
cy
linde
rs
py
ram
ids
Cha
ract
eris
tics
of o
bjec
ts
sh
apes
of f
aces
flat a
nd c
urve
d su
rface
s
Furt
her a
ctiv
ities
Mak
e 3-
D m
odel
s us
ing
cut o
ut p
olyg
ons
3-D
obj
ects
R
ange
of O
bjec
ts:
re
ctan
gula
r pris
ms
and
othe
r pris
ms
cu
bes
cy
linde
rs
co
nes
py
ram
ids
si
mila
ritie
s an
d di
ffere
nces
bet
wee
n cu
bes
and
rect
angu
lar p
rism
s C
hara
cter
istic
s of
obj
ects
shap
e of
face
s
num
ber o
f fac
es
fla
t and
cur
ved
surfa
ces
Furt
her a
ctiv
ities
Mak
e 3-
D m
odel
s us
ing
c
ut o
ut p
olyg
ons
ne
ts
3-D
obj
ects
R
ange
of O
bjec
ts:
re
ctan
gula
r pris
ms
cu
bes
te
trahe
dron
s
pyra
mid
s
sim
ilarit
ies
and
diffe
renc
es b
etw
een
tetra
hedr
ons
and
othe
r pyr
amid
s C
hara
cter
istic
s of
obj
ects
num
ber a
nd s
hape
of f
aces
num
ber o
f ver
tices
num
ber o
f edg
es
Furt
her a
ctiv
ities
• Mak
e 3-
D m
odel
s us
ing:
drin
king
stra
ws,
toot
hpic
ks e
tc
ne
ts
1 Fo
rmal
SB
A Ta
sk: E
xam
inat
ion
Form
al S
BA
Task
: Exa
min
atio
n Fo
rmal
SB
A Ta
sk: E
xam
inat
ion
6 R
evis
ion
R
evis
ion
R
evis
ion
56
TOTA
L H
OU
RS
IMPO
RTAN
T NO
TE: A
lway
s co
nsul
t the
CAP
S to
est
ablis
h a
deta
iled
prog
ress
ion
acro
ss th
e gr
ades
and
the
dept
hs w
ithin
the
grad
e re
gard
ing
topi
cs, c
once
pts
and
skills
.
12 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
T ER
M 3
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
3
Who
le n
umbe
rs:
C
ount
ing
Ord
er, c
ompa
re a
nd re
pres
ent n
umbe
rs;
Odd
and
eve
n nu
mbe
rs;
Plac
e va
lue;
M
ultip
les
;
R
ound
ing
off;
Who
le n
umbe
rs:
Cou
ntin
g
O
rder
, com
pare
and
repr
esen
t num
bers
;
O
dd a
nd e
ven
num
bers
;
Pl
ace
valu
e;
M
ultip
les;
Fact
ors;
Rou
ndin
g of
f;
Who
le n
umbe
rs:
Cou
ntin
g
O
rder
, com
pare
and
repr
esen
t num
bers
;
Pr
ime
num
bers
;
Pl
ace
valu
e;
M
ultip
les
;
Fact
ors;
Rou
ndin
g of
f 1
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
8 Ad
ditio
n an
d su
btra
ctio
n of
who
le n
umbe
rs
Ad
ditio
n an
d su
btra
ctio
n of
who
le n
umbe
rs
Ad
ditio
n an
d su
btra
ctio
n of
who
le n
umbe
rs
7 M
ultip
licat
ion
and
divi
sion
of w
hole
nu
mbe
rs
Mul
tiplic
atio
n an
d di
visi
on o
f who
le
num
bers
M
ultip
licat
ion
and
divi
sion
of w
hole
nu
mbe
rs
1 Fo
rmal
SB
A Ta
sk: P
roje
ct
Form
al S
BA
Task
: Pro
ject
Fo
rmal
SB
A Ta
sk: P
roje
ct
IMPO
RTAN
T N
OTE
: Alw
ays
cons
ult t
he C
APS
to e
stab
lish
a de
taile
d pr
ogre
ssio
n ac
ross
the
grad
es a
nd th
e de
pths
with
in th
e gr
ade
rega
rdin
g to
pics
, con
cept
s an
d sk
ills.
6
Geo
met
ric P
atte
rns
Inve
stig
ate
and
exte
nd p
atte
rns
for
rela
tions
hips
or r
ules
of p
atte
rns.
In
put a
nd o
utpu
t val
ues
Equi
vale
nt fo
rms
ve
rbal
ly
in
a fl
ow d
iagr
am
by
a n
umbe
r sen
tenc
e
Geo
met
ric P
atte
rns
Inve
stig
ate
and
exte
nd p
atte
rns
for
rela
tions
hips
or r
ules
of p
atte
rns.
In
put a
nd o
utpu
t val
ues
Equi
vale
nt fo
rms
ve
rbal
ly
in
a fl
ow d
iagr
am
by
a n
umbe
r sen
tenc
e
Geo
met
ric P
atte
rns
Inve
stig
ate
and
exte
nd p
atte
rns
for
rela
tions
hips
or r
ules
of p
atte
rns.
In
put a
nd o
utpu
t val
ues
Equi
vale
nt fo
rms
ve
rbal
ly
in
a fl
ow d
iagr
am
in
tabl
es
by
a n
umbe
r sen
tenc
e IM
PORT
ANT
NO
TE: A
lway
s co
nsul
t the
CAP
S to
est
ablis
h a
deta
iled
prog
ress
ion
acro
ss th
e gr
ades
and
the
dept
hs w
ithin
the
grad
e re
gard
ing
topi
cs c
once
pts
and
skills
.
13MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
8 2
- D s
hape
s,
Rec
ogni
ze, v
isua
lize
and
nam
e 2-
D s
hape
s in
regu
lar a
nd ir
regu
lar p
olyg
ons
– tri
angl
es,
squa
res,
rect
angl
es, o
ther
qua
drila
tera
ls,
pent
agon
s, h
exag
ons
and
circ
les
Cha
ract
eris
tics
of s
hape
s
stra
ight
sid
es
cu
rved
sid
es
nu
mbe
r of s
ides
D
raw
2-D
sha
pes
on g
rid p
aper
Tr
ansf
orm
atio
ns
Bu
ild c
ompo
site
sha
pes
Te
ssel
latio
ns
D
escr
ibe
patte
rns
Posi
tion
and
view
s Lo
catio
n an
d di
rect
ions
2 -
D s
hape
s,
Rec
ogni
ze, v
isua
lize
and
nam
e 2-
D s
hape
s in
regu
lar a
nd ir
regu
lar p
olyg
ons
– tri
angl
es,
squa
res,
rect
angl
es, o
ther
qua
drila
tera
ls,
pent
agon
s, h
exag
ons,
hep
tago
ns a
nd
circ
les
si
mila
ritie
s an
d di
ffere
nces
bet
wee
n sq
uare
s an
d re
ctan
gles
C
hara
cter
istic
s of
sha
pes
st
raig
ht s
ides
curv
ed s
ides
num
ber o
f sid
es
an
gles
in s
hape
D
raw
2-D
sha
pes
on g
rid p
aper
In
volv
ing
angl
es
Rec
ogni
ze a
nd d
escr
ibe
angl
es in
2-D
sha
pes
Tran
sfor
mat
ions
Use
tran
sfor
mat
ions
to m
ake
com
posi
te
shap
es
U
se tr
ansf
orm
atio
ns to
mak
e te
ssel
latio
ns
D
escr
ibe
patte
rns
Posi
tion
and
view
s Lo
catio
n an
d di
rect
ions
2 - D
sha
pes,
R
ecog
nize
, vis
ualiz
e an
d na
me
2-D
sha
pes
in
re
gula
r and
irre
gula
r pol
ygon
s - t
riang
les,
sq
uare
s, re
ctan
gles
, par
alle
logr
ams,
oth
er
quad
rilat
eral
s, p
enta
gons
, hex
agon
s,
hept
agon
s, o
ctag
ons
si
mila
ritie
s an
d di
ffere
nces
bet
wee
n re
ctan
gles
and
par
alle
logr
ams
Cha
ract
eris
tics
of s
hape
s
num
ber o
f sid
es
le
ngth
s in
sid
es
si
zes
of a
ngle
s D
raw
2-D
sha
pes
on g
rid p
aper
In
volv
ing
angl
es
Rec
ogni
ze a
nd d
escr
ibe
angl
es in
2-D
sha
pes
Tran
sfor
mat
ions
Use
tran
sfor
mat
ions
to m
ake
com
posi
te
shap
es
E
nlar
gem
ent a
nd re
duct
ions
Des
crib
e pa
ttern
s Po
sitio
n an
d vi
ews
Loca
tion
and
dire
ctio
ns
1 In
form
al a
sses
smen
t In
form
al a
sses
smen
t In
form
al a
sses
smen
t IM
PORT
ANT
NO
TE: A
lway
s co
nsul
t the
CAP
S to
est
ablis
h a
deta
iled
prog
ress
ion
acro
ss th
e gr
ades
and
the
dept
hs w
ithin
the
grad
e re
gard
ing
topi
cs, c
once
pts
and
skills
.
14 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6 4
Leng
th
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
leng
th
Leng
th
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
leng
th
Leng
th
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
leng
th
M
ass
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts ((
milli
litre
s, li
tres)
Cal
cula
tions
and
pro
blem
sol
ving
invo
lvin
g m
ass
Mas
s
Prac
tical
mea
surin
g of
2-D
sha
pes
and
3-D
ob
ject
s
Mea
surin
g in
stru
men
ts
U
nits
(milli
litre
s, li
tres)
Cal
cula
tions
and
pro
blem
sol
ving
invo
lvin
g m
ass
Mas
s
Prac
tical
mea
surin
g of
2-D
sha
pes
and
3-D
ob
ject
s
Mea
surin
g in
stru
men
ts
U
nits
(milli
litre
s, li
tres,
kilo
litre
s)
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
mas
s (in
clud
e fra
ctio
n an
d de
cim
al fo
rms
to
2 de
cim
al p
lace
s)
C
apac
ity/V
olum
e
Prac
tical
mea
surin
g of
2-D
sha
pes
and
3-D
ob
ject
s
Mea
surin
g in
stru
men
ts
U
nits
Cal
cula
tions
and
pro
blem
sol
ving
invo
lvin
g ca
paci
ty/v
olum
e
Cap
acity
/Vol
ume
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
capa
city
/vol
ume
Cap
acity
/Vol
ume
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D
obje
cts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng in
volv
ing
capa
city
/vol
ume
IM
PORT
ANT
NO
TE: A
lway
s co
nsul
t the
CAP
S to
est
ablis
h a
deta
iled
prog
ress
ion
acro
ss th
e gr
ades
and
the
dept
hs w
ithin
the
grad
e re
gard
ing
topi
cs, c
once
pts
and
skills
.
15MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
12
Com
mon
frac
tions
D
escr
ibin
g an
d or
derin
g fr
actio
ns:
• C
ompa
re a
nd o
rder
(hal
ves;
third
s,
quar
ters
; fift
hs; s
ixth
s; s
even
ths;
eig
hths
)
• Com
mon
frac
tions
in d
iagr
am fo
rm
Cal
cula
tions
with
frac
tions
:
Addi
tion
of c
omm
on fr
actio
ns w
ith th
e sa
me
deno
min
ator
s
Equi
vale
nce
of d
ivis
ion
and
fract
ions
So
lvin
g pr
oble
ms
So
lve
prob
lem
s in
con
text
s in
volv
ing
fract
ions
, inc
ludi
ng g
roup
ing
and
equa
l sh
arin
g Eq
uiva
lent
form
s:
Com
mon
frac
tions
D
escr
ibin
g an
d or
derin
g fr
actio
ns:
C
ount
forw
ards
and
bac
kwar
ds
C
ompa
re a
nd o
rder
com
mon
frac
tions
to a
t le
ast t
wel
fths
Cal
cula
tions
with
frac
tions
:
Addi
tion
and
subt
ract
ion
of c
omm
on
fract
ions
with
the
sam
e de
nom
inat
ors
Ad
ditio
n an
d su
btra
ctio
n of
mix
ed n
umbe
rs
Fr
actio
ns o
f who
le n
umbe
rs
Eq
uiva
lenc
e of
div
isio
n an
d fra
ctio
ns
Solv
ing
prob
lem
s
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g co
mm
on fr
actio
ns, i
nclu
ding
gro
upin
g an
d sh
arin
g Eq
uiva
lent
form
s:
Com
mon
frac
tions
, dec
imal
frac
tions
and
pe
rcen
tage
s
Com
pare
and
ord
er c
omm
on fr
actio
ns,
incl
udin
g te
nths
and
hun
dred
ths
Cal
cula
tions
with
frac
tions
:
Addi
tion
and
subt
ract
ion
of c
omm
on
fract
ions
in
w
hich
one
den
omin
ator
is a
mul
tiple
of
anot
her
Ad
ditio
n an
d su
btra
ctio
n of
mix
ed n
umbe
rs
Fr
actio
ns o
f who
le n
umbe
rs
Solv
ing
prob
lem
s
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g co
mm
on fr
actio
ns, i
nclu
ding
gro
upin
g an
d sh
arin
g Eq
uiva
lent
form
s:
Perc
enta
ges
Fi
nd p
erce
ntag
es o
f who
le n
umbe
rs
1 Fo
rmal
SB
A Ta
sk: T
est
Form
al S
BA
Task
: Tes
t Fo
rmal
SB
A Ta
sk: T
est
4 R
evis
ion
Rev
isio
n R
evis
ion
56
IM
PORT
ANT
NO
TE: A
lway
s co
nsul
t the
CAP
S to
est
ablis
h a
deta
iled
prog
ress
ion
acro
ss th
e gr
ades
and
the
dept
hs w
ithin
the
grad
e re
gard
ing
topi
cs, c
once
pts
and
skills
.
16 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
T ER
M 4
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
3
Who
le n
umbe
rs:
C
ount
ing
Ord
er, c
ompa
re a
nd re
pres
ent n
umbe
rs;
Odd
and
eve
n nu
mbe
rs;
Plac
e va
lue;
M
ultip
les
;
R
ound
ing
off;
Who
le n
umbe
rs:
Cou
ntin
g
O
rder
, com
pare
and
repr
esen
t num
bers
;
O
dd a
nd e
ven
num
bers
;
Pl
ace
valu
e;
M
ultip
les;
Fact
ors;
Rou
ndin
g of
f;
Who
le n
umbe
rs:
Cou
ntin
g
O
rder
, com
pare
and
repr
esen
t num
bers
;
Pr
ime
num
bers
;
Pl
ace
valu
e;
M
ultip
les
;
Fact
ors;
Rou
ndin
g of
f 1
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
6 Ad
ditio
n an
d su
btra
ctio
n of
who
le n
umbe
rs
Addi
tion
and
subt
ract
ion
of w
hole
num
bers
Ad
ditio
n an
d su
btra
ctio
n of
who
le n
umbe
rs
6 M
ultip
licat
ion
and
divi
sion
of w
hole
nu
mbe
rs
Mul
tiplic
atio
n an
d di
visi
on o
f who
le
num
bers
M
ultip
licat
ion
and
divi
sion
of w
hole
nu
mbe
rs
6
3-D
obj
ects
R
ange
of O
bjec
ts:
re
ctan
gula
r pris
ms,
sphe
res
cy
linde
rs
py
ram
ids
3-D
obj
ects
R
ange
of O
bjec
ts:
re
ctan
gula
r pris
ms
and
othe
r pris
ms
cu
bes
cy
linde
rs
co
nes
py
ram
ids
si
mila
ritie
s an
d di
ffere
nces
bet
wee
n cu
bes
and
rect
angu
lar p
rism
s
3-D
obj
ects
R
ange
of O
bjec
ts:
re
ctan
gula
r pris
ms
cu
bes
te
trahe
dron
s
pyra
mid
s
sim
ilarit
ies
and
diffe
renc
es b
etw
een
tetra
hedr
ons
and
othe
r pyr
amid
s
1
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
Info
rmal
ass
essm
ent
IMPO
RTAN
T N
OTE
: Alw
ays
cons
ult t
he C
APS
to e
stab
lish
a de
taile
d pr
ogre
ssio
n ac
ross
the
grad
es a
nd th
e de
pths
with
in th
e gr
ade
rega
rdin
g to
pics
, con
cept
s an
d sk
ills.
17MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
char
acte
ristic
s of
obj
ects
shap
es o
f fac
es
fla
t and
cur
ved
surfa
ces
Furt
her a
ctiv
ities
Mak
e 3-
D m
odel
s us
ing
cut o
ut p
olyg
ons
char
acte
ristic
s of
obj
ects
shap
e of
face
s
num
ber o
f fac
es
fla
t and
cur
ved
surfa
ces
Fu
rthe
r act
iviti
es
M
ake
3-D
mod
els
usin
g
cu
t out
pol
ygon
s
nets
char
acte
ristic
s of
obj
ects
num
ber a
nd s
hape
of f
aces
num
ber o
f ver
tices
num
ber o
f edg
es
Furt
her a
ctiv
ities
Mak
e 3-
D m
odel
s us
ing:
drin
king
stra
ws,
toot
hpic
ks e
tc
ne
ts
1 Fo
rmal
SB
A Ta
sk: I
nves
tigat
ion
Form
al S
BA
Task
: Inv
estig
atio
n Fo
rmal
SB
A Ta
sk: I
nves
tigat
ion
IMPO
RTAN
T N
OTE
: Alw
ays
cons
ult t
he C
APS
to e
stab
lish
a de
taile
d pr
ogre
ssio
n ac
ross
the
grad
es a
nd th
e de
pths
with
in th
e gr
ade
rega
rdin
g to
pics
, con
cept
s an
d sk
ills.
8
Perim
eter
M
easu
re p
erim
eter
usi
ng ru
lers
or m
easu
ring
tape
s M
easu
rem
ent o
f are
a
Find
are
as o
f reg
ular
and
irre
gula
r sha
pes
by c
ount
ing
squa
res
on g
rids
in o
rder
to
deve
lop
an u
nder
stan
ding
of s
quar
e un
its
Mea
sure
men
t of v
olum
e
Find
vol
ume/
capa
city
of o
bjec
ts b
y pa
ckin
g or
fillin
g th
em in
ord
er to
dev
elop
an
unde
rsta
ndin
g of
cub
ic u
nits
Perim
eter
M
easu
re p
erim
eter
usi
ng ru
lers
or m
easu
ring
tape
s M
easu
rem
ent o
f are
a
Find
are
as o
f reg
ular
and
irre
gula
r sha
pes
by c
ount
ing
squa
res
on g
rids
in o
rder
to
deve
lop
an u
nder
stan
ding
of s
quar
e un
its
Mea
sure
men
t of v
olum
e
Find
vol
ume/
capa
city
of o
bjec
ts b
y pa
ckin
g or
fillin
g th
em in
ord
er to
dev
elop
an
unde
rsta
ndin
g of
cub
ic u
nits
Perim
eter
M
easu
re p
erim
eter
usi
ng ru
lers
or m
easu
ring
tape
s M
easu
rem
ent o
f are
a
Con
tinue
to fi
nd a
reas
of r
egul
ar a
nd
irreg
ular
sha
pes
by c
ount
ing
squa
res
on
grid
s
Dev
elop
rule
s fo
r cal
cula
ting
the
area
s of
sq
uare
s an
d re
ctan
gles
M
easu
rem
ent o
f vol
ume
C
ontin
ue to
find
vol
ume/
capa
city
of o
bjec
ts
by p
acki
ng o
r filli
ng th
em
D
evel
op a
n un
ders
tand
ing
of w
hy th
e vo
lum
e of
rect
angu
lar p
rism
s is
giv
en b
y le
ngth
mul
tiplie
d by
wid
th m
ultip
lied
by
heig
ht
Inve
stig
ate
R
elat
ions
hip
betw
een
perim
eter
and
are
a of
re
ctan
gles
and
squ
ares
.
Rel
atio
nshi
p be
twee
n su
rface
are
a an
d vo
lum
e of
rect
angu
lar p
rism
s
18 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
6
Dat
a ha
ndlin
g
Col
lect
ing
and
orga
nizi
ng d
ata
R
epre
sent
ing
data
Anal
ysin
g, in
terp
retin
g an
d re
porti
ng d
ata
Pr
obab
ility
Toss
ing
a co
in &
rollin
g a
die
Dat
a ha
ndlin
g
Col
lect
ing
and
orga
nizi
ng d
ata
R
epre
sent
ing
data
Anal
ysin
g, in
terp
retin
g an
d re
porti
ng d
ata
U
ngro
uped
dat
a
Prob
abilit
y
To
ssin
g a
coin
& ro
lling
a di
e
spin
ning
a s
pinn
er
Dat
a ha
ndlin
g
Col
lect
ing
and
orga
nizi
ng d
ata
R
epre
sent
ing
data
Anal
ysin
g, in
terp
retin
g an
d re
porti
ng d
ata
in
clud
ing
doub
le b
ar g
raph
s
cent
ral t
ende
ncie
s –
(mod
e an
d m
edia
n)
U
ngro
uped
dat
a
Prob
abilit
y
To
ssin
g a
coin
& ro
lling
a di
e
spin
ning
a s
pinn
er
4
Com
mon
frac
tions
D
escr
ibin
g an
d or
derin
g fr
actio
ns:
C
ompa
re a
nd o
rder
(hal
ves;
third
s, q
uarte
rs;
fifth
s; s
ixth
s; s
even
ths;
eig
hths
)
Com
mon
frac
tions
in d
iagr
am fo
rm
Cal
cula
tions
with
frac
tions
:
Addi
tion
of c
omm
on fr
actio
ns w
ith th
e sa
me
deno
min
ator
s
Equi
vale
nce
of d
ivis
ion
and
fract
ions
So
lvin
g pr
oble
ms
So
lve
prob
lem
s in
con
text
s in
volv
ing
fract
ions
, inc
ludi
ng g
roup
ing
and
equa
l sh
arin
g Eq
uiva
lent
form
s:
Com
mon
frac
tions
D
escr
ibin
g an
d or
derin
g fr
actio
ns:
C
ount
forw
ards
and
bac
kwar
ds
C
ompa
re a
nd o
rder
com
mon
frac
tions
to a
t le
ast t
wel
fths
Cal
cula
tions
with
frac
tions
:
Addi
tion
and
subt
ract
ion
of c
omm
on
fract
ions
with
the
sam
e de
nom
inat
ors
Ad
ditio
n an
d su
btra
ctio
n of
mix
ed n
umbe
rs
Fr
actio
ns o
f who
le n
umbe
rs
Eq
uiva
lenc
e of
div
isio
n an
d fra
ctio
ns
Solv
ing
prob
lem
s
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g co
mm
on fr
actio
ns, i
nclu
ding
gro
upin
g an
d sh
arin
g Eq
uiva
lent
form
s:
Com
mon
frac
tions
, dec
imal
frac
tions
and
pe
rcen
tage
s C
ompa
re a
nd o
rder
com
mon
frac
tions
, in
clud
ing
tent
hs a
nd h
undr
edth
s C
alcu
latio
ns w
ith fr
actio
ns:
Ad
ditio
n an
d su
btra
ctio
n of
com
mon
fra
ctio
ns in
whi
ch o
ne d
enom
inat
or is
a
mul
tiple
of a
noth
er
Ad
ditio
n an
d su
btra
ctio
n of
mix
ed n
umbe
rs
Fr
actio
ns o
f who
le n
umbe
rs
Solv
ing
prob
lem
s
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g co
mm
on fr
actio
ns, i
nclu
ding
gro
upin
g an
d sh
arin
g Eq
uiva
lent
form
s:
Perc
enta
ges
Fi
nd p
erce
ntag
es o
f who
le n
umbe
rs
IMPO
RTAN
T N
OTE
: Alw
ays
cons
ult t
he C
APS
to e
stab
lish
a de
taile
d pr
ogre
ssio
n ac
ross
the
grad
es a
nd th
e de
pths
with
in th
e gr
ade
rega
rdin
g to
pics
, con
cept
s an
d sk
ills.
19MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TIM
E
(HO
UR
S)
GR
ADE
4 G
RAD
E 5
GR
ADE
6
3
Num
ber s
ente
nces
nu
mbe
r sen
tenc
es d
escr
ibin
g pr
oble
m
situ
atio
ns
So
lve
and
com
plet
e nu
mbe
r sen
tenc
es
by in
spec
tion,
-tria
l and
impr
ovem
ent,
chec
k so
lutio
n by
sub
stitu
tion
Num
ber s
ente
nces
nu
mbe
r sen
tenc
es d
escr
ibin
g pr
oble
m
situ
atio
ns
so
lve
and
com
plet
e nu
mbe
r sen
tenc
es
by in
spec
tion,
tria
l and
impr
ovem
ent,
chec
k so
lutio
n by
sub
stitu
tion
Num
ber s
ente
nces
nu
mbe
r sen
tenc
es d
escr
ibin
g pr
oble
m
situ
atio
ns
So
lve
and
com
plet
e nu
mbe
r sen
tenc
es
by in
spec
tion,
tria
l and
impr
ovem
ent,
chec
k so
lutio
n by
sub
stitu
tion
1 Fo
rmal
SB
A Ta
sk: A
ssig
nmen
t Fo
rmal
SB
A Ta
sk: A
ssig
nmen
t Fo
rmal
SB
A Ta
sk: A
ssig
nmen
t
End
of y
ear e
xam
En
d of
yea
r exa
m
End
of y
ear e
xam
6 R
evis
ion
Rev
isio
n R
evis
ion
52
TOTA
L H
OU
RS
IMPO
RTA
NT
NO
TE: A
lway
s co
nsul
t the
CAP
S to
est
ablis
h a
deta
iled
prog
ress
ion
acro
ss th
e gr
ades
and
the
dept
hs w
ithin
the
grad
e re
gard
ing
topi
cs, c
once
pts
and
skills
.
20 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LE
SSO
N P
LAN
S: T
ERM
1
21MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
1
TER
M 1
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E: fr
om
……
… to
……
…
Tim
e: 5
HO
UR
S G
RAD
E 4
CAP
S pp
. 37
- 38
5 C
APS
pp. 1
25 -1
26
6 C
APS
pp. 2
15 –
216
TO
PIC
W
hole
num
bers
C
once
pts,
Ski
lls a
nd
know
ledg
e
Cou
nt fo
rwar
ds a
nd b
ackw
ards
in 2
s,
3s, 5
s, 1
0s, 2
5s, 5
0s, 1
00s
betw
een
0 an
d at
leas
t 1 0
00
O
rder
, com
pare
and
repr
esen
t nu
mbe
rs to
at l
east
0 -
999.
Rep
rese
nt o
dd a
nd e
ven
num
bers
to
at le
ast 1
000
Rec
ogni
ze th
e pl
ace
valu
e of
dig
its
in w
hole
num
bers
to a
t lea
st 3
-dig
it nu
mbe
rs
Rou
nd o
ff to
the
near
est 1
0, 1
00 a
nd
1 00
0
C
ount
forw
ards
and
bac
kwar
ds in
w
hole
num
ber i
nter
vals
up
to a
t lea
st
10 0
00
O
rder
, com
pare
and
repr
esen
t nu
mbe
rs to
at l
east
4-d
igit
num
bers
Rep
rese
nt o
dd a
nd e
ven
num
bers
to
at le
ast 1
000
.
Rec
ogni
ze th
e pl
ace
valu
e of
dig
its
in w
hole
num
bers
to a
t lea
st 6
dig
it nu
mbe
rs.
R
ound
off
to th
e ne
ares
t 5, 1
0, 1
00
and
1 00
0
C
ount
forw
ards
and
bac
kwar
ds in
w
hole
num
ber i
nter
vals
up
to a
t lea
st
10 0
00
O
rder
, com
pare
and
repr
esen
t nu
mbe
rs to
at l
east
9-d
igit
num
bers
Rep
rese
nt p
rime
num
bers
to a
t lea
st
100
R
ecog
nizi
ng th
e pl
ace
valu
e of
dig
its
in w
hole
num
bers
to a
t lea
st 9
-dig
it nu
mbe
rs
R
ound
off
to th
e ne
ares
t 5, 1
0, 1
00,
1 00
0, 1
00 0
00, a
nd 1
000
000
22 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
SUG
GES
TED
M
ETH
OD
OLO
GY
Expl
ain
from
kno
wn
(low
num
ber r
ange
); w
ork
with
con
cret
e LT
SM
Cou
ntin
g, o
rder
ing,
com
parin
g, re
pres
entin
g of
dig
its
St
art w
ith 2
-dig
it nu
mbe
rs a
nd b
uild
up
to 3
-dig
it nu
mbe
rs
Not
e: A
ccor
ding
to C
APS
num
ber r
ange
per
gra
de p
er te
rm a
s in
con
tent
cla
rific
atio
n
R
ead,
say
and
writ
e up
to a
t lea
st 4
-dig
it nu
mbe
rs, (
Lear
ners
can
writ
e nu
mbe
rs w
ith fi
nger
s in
the
air w
hile
they
are
read
ing
/ say
ing
the
wor
ds.)
e.g.
Tw
enty
-nin
e
C
onve
rt fro
m w
ords
to n
umbe
rs a
nd n
umbe
rs to
wor
ds
W
rite
the
num
ber t
hat i
s eq
uiva
lent
to:
Ar
rang
e th
e nu
mbe
rs b
elow
from
the
smal
lest
to th
e bi
gges
t: 11
1; 1
101
; 1 1
10; 1
011
M
ake
the
bigg
est/s
mal
lest
num
ber y
ou c
an w
ith th
ese
digi
ts: 3
, 2, 5
, 4, 0
.
Odd
and
eve
n nu
mbe
rs:
Ex
plor
e pr
actic
ally
by
wor
king
with
num
bers
to b
e ab
le to
des
crib
e th
e pa
ttern
e.g
. all
odd
num
bers
end
in 1
, 3, 5
, 7 o
r 9
ther
efor
e 20
1, 2
03, 2
05, 2
07, 2
09 a
re a
ll od
d nu
mbe
rs
Prim
e nu
mbe
rs in
trod
uced
to G
rade
6
U
se n
umbe
r cha
rt to
isol
ate
prim
e nu
mbe
rs fr
om c
ompo
site
num
bers
Mul
tiple
s:
If
you
coun
t in
mul
tiple
s of
3, u
p to
100
.
o W
ill yo
u co
unt t
he n
umbe
r 13?
Why
?
o W
ill yo
u co
unt t
he n
umbe
r 42?
Why
?
23MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Plac
e va
lue:
D
istin
guis
h be
twee
n nu
mer
ic v
alue
and
pla
ce v
alue
U
se p
lace
val
ue c
ards
to b
uild
up
and
brea
k do
wn
num
bers
Wha
t is
diffe
rent
to G
rade
3?
R
ound
ing
off t
o th
e ne
ares
t
Rou
ndin
g of
f:
R
ound
off
to th
e ne
ares
t te
n, h
undr
ed a
nd th
ousa
nd (u
se b
ase
ten
bloc
ks, n
umbe
r lin
es, p
lace
val
ue)
Pl
ace
valu
e Ta
ble
U
se th
e co
ncep
t of r
ound
ing
off
in p
robl
em s
olvi
ng c
onte
xt
Gra
de 4
and
5:
In T
erm
1, l
earn
ers
shou
ld r
evis
e an
d co
nsol
idat
e w
ork
done
in G
rade
3. R
ecom
men
ded
spec
ifica
tions
are
pro
vide
d be
low.
Cou
ntin
g
Cou
nt fo
rwar
ds a
nd b
ackw
ards
in 2
s, 3
s, 5
s, 1
0s, 2
5s, 5
0s, 1
00s
betw
een
0 an
d at
leas
t 1 0
00
C
ount
ing
shou
ld n
ot o
nly
be th
ough
t of a
s ve
rbal
cou
ntin
g. L
earn
ers
shou
ld c
ount
usi
ng a
ppar
atus
suc
h as
o C
ount
ers
o co
untin
g be
ads
o nu
mbe
r grid
s
o st
ruct
ured
, sem
i-stru
ctur
ed a
nd e
mpt
y nu
mbe
r lin
es
o pi
ctur
es o
f obj
ects
, esp
ecia
lly p
ictu
res
of la
rge
num
bers
of o
bjec
ts th
at a
re p
rese
nted
in a
gro
uped
or s
truct
ured
way
. An
exam
ple
of a
pic
ture
of o
bjec
ts s
uita
ble
for c
ount
ing
is p
rovi
ded
at th
e en
d of
the
Gra
de 4
sec
tion
of
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
.
o ar
rays
or d
iagr
ams
of a
rrays
e.g
.
24 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
ot
her d
iagr
ams
for c
ount
ing
e.g.
Cou
ntin
g sh
ould
not
alw
ays
star
t on
the
first
mul
tiple
, nor
sho
uld
it al
way
s st
art o
n an
y ot
her m
ultip
le e
.g. c
ount
ing
in 2
s
can
star
t fro
m 5
or 2
7 or
348
.
Plac
e va
lue
(num
ber r
ange
0 to
999
)
Le
arne
rs s
houl
d be
abl
e to
bre
ak u
p nu
mbe
rs in
to h
undr
eds,
tens
and
uni
ts u
sing
o th
e nu
mbe
r nam
es (n
umbe
r wor
ds)
o pl
ace
valu
e or
flas
h ca
rds
o ex
pand
ed n
otat
ion
R
ecom
men
ded
appa
ratu
s: p
lace
val
ue/fl
ash
card
s; D
iene
s bl
ocks
Com
pare
and
ord
er (n
umbe
r ran
ge 0
to 9
99)
Le
arne
rs s
houl
d be
giv
en a
rang
e of
exe
rcis
es s
uch
as:
o Ar
rang
e th
e gi
ven
num
bers
bel
ow fr
om th
e sm
alle
st to
the
bigg
est o
r big
gest
to s
mal
lest
o Fi
ll in
mis
sing
num
bers
in
◊ a
sequ
ence
◊ on
a n
umbe
r grid
25MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
o Sh
ow a
giv
en n
umbe
r on
a st
ruct
ured
or s
emi-s
truct
ured
num
ber l
ine,
e.g
. sho
w w
hich
num
ber i
s ha
lfway
bet
wee
n
340
and
350
on a
num
ber l
ine
o In
dica
te w
hich
of t
wo
num
bers
is g
reat
er o
r sm
alle
r e.g
. 5 4
31 o
r 5 4
13
o R
epla
ce *
with
<,=
or >
Exa
mpl
e: 8
9 * 9
8, 1
09 *
190
A
ll w
ork
deve
lope
d he
re c
an b
e pr
actis
ed th
roug
hout
the
year
in th
e M
enta
l Mat
hem
atic
s pr
ogra
mm
e.
Gra
de 6
: Pl
ace
valu
e (n
umbe
r ran
ge 0
to 9
99 9
99)
Le
arne
rs s
houl
d be
abl
e to
bre
ak u
p nu
mbe
rs in
to h
undr
eds,
tens
and
uni
ts u
sing
o th
e nu
mbe
r nam
es (n
umbe
r wor
ds)
o pl
ace
valu
e or
flas
h ca
rds
o ex
pand
ed n
otat
ion
R
ecom
men
ded
appa
ratu
s: p
lace
val
ue, f
lash
car
ds, D
iene
s bl
ocks
Com
pare
and
ord
er
Her
e le
arne
rs s
houl
d be
giv
en a
rang
e of
exe
rcis
es
Ar
rang
e th
e gi
ven
num
bers
bel
ow f
rom
the
smal
lest
to th
e bi
gges
t: or
big
gest
to s
mal
lest
Fi
ll in
mis
sing
num
bers
in
o a
sequ
ence
o on
a n
umbe
r grid
◊ Sh
ow a
giv
en n
umbe
r on
a nu
mbe
r lin
e –
stru
ctur
ed o
r sem
i-stru
ctur
ed e
.g. s
how
on
a nu
mbe
r lin
e w
hich
num
ber i
s ha
lfway
bet
wee
n 47
1 34
0 an
d 47
1 35
0.
In
dica
te w
hich
of t
wo
num
bers
is g
reat
er o
r sm
alle
r: 39
5431
or 3
9541
3?
Fi
ll in
<, =
or >
a)
247
889
* 2
47 8
98
26 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
b)
784
109
* 7
85 1
90
All w
ork
deve
lope
d he
re c
an b
e pr
actis
ed th
roug
hout
the
year
in th
e M
enta
l Mat
hem
atic
s pr
ogra
mm
e.
LTSM
Res
ourc
es
Num
ber l
ines
: 0 –
120
, Stru
ctur
ed -,
sem
i- st
ruct
ured
- , u
nstru
ctur
ed n
umbe
r lin
es; C
ount
ers,
Pic
ture
s, a
rrays
/ dia
gram
s, F
lash
card
s, B
ase
10 b
lock
s, 1
00 c
harts
, mul
tiplic
atio
n ta
ble,
aba
cus
, bea
ds
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
WB
1: p
p. 2
– 7
A
ctiv
ities
: 1a&
b; 2
W
B 1
: pp.
2
Activ
ities
: 1a&
b W
B 1
: pp.
2 –
4
Activ
ities
: 1a&
b, 2
, 3
DB
E Te
xtbo
ok re
fere
nce
Term
1: U
nit 1
: Who
le N
umbe
rs p
. 3
Term
1: U
nit 1
: Who
le N
umbe
rs p
. 3
Term
1: U
nit 1
: Who
le N
umbe
rs p
. 3
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
Test
27MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
2
TER
M 1
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to
……
…
Tim
e: 6
HO
UR
S G
RAD
E 4
CAP
S pp
. 39
– 42
5
CAP
S pp
. 127
-131
6
CAP
S pp
. 217
– 2
22
TOPI
C
Num
ber s
ente
nces
C
once
pts,
Ski
lls a
nd
know
ledg
e
• W
rite
num
ber s
ente
nces
to
desc
ribe
prob
lem
situ
atio
ns
•
Solv
e an
d co
mpl
ete
num
ber
sent
ence
s by
- in
spec
tion
-
trial
and
impr
ovem
ent
• C
heck
sol
utio
n by
sub
stitu
tion
• W
rite
num
ber s
ente
nces
to
desc
ribe
prob
lem
situ
atio
ns
• So
lve
and
com
plet
e nu
mbe
r se
nten
ces
by
-
insp
ectio
n
- tri
al a
nd im
prov
emen
t •
Che
ck s
olut
ion
by s
ubst
itutio
n
• W
rite
num
ber s
ente
nces
to
desc
ribe
prob
lem
situ
atio
ns
• So
lve
and
com
plet
e nu
mbe
r se
nten
ces
by
-
insp
ectio
n
- tri
al a
nd im
prov
emen
t •
Che
ck s
olut
ion
by s
ubst
itutio
n
SUG
GES
TED
M
ETH
OD
OLO
GY
U
se n
umbe
r sen
tenc
es to
des
crib
e pr
oble
m s
ituat
ions
. Ex
ampl
e: P
robl
em s
ituat
ion:
I bo
ught
750
g of
sw
eets
and
div
ided
them
am
ong
25 c
hild
ren.
Num
ber s
ente
nce:
750
÷25
U
se n
umbe
r sen
tenc
es a
s eq
uiva
lent
form
of e
xpre
ssio
n to
sec
tions
of f
low
dia
gram
or t
able
s.
Exam
ple:
Tab
le
1 2
3 4
×3
28 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Flow
dia
gram
E
quiv
alen
t rep
rese
ntat
ion
of th
e ta
ble
and
the
flow
dia
gram
: ×
3
• U
sing
num
ber
sent
ence
s to
hel
p le
arne
rs u
nder
stan
d an
d us
e th
e fa
ct t
hat
addi
tion
and
subt
ract
ion
are
inve
rse
oper
atio
ns
Exa
mpl
e: 3
7 –
4 +
4 =
∆ •
Use
num
ber s
ente
nces
hel
ps le
arne
rs d
evel
op a
dditi
on a
nd s
ubtra
ctio
n te
chni
ques
Exa
mpl
e: 3
6+13
= th
eref
ore
49 –
13
=
•
Com
mut
ativ
e pr
oper
ty o
f add
ition
Num
bers
can
be
adde
d in
any
ord
er.
Exam
ple:
29
+ 19
= 1
9 +
26
T
here
fore
13
+ 49
= o
r 49
+ 1
3 =
•
Ass
ocia
tive
prop
erty
of a
dditi
on
Th
e as
soci
ativ
e pr
oper
ty a
llow
s nu
mbe
rs t
o be
gro
uped
in
diffe
rent
way
s w
hen
addi
ng m
ore
than
wo
num
bers
, with
out i
t af
fect
ing
the
answ
er.
Exa
mpl
e: (3
1 +
26) +
19=
i
s th
e sa
me
as 3
1 +(
26+
19) =
• U
se n
umbe
r sen
tenc
es to
hel
p le
arne
rs s
ee a
nd u
se p
atte
rns
in a
dditi
on a
nd s
ubtra
ctio
n nu
mbe
r bon
ds fo
r:
- 10
- m
ultip
les
of 1
0
- m
ultip
les
of 1
00
29MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
E
xam
ples
:
- Te
n
3 +
7=
4
+ 6
= 2
+ 8
=
5 +
5 =
- M
ultip
les
of 1
0
1
3 +
7 =
14
+ 6
=
12
+ 8=
15 +
5 =
- M
ultip
les
of 1
00
Sim
ilar e
xam
ples
can
be
give
n fo
r mul
tiple
s of
100
suc
h as
200
; 300
; 400
; 500
; 600
; 700
; 800
; 900
[S
ee C
APS
at th
e in
dica
ted
page
s fo
r mor
e ex
ampl
e / d
etai
ls]
LTSM
R
esou
rces
N
umbe
r lin
es, S
truct
ured
-, s
emi-
stru
ctur
ed -
, uns
truct
ured
num
ber l
ines
; Cou
nter
s, A
bacu
s, P
ictu
res,
arra
ys/ d
iagr
ams,
flow
di
agra
ms,
mat
hs v
ideo
clip
s, E
lear
ning
reso
urce
s on
line,
Mat
hs g
ames
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
WB
1: p
p. 1
4 - 1
6
Activ
ities
: 6 a
& b
; 29
WB
1: p
p. 1
0 –
12
Activ
ities
: 4 a
nd 5
W
B 1
: pp.
73
-74
Ac
tivity
: 4
DB
E Te
xtbo
ok
refe
renc
e Te
rm 1
: Uni
t 2: N
umbe
r Sen
tenc
es p
. 18
Term
1: U
nit 2
: Num
ber s
ente
nces
p.
13
Term
1: U
nit 2
: Num
ber s
ente
nces
p.
18
HO
MEW
OR
K
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
30 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
3
TER
M 1
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to
……
…
Tim
e: 7
HO
UR
S G
RAD
E 4
CAP
S pp
. 43
– 45
5
CAP
S pp
. 132
-135
6
CAP
S pp
. 222
– 2
25
TOPI
C
Addi
tion
and
subt
ract
ion
of w
hole
num
bers
C
once
pts,
Ski
lls a
nd
know
ledg
e
Addi
tion
and
subt
ract
ion
of w
hole
nu
mbe
rs o
f at l
east
4 d
igits
C
alcu
latio
n te
chni
ques
U
se a
rang
e of
tech
niqu
es to
per
form
an
d ch
eck
writ
ten
and
men
tal
calc
ulat
ions
of w
hole
num
bers
in
clud
ing:
•
estim
atio
n
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
roun
ding
off
and
com
pens
atin
g •
doub
ling
and
halv
ing
• us
ing
a nu
mbe
r lin
e •
usin
g ad
ditio
n an
d su
btra
ctio
n as
inve
rse
oper
atio
ns
Addi
tion
and
subt
ract
ion
of w
hole
nu
mbe
rs o
f at l
east
5 d
igits
C
alcu
latio
n te
chni
ques
U
sing
a ra
nge
of te
chni
ques
to
perfo
rm a
nd c
heck
writ
ten
and
men
tal
calc
ulat
ions
with
who
le n
umbe
rs
incl
udin
g:
• es
timat
ion
• ad
ding
and
sub
tract
ing
in c
olum
ns
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
roun
ding
off
and
com
pens
atin
g •
doub
ling
and
halv
ing
• us
ing
a nu
mbe
r lin
e •
usin
g ad
ditio
n an
d su
btra
ctio
n as
inve
rse
oper
atio
ns
• A
dditi
on a
nd s
ubtra
ctio
n of
who
le
num
bers
with
at l
east
6-d
igit
num
ber
• M
ultip
le o
pera
tions
on
who
le
num
bers
with
or w
ithou
t br
acke
ts
Cal
cula
tion
tech
niqu
es
Usi
ng a
rang
e of
tech
niqu
es to
pe
rform
and
che
ck w
ritte
n an
d m
enta
l cal
cula
tions
with
who
le
num
bers
incl
udin
g:
• es
timat
ion
• ad
ding
, sub
tract
ing
in c
olum
ns
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
roun
ding
off
and
com
pens
atin
g
• us
ing
addi
tion
and
subt
ract
ion
as in
vers
e op
erat
ions
•
usin
g a
calc
ulat
or
31MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Prop
ertie
s of
who
le n
umbe
rs
Rec
ogni
ze a
nd u
se th
e co
mm
utat
ive
and
asso
ciat
ive
prop
ertie
s of
who
le n
umbe
rs
Sol
ving
pro
blem
s So
lve
prob
lem
s in
con
text
s in
volv
ing
who
le n
umbe
rs, i
nclu
ding
fina
ncia
l co
ntex
ts
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e pr
oper
ties
with
w
hole
num
bers
•
0 in
term
s of
its
addi
tive
prop
erty
•
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
finan
cial
con
text
s
mea
sure
men
t con
text
s
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
•
0 in
term
s of
its
addi
tive
prop
erty
So
lvin
g pr
oble
ms
• So
lve
prob
lem
s in
volv
ing
who
le n
umbe
rs a
nd d
ecim
al
fract
ions
, inc
ludi
ng
fin
anci
al c
onte
xts
m
easu
rem
ent c
onte
xts
• So
lve
prob
lem
s in
volv
ing
who
le
num
bers
, inc
ludi
ng
com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(ra
tio)
SUG
GES
TED
M
ETH
OD
OLO
GY
• R
evis
e an
d co
nsol
idat
e w
ork
done
in G
rade
3.
• Le
arne
rs s
houl
d so
lve
prob
lem
s in
con
text
s an
d do
con
text
free
cal
cula
tions
. •
Lear
ners
sho
uld
be tr
aine
d to
judg
e th
e re
ason
able
ness
of s
olut
ions
. •
Lear
ners
sho
uld
know
that
they
can
: o
chec
k an
add
ition
cal
cula
tion
by s
ubtra
ctio
n.
Exam
ple:
If 9
6 +4
8 =1
44, t
hen
144
– 48
= 9
6 o
chec
k a
subt
ract
ion
calc
ulat
ion
by a
ddin
g.
Exa
mpl
e:14
4 –
48 =
96,
then
96
+ 48
= 1
44
32 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Cal
cula
tion
tech
niqu
es
• B
reak
ing
dow
n al
l num
bers
acc
ordi
ng to
pla
ce v
alue
par
ts to
add
.
Exam
ple:
Cal
cula
te 3
62 +
486
36
2 +
486
= 30
0 +
60 +
2 +
400
+ 8
0 +
6
2
+ 6
=
8
=
300
+ 40
0 +
60 +
80
+ 2
+ 6
or
and
60
+ 8
0
= 1
4
= 70
0 +
140
+ 8
an
d
30
0 +
400
= 70
0
= 84
8
mea
ns 3
62 +
486
= 8
48
• A
ddin
g on
(by
brea
king
dow
n th
e nu
mbe
r to
be a
dded
) Ex
ampl
e: C
alcu
late
362
+ 4
86
362
+ 40
0 →
762
+ 8
0 →
842
+ 6
→ 8
48
• Fi
lling
up
tens
(by
brea
king
dow
n th
e nu
mbe
r to
be a
dded
). Th
is c
an a
lso
be c
alle
d ro
undi
ng o
ff an
d co
mpe
nsat
ing.
Exa
mpl
e: C
alcu
late
96
+ 48
9
6 +
48 =
96
+ 4
– 4
+ 48
= 1
00 +
48
– 4
= 10
0 +
44 =
144
• B
reak
ing
dow
n bo
th n
umbe
rs a
ccor
ding
to p
lace
val
ue p
arts
to s
ubtr
act.
Ex
ampl
e: C
alcu
late
687
– 1
43
687
– 14
3 =
600
+ 80
+ 7
– 1
00 –
40
– 3
7 –
3
= 4
= 6
00 –
100
+ 8
0 –
40 +
7 –
3
or
and
80 –
40
=
40
= 5
00 +
40
+ 4
and
6
00 –
100
= 5
00
= 5
44
mea
ns 6
87 –
143
= 5
44
• B
reak
ing
dow
n al
l num
bers
acc
ordi
ng to
pla
ce v
alue
par
ts to
add
usi
ng c
ompe
nsat
ion
(cou
nter
bala
nce)
Le
arne
rs c
anno
t sub
tract
4 fr
om 3
or 8
0 fro
m 4
0. In
stea
d of
bre
akin
g do
wn
743
into
700
+ 4
0 +
3 th
ey w
ill br
eak
dow
n 74
3 in
to 6
00 +
130
+ 1
3. T
hen
they
can
sub
tract
4 fr
om 1
3 an
d 80
from
130
. Ex
ampl
e: C
alcu
late
: 743
– 6
84
743
– 68
4 =
700
+ 40
+ 3
– 6
00 –
80
– 4
= 60
0 +
130
+ 13
– 6
00 –
80
– 4
(Bre
ak u
p 74
3 in
to 6
00 +
130
+ 1
3)
= 60
0 - 6
00 +
130
– 8
0 +
13 –
4
= 5
0 +
9 =
59
33MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• Su
btra
ctin
g by
bre
akin
g do
wn
the
num
ber t
o be
sub
trac
ted
exam
ple:
C
alcu
late
687
– 1
43
687
– 10
0 →
587
– 4
0 →
547
– 3
= 5
44
or
687
– 14
0 –
3 =
547
– 3
= 54
4 •
Col
umn
met
hod
for a
ddin
g By
Gra
de 6
lear
ners
sho
uld
have
had
eno
ugh
expe
rienc
e w
ith b
reak
ing
up n
umbe
rs to
add
and
sub
tract
them
. The
ho
rizon
tal m
etho
d of
exp
andi
ng n
umbe
rs b
efor
e ad
ding
them
can
get
unw
ield
y w
hen
mor
e th
an tw
o 5-
digi
t num
bers
are
ad
ded.
Ter
m 1
lear
ners
can
revi
sit t
he e
xpan
ded
verti
cal m
etho
d, a
nd th
en m
ove
on to
the
tradi
tiona
l col
umn
met
hod
• Ex
pand
ed v
ertic
al c
olum
n m
etho
d to
add
5
6 42
3 =
5
0 00
0 +
6 00
0 +
400
+
20
+
3
+
7 58
1 =
7
000
+
5
00
+
80
+
1
+21
479
=
20
000
+
1
000
+
4
00
+
70
+
9
Tot
al
=
70 0
00
+
14 0
00
+
1 3
00
+
170
+
13
This
can
be
writ
ten
as 7
0 00
0 +
10 0
00 +
5 0
00 +
400
+ 8
0 +
3 =
85 4
83
• Th
e ve
rtic
al c
olum
n m
etho
d to
add
.
1 1
1 1
56 4
23
+ 2
1 47
9 +
7 5
81
85 48
3 •
Expa
nded
ver
tical
col
umn
met
hod
to s
ubtr
act e
xam
ple:
Cal
cula
te: 9
8 74
3 –
45 6
84
600
130
13
98
743
=
90
000
+
8
000
+
7
00
+
40
+
3
– 45
684
=
40 0
00
+
5 0
00
+
600
+
80
+
4
T
otal
=
5
0 00
0 +
3 00
0 +
0
+
50
+
9
Th
eref
ore
50 0
00 +
3 0
00 +
0 +
50
+ 9
= 53
059
34 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• T
he v
ertic
al c
olum
n m
etho
d to
sub
trac
t
6 1
3 13
98
743
– 4
5 684
53 05
9
Wor
king
with
cal
cula
tors
•
The
men
tal m
athe
mat
ics
prog
ram
me
cont
ains
wor
k on
num
ber c
once
pt, n
umbe
r fac
ts a
nd m
enta
l cal
cula
tion
tech
niqu
es.
Dai
ly w
ork
on m
enta
l Mat
hem
atic
s co
mbi
ned
with
dai
ly w
ritte
n ca
lcul
atio
ns w
ill pr
even
t lea
rner
s fro
m b
ecom
ing
depe
nden
t on
cal
cula
tors
and
not
kno
win
g ho
w to
cal
cula
te w
ithou
t the
m.
• C
alcu
lato
rs a
re a
use
ful w
ay fo
r lea
rner
s to
exp
lore
num
ber p
atte
rns
and
whe
n w
orki
ng w
ith v
ery
larg
e nu
mbe
rs.
• Le
arne
rs s
houl
d be
taug
ht h
ow to
use
cal
cula
tors
incl
udin
g ho
w to
cle
ar a
n in
corre
ctly
ent
ered
num
ber.
Lear
ners
sho
uld
alw
ays
estim
ate
answ
ers
befo
re d
oing
a c
alcu
latio
n on
a c
alcu
lato
r. Le
arne
rs s
houl
d es
timat
e w
heth
er th
eir a
nsw
ers
will
be
in te
ns, h
undr
eds,
thou
sand
s, te
n th
ousa
nds,
hun
dred
thou
sand
s or
milli
ons.
For
exa
mpl
e w
hen
addi
ng 1
2 34
5 an
d 87
654
th
ey s
houl
d es
timat
e th
at th
e an
swer
will
be b
etw
een
90 a
nd 1
00 th
ousa
nd.
Kin
ds o
f pro
blem
s •
Sum
mat
ion,
incr
ease
and
dec
reas
e, c
ompa
rison
by
diffe
renc
e •
See
the
desc
riptio
n of
pro
blem
type
s at
the
end
of th
e gr
ade
note
s LT
SM
Res
ourc
es
Num
ber l
ines
: 0 –
120
, Stru
ctur
ed -,
sem
i- st
ruct
ured
- , u
nstru
ctur
ed n
umbe
r lin
es; C
ount
ers,
Pic
ture
s, a
rrays
/ dia
gram
s, F
lash
ca
rds,
Bas
e 10
blo
cks,
100
cha
rts, m
aths
vid
eo c
lips,
E le
arni
ng re
sour
ces
onlin
e, M
aths
gam
es
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
WB
1: p
p. 1
8 –
38
Activ
ities
: 7 a
&b –
11a&
b; 1
2
WB
1: p
p. 1
4 -2
8 Ac
tiviti
es: 6
a&b
; 7a&
b; 8
a&b;
9a&
b p
98
Activ
ity: 3
1
WB
1: p
p. 1
4 - 2
4 Ac
tiviti
es: 6
a&b;
7a&
b
DB
E Te
xtbo
ok re
fere
nce
Term
1: U
nit 3
: Add
ition
and
su
btra
ctio
n, p
. 26
Term
1: U
nit 3
: Add
ition
and
su
btra
ctio
n, p
. 21
Term
1: U
nit 3
: Add
ition
and
su
btra
ctio
n, p
. 25
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
35MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
4
TER
M 1
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
……
T
ime:
3 H
OU
RS
GR
ADE
4 C
APS
pp. 4
6 –
51
5 C
APS
pp. 1
36 -1
39
6 C
APS
pp. 2
35 –
238
TO
PIC
N
umer
ic a
nd g
eom
etric
pat
tern
s C
once
pts,
Ski
lls a
nd
know
ledg
e
Inve
stig
ate
and
exte
nd p
atte
rns
• In
vest
igat
e an
d ex
tend
num
eric
pa
ttern
s lo
okin
g fo
r rel
atio
nshi
ps
or ru
les
of p
atte
rns:
-
sequ
ence
s in
volv
ing
a co
nsta
nt d
iffer
ence
or r
atio
-
of le
arne
r’s o
wn
crea
tion
• D
escr
ibe
obse
rved
rela
tions
hips
or
rule
s in
lear
ner’s
ow
n w
ords
In
put a
nd o
utpu
t val
ues
Det
erm
ine
inpu
t val
ues,
out
put v
alue
s an
d ru
les
for p
atte
rns
and
rela
tions
hips
usi
ng fl
ow d
iagr
ams
Equi
vale
nt fo
rms
Det
erm
ine
equi
vale
nce
of d
iffer
ent
desc
riptio
ns o
f the
sam
e re
latio
nshi
p or
rule
pre
sent
ed:
• ve
rbal
ly
• in
a fl
ow d
iagr
am
• by
a n
umbe
r sen
tenc
e
Inve
stig
ate
and
exte
nd p
atte
rns
• In
vest
igat
e an
d ex
tend
num
eric
pa
ttern
s lo
okin
g fo
r rel
atio
nshi
ps
or ru
les
of p
atte
rns
- se
quen
ces
inv
olvi
ng
a
cons
tant
diff
eren
ce o
r rat
io
- of
lear
ner’s
ow
n cr
eatio
n •
Des
crib
e ob
serv
ed re
latio
nshi
ps o
r ru
les
in le
arne
r’s o
wn
wor
ds
Inpu
t and
out
put v
alue
s D
eter
min
e in
put v
alue
s, o
utpu
t val
ues
and
rule
s fo
r pat
tern
s an
d re
latio
nshi
ps
usin
g flo
w d
iagr
ams
Equi
vale
nt fo
rms
Det
erm
ine
equi
vale
nce
of d
iffer
ent
desc
riptio
ns o
f the
sam
e re
latio
nshi
p or
rule
pre
sent
ed
• ve
rbal
ly
• in
a fl
ow d
iagr
am
• by
a n
umbe
r sen
tenc
e
Inve
stig
ate
and
exte
nd p
atte
rns
• In
vest
igat
e an
d ex
tend
num
eric
pa
ttern
s lo
okin
g fo
r rel
atio
nshi
ps o
r ru
les
of p
atte
rns
- se
quen
ces
invo
lvin
g a
co
nsta
nt d
iffer
ence
or r
atio
-
of le
arne
r’s o
wn
crea
tion
• D
escr
ibe
obse
rved
rela
tions
hips
or
rule
s in
lear
ner’s
ow
n w
ords
In
put a
nd o
utpu
t val
ues
Det
erm
ine
inpu
t val
ues,
out
put v
alue
s an
d ru
les
for p
atte
rns
and
rela
tions
hips
us
ing
flow
dia
gram
s Eq
uiva
lent
form
s D
eter
min
e eq
uiva
lenc
e of
diff
eren
t de
scrip
tions
of t
he s
ame
rela
tions
hip
or
rule
pre
sent
ed
• ve
rbal
ly
• in
a fl
ow d
iagr
am
• by
a n
umbe
r sen
tenc
e
36 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
SUG
GES
TED
M
ETH
OD
OLO
GY
Num
eric
pat
tern
s:
All
grad
es:
Rem
embe
r tha
t pro
gres
sion
is ta
king
pla
ce in
the
resp
ectiv
e gr
ades
as
indi
cate
d in
the
CAP
S do
cum
ent.
Sequ
ence
s of
num
bers
: Ex
ampl
es o
f the
abo
ve a
re il
lust
rate
d in
Ter
m 3
. For
Ter
m 1
the
reco
mm
enda
tion
is to
focu
s on
usi
ng in
put-o
utpu
t dia
gram
s,
with
a fo
cus
on d
evel
opin
g m
ultip
licat
ion
tabl
es a
nd th
e pr
oper
ties
of o
pera
tions
.
Patte
rns
give
n in
inpu
t-out
put d
iagr
ams
Inpu
t-out
put d
iagr
ams
are
som
etim
es c
alle
d fu
nctio
n di
agra
ms,
func
tion
mac
hine
s or
flow
dia
gram
s be
caus
e th
ey a
re a
way
of in
trodu
cing
lear
ners
to fu
nctio
nal r
elat
ions
hips
dia
gram
mat
ical
ly. F
unct
iona
l rel
atio
nshi
ps b
ecom
e ve
ry im
porta
nt in
the
Seni
or P
hase
and
FET
Mat
hem
atic
s.
The
form
s of
inpu
t-out
put d
iagr
ams
that
lear
ners
use
in th
e In
term
edia
te P
hase
mos
t ofte
n ar
e flo
w d
iagr
ams
or s
pide
rgra
ms.
Whe
n us
ing
flow
dia
gram
s, th
e co
rresp
onde
nce
betw
een
inpu
t and
out
put v
alue
s sh
ould
be
clea
r in
its re
pres
enta
tiona
l for
m
i.e. t
he fi
rst i
nput
pro
duce
s th
e fir
st o
utpu
t, th
e se
cond
inpu
t pro
duce
s th
e se
cond
out
put,
etc.
Exa
mp
le
37MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
An in
put-o
utpu
t dia
gram
can
allo
w le
arne
rs to
see
or w
ork
out t
he
• in
put v
alue
s, if
the
rule
and
a c
orre
spon
ding
out
put v
alue
are
giv
en
• ou
tput
val
ues,
if th
e ru
le a
nd a
cor
resp
ondi
ng in
put v
alue
s ar
e gi
ven
• ru
le, i
f the
rule
wor
ks fo
r eve
ry g
iven
inpu
t val
ue a
nd it
s co
rresp
ondi
ng o
utpu
t val
ue
Tabl
es a
re a
use
ful w
ay to
reco
rd p
atte
rns
in G
rade
s 4
& 5.
In G
rade
4 it
is u
sefu
l to
som
etim
es in
clud
e th
e ru
le in
a ta
ble.
Exa
mpl
e:
In T
erm
1 it
is re
com
men
ded
that
num
ber p
atte
rns
be u
sed
to d
evel
op c
once
pts
and
skills
that
will
be u
sed
in m
ultip
licat
ion
and
divi
sion
. The
focu
s ca
n be
on
inpu
t-out
put f
low
dia
gram
s th
at h
elp
lear
ners
to u
nder
stan
d an
d le
arn
abou
t
• th
e in
vers
e op
erat
ion
betw
een
mul
tiplic
atio
n an
d di
visi
on
• th
e m
ultip
licat
ion
of u
nits
by
mul
tiple
s of
ten
• th
e as
soci
ativ
e pr
oper
ty w
ith w
hole
num
bers
and
how
we
can
use
this
pro
perty
whe
n w
e m
ultip
ly b
y m
ultip
les
of 1
0
Usi
ng fl
ow d
iagr
ams
help
lear
ners
to u
nder
stan
d an
d us
e th
e fa
ct th
at m
ultip
licat
ion
and
divi
sion
are
inve
rse
oper
atio
ns
Lear
ners
are
not
exp
ecte
d to
use
the
expr
essi
on “i
nver
se o
pera
tions
”. Th
ey a
re e
xpec
ted
to k
now
that
• th
ey c
an u
se m
ultip
licat
ion
to c
heck
div
isio
n ca
lcul
atio
ns
• th
ey c
an u
se d
ivis
ion
to c
heck
mul
tiplic
atio
n ca
lcul
atio
ns
38 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Afte
r com
plet
ing
a nu
mbe
r of s
imila
r exa
mpl
es, l
earn
ers
can
be a
sked
to e
xpla
in w
hat t
hey
notic
e in
thei
r ow
n w
ords
. If l
earn
ers
writ
e pa
irs o
f mat
chin
g nu
mbe
r sen
tenc
es b
ased
on
the
inpu
t and
out
put v
alue
s in
the
flow
dia
gram
s, th
ey c
an d
iscu
ss u
sing
mul
tiplic
atio
n to
che
ck d
ivis
ion
and
usin
g di
visi
on to
che
ck m
ultip
licat
ion.
Furt
her e
xam
ple
Lear
ners
can
use
the
abov
e kn
owle
dge
to in
dica
te h
ow th
ey c
ould
com
plet
e th
e m
issi
ng in
put n
umbe
rs in
a fl
ow d
iagr
am
O
nce
lear
ners
hav
e co
mpl
eted
the
flow
dia
gram
, the
y ca
n di
scus
s ho
w th
ey fo
und
the
mis
sing
inpu
t val
ues
from
the
corre
spon
ding
out
put v
alue
s an
d ru
le.
39MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Usi
ng fl
ow d
iagr
ams
to h
elp
lear
ners
dev
elop
mul
tiplic
atio
n an
d di
visi
on te
chni
ques
Ass
ocia
tive
prop
erty
Num
bers
can
be
mul
tiplie
d in
any
ord
er.
Exam
ple:
11
x (3
x 2
) = (1
1 x
3) x
2
Lear
ners
can
dis
cuss
wha
t the
y no
tice
whe
n th
ey c
ompa
re th
e ex
ampl
es. L
earn
ers
are
not r
equi
red
to k
now
the
nam
es o
f
the
prop
ertie
s. T
hey
are
only
exp
ecte
d to
use
them
to m
ake
calc
ulat
ions
eas
ier o
r use
equ
ival
ent n
umbe
r sen
tenc
es.
Usi
ng fl
ow d
iagr
ams
to h
elp
lear
ners
thin
k ab
out a
nd u
se te
chni
ques
for m
ultip
lyin
g by
10
Lear
ners
com
plet
e a
flow
dia
gram
like
the
one
belo
w. T
hey
then
exp
lain
usi
ng th
eir o
wn
wor
ds w
hat t
hey
notic
e ab
out t
he in
put
and
outp
ut v
alue
40 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Lear
ners
can
then
be
aske
d: “W
hat i
s an
othe
r way
to m
ultip
ly b
y 6?
”
Lear
ners
can
dev
elop
fast
men
tal a
nd w
ritte
n te
chni
ques
bas
ed o
n th
is.
All c
once
pts
and
calc
ulat
ing
tech
niqu
es d
evel
oped
her
e ca
n be
pra
ctic
ed th
roug
hout
the
year
in th
e m
enta
l Mat
hem
atic
s
prog
ram
me.
Gra
de 6
: C
omm
utat
ive
prop
erty
Num
bers
can
be
mul
tiplie
d in
any
ord
er.
Exam
ple:
13
x 5
x 2
= 13
x 2
x 5
..
41MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Lear
ners
can
dis
cuss
wha
t the
y no
tice
whe
n th
ey c
ompa
re th
e
exam
ples
. Lea
rner
s ar
e no
t req
uire
d to
kno
w th
e na
me
of th
e
com
mut
ativ
e pr
oper
ty. T
hey
are
only
exp
ecte
d to
be
able
to u
se
it to
sim
plify
cal
cula
tions
or t
o us
e eq
uiva
lent
sta
tem
ents
.
Geo
met
ric p
atte
rns
LTSM
Res
ourc
es
Num
ber l
ines
: 0 –
120
, Stru
ctur
ed -,
sem
i- st
ruct
ured
- , u
nstru
ctur
ed n
umbe
r lin
es; C
ount
ers,
Pic
ture
s, a
rrays
/ dia
gram
s, F
lash
ca
rds,
Bas
e 10
blo
cks,
100
cha
rts, m
ultip
licat
ion
tabl
e, m
aths
vid
eo c
lips,
E le
arni
ng o
nlin
e re
sour
ces,
Mat
hs g
ames
Gra
de 4
G
rade
5
Gra
de 6
W
orkb
ook
refe
renc
e W
B 1
: pp
. 40
– 42
Ac
tiviti
es: 1
3 &
14
pp. 1
36 –
138
Ac
tiviti
es: 5
1, 5
2
WB
1:
pp
. 34
- 40
Activ
ities
11;
12;
13
& 14
pp
. 152
– 1
54
Activ
ities
55,
56
WB
1:
pp. 7
2 –
74 ;
98 -
102
Activ
ities
: 24
a&b)
; 35
- 37
DB
E Te
xtbo
ok re
fere
nce
Te
rm 1
: Uni
t 4: N
umer
ic P
atte
rns,
p. 5
1 Te
rm 2
: Uni
t 7: G
eom
etric
Pat
tern
s, p
. 18
1
Term
1: U
nit 4
: Num
eric
Pat
tern
s, p
. 4
Term
2: U
nit 7
: Geo
met
ric P
atte
rns,
p.
176
Term
1: U
nit 8
: Num
eric
Pat
tern
s, p
. 10
8 Te
rm 2
: Uni
t 4: G
eom
etric
Pat
tern
s,
p. 1
52
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent –
Te
st
42 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
5
TER
M 1
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to
……
…
Tim
e: 5
HO
UR
S G
RAD
E 4
CAP
S pp
. 52
– 55
5
CAP
S pp
. 140
-143
6
CAP
S pp
. 241
– 2
43 &
pp.
250
- 25
1 TO
PIC
M
ultip
licat
ion
and
divi
sion
of w
hole
num
bers
C
once
pts,
Ski
lls a
nd
know
ledg
e
Mul
tiplic
atio
n of
at l
east
who
le
2-di
git b
y 2-
digi
t num
bers
Div
isio
n of
at l
east
who
le 3
-dig
it by
1-
digi
t num
bers
C
alcu
latio
n te
chni
ques
U
se a
rang
e of
tech
niqu
es to
per
form
an
d ch
eck
writ
ten
and
men
tal
calc
ulat
ions
of w
hole
num
bers
incl
udin
g:
es
timat
ion
bu
ildin
g up
and
bre
akin
g do
wn
num
bers
roun
ding
off
and
com
pens
atin
g
doub
ling
and
halv
ing
us
ing
a nu
mbe
r lin
e
usin
g ad
ditio
n an
d su
btra
ctio
n as
in
vers
e op
erat
ions
usin
g m
ultip
licat
ion
and
divi
sion
as
inve
rse
oper
atio
ns
M
ultip
licat
ion
of a
t lea
st w
hole
3
-di
git b
y 2-
digi
t num
bers
Div
isio
n of
at l
east
who
le 3
-dig
it by
2-
digi
t num
bers
C
alcu
latio
n te
chni
ques
U
sing
a ra
nge
of te
chni
ques
to p
erfo
rm
and
chec
k w
ritte
n an
d m
enta
l ca
lcul
atio
ns o
f who
le n
umbe
rs in
clud
ing:
estim
atio
n
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
us
ing
a nu
mbe
r lin
e
roun
ding
off
and
com
pens
atin
g
doub
ling
and
halv
ing
us
ing
addi
tion
and
subt
ract
ion
as
inve
rse
oper
atio
ns
us
ing
mul
tiplic
atio
n an
d di
visi
on a
s in
vers
e op
erat
ions
M
ultip
licat
ion
of a
t lea
st w
hole
4-
digi
t by
3-di
git n
umbe
rs
D
ivis
ion
of a
t lea
st w
hole
4-d
igit
by
3-di
git n
umbe
rs
M
ultip
le o
pera
tions
on
who
le
num
bers
with
or w
ithou
t bra
cket
s Cal
cula
tion
tech
niqu
es in
clud
e U
sing
a ra
nge
of te
chni
ques
to p
erfo
rm
and
chec
k w
ritte
n an
d m
enta
l ca
lcul
atio
ns o
f who
le n
umbe
rs in
clud
ing:
estim
atio
n
mul
tiply
ing
in c
olum
ns
bu
ildin
g up
and
bre
akin
g do
wn
num
bers
roun
ding
off
and
com
pens
atin
g
usin
g a
calc
ulat
or
us
ing
the
reci
proc
al re
latio
nshi
p be
twee
n m
ultip
licat
ion
and
divi
sion
long
div
isio
n
43MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s M
ultip
les
of 1
-dig
it nu
mbe
rs to
at l
east
10
0 Pr
oper
ties
of w
hole
num
bers
R
ecog
nize
and
use
the
com
mut
ativ
e;
asso
ciat
ive;
and
dis
tribu
tive
prop
ertie
s of
who
le n
umbe
rs
Solv
ing
prob
lem
s
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g w
hole
num
bers
: -
finan
cial
con
text
s -
mea
sure
men
t con
text
s
So
lve
prob
lem
s in
volv
ing
who
le
num
bers
: -
com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(ra
tio)
- co
mpa
ring
two
quan
titie
s of
di
ffere
nt k
inds
(rat
e)
- gr
oupi
ng a
nd e
qual
sha
ring
with
rem
aind
ers
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s
Mul
tiple
s of
2-d
igit
who
le n
umbe
rs
to a
t lea
st 1
00
Fa
ctor
s of
2-d
igit
who
le n
umbe
rs to
at
leas
t 100
Prop
ertie
s of
who
le n
umbe
rs
R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
0 in
term
s of
its
addi
tive
prop
erty
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
-
finan
cial
con
text
s -
mea
sure
men
t con
text
s
So
lve
prob
lem
s in
volv
ing
who
le
num
bers
, inc
ludi
ng:
- co
mpa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd
(ratio
) -
com
parin
g tw
o qu
antit
ies
of
diffe
rent
kin
ds (r
ate)
-
grou
ping
and
equ
al s
harin
g w
ith re
mai
nder
s
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s
Mul
tiple
s of
2-d
igit
and
3-di
git
num
bers
Fact
ors
of 2
-dig
it an
d 3-
digi
t who
le
num
bers
Prim
e fa
ctor
s of
num
bers
to a
t le
ast 1
00
Prop
ertie
s of
who
le n
umbe
rs
R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
0 in
term
s of
its
addi
tive
prop
erty
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs a
nd d
ecim
al fr
actio
ns,
incl
udin
g -
finan
cial
con
text
s -
mea
sure
men
t con
text
s
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
-
com
parin
g tw
o or
mor
e qu
antit
ies
of
the
sam
e ki
nd
(ratio
) -
com
parin
g tw
o qu
antit
ies
of
diffe
rent
kin
ds (r
ate)
-
grou
ping
and
equ
al s
harin
g w
ith re
mai
nder
s
44 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
SUG
GES
TED
M
ETH
OD
OLO
GY
Le
arne
rs s
houl
d do
roun
ding
off
to th
e ne
ares
t 10,
to e
stim
ate
answ
ers.
Lear
ners
sho
uld
do c
onte
xt fr
ee c
alcu
latio
ns a
nd s
olve
pro
blem
s in
con
text
s
Judg
ing
reas
onab
lene
ss o
f sol
utio
ns
Lear
ners
sho
uld
estim
ate
thei
r ans
wer
s be
fore
cal
cula
ting.
The
y co
uld
roun
d of
f the
num
bers
invo
lved
in th
e ca
lcul
atio
ns.
Le
arne
rs c
an ro
und
off t
o th
e ne
ares
t 10
whe
n m
ultip
lyin
g or
div
idin
g w
ith 2
-dig
it nu
mbe
rs
Che
ckin
g so
lutio
ns
Le
arne
rs s
houl
d kn
ow th
at th
ey c
an c
heck
a d
ivis
ion
calc
ulat
ion
by m
ultip
lyin
g Ex
ampl
e: If
69
÷ 3
= 23
; the
n 23
x 3
= 6
9
Lear
ners
sho
uld
know
that
to c
heck
a d
ivis
ion
calc
ulat
ion
with
a re
mai
nder
, the
y sh
ould
firs
t mul
tiply
div
iden
d by
the
divi
sor
and
then
add
the
rem
aind
er
Exam
ple:
If 7
0 ÷
3 =
23 re
mai
nder
1; t
hen
23 x
3 =
69
ther
efor
e 69
+ 1
=70
Usi
ng th
e in
vers
e op
erat
ion
to c
heck
sol
utio
ns is
one
reas
on fo
r tea
chin
g m
ultip
licat
ion
and
divi
sion
toge
ther
. Ano
ther
reas
on
for l
ooki
ng a
t mul
tiplic
atio
n an
d di
visi
on to
geth
er is
that
we
alm
ost a
lway
s us
e m
ultip
licat
ion
to s
olve
div
isio
n.
In G
rade
4 le
arne
rs b
reak
up
num
bers
to m
ultip
ly. T
here
are
diff
eren
t way
s of
doi
ng th
is.
Som
etim
es th
e nu
mbe
rs in
volv
ed
in th
e ca
lcul
atio
n m
ake
diffe
rent
met
hods
eas
ier
or m
ore
diffi
cult.
Lea
rner
s ha
ve a
lread
y se
en h
ow to
use
the
asso
ciat
ive
and
com
mut
ativ
e pr
oper
ties
to m
ake
mul
tiplic
atio
n ea
sier
. Mul
tiplic
atio
n an
d th
e di
strib
utiv
e pr
oper
ty o
f mul
tiplic
atio
n ov
er a
dditi
on/s
ubtr
actio
n O
ne w
ay fo
r lea
rner
s to
und
erst
and
how
and
why
the
dist
ribut
ive
prop
erty
wor
ks, i
s to
bre
ak u
p ar
rays
and
writ
e nu
mbe
r se
nten
ces
to d
escr
ibe
the
arra
ys.
9
x 5
=
5 x
5
+
4
x 5
45MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
The
dist
ribut
ive
law
allo
ws
lear
ners
to s
plit
the
num
ber a
nd th
en m
ultip
ly e
ach
part
sepa
rate
ly.
Usi
ng fa
ctor
s to
mul
tiply
Ex
ampl
e:
Cal
cula
te 4
7 x
6 47
x 6
= 4
7 x
2 x
3 =
94 x
3
= (9
0 +
4) x
3
= 90
x 3
+ 4
x 3
=
270
+ 12
=
282
Usi
ng th
e di
strib
utiv
e pr
oper
ty to
mul
tiply
Ex
ampl
e:
47 x
5 =
40
x 5
+ 7
x 5
(
usi
ng th
e di
strib
utiv
e pr
oper
ty)
= 4
x 10
x 5
+ 3
5 =
4 x
5 x
10 +
35
= 20
0 +
35
=
235
or
47 x
5 =
(50
– 3)
x 5
(usi
ng th
e di
strib
utiv
e pr
oper
ty)
= (5
0 x
5) –
(3 x
5)
= 5
x 5
x 10
– 1
5 =
250
– 1
5 =
235
Div
idin
g Le
arne
rs u
se w
hat t
hey
know
abo
ut m
ultip
licat
ion
to d
o di
visi
on.
Exam
ple
75 ÷
4
46 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Lear
ners
can
writ
e ou
t a “
clue
boa
rd”
of w
hat t
hey
know
abo
ut m
ultip
lyin
g by
4
Exam
ple:
4
x 10
= 4
0 4
x 20
= 8
0 (d
oubl
ing
the
first
sta
tem
ent)
4 x
5 =
20 (h
alvi
ng th
e fir
st s
tate
men
t) 4
x 4
= 16
4
x 3
= 12
75
cou
ld b
e w
ritte
n as
40
+ 20
+ 1
2 +
3 =
4×
10+
4×
5+
4×3
+3
The
refo
re, 7
5 ÷
4 =
40÷
4+20
÷4+
12÷
4+𝑡𝑡ℎ𝑒𝑒 𝑟𝑟
𝑒𝑒𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑒𝑒𝑟𝑟 𝑜𝑜𝑜𝑜
3 =
10
+ 5
+ 3
+ re
mai
nder
3 =
18
rem
aind
er 3
Le
arne
rs s
houl
d ch
eck
thei
r cal
cula
tions
by
mul
tiply
ing
and
addi
ng th
e re
mai
nder
: 18
x 4
= 72
and
72
+ 3
= 75
. K
inds
of p
robl
ems
Shar
ing,
gro
upin
g, tr
eatin
g gr
oups
as
units
, rat
e,
See
the
desc
riptio
n of
pro
blem
typ
es a
t th
e en
d of
the
gra
de
note
s LT
SM
Res
ourc
es
Num
ber l
ines
: 0 –
120
, Stru
ctur
ed -,
sem
i- st
ruct
ured
- , u
nstru
ctur
ed n
umbe
r lin
es; C
ount
ers,
Pic
ture
s, a
rrays
/ dia
gram
s, F
lash
ca
rds,
Bas
e 10
blo
cks,
100
cha
rts, m
ultip
licat
ion
tabl
e, m
aths
vid
eo c
lips,
E le
arni
ng o
nlin
e re
sour
ces,
Mat
hs g
ames
, cal
cula
tors
Gra
de 4
G
rade
5
Gra
de 6
W
orkb
ook
refe
renc
e W
B 1
: pp
. 118
– 1
24
Activ
ities
: 44a
&b; 4
5a&b
pp
. 158
– 1
60
Activ
ities
: 62,
63
WB
1:
pp. 4
2 –
48
Activ
ities
: 15a
&b, 1
6 a&
b pp
. 128
Ac
tiviti
es: 4
4a&b
WB
1:
pp. 8
4 –
86
Activ
ities
28;
29
pp
. 122
- 12
4
Activ
ities
45,
46
DB
E Te
xtbo
ok
refe
renc
e Te
rm 1
: Uni
t 5: M
ultip
licat
ion
and
divi
sion
of
who
le n
umbe
rs, p
. 60
Term
1: U
nit 9
: Who
le N
umbe
r: M
ultip
licat
ion
and
divi
sion
, p. 1
04
Term
1: U
nit 5
: Mul
tiplic
atio
n an
d di
visi
on o
f who
le n
umbe
rs, p
. 55
Term
2: U
nit 2
: Mul
tiplic
atio
n of
who
le
num
bers
, p. 1
25
Term
2: U
nit 6
: Div
isio
n of
who
le
num
bers
, p. 1
65
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
47MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTIG
RAD
E LE
SSO
N P
LAN
6
TER
M 1
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
……
Tim
e: 6
HO
UR
S G
RAD
E 4
CAP
S p.
55
5 C
APS
pp. 1
44 &
186
6 C
APS
pp. 2
28 &
266
TO
PIC
Ti
me
Con
cept
s, S
kills
and
kn
owle
dge
Rea
ding
tim
e an
d tim
e in
stru
men
ts
Rea
d, te
ll an
d w
rite
time
in 1
2-ho
ur a
nd
24-h
our f
orm
ats
on b
oth
anal
ogue
and
di
gita
l ins
trum
ents
in:
• ho
urs
• m
inut
es
• se
cond
s In
stru
men
ts in
clud
e cl
ocks
and
wat
ches
R
eadi
ng c
alen
dars
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng
with
tim
e in
clud
e •
Cal
cula
tion
of
the
num
ber
of
days
be
twee
n an
y tw
o da
tes
with
in t
he s
ame
or c
onse
cutiv
e ye
ars
•
Cal
cula
tion
of ti
me
inte
rval
s w
here
tim
e is
giv
en in
min
utes
or h
ours
on
ly
Rea
ding
tim
e an
d tim
e in
stru
men
ts
Rea
d, te
ll an
d w
rite
time
in 1
2-ho
ur
and
24-h
our f
orm
ats
on b
oth
anal
ogue
an
d di
gita
l ins
trum
ents
in
• ho
urs
• m
inut
es
• se
cond
s In
stru
men
ts in
clud
e cl
ocks
, wat
ches
an
d st
opw
atch
es
Rea
ding
cal
enda
rs
Cal
cula
tions
and
pro
blem
sol
ving
re
late
d to
tim
e in
clud
e C
alcu
latio
n of
tim
e in
terv
als
whe
re
time
is g
iven
in
• se
cond
s an
d/or
min
utes
Rea
ding
tim
e an
d tim
e in
stru
men
ts
Rea
d, te
ll an
d w
rite
time
in 1
2-ho
ur a
nd
24-h
our f
orm
ats
on b
oth
anal
ogue
and
di
gita
l ins
trum
ents
in
• ho
urs
• m
inut
es
• se
cond
s In
stru
men
ts in
clud
e cl
ocks
, wat
ches
an
d st
opw
atch
es
Rea
ding
cal
enda
rs
Cal
cula
tions
and
pro
blem
-sol
ving
re
late
d to
tim
e •
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g tim
e •
Rea
d tim
e zo
ne m
aps
and
calc
ulat
ing
time
diffe
renc
es
base
d on
tim
e zo
nes
• C
alcu
latio
n of
tim
e in
terv
als
whe
re
time
is g
iven
in
• se
cond
s an
d/or
min
utes
;
48 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
His
tory
of t
ime
Know
s ho
w ti
me
was
mea
sure
d an
d re
pres
ente
d in
anc
ient
tim
es
• m
inut
es a
nd/o
r hou
rs
• ho
urs
and/
or d
ays
• da
ys a
nd/o
r wee
ks a
nd/o
r mon
ths
• m
onth
s an
d/or
yea
rs
• ye
ars
and/
or d
ecad
es
His
tory
of t
ime
Know
how
tim
e w
as m
easu
red
and
expr
esse
d in
anc
ient
tim
es.
Prac
tical
mea
surin
g of
tem
pera
ture
by
es
timat
ing,
mea
surin
g, re
cord
ing,
co
mpa
ring
and
orde
ring
Mea
surin
g in
stru
men
ts:
ther
mom
eter
s U
nits
de
gree
s C
elsi
us (o
C)
Cal
cula
tions
and
pro
blem
-so
lvin
g re
late
d to
tem
pera
ture
•
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g to
tem
pera
ture
•
Cal
cula
te te
mpe
ratu
re d
iffer
ence
s lim
ited
to p
ositi
ve w
hole
num
bers
• m
inut
es a
nd/o
r hou
rs
• ho
urs
and
/or d
ays
• da
ys a
nd/o
r wee
ks a
nd/o
r mon
ths
• ye
ars
and/
or d
ecad
es
• ce
ntur
ies,
dec
ades
and
yea
rs
His
tory
of t
ime
Know
som
e w
ays
in w
hich
tim
e w
as
mea
sure
d an
d re
pres
ente
d in
the
past
.
Prac
tical
mea
surin
g of
tem
pera
ture
by
es
timat
ing,
mea
surin
g, re
cord
ing,
co
mpa
ring
and
orde
ring
M
easu
ring
inst
rum
ents
ther
mom
eter
s (a
nalo
gue
and
digi
tal)
Uni
ts
degr
ees
Cel
sius
(oC
) C
alcu
latio
ns a
nd p
robl
em-
solv
ing
rela
ted
tem
pera
ture
So
lvin
g pr
oble
ms
in c
onte
xts
rela
ted
to
tem
pera
ture
s
SUG
GES
TED
M
ETH
OD
OLO
GY
Tim
e:
Lear
ners
sho
uld
cont
inue
to re
ad c
lock
s an
d te
ll th
e tim
e at
freq
uent
inte
rval
s du
ring
the
entir
e ye
ar. T
his
can
be d
one
durin
g th
e M
enta
l Mat
hem
atic
s tim
e or
just
bef
ore
or a
fter b
reak
tim
e or
bef
ore
lear
ners
go
hom
e, o
r whe
n th
ey c
ome
in fr
om a
cla
ss in
an
othe
r ven
ue.
All g
rade
s In G
rade
3 le
arne
rs w
ork
with
ana
logu
e an
d di
gita
l clo
cks
usin
g 12
-hou
r for
mat
. In
Gra
de 4
lear
ners
mov
e on
to d
igita
l 24
-hou
r for
mat
.
49MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Onc
e le
arne
rs h
ave
been
lear
nt to
tell
the
time,
furth
er p
ract
ise
can
take
pla
ce d
urin
g m
enta
l mat
hem
atic
s tim
e.
Lear
ners
con
tinue
to re
ad c
alen
dars
. C
alcu
latio
ns a
nd p
robl
em-s
olvi
ng w
ith ti
me
incl
ude
• ca
lcul
atio
n of
the
num
ber o
f day
s be
twee
n an
y tw
o da
tes
with
in th
e sa
me
or c
onse
cutiv
e ye
ars
• ca
lcul
atio
n of
tim
e in
terv
als
whe
re ti
me
is g
iven
in m
inut
es a
nd/o
r hou
rs o
nly
• ca
lcul
atio
ns s
houl
d be
lim
ited
to w
hole
num
bers
and
com
mon
frac
tions
Le
arne
rs s
houl
d co
ntin
ue to
read
clo
cks
and
tell
the
time
at fr
eque
nt in
terv
als
durin
g th
e en
tire
year
. Thi
s ca
n be
don
e du
ring
the
men
tal M
athe
mat
ics
time
or ju
st b
efor
e or
afte
r bre
ak ti
me
or b
efor
e le
arne
rs g
o ho
me,
or w
hen
they
com
e in
from
a c
lass
in
anot
her v
enue
. G
rade
s 5
and
6:
Stop
wat
ches
are
intro
duce
d.
Lear
ners
can
eith
er u
se s
topw
atch
es th
at o
ccur
as
sing
le in
stru
men
ts, o
r sto
pwat
ches
on
cell
phon
es o
r wris
t wat
ches
. Le
arne
rs c
ontin
ue to
read
, rec
ord
and
calc
ulat
e tim
e in
12-h
our a
nd 2
4-ho
ur fo
rmat
s an
d to
wor
k w
ith a
nalo
gue
and
digi
tal
inst
rum
ents
. Th
is is
pra
ctis
ed re
gula
rly. O
nce
lear
ners
hav
e be
en ta
ught
to te
ll th
e tim
e, it
can
be
prac
tised
dur
ing
the
men
tal m
athe
mat
ics
sect
ion
of th
e le
sson
, and
freq
uent
ly a
t oth
er ti
mes
dur
ing
the
day.
Le
arne
rs c
ontin
ue to
read
cal
enda
rs
Cal
cula
tions
and
pro
blem
-sol
ving
rela
ted
to ti
me
Dec
ades
are
intro
duce
d.
Cal
cula
tions
sho
uld
be li
mite
d to
who
le n
umbe
rs a
nd fr
actio
ns.
Gra
de 6
: W
hat i
s di
ffere
nt to
Gra
de 5
? • T
ime
zone
s ar
e in
trodu
ced.
50 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• C
entu
ries
are
intro
duce
d O
nce
lear
ners
hav
e be
en ta
ught
to te
ll th
e tim
e, th
is c
an b
e pr
actis
ed d
urin
g th
e m
enta
l Mat
hem
atic
s se
ctio
n of
the
less
on.
Lear
ners
con
tinue
to re
ad c
alen
dars
, and
do
calc
ulat
ions
bas
ed o
n da
tes.
C
alcu
latio
ns a
nd p
robl
em-s
olvi
ng re
late
d to
tim
e in
clud
e C
alcu
latio
ns w
ith a
nd c
onve
rsio
ns b
etw
een
all t
he u
nits
men
tione
d in
the
colu
mn
on th
e le
ft.
Tim
e zo
nes
Lear
ners
sho
uld
be a
ble
to:
• rea
d tim
e zo
ne m
aps
and
do c
alcu
latio
ns u
sing
zon
ed m
aps.
Hel
p le
arne
rs to
und
erst
and
why
ther
e ar
e tim
e zo
ne
diffe
renc
es b
etw
een
diffe
rent
pla
ces
in th
e w
orld
• c
alcu
late
tim
e di
ffere
nces
whe
n gi
ven
cloc
k fa
ces
show
ing
the
times
in d
iffer
ent p
lace
s.
Tem
pera
ture
: Intro
duce
dec
ades
in G
rade
5. C
alcu
latio
ns s
houl
d be
lim
ited
to w
hole
num
bers
and
frac
tions
. G
rade
5 a
nd 6
lear
ners
sho
uld
also
use
com
mon
tem
pera
ture
refe
rent
s e.
g.
• th
e fre
ezin
g po
int o
f pur
e w
ater
is 0
o C
• th
e bo
iling
poin
t of p
ure
wat
er is
100
o C
• th
e av
erag
e no
rmal
hum
an b
ody
tem
pera
ture
is 3
7oC
•
the
daily
env
ironm
enta
l tem
pera
ture
s.
Lear
ners
sho
uld
read
tem
pera
ture
s on
pic
ture
s of
ther
mom
eter
s. W
here
pos
sibl
e le
arne
rs s
houl
d re
ad te
mpe
ratu
res
on re
al
ther
mom
eter
s.
Rea
ding
ana
logu
e th
erm
omet
ers
requ
ires
lear
ners
to re
ad th
e te
mpe
ratu
re o
n nu
mbe
red
and
un-n
umbe
red
grad
atio
n lin
es.
In th
erm
omet
ers
desi
gned
to re
ad th
e en
viro
nmen
tal t
empe
ratu
res
the
unnu
mbe
red
grad
atio
n lin
es o
ften
refe
r to
who
le
degr
ees.
In th
erm
omet
ers
desi
gned
to re
ad h
uman
bod
y te
mpe
ratu
re th
e un
num
bere
d gr
adat
ion
lines
ofte
n re
fer t
o fra
ctio
ns
of d
egre
es.
Rec
ordi
ng a
nd re
port
ing
on te
mpe
ratu
re m
easu
rem
ents
51MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Lear
ners
sho
uld
reco
rd a
nd re
port
on te
mpe
ratu
re m
easu
rem
ents
they
hav
e re
ad o
ff th
erm
omet
ers
in w
hole
num
bers
. Thi
s m
ay in
volv
e ro
undi
ng u
p or
dow
n. T
hey
can
also
reco
rd a
nd re
port
tem
pera
ture
s by
usi
ng fr
actio
n no
tion.
G
rade
6 le
arne
rs s
houl
d do
cal
cula
tions
with
and
con
vers
ions
bet
wee
n tim
e zo
nes.
The
y sh
ould
be
able
to:
• re
ad ti
me
zone
map
s an
d do
cal
cula
tions
usi
ng z
oned
map
s. H
elp
lear
ners
to u
nder
stan
d w
hy th
ere
are
time
zone
di
ffere
nces
bet
wee
n di
ffere
nt p
lace
s in
the
wor
ld
• ca
lcul
ate
time
diffe
renc
es w
hen
give
n cl
ock
face
s sh
owin
g th
e tim
es in
diff
eren
t pla
ces.
Cal
cula
tions
and
pro
blem
-sol
ving
with
tim
e an
d te
mpe
ratu
re in
clud
e •
calc
ulat
ion
of th
e nu
mbe
r of d
ays
betw
een
any
two
date
s w
ithin
the
sam
e or
con
secu
tive
year
s •
calc
ulat
ion
of ti
me
inte
rval
s w
here
tim
e is
giv
en in
min
utes
and
/or h
ours
onl
y •
calc
ulat
ions
lim
ited
to w
hole
num
bers
and
com
mon
frac
tions
for G
rade
4 a
nd 5
(Gra
de 6
sho
uld
do p
robl
ems
that
invo
lve
de
cim
al fr
actio
ns).
LTSM
Res
ourc
es
Anal
ogue
and
dig
ital c
lock
s, c
alen
dar,
stop
wat
ch, c
ellp
hone
, wor
ld ti
me
zone
cha
rts, t
herm
omet
er, n
ewsp
aper
wea
ther
repo
rts,
vide
o cl
ips,
E le
arni
ng o
nlin
e re
sour
ces,
Mat
hs g
ames
,
Gra
de 4
G
rade
5
Gra
de 6
W
orkb
ook
refe
renc
e W
B 1
: pp
50
– 56
Ac
tiviti
es: 1
8a&b
,19a
&b
WB
1:
pp. 6
0 -6
4
Activ
ities
: (20
a&b;
21)
W
B 2
: pp
. 68
- 70
Activ
ities
: 94
, 95
WB
1:
pp. 4
6 - 5
2 ; 1
44
Activ
ities
: 16a
&b; 1
7a&b
, 54
WB
2:
pp. 6
2 –
66
Activ
ity: 8
5a&b
, 86
DB
E Te
xtbo
ok re
fere
nce
Te
rm 1
: Uni
t 6: T
ime,
p. 7
3
Term
1: U
nit 6
: Tim
e, p
. 69
Term
3: U
nit 8
: Tem
pera
ture
, p. 2
52
Term
1: U
nit 5
: Tim
e, p
. 72
Term
3: U
nit 7
: Tem
pera
ture
, p. 2
58
HO
MEW
OR
K
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
52 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
7
TER
M 1
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
……
T
ime:
6 H
OU
RS
GR
ADE
4 C
APS
pp. 5
7 - 5
8 5
CAP
S pp
. 145
-146
6
CAP
S pp
. 233
TO
PIC
D
ata
hand
ling
Con
cept
s, S
kills
and
kn
owle
dge
• C
olle
ct d
ata
usin
g ta
lly m
arks
and
ta
bles
for r
ecor
ding
•
Dra
w a
var
iety
of g
raph
s to
dis
play
an
d in
terp
ret d
ata
incl
udin
g:
- pi
ctog
raph
s (o
ne-
to-o
ne
repr
esen
tatio
n)
- ba
r gra
phs
• C
ritic
ally
read
and
inte
rpre
t dat
a re
pres
ente
d in
-
wor
ds
- pi
ctog
raph
s -
bar g
raph
s -
pie
char
ts
• C
olle
ct d
ata
usin
g ta
lly m
arks
and
ta
bles
for r
ecor
ding
•
Ord
er d
ata
from
sm
alle
st g
roup
to
larg
est g
roup
•
Dra
w a
var
iety
of g
raph
s to
dis
play
an
d in
terp
ret d
ata
incl
udin
g -
pict
ogra
phs
(man
y-to
-one
co
rresp
onde
nce)
-
bar g
raph
s •
Crit
ical
ly re
ad a
nd in
terp
ret d
ata
repr
esen
ted
in
- w
ords
-
pict
ogra
phs
- ba
r gra
phs
- pi
e ch
arts
• C
olle
ct d
ata
- U
se ta
lly m
arks
and
tabl
es fo
r re
cord
ing
- U
se s
impl
e qu
estio
nnai
res
(yes
/no
type
resp
onse
) •
Ord
er d
ata
from
sm
alle
st g
roup
to
larg
est g
roup
•
Dra
w a
var
iety
of g
raph
s to
dis
play
an
d in
terp
ret d
ata
incl
udin
g -
pict
ogra
phs
with
man
y-to
-one
repr
esen
tatio
ns
- ba
r gra
phs
and
doub
le b
ar
grap
hs
• C
ritic
ally
read
and
inte
rpre
t dat
a re
pres
ente
d in
-
wor
ds
- pi
ctog
raph
s -
bar g
raph
s -
doub
le b
ar g
raph
s -
pie
char
ts
53MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• An
alys
e da
ta b
y an
swer
ing
ques
tions
re
late
d to
dat
a ca
tego
ries
• An
alys
e da
ta b
y an
swer
ing
ques
tions
re
late
d to
- da
ta c
ateg
orie
s -
data
sou
rces
and
con
text
s •
Sum
mar
ise
data
ver
bally
and
in s
hort
writ
ten
para
grap
hs th
at in
clud
e -
draw
ing
conc
lusi
ons
abou
t the
da
ta
- m
akin
g pr
edic
tions
bas
ed o
n th
e da
ta
• Ex
amin
e un
grou
ped
num
eric
al d
ata
to d
eter
min
e th
e m
ost f
requ
ently
oc
curri
ng s
core
in th
e da
ta s
et
(mod
e)
• An
alys
e da
ta b
y an
swer
ing
ques
tions
rela
ted
to
-
data
cat
egor
ies,
incl
udin
g da
ta
inte
rval
s -
data
sou
rces
and
con
text
s -
cent
ral t
ende
ncie
s –
(mod
e an
d m
edia
n)
• Su
mm
aris
e da
ta v
erba
lly a
nd in
sh
ort w
ritte
n pa
ragr
aphs
that
incl
ude
- dr
awin
g co
nclu
sion
s ab
out t
he
data
-
mak
ing
pred
ictio
ns b
ased
on
the
data
LTSM
R
esou
rces
Ex
empl
ers
of p
icto
grap
hs, b
ar g
raph
s, p
ie c
harts
– (c
onte
xt s
ensi
tive)
, IC
T –
Exce
l wor
kshe
ets
with
gra
phs,
vid
eo
clip
s, E
lear
ning
onl
ine
reso
urce
s, M
aths
gam
es,
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
WB
1:
pp. 5
8 -6
2 Ac
tiviti
es: 2
0; 2
1a&b
WB
1:
pp. 6
6 –
68
Activ
ities
: 22a
&b
WB
1:
pp. 7
8 –
88
Activ
ities
: 92a
&b, 9
3, 9
4, 9
5, 9
5 D
BE
Text
book
refe
renc
e Te
rm 1
: Uni
t 7: D
ata
hand
ling,
p. 8
6
Term
1: U
nit 7
: Dat
a ha
ndlin
g, p
. 81
Term
1: U
nit 7
: Dat
a ha
ndlin
g, p
. 97
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
54 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
8
TER
M 1
EDU
CAT
OR
: ……
……
……
……
……
DAT
E : f
rom
…
……
to
……
…
Tim
e: 6
HO
UR
S G
RAD
E 4
CAP
S pp
. 59
- 61
5 C
APS
pp. 1
47 -1
49
6 C
APS
pp. 2
29 –
232
TO
PIC
Pr
oper
ties
of 2
D s
hape
s C
once
pts,
Ski
lls a
nd
know
ledg
e Sh
apes
lear
ners
nee
d to
kno
w a
nd
nam
e •
Reg
ular
and
irre
gula
r pol
ygon
s:
- tri
angl
es
- sq
uare
s, re
ctan
gles
-
othe
r qua
drila
tera
ls
- pe
ntag
ons
- he
xago
ns
• C
ircle
s Th
e ch
arac
teris
tics
whi
ch le
arne
rs
use
to d
istin
guis
h, d
escr
ibe,
sor
t an
d co
mpa
re s
hape
s •
stra
ight
and
/cur
ved
side
s •
num
ber o
f sid
es
Shap
es le
arne
rs n
eed
to k
now
and
na
me
• R
egul
ar a
nd ir
regu
lar p
olyg
ons
- tri
angl
es, s
quar
es, r
ecta
ngle
s, o
ther
qu
adril
ater
als,
pen
tago
ns, h
exag
ons,
he
ptag
ons,
•
Circ
les
• Si
mila
ritie
s an
d di
ffere
nces
be
twee
n sq
uare
s an
d re
ctan
gles
C
hara
cter
istic
s le
arne
rs u
se t
o di
stin
guis
h, d
escr
ibe,
sor
t an
d co
mpa
re s
hape
s •
Stra
ight
and
/ cu
rved
sid
es
• N
umbe
r of s
ides
•
Leng
th o
f sid
es
• An
gles
: lim
ited
to
- rig
ht a
ngle
s -
angl
es s
mal
ler t
han
right
ang
les
- an
gles
gre
ater
than
righ
t ang
les
Shap
es le
arne
rs n
eed
to k
now
and
na
me
• R
egul
ar a
nd ir
regu
lar p
olyg
ons
- tria
ngle
s, s
quar
es, r
ecta
ngle
s,
para
llelo
gram
s, o
ther
qua
drila
tera
ls,
pent
agon
s, h
exag
ons,
hep
tago
ns,
octa
gons
•
Sim
ilarit
ies
and
diffe
renc
es
betw
een
rect
angl
es a
nd
para
llelo
gram
s
Feat
ures
of s
hape
s D
escr
ibe,
sor
t and
com
pare
2-D
sh
apes
in te
rms
of
• nu
mbe
r of s
ides
•
leng
th o
f sid
es
• si
ze o
f ang
les
- ac
ute
- rig
ht
- ob
tuse
-
stra
ight
55MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Furt
her a
ctiv
ities
to fo
cus
on th
e ch
arac
teris
tics
of s
hape
s D
raw
2-D
sha
pes
on g
rid p
aper
Furt
her a
ctiv
ities
to fo
cus
lear
ners
on
cha
ract
eris
tics
of s
hape
s D
raw
2-D
sha
pes
on g
rid p
aper
A
ngle
s
Lim
ited
to
• rig
ht a
ngle
s •
angl
es s
mal
ler t
han
right
ang
les
• A
ngle
s gr
eate
r tha
n rig
ht a
ngle
s
- re
flex
-
revo
lutio
n
Furt
her a
ctiv
ities
•
Dra
w 2
-D s
hape
s on
grid
pap
er
• D
raw
circ
les,
pat
tern
s in
circ
les
and
patte
rns
with
circ
les
usin
g a
pair
of c
ompa
sses
Ang
les
Rec
ogni
ze a
nd n
ame
the
follo
win
g an
gles
in 2
-D s
hape
s:
-
acut
e
- rig
ht
-
obtu
se
-
stra
ight
- re
flex
-
revo
lutio
n
Furt
her a
ctiv
ities
to fo
cus
lear
ners
on
cha
ract
eris
tics
of s
hape
s •
Dra
w
2-D
sh
apes
on
gr
id
pape
r •
Dra
w
circ
les,
pa
ttern
s in
ci
rcle
s an
d pa
ttern
s w
ith
circ
les
usin
g a
pair
of
com
pass
es
LTSM
R
esou
rces
Va
riety
of r
egul
ar a
nd ir
regu
lar p
olyg
ons:
( To
cut
out
) - t
riang
les,
squ
ares
, rec
tang
les,
par
alle
logr
ams,
oth
er q
uadr
ilate
rals
, pen
tago
ns, h
exag
ons,
hep
tago
ns, o
ctag
ons
- Tan
gram
s pa
ir of
com
pass
es, g
eobo
ards
56 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
WB
1:
pp 6
4 -6
6 Ac
tiviti
es: 2
2a&b
WB
1:
pp 7
0 –
72
Activ
ities
: 22a
, 23
a&b
WB
1:
pp 5
4 –
58
Activ
ities
: 18a
, b, c
D
BE
Text
book
refe
renc
e Te
rm 1
: Uni
t 8: P
rope
rties
of
two
- di
imen
sion
al s
hape
s, p
. 96
Term
1: U
nit 8
: Pro
perti
es o
f tw
o -
diim
ensi
onal
sha
pes,
p. 9
1
Term
1: U
nit 6
: Pro
perti
es o
f tw
o -
diim
ensi
onal
sha
pes,
p. 8
6
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
Test
57MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LE
SSO
N P
LAN
S: T
ERM
2
58 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
1
TER
M:
2
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E: fr
om
……
… to
……
…
Tim
e: 3
HO
UR
S G
RAD
E 4
CAP
S pp
. 68
5 C
APS
pp. 1
56
6 C
APS
pp. 2
40
TOPI
C
Who
le n
umbe
rs
Con
cept
s, S
kills
and
kn
owle
dge
C
ount
forw
ards
and
bac
kwar
ds in
2s,
3s
, 5s,
10s
, 25s
, 50s
, 100
s be
twee
n 0
and
at le
ast 1
0 00
0
O
rder
, com
pare
and
repr
esen
t
nu
mbe
rs to
at l
east
4-d
igit
num
bers
Rep
rese
nt o
dd a
nd e
ven
num
bers
to
at le
ast 1
000
Rec
ogni
ze th
e pl
ace
valu
e of
dig
its in
w
hole
num
bers
to a
t lea
st 4
-dig
it nu
mbe
rs
R
ound
off
to th
e ne
ares
t 10,
100
,
1 00
0
C
ount
forw
ards
and
bac
kwar
ds in
w
hole
num
ber i
nter
vals
up
to a
t lea
st
10 0
00
O
rder
, com
pare
and
repr
esen
t nu
mbe
rs to
at l
east
6-d
igit
num
bers
Rep
rese
nt o
dd a
nd e
ven
num
bers
to
at le
ast 1
000
.
Rec
ogni
ze th
e pl
ace
valu
e of
dig
its in
w
hole
num
bers
to a
t lea
st 6
dig
it nu
mbe
rs.
R
ound
off
to th
e ne
ares
t 5, 1
0, 1
00
and
1 00
0
C
ount
forw
ards
and
bac
kwar
ds in
w
hole
num
ber i
nter
vals
up
to a
t lea
st
10 0
00
O
rder
, com
pare
and
repr
esen
t nu
mbe
rs to
at l
east
9-d
igit
num
bers
Rep
rese
nt p
rime
num
bers
to a
t lea
st
100
R
ecog
nizi
ng th
e pl
ace
valu
e of
dig
its
in w
hole
num
bers
to a
t lea
st 9
-dig
it nu
mbe
rs
R
ound
off
to th
e ne
ares
t 5, 1
0, 1
00,
1 00
0
SUG
GES
TED
Se
e Te
rm 1
not
es:
59MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MET
HO
DO
LOG
Y Ex
plai
n fro
m k
now
n (lo
w n
umbe
r ran
ge) t
o an
incr
ease
d nu
mbe
r ran
ge; w
ork
with
con
cret
e LT
SM
Gra
de 4
:
Cou
ntin
g nu
mbe
r ran
ge in
crea
sed
to 1
0 00
0
Rou
ndin
g of
f to
the
near
est 1
0 an
d 10
0
Num
ber r
ange
for p
lace
val
ue, o
rder
ing,
com
parin
g an
d re
pres
entin
g nu
mbe
rs in
crea
sed
to 4
dig
its.
Gra
de 5
and
6:
C
ount
ing
num
ber r
ange
incr
ease
d –
lear
ners
cou
nt fo
rwar
ds a
nd b
ackw
ards
in 2
s, 3
s, 5
s, 1
0s, 2
5s, 5
0s, 1
00s
betw
een
0 an
d at
leas
t 10
000.
Lear
ners
als
o co
unt i
n fra
ctio
ns (a
fter t
he to
pic
of fr
actio
ns h
as b
een
cove
red
in th
e m
ain
less
on –
see
com
men
t in
that
se
ctio
n ab
out c
ount
ing
in fr
actio
ns)
R
ound
ing
off t
o th
e ne
ares
t 10,
100
, 1 0
00
N
umbe
r ran
ge fo
r pla
ce v
alue
, ord
erin
g, c
ompa
ring
and
repr
esen
ting
num
bers
incr
ease
d to
6 d
igits
Se
e fu
rther
not
es in
Ter
m 1
, but
be
awar
e th
at n
umbe
r ran
ges
have
incr
ease
d in
Ter
m 2
. The
incr
ease
d nu
mbe
r ran
ges
are
show
n in
the
colu
mn
on th
e le
ft.
LTSM
R
esou
rces
N
umbe
r lin
es: 0
– 1
20, S
truct
ured
-, s
emi-
stru
ctur
ed -
, uns
truct
ured
num
ber l
ines
; Cou
nter
s, P
ictu
res,
arra
ys/ d
iagr
ams,
Fla
sh
card
s, B
ase
10 b
lock
s, 1
00 c
harts
W
orkb
ook
refe
renc
e W
B 1
: pp
. 8 –
12
Ac
tiviti
es: 3
, 4, 5
WB
1:
pp. 3
– 8
Ac
tiviti
es: 2
, 3
WB
1:
pp. 6
– 8
; 80
- 82
Activ
ities
: 25a
&b; 2
6; 2
7
DB
E Te
xtbo
ok re
fere
nce
Te
rm 2
: Uni
t 1: W
hole
Num
bers
, p. 1
19
Te
rm 2
: Uni
t 1: W
hole
Num
bers
, p.
115
Term
2: U
nit 1
: Who
le N
umbe
rs, p
. 11
9 H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
60 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
2
TER
M:
2
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E: fr
om
……
… to
……
…
Tim
e: 3
HO
UR
S G
RAD
E 4
CAP
S pp
. 69
5 C
APS
pp. 1
57
6 C
APS
pp. 2
22
TOPI
C
Addi
tion
and
Subt
ract
ion
of W
hole
num
bers
C
once
pts,
Ski
lls a
nd
know
ledg
e N
umbe
r ra
nge
for c
alcu
latin
g Ad
ditio
n an
d su
btra
ctio
n of
who
le
num
bers
of a
t lea
st 4
-dig
its.
Cal
cula
tion
tech
niqu
es
Use
a ra
nge
of te
chni
ques
to
perfo
rm a
nd c
heck
writ
ten
and
men
tal c
alcu
latio
ns w
ith w
hole
nu
mbe
rs in
clud
ing
• es
timat
ion
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
roun
ding
off
and
com
pens
atin
g •
doub
ling
and
halv
ing
• us
ing
a nu
mbe
r lin
e •
usin
g ad
ditio
n an
d su
btra
ctio
n as
inve
rse
oper
atio
ns
Prop
ertie
s of
who
le n
umbe
rs
Rec
ogni
ze a
nd u
se th
e co
mm
utat
ive
and
asso
ciat
ive
prop
ertie
s of
who
le n
umbe
rs
Num
ber
rang
e fo
r cal
cula
tions
Ad
ditio
n an
d su
btra
ctio
n of
who
le
num
bers
with
at l
east
5-d
igit
num
bers
C
alcu
latio
n te
chni
ques
U
sing
a ra
nge
of te
chni
ques
to
perfo
rm a
nd c
heck
writ
ten
and
men
tal c
alcu
latio
ns o
f who
le
num
bers
incl
udin
g:
• es
timat
ion
• ad
ding
and
sub
tract
ing
in c
olum
ns
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
usin
g a
num
ber l
ine
• ro
undi
ng o
ff an
d co
mpe
nsat
ing
• do
ublin
g an
d ha
lvin
g •
usin
g ad
ditio
n an
d su
btra
ctio
n as
inve
rse
oper
atio
ns
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
who
le
Num
ber
rang
e fo
r cal
cula
tions
•
Addi
tion
and
subt
ract
ion
of w
hole
nu
mbe
rs o
f at l
east
6-d
igit
num
bers
•
mul
tiple
ope
ratio
ns o
n w
hole
nu
mbe
rs w
ith o
r with
out b
rack
ets
Cal
cula
tion
tech
niqu
es
Usi
ng a
rang
e of
tech
niqu
es to
pe
rform
and
che
ck w
ritte
n an
d m
enta
l cal
cula
tions
of w
hole
nu
mbe
rs in
clud
ing:
•
estim
atio
n
61MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Solv
ing
prob
lem
s So
lve
prob
lem
s in
con
text
s in
volv
ing
who
le n
umbe
rs, i
nclu
ding
fina
ncia
l co
ntex
ts
num
bers
0 in
term
s of
its
addi
tive
prop
erty
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s So
lve
prob
lem
s in
volv
ing
who
le
num
bers
, inc
ludi
ng th
e fo
llow
ing:
•
finan
cial
con
text
s •
mea
sure
men
t con
text
s SU
GG
ESTE
D
MET
HO
DO
LOG
Y Al
l gra
des:
In
Ter
m 2
, lea
rner
s ad
d an
d su
btra
ct n
umbe
rs u
p to
4 d
igits
. R
ound
ing-
off i
nclu
des
roun
ding
off
to th
e ne
ares
t 1 0
00 a
s a
way
of e
stim
atin
g an
swer
s.
Lear
ners
sho
uld
solv
e pr
oble
ms
in c
onte
xts
and
do c
onte
xt fr
ee c
alcu
latio
ns
Lear
ners
con
tinue
to
• ch
eck
thei
r sol
utio
ns th
emse
lves
by
usin
g th
e in
vers
e op
erat
ion
• ju
dge
the
reas
onab
lene
ss o
f the
ir so
lutio
ns b
y ro
undi
ng o
ff nu
mbe
rs a
nd e
stim
atin
g an
swer
s.
The
calc
ulat
ion
tech
niqu
es c
ontin
ue to
mos
tly in
volv
e br
eaki
ng d
own
num
bers
. As
the
num
bers
lear
ners
wor
k w
ith g
et la
rger
, lea
rner
s m
ay b
egin
to lo
se tr
ack
of s
ome
num
bers
whe
n th
ey b
reak
up
num
bers
to
do c
alcu
latio
ns. U
sing
bra
cket
s is
hel
pful
to s
how
gro
upin
g of
num
bers
and
so
help
s le
arne
rs k
eep
track
of w
hat t
hey
are
doin
g.
Sinc
e th
e op
erat
ions
in b
rack
ets
have
to b
e do
ne fi
rst,
it re
mov
es a
ny c
onfu
sion
abo
ut th
e or
der o
f ope
ratio
ns. L
earn
ers
thus
do
not h
ave
to le
arn
rule
s su
ch a
s BO
DM
AS if
bra
cket
s ar
e us
ed ro
utin
ely
to in
dica
te w
hich
ope
ratio
ns h
ave
to b
e do
ne fi
rst.
• B
reak
ing
dow
n al
l num
bers
acc
ordi
ng to
pla
ce v
alue
par
ts to
add
E
xam
ple
Cal
cula
te 5
362
+ 2
486
5 36
2 +
2 48
6 =
5 00
0 +
300
+ 60
+ 2
+ 2
000
+ 4
00 +
80
+ 6
2
+
6 =
8
=
5 00
0 +
2 00
0 +
300
+ 40
0 +
60 +
80
+ 2
+ 6
o
r
an
d 60
+
80 =
1
40
= 7
000
+ 70
0 +
140
+ 8
and
300
+ 4
00 =
70
0 =
7 84
8
and
5 00
0 +
2 00
0 =
7 00
0 m
eans
5 3
62 +
2 4
86 =
7 8
48
62 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• A
ddin
g on
by
brea
king
dow
n th
e nu
mbe
r to
be a
dded
Ex
ampl
e C
alcu
late
5 3
62 +
2 4
86
5 36
2 +
2 00
0 →
7 3
62 +
400
→ 7
762
+ 8
0 →
7 6
842
+ 6
→ 7
848
•
Filli
ng u
p te
ns b
y br
eaki
ng d
own
the
num
ber t
o be
add
ed.
This
can
als
o be
cal
led
roun
ding
off
and
com
pens
atin
g. H
ere,
com
pens
atin
g m
eans
that
wha
teve
r is
adde
d, m
ust b
e su
btra
cted
aga
in s
o th
at th
e st
atem
ents
rem
ain
equi
vale
nt.
Exa
mpl
e C
alcu
late
2 4
86 +
48
2
486
+ 48
= (2
486
+ 1
4) –
14
+ 48
= 2
500
+ (4
8 –1
4) =
2 5
00 +
34
= 2
534
• B
reak
ing
dow
n bo
th n
umbe
rs to
sub
trac
t Ex
ampl
e C
alcu
late
4 6
87 –
2 1
43
4 68
7 –
2 14
3 =
4 00
0 +
600
+ 80
+ 7
– 2
000
- 10
0 –
40 –
3
o
r
7
–
3 =
4
= (4
000
– 2
000
) + (6
00 –
100
) + (8
0 –
40) +
(7 –
3)
an
d 80
–
40 =
40
=
2 00
0 +
500
+ 40
+ 4
a
nd 6
00 –
100
= 5
00
= 2
544
and
4 0
00 –
2 0
00 =
2 0
00
This
mea
ns th
at:
4
687
– 2
143
= 2
000
+ 50
0 +
40 +
4
= 2
544
• B
reak
ing
dow
n al
l the
num
bers
to a
dd u
sing
com
pens
atio
n (c
ount
erba
lanc
e)
Lear
ners
can
not s
ubtra
ct 4
from
3 o
r 80
from
40.
Inst
ead
of b
reak
ing
dow
n 74
3 in
to 7
00 +
40
+ 3
they
will
brea
k do
wn
743
into
600
+ 1
30 +
13.
The
n th
ey c
an s
ubtra
ct 4
from
13
and
80 fr
om 1
30.
C
alcu
late
: 8 7
43 –
5 6
84
8 74
3 –
5 68
4 =
(8 0
00 +
700
+ 4
0 +
3) –
5 0
00 –
600
– 8
0 –
4 =
(8 0
00 +
600
+ 1
30 +
13)
– 5
000
– 6
00 –
80
– 4
(bre
akin
g up
743
into
600
+ 1
30 +
13)
=
(8 0
00 –
5 0
00) +
(600
– 6
00) +
(130
– 8
0) +
(13
– 4)
= 3
000
+ 0
+ 5
0
+ 9
= 3
059
•
Subt
ract
ing
by b
reak
ing
dow
n th
e nu
mbe
r to
be s
ubtr
acte
d C
alcu
late
4 6
87 –
2 1
43
4 68
7 –
2 00
0 →
2 6
87 –
100
→ 2
587
– 4
0 →
2 5
47 –
3 →
2 5
44
63MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Kin
ds o
f pro
blem
s •
Sum
mat
ion,
Incr
ease
and
dec
reas
e, c
ompa
rison
by
diffe
renc
e; c
ompa
rison
by
ratio
•
See
the
desc
riptio
n of
pro
blem
type
s at
the
end
of th
e gr
ade
note
s G
rade
5 a
nd 6
: •
In T
erm
2, l
earn
ers
add
and
subt
ract
num
bers
with
up
to 5
dig
its.
• R
ound
ing
off a
s a
way
of e
stim
atin
g an
swer
s to
incl
ude
roun
ding
off
to th
e ne
ares
t 1 0
00 a
s w
ell a
s ro
undi
ng o
ff to
the
near
est 1
0, 1
00
Le
arne
rs s
houl
d so
lve
prob
lem
s in
con
text
s an
d do
con
text
free
cal
cula
tions
As
num
ber r
ange
s ge
t lar
ger m
any
lear
ners
tend
to lo
se th
e pa
rts o
f the
num
ber t
hat t
hey
brea
k up
, whe
n th
ey tr
y to
co
mbi
ne a
gain
. Thi
s is
esp
ecia
lly th
e ca
se w
hen
mor
e th
an tw
o 5-
digi
t num
bers
are
bei
ng a
dded
. It i
s fo
r thi
s re
ason
that
co
lum
n ad
ditio
n an
d co
lum
n su
btra
ctio
n ar
e in
trodu
ced
in G
rade
5. I
n Te
rm 2
one
can
stil
l enc
oura
ge le
arne
rs to
exp
and
the
num
bers
as
they
writ
e th
em in
col
umns
. In
Term
1, a
n op
tion
of a
col
umn
met
hod
was
pro
vide
d, b
ut it
con
sist
ed o
f pu
tting
diff
eren
t pla
ce v
alue
s in
to d
iffer
ent r
ows.
Le
arne
rs c
ontin
ue to
: •
chec
k th
eir s
olut
ions
them
selv
es e
.g. b
y us
ing
the
inve
rse
oper
atio
n •
judg
e th
e re
ason
able
ness
of t
heir
solu
tions
e.g
. by
roun
ding
off
num
bers
and
est
imat
ing
answ
ers
Exa
mpl
e:
Cal
cula
te: 5
6 42
3 +7
581
+21
479
•
Brea
king
dow
n al
l the
num
bers
to a
dd
Addi
ng in
a ro
w (h
oriz
onta
lly)
50 0
00+6
000
+400
+20+
3+7
000+
500+
80+1
+20
000+
1 00
0+40
0 +7
0+9
= 50
000
+20
000+
6 0
00+7
000
+1 0
00+4
00+5
00 +
4 00
+20+
80
+70+
3+1
+9
= 70
000
+ 1
4 00
0 +
1 30
0 +
170
+ 14
=
70 0
00 +
10
000
+ 4
000
+ 1
000
+ 30
0 +
100
+ 70
+ 1
0 +
4 =
80 0
00 +
5 0
00 +
400
+ 8
0+ 4
=
8548
4
The
horiz
onta
l met
hod
may
get
unw
ield
y w
hen
mor
e th
an tw
o 5-
digi
t num
bers
are
add
ed. T
he a
ltern
ativ
e is
to u
se th
e ex
pand
ed v
ertic
al m
etho
d.
•
Expa
nded
ver
tical
met
hod
56
423
= 5
0 00
0 +
6 00
0 +
400
+
20
+ +
7
581
=
7 00
0 +
500
+
80
+ 1
+ 21
479
= 2
0 00
0+ 1
000
+
400
+ 7
0 +
9
70 0
00+
14 0
00 +
130
0 +
170
+ 10
64 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
= 70
000
+ 1
0 00
0 +
5 00
0 +
400
+ 80
+ 4
= 85
484
• Ad
ding
on
(by
brea
king
dow
n th
e nu
mbe
r to
be a
dded
) C
alcu
late
: 56
423
+ 7
581
56
423
+ 7
000
→ 6
3 42
3 +
500
→ 6
3 92
3 +
80 →
64
003
+ 1
→ 6
4 00
4 Th
is te
nds
to w
ork
bette
r if o
nly
two
num
bers
are
add
ed. I
f a th
ird o
r fou
rth n
umbe
r is
adde
d, th
ey c
an b
e br
oken
up
and
adde
d on
e at
a ti
me,
but
the
expa
nded
col
umn
met
hod
is m
ore
effic
ient
. •
Bre
akin
g do
wn
all t
he n
umbe
rs c
ordi
ng to
pla
ce v
alue
par
ts to
sub
trac
t usi
ng c
ompe
nsat
ion
(cou
nter
bala
nce)
E
xam
ple:
C
alcu
late
: 8 7
43 –
5 6
84
8 74
3 –
5 68
4 =
8 00
0 +
700
+ 40
+ 3
– 5
000
– 6
00 –
80
– 4
= 8
000
+ 60
0 +
130
+ 13
– 5
000
– 6
00 –
80
– 4
(by
brea
king
up
743
into
600
+ 1
30 +
13)
=
8 00
0 –
5 00
0 +
600
– 60
0 +
130
– 80
+ 1
3 –
4 =
3 00
0
+
0
+
50
= 3
059
• B
reak
ing
dow
n nu
mbe
rs a
nd u
sing
the
expa
nded
col
umn
met
hod
Exam
ple:
C
alcu
late
: 98
743
– 45
684
Le
arne
rs c
anno
t sub
tract
4 fr
om 3
or 8
0 fro
m 4
0. In
stea
d of
bre
akin
g do
wn
743
into
700
+ 4
0 +
3 th
ey w
ill br
eak
dow
n 74
3 in
to 6
00 +
130
+ 1
3. T
hen
they
can
sub
tract
4 fr
om 1
3 an
d 80
from
130
.
600
130
13
9
8 7
4 3
= 9
0 00
0+
8 0
00 +
700
+
40
+
3 –
4 5
6 8
4
=
40
000+
5
000
+
6
00 +
8
0 +
4
50 00
0+
3 0
00 +
0
+
50 +
9 =
53
059
• Su
btra
ctin
g by
bre
akin
g do
wn
num
ber t
o be
sub
trac
ted
Exam
ple:
C
alcu
late
74
687
– 52
143
74
687
– 5
0 00
0→24
687
– 2
000
→ 2
2 68
7 –
100
→ 2
2 58
7 –
40 →
22
547
– 3
= 22
544
OR
65MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
25
746
– 1
0 00
0 –
4 00
0 –
500
– 30
– 2
= (1
5 74
6 –
4 00
0) –
500
– 3
0 –
2
= (1
1 74
6 –
500)
– 3
0 –
2
= (1
1 24
6 –
30) –
2
= 11
216
– 2
=
11 2
14
This
tend
s to
wor
k be
tter i
f onl
y on
e nu
mbe
r is
subt
ract
ed fr
om a
noth
er. I
f a s
econ
d or
third
num
ber i
s su
btra
cted
, the
y ca
n be
br
oken
up
and
subt
ract
ed o
ne a
t a ti
me,
but
the
expa
nded
col
umn
met
hod
is m
ore
effic
ient
. Pr
oble
ms
• Su
mm
atio
n, in
crea
se a
nd d
ecre
ase,
com
paris
on b
y di
ffere
nce;
com
paris
on b
y ra
tio
• Se
e th
e de
scrip
tion
of p
robl
em ty
pes
at th
e en
d of
the
grad
e no
tes
Gra
de 6
: C
heck
ing
solu
tions
Le
arne
rs s
houl
d kn
ow th
at th
ey c
an
• ch
eck
an a
dditi
on c
alcu
latio
n by
sub
trac
tion.
Ex
ampl
e: If
45
362
+ 32
488
= 7
7 84
8; th
en 7
7 84
8 –
32 4
88 =
45
362
• ch
eck
a su
btra
ctio
n ca
lcul
atio
n by
add
ition
Ex
ampl
e: If
54
687
– 32
134
= 2
2 54
4, th
en 2
2 54
4 +
32 1
34 =
54
687
Usi
ng th
e in
vers
e op
erat
ion
to c
heck
sol
utio
ns is
one
reas
on fo
r tea
chin
g ad
ditio
n an
d su
btra
ctio
n si
mul
tane
ousl
y.
Anot
her r
easo
n fo
r doi
ng th
e tw
o op
erat
ions
at t
he s
ame
time
is th
at w
hen
lear
ners
sol
ve p
robl
ems,
it is
som
etim
es p
ossi
ble
to
solv
e th
e sa
me
prob
lem
by
doin
g ei
ther
add
ition
or s
ubtra
ctio
n.
Ex
ampl
e: V
eli’s
sho
ppin
g co
sts
R16
3. H
e pa
ys w
ith a
R20
0 no
te. H
ow m
uch
chan
ge d
oes
he g
et”?
So
me
lear
ners
may
add
on
from
R16
3 to
get
R20
0 as
follo
ws:
R
163
+ R
7= R
170,
then
R17
0 +
R30
= R
200.
Ve
li ge
ts R
37 c
hang
e.
E
xam
ple:
C
alcu
late
: 56
423
+ 7
581
+ 2
1 47
9 •
Col
umn
met
hod
for a
ddin
g By
Gra
de 6
lear
ners
sho
uld
have
had
eno
ugh
expe
rienc
e w
ith b
reak
ing
up n
umbe
rs to
add
and
sub
tract
them
. The
hor
izon
tal
66 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
met
hod
of e
xpan
ding
num
bers
bef
ore
addi
ng th
em c
an g
et u
nwie
ldy
whe
n m
ore
than
two
5-di
git n
umbe
rs a
re a
dded
. Ter
m 1
le
arne
rs c
an re
visi
t the
exp
ande
d ve
rtica
l met
hod,
and
then
mov
e on
to th
e tra
ditio
nal c
olum
n m
etho
d •
Expa
nded
ver
tical
col
umn
met
hod
to a
dd
56
423
=
50
000
+
6
000
+
400
+
20
+
3
+7
581
=
7
000
+
5
00
+
80
+
1
+21
479
=
20
000
+
1
000
+
400
+
70
+
9
Tot
al
=
70 0
00
+
14 0
00
+
1 3
00
+
170
+
13
This
can
be
writ
ten
as 7
0 00
0 +
10 0
00 +
5 0
00 +
400
+ 8
0 +
3 =
85 4
83
• T
he v
ertic
al c
olum
n m
etho
d to
add
.
1 1
1 1
5
6 42
3
+ 21
479
+
7 58
1
85 48
3 •
Expa
nded
ver
tical
col
umn
met
hod
to s
ubtr
act
Exam
ple:
Cal
cula
te: 9
8 74
3 –
45 6
84
600
130
13
9
8 74
3 =
90 0
00
+
8 0
00
+
700
+
40
+
3
–
45 6
84
=
40
000
+
5
000
+
6
00
+
80
+
4
Tot
al =
50 0
00
+
3 0
00
+
0 +
50
+
9
Th
eref
ore
50 0
00 +
3 0
00 +
0 +
50
+ 9
= 53
059
•
The
ver
tical
col
umn
met
hod
to s
ubtr
act
6
13
13
98 7
43
– 45
684
53
059
Prob
lem
s •
Sum
mat
ion,
incr
ease
and
dec
reas
e, c
ompa
rison
by
diffe
renc
e; c
ompa
rison
by
ratio
•
See
the
desc
riptio
n of
pro
blem
type
s at
the
end
of th
e G
rade
6 n
otes
67MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Wor
king
with
cal
cula
tors
•
The
men
tal m
athe
mat
ics
prog
ram
me
cont
ains
wor
k on
num
ber c
once
pt, n
umbe
r fac
ts a
nd m
enta
l cal
cula
tion
tech
niqu
es.
Dai
ly w
ork
on m
enta
l Mat
hem
atic
s co
mbi
ned
with
dai
ly w
ritte
n ca
lcul
atio
ns w
ill pr
even
t lea
rner
s fro
m b
ecom
ing
depe
nden
t on
cal
cula
tors
and
not
kno
win
g ho
w to
cal
cula
te w
ithou
t the
m.
• C
alcu
lato
rs a
re a
use
ful w
ay fo
r lea
rner
s to
exp
lore
num
ber p
atte
rns
and
whe
n w
orki
ng w
ith v
ery
larg
e nu
mbe
rs.
LTS
M
Res
ourc
es
Num
ber l
ines
: Stru
ctur
ed -,
sem
i- st
ruct
ured
- , u
nstru
ctur
ed n
umbe
r lin
es; C
ount
ers,
Pic
ture
s, a
rrays
/ dia
gram
s, F
lash
car
ds,
Base
10
bloc
ks, 1
00 c
harts
,
Gra
de 4
G
rade
5
Gra
de 6
W
orkb
ook
refe
nce
WB
1:
pp. 2
6 –
38
Activ
ities
: 9, 1
0a&b
; 12
pp
. 92
– 96
Ac
tiviti
es: 3
2a&b
; 33
WB
1:
pp 3
0 –
32
Activ
ities
: 10a
&b
pp 9
0 –
96
Activ
ities
: 29a
&b, 3
0a&b
WB
1:
pp.
14 -
24
Activ
ities
: 8a&
b
DB
E Te
xtbo
ok re
fere
nce
Term
2: U
nit 2
: Who
le N
umbe
rs:
Addi
tion
and
subt
ract
ion,
p. 1
28
Term
2: U
nit 2
: Who
le N
umbe
rs:
Addi
tion
and
subt
ract
ion,
p. 1
21
Term
1: U
nit 3
: Who
le N
umbe
rs:
Addi
tion
and
subt
ract
ion,
p. 2
5 H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent –
Te
st
68 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
3
TER
M:
2
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E: fr
om
……
… to
……
…
Tim
e: 3
HO
UR
S G
RAD
E 4
CAP
S pp
. 67
- 77
5 C
APS
pp. 1
66
6 C
APS
pp. 2
40
TOPI
C
Mul
tiplic
atio
n of
Who
le N
umbe
rs
Con
cept
s, S
kills
and
kn
owle
dge
Num
ber
rang
e fo
r cal
cula
tions
•
Mul
tiplic
atio
n of
at l
east
who
le 2
-di
git b
y 2-
digi
t num
bers
C
alcu
latio
n te
chni
ques
U
se a
rang
e of
tech
niqu
es to
pe
rform
and
che
ck w
ritte
n an
d m
enta
l cal
cula
tions
with
who
le
num
bers
incl
udin
g:
• es
timat
ion
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
roun
ding
off
and
com
pens
atin
g •
doub
ling
and
halv
ing
Num
ber
rang
e fo
r cal
cula
tions
M
ultip
licat
ion
of a
t lea
st w
hole
3-d
igit
by
2-di
git n
umbe
rs
Cal
cula
tion
tech
niqu
es
Usi
ng a
rang
e of
tech
niqu
es to
pe
rform
and
che
ck w
ritte
n an
d m
enta
l cal
cula
tions
of w
hole
nu
mbe
rs in
clud
ing:
•
estim
atio
n •
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
• us
ing
a nu
mbe
r lin
e •
roun
ding
off
and
com
pens
atin
g •
doub
ling
and
halv
ing
Num
ber
rang
e fo
r cal
cula
tions
•
Mul
tiplic
atio
n of
at l
east
who
le 4
-di
git b
y 3-
digi
t num
bers
•
Mul
tiple
ope
ratio
ns o
n w
hole
nu
mbe
rs w
ith o
r with
out
brac
kets
C
alcu
latio
n te
chni
ques
incl
ude
• es
timat
ion
• m
ultip
lyin
g in
col
umns
•
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
• ro
undi
ng o
ff an
d co
mpe
nsat
ing
• us
ing
a ca
lcul
ator
69MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s M
ultip
les
of 1
-dig
it nu
mbe
rs to
at l
east
10
0 Prop
ertie
s of
who
le n
umbe
rs
R
ecog
nize
and
use
the
com
mut
ativ
e;
asso
ciat
ive;
and
dis
tribu
tive
prop
ertie
s of
who
le n
umbe
rs
So
lvin
g pr
oble
ms
So
lve
prob
lem
s in
con
text
s in
volv
ing
who
le n
umbe
rs, i
nclu
ding
fina
ncia
l co
ntex
ts
So
lve
prob
lem
s in
volv
ing
who
le
num
bers
, inc
ludi
ng
co
mpa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd (r
atio
)
com
parin
g tw
o qu
antit
ies
of d
iffer
ent
kind
s (ra
te)
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
2-d
igits
who
le
num
bers
to a
t lea
st 1
00
• Fa
ctor
s of
2-d
igit
who
le n
umbe
rs
to a
t lea
st 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
an
d us
e th
e co
mm
utat
ive;
as
soci
ativ
e an
d di
strib
utiv
e pr
oper
ties
with
who
le
num
bers
•
0 in
term
s of
its
addi
tive
prop
erty
•
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
finan
cial
con
text
s
mea
sure
men
t con
text
s
So
lve
prob
lem
s in
volv
ing
who
le
num
bers
, inc
ludi
ng c
ompa
ring
two
or
mor
e qu
antit
ies
of th
e sa
me
kind
(ra
tio)
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
2-d
igit
and
3-di
git
num
bers
•
Fact
ors
of 2
-dig
it an
d 3-
digi
t who
le
num
bers
•
Prim
e fa
ctor
s of
num
bers
to a
t lea
st
100
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
w
hole
num
bers
•
0 in
term
s of
its
addi
tive
prop
erty
•
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
num
bers
and
dec
imal
fra
ctio
ns, i
nclu
ding
-
finan
cial
con
text
s -
mea
sure
men
t con
text
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
num
bers
, inc
ludi
ng
co
mpa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd (r
atio
)
com
parin
g tw
o qu
antit
ies
of d
iffer
ent k
inds
(rat
e)
70 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LTSM
R
esou
rces
N
umbe
r lin
es: 0
– 1
20, S
truct
ured
-, s
emi-
stru
ctur
ed -
, uns
truct
ured
num
ber l
ines
; Cou
nter
s, P
ictu
res,
arra
ys/ d
iagr
ams,
Fl
ash
card
s, B
ase
10 b
lock
s, 1
00 c
harts
, mul
tiplic
atio
n ta
ble
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
WB
1:
pp. 1
26 –
128
Ac
tiviti
es:
46,4
7 p.
162
Ac
tiviti
es: 6
4
WB
1:
pp. 5
0 –
52
Activ
ities
: 17a
&b
pp. 1
40
Activ
ity: 4
9 pp
. 172
- 17
4
Activ
ities
: 63,
64
WB
1:
pp. 8
8 - 9
2 Ac
tiviti
es: 3
0; 3
1; 3
2;
p. 1
26
Activ
ities
: 47
DB
E Te
xtbo
ok re
fere
nce
Term
2: U
nit 5
: Who
le N
umbe
rs:
Mul
tiplic
atio
n, p
. 161
Term
2: U
nit 2
: Who
le N
umbe
rs:
Mul
tiplic
atio
n, p
. 157
Term
2: U
nit 2
: Who
le N
umbe
rs:
Mul
tiplic
atio
n, p
. 125
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
Test
71MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
M
ULT
I GR
ADE
LESS
ON
PLA
N 4
TE
RM
: 2
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E: fr
om
……
… to
……
…
Tim
e: 3
HO
UR
S G
RAD
E 4
CAP
S pp
. 84
- 85
5 C
APS
pp. 1
72 -
173
6 C
APS
pp. 2
50 -
251
TOPI
C
Div
isio
n of
Who
le N
umbe
rs
Con
cept
s, S
kills
and
kn
owle
dge
Num
ber
rang
e fo
r cal
cula
tions
•
Div
isio
n of
at l
east
who
le 3
-dig
it by
1-
digi
t num
bers
. Cal
cula
tion
tech
niqu
es
• U
se a
rang
e of
tech
niqu
es to
pe
rform
and
che
ck w
ritte
n an
d m
enta
l cal
cula
tions
of w
hole
nu
mbe
rs in
clud
ing
- es
timat
ion
- bu
ildin
g u
p a
nd
brea
king
do
wn
num
bers
-
roun
ding
off
and
com
pens
atin
g -
doub
ling
and
halv
ing
- us
ing
mul
tiplic
atio
n an
d di
visi
on
as in
vers
e op
erat
ions
N
umbe
r ra
nge
for m
ultip
les
and
fact
ors
• M
ultip
les
of 1
-dig
it nu
mbe
rs to
at
leas
t 100
Num
ber
rang
e fo
r cal
cula
tions
D
ivis
ion
of a
t lea
st w
hole
3-d
igit
by
2-di
git n
umbe
rs
Cal
cula
tion
tech
niqu
es
Use
a ra
nge
of te
chni
ques
to
perfo
rm a
nd c
heck
writ
ten
and
men
tal c
alcu
latio
ns w
ith w
hole
nu
mbe
rs in
clud
ing
• es
timat
ion
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
usin
g m
ultip
licat
ion
and
divi
sion
as
inve
rse
oper
atio
ns
Num
ber
rang
e fo
r co
untin
g, o
rder
ing
and
repr
esen
ting,
and
pla
ce v
alue
of
digi
ts
• Rec
ogni
ze th
e pl
ace
valu
e of
dig
its
in w
hole
num
bers
to a
t lea
st 6
-dig
it nu
mbe
rs.
• R
ound
off
to th
e ne
ares
t 10,
100
, 1
000
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
2-d
igit
num
bers
to a
t
Num
ber
rang
e fo
r cal
cula
tions
•
Div
isio
n of
at l
east
who
le 4
-dig
it by
3-
digi
t num
bers
•
mul
tiple
ope
ratio
ns o
n w
hole
nu
mbe
rs w
ith o
r with
out b
rack
ets
Cal
cula
tion
tech
niqu
es
• es
timat
ion
• us
ing
the
reci
proc
al re
latio
nshi
p be
twee
n m
ultip
licat
ion
and
divi
sion
•
long
div
isio
n •
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
• ro
undi
ng o
ff an
d co
mpe
nsat
ing
• us
ing
a ca
lcul
ator
N
umbe
r ra
nge
for m
ultip
les
and
fact
ors
• M
ultip
les
of 2
-dig
it an
d 3-
digi
t
72 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e; a
nd
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
So
lvin
g pr
oble
ms
• So
lve
prob
lem
s in
co
ntex
ts
invo
lvin
g w
hole
num
bers
-
finan
cial
con
text
s -
mea
sure
men
t con
text
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
-
grou
ping
and
equ
al s
harin
g w
ith
rem
aind
ers
- co
mpa
ring
two
or m
ore
quan
titie
s of
th
e sa
me
kind
(rat
io)
- co
mpa
ring
two
quan
titie
s of
diff
eren
t ki
nds
(rate
)
leas
t 100
•
Fact
ors
of 2
-dig
it w
hole
num
bers
to
at l
east
100
M
ultip
licat
ion
fact
s •
Uni
ts b
y m
ultip
les
of 1
0 •
Uni
ts b
y m
ultip
les
of 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e; a
nd
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
•
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
in
cont
exts
in
volv
ing
who
le
num
bers
, in
clud
ing
finan
cial
con
text
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
-
com
parin
g tw
o or
mor
e qu
antit
ies
of
the
sam
e ki
nd (r
atio
) - c
ompa
ring
two
quan
titie
s of
diff
eren
t ki
nds
(rate
) - g
roup
ing
and
equa
l sha
ring
with
re
mai
nder
s
num
bers
•
Fact
ors
of 2
-dig
it an
d 3-
digi
t who
le
num
bers
•
Prim
e fa
ctor
s of
num
bers
up
to a
t le
ast 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
•
0 in
term
s of
its
addi
tive
prop
erty
•
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs a
nd d
ecim
al fr
actio
ns,
incl
udin
g -
finan
cial
con
text
s -
mea
sure
men
t con
text
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
-
com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(rat
io)
- co
mpa
ring
two
quan
titie
s of
di
ffere
nt k
inds
(rat
e)
- gr
oupi
ng a
nd e
qual
sha
ring
with
re
mai
nder
s
73MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LTSM
Res
ourc
es
Num
ber l
ines
: Stru
ctur
ed -,
sem
i- st
ruct
ured
- , u
nstru
ctur
ed n
umbe
r lin
es; C
ount
ers,
Pic
ture
s, a
rrays
/ dia
gram
s, F
lash
car
ds,
Base
10
bloc
ks, 1
00 c
harts
, mul
tiplic
atio
n ta
ble
G
rade
4
Gra
de 5
G
rade
6
W
B 1
: p.
162
Ac
tiviti
es 6
4
WB
1:
pp. 1
40
Activ
ity: 4
9 pp
. 172
- 17
4
Activ
ities
: 63,
64
WB
1:
p. 1
26
Activ
ities
: 47
DB
E TE
XTB
OO
K
REF
EREN
CE
Term
2: U
nit 1
0: W
hole
Num
bers
: D
ivis
ion,
p. 2
00
Term
2: U
nit 9
: Who
le N
umbe
rs:
Div
isio
n, p
. 187
Term
2: U
nit 6
: Who
le N
umbe
rs:
Div
isio
n, p
. 165
HO
MEW
OR
K
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent –
Te
st
74 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
5
TER
M:
2
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E: fr
om
……
… to
……
…
Tim
e: 9
HO
UR
S G
RAD
E 4
CAP
S pp
. 71
- 72
5 C
APS
pp. 1
72 -
173
6 C
APS
pp. 2
80 (F
ract
ions
) C
APS
pp. 2
52 (D
ecim
al F
ract
ions
) TO
PIC
C
omm
on F
ract
ions
and
Dec
imal
Fra
ctio
ns
Con
cept
s, S
kills
and
kn
owle
dge
Des
crib
ing
and
orde
ring
frac
tions
•
Com
pare
and
ord
er c
omm
on fr
actio
ns
of d
iffer
ent d
enom
inat
ors
(hal
ves,
th
irds,
qua
rters
, fift
hs, s
ixth
s, s
even
ths,
ei
ghth
s)
• D
escr
ibe
and
com
pare
com
mon
fra
ctio
ns in
dia
gram
for
m
Cal
cula
tions
with
frac
tions
: •
Rec
ogni
ze, d
escr
ibe
and
use
the
equi
vale
nce
of d
ivis
ion
and
fract
ions
•
Addi
tion
of c
omm
on fr
actio
ns w
ith
sam
e de
nom
inat
ors
Solv
ing
prob
lem
s
• D
escr
ibin
g an
d or
derin
g fr
actio
ns
• C
ount
forw
ards
and
bac
kwar
ds in
fra
ctio
ns
• C
ompa
re a
nd o
rder
com
mon
fra
ctio
ns to
at l
east
twel
fths
Cal
cula
tions
with
frac
tions
•
Addi
tion
of c
omm
on fr
actio
ns w
ith th
e sa
me
deno
min
ator
•
Rec
ogni
ze, d
escr
ibe
and
use
the
equi
vale
nce
of d
ivis
ion
and
fract
ions
So
lvin
g pr
oble
ms
Des
crib
ing
and
orde
ring
frac
tions
•
Com
pare
and
ord
er c
omm
on
fract
ions
, inc
ludi
ng s
peci
fical
ly te
nths
an
d hu
ndre
dths
C
alcu
latio
ns u
sing
frac
tions
• A
dditi
on a
nd s
ubtra
ctio
n of
com
mon
fra
ctio
ns w
ith d
enom
inat
ors
whi
ch a
re
mul
tiple
s of
eac
h ot
her.
• Ad
ditio
n an
d su
btra
ctio
n of
mix
ed
num
bers
•
Frac
tions
of w
hole
num
bers
So
lvin
g pr
oble
ms
75MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g fra
ctio
ns, i
nclu
ding
gro
upin
g an
d eq
ual
shar
ing
Equi
vale
nt fo
rms:
R
ecog
nize
and
use
equ
ival
ent f
orm
s of
co
mm
on fr
actio
ns (d
enom
inat
ors
whi
ch
are
mul
tiple
s of
eac
h ot
her)
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g co
mm
on fr
actio
ns, i
nclu
ding
gro
upin
g an
d sh
arin
g Eq
uiva
lent
form
s:
Rec
ogni
ze a
nd u
se e
quiv
alen
t for
ms
of
com
mon
frac
tions
with
den
omin
ator
s w
hich
are
mul
tiple
s of
eac
h ot
her.
• So
lve
prob
lem
s in
con
text
s in
volv
ing
com
mon
frac
tions
, inc
ludi
ng g
roup
ing
and
shar
ing
Perc
enta
ges
• C
alcu
late
per
cent
ages
of w
hole
nu
mbe
rs
Equi
vale
nt fo
rms:
•
Rec
ogni
ze a
nd u
se e
quiv
alen
t fo
rms
of c
omm
on fr
actio
ns w
ith
1-di
git o
r 2-d
igit
deno
min
ator
s w
ith
deno
min
ator
s w
hich
are
mul
tiple
s of
ea
ch o
ther
•
Rec
ogni
ze e
quiv
alen
ce b
etw
een
com
mon
frac
tion
and
deci
mal
frac
tion
form
s of
the
sam
e nu
mbe
r • R
ecog
nize
equ
ival
ence
bet
wee
n co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r. D
ecim
al fr
actio
ns
Rec
ogni
zing
, ord
erin
g an
d pl
ace
valu
e of
dec
imal
frac
tions
•
Cou
nt fo
rwar
ds a
nd b
ackw
ards
in
deci
mal
frac
tions
to a
t lea
st tw
o de
cim
al p
lace
s •
Com
pare
and
ord
er d
ecim
al fr
actio
ns
to a
t lea
st tw
o de
cim
al p
lace
s •
Plac
e va
lue
of d
igits
to a
t lea
st tw
o de
cim
al p
lace
s C
alcu
latio
ns w
ith d
ecim
al fr
actio
ns
• Ad
ditio
n an
d su
btra
ctio
n of
dec
imal
fra
ctio
ns o
f at l
east
two
deci
mal
pl
aces
•
Mul
tiply
dec
imal
frac
tions
by
10 a
nd
100
76 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Solv
ing
prob
lem
s So
lve
prob
lem
s in
con
text
invo
lvin
g de
cim
al fr
actio
ns
SUG
GES
TED
M
ETH
OD
OLO
GY
All l
earn
ers
can
star
t of w
ith th
e ea
sier
pro
blem
s. G
rade
4 le
arne
rs a
re tr
eatin
g th
e w
ork
as n
ew w
hile
the
Gra
de 5
an
d G
rade
6 le
arne
rs c
an m
ove
on to
mor
e co
mpl
ex p
robl
ems
as in
dica
ted
in th
e C
APS
polic
y do
cum
ent.
All g
rade
s:
Seve
nths
are
new
. Th
ere
are
diffe
rent
way
s to
und
erst
and
fract
ions
. Thi
s m
eans
that
lear
ners
sho
uld
deve
lop
the
conc
ept o
f fra
ctio
ns in
a v
arie
ty
of w
ays.
Pro
blem
-sol
ving
con
text
s ca
n he
lp l
earn
ers
to u
nder
stan
d m
any
way
s of
thi
nkin
g ab
out
fract
ions
. A
varie
ty o
f pr
oble
ms
shou
ld b
e gi
ven
to le
arne
rs. S
ee th
e ty
pes
of fr
actio
ns p
robl
ems
stat
ed a
t the
end
of t
he G
rade
not
es. T
he c
once
pt
of a
frac
tion
shou
ld fi
rst b
e de
velo
ped
befo
re le
arne
rs fo
cus
on e
quiv
alen
ce a
nd c
alcu
latin
g.
Lear
ners
can
als
o w
ork
with
app
arat
us a
nd d
iagr
ams.
Diff
eren
t di
agra
ms
or a
ppar
atus
dev
elop
diff
eren
t w
ays
of th
inki
ng
abou
t fra
ctio
ns:
R
egio
n or
are
a m
odel
s de
velo
p th
e co
ncep
t of f
ract
ions
as
part
of a
who
le. I
f use
d in
par
ticul
ar w
ays
they
can
als
o de
velo
p th
e co
ncep
t of a
frac
tion
as a
mea
sure
. Exa
mpl
es o
f are
a m
odel
s in
clud
e ci
rcle
s cu
t int
o fra
ctio
n pi
eces
or
diag
ram
s of
pie
s, re
ctan
gles
or o
ther
geo
met
ric s
hape
s di
vide
d in
to fr
actio
n pi
eces
(pap
er fo
ldin
g), f
ract
ions
usi
ng
squa
re o
r dot
ty g
rid p
aper
, geo
boar
ds
Le
ngth
or m
easu
rem
ent m
odel
s ca
n be
use
d to
dev
elop
the
conc
ept o
f fra
ctio
ns a
s pa
rt of
a w
hole
and
if u
sed
in
parti
cula
r way
s al
so fr
actio
n as
a m
easu
re. E
xam
ples
of l
engt
h m
odel
s in
clud
e fra
ctio
n st
rips,
Cui
sena
ire ro
ds,
num
ber l
ines
Set m
odel
s de
velo
p th
e co
ncep
t of a
frac
tion
of a
col
lect
ion
of o
bjec
ts a
nd c
an la
y th
e ba
sis
for t
hink
ing
abou
t a
fract
ion
of a
num
ber e
.g.1 3
of 1
2. E
xam
ples
of s
et m
odel
s in
clud
e co
unte
rs o
f any
kin
d in
diff
eren
t arra
ngem
ents
.
Lear
ners
sho
uld
not
only
wor
k w
ith o
ne k
ind
of m
odel
, be
caus
e th
is c
an li
mit
thei
r un
ders
tand
ing
of f
ract
ions
. Fo
r ex
ampl
e,
fract
ions
in d
iagr
am fo
rms
shou
ld in
clud
e re
gion
mod
els
(circ
les
and
othe
r geo
met
ric s
hape
s di
vide
d in
to fr
actio
n pa
rts),
leng
th
mod
els
(incl
udin
g nu
mbe
r lin
es) a
nd s
et m
odel
s (w
hich
sho
w c
olle
ctio
ns o
f obj
ects
). In
Ter
m 1
lear
ners
sho
uld
revi
se a
nd c
onso
lidat
e w
hat t
hey
lear
ned
abou
t fra
ctio
ns in
Gra
de 3
. Le
arne
rs s
houl
d so
lve
prob
lem
s as
wel
l as
wor
k w
ith a
ppar
atus
and
dia
gram
s in
volv
ing
area
, len
gth
and
set m
odel
s to
ens
ure
that
they
:
unde
rsta
nd th
e re
latio
nshi
p be
twee
n fra
ctio
ns a
nd d
ivis
ion
i.e. i
f you
sha
re a
mon
gst 3
lear
ners
you
will
be
mak
ing
third
s
are
able
to n
ame
fract
ions
. Ter
min
olog
y lik
e “3
ove
r 4” s
houl
d be
avo
ided
as
it te
nds
to e
ncou
rage
lear
ners
to
thin
k ab
out e
ach
fract
ion
as tw
o di
ffere
nt n
umbe
rs, r
athe
r tha
n 3 4
bein
g a
num
ber w
hich
is g
reat
er 1 2
than
but
less
77MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
than
1.
Whe
n na
min
g fra
ctio
n pa
rts it
is u
sefu
l for
lear
ners
to ra
ther
use
the
form
“3 q
uarte
rs”.
Lear
ners
sho
uld,
thro
ugh
wor
k w
ith a
ppar
atus
, dia
gram
s an
d so
lvin
g pr
oble
ms,
lear
n th
e ne
w f
ract
ions
that
the
y w
ill de
al
with
in G
rade
4.
G
rade
5 a
nd 6
: W
hat i
s di
ffere
nt to
Gra
de 4
?
Nin
ths,
tent
hs, e
leve
nths
and
twel
fths
Le
arne
rs c
ount
in fr
actio
ns
Su
btra
ctio
n of
frac
tions
with
the
sam
e de
nom
inat
ors
Ad
ditio
n an
d su
btra
ctio
n of
mix
ed n
umbe
rs
Fr
actio
ns o
f who
le n
umbe
rs th
at re
sult
in w
hole
num
bers
M
ost
of t
he n
ew w
ork
men
tione
d ab
ove
can
be d
evel
oped
in
Term
s 3
and
4. H
owev
er,
lear
ners
can
beg
in t
o co
unt
in
fract
ions
Le
arne
rs s
houl
d de
velo
p th
e co
ncep
t of f
ract
ions
in a
var
iety
of w
ays.
Pro
blem
sol
ving
con
text
s ca
n he
lp le
arne
rs to
und
erst
and
man
y w
ays
of th
inki
ng a
bout
frac
tions
. A v
arie
ty o
f pro
blem
s sh
ould
be
give
n to
lear
ners
. See
the
type
s of
frac
tions
pro
blem
s st
ated
at t
he e
nd o
f the
gra
de n
otes
. Le
arne
rs c
an a
lso
wor
k w
ith a
ppar
atus
and
dia
gram
s. D
iffer
ent d
iagr
ams
or a
ppar
atus
dev
elop
diff
eren
t way
s of
thin
king
abo
ut
fract
ions
.
Reg
ion
or a
rea
mod
els
deve
lop
the
conc
ept o
f fra
ctio
ns a
s pa
rt of
a w
hole
. If u
sed
in p
artic
ular
way
s th
ey c
an a
lso
deve
lop
the
conc
ept
of f
ract
ion
as a
mea
sure
. Ex
ampl
es o
f ar
ea m
odel
s in
clud
e ci
rcle
s cu
t in
to f
ract
ion
piec
es (
or
diag
ram
s of
pie
s),
rect
angl
es o
r ot
her
geom
etric
sha
pes
divi
ded
into
fra
ctio
n pi
eces
(pa
per
fold
ing)
, fra
ctio
ns u
sing
sq
uare
or d
otty
grid
pap
er, g
eobo
ards
.
Leng
th o
r m
easu
rem
ent
mod
els
can
be u
sed
to d
evel
op t
he c
once
pt o
f fra
ctio
ns a
s pa
rt of
a w
hole
and
if u
sed
in
parti
cula
r way
s al
so fr
actio
n as
a m
easu
re. E
xam
ples
of l
engt
h m
odel
s in
clud
e fra
ctio
n st
rips,
Cui
sena
ire ro
ds, n
umbe
r lin
es.
Se
t mod
els
deve
lop
the
conc
ept o
f fra
ctio
n of
a c
olle
ctio
n of
obj
ects
(and
can
lay
the
basi
s fo
r thi
nkin
g ab
out a
frac
tion
of a
num
ber e
.g. 1 3
of 1
2). E
xam
ples
of s
et m
odel
s in
clud
e co
unte
rs o
f any
kin
d in
diff
eren
t arra
ngem
ents
. Le
arne
rs s
houl
d no
t on
ly w
ork
with
one
kin
d of
mod
el,
beca
use
this
can
lim
it th
eir
unde
rsta
ndin
g of
fra
ctio
ns.
For
exam
ple
fract
ions
in d
iagr
am fo
rms
shou
ld in
clud
e re
gion
mod
el (c
ircle
s an
d ot
her g
eom
etric
sha
pes
divi
ded
into
frac
tion
parts
), le
ngth
m
odel
s (in
clud
ing
num
ber l
ines
) and
set
mod
els
(whi
ch s
how
col
lect
ions
of o
bjec
ts).
In T
erm
2 le
arne
rs s
houl
d re
vise
and
con
solid
ate
wha
t the
y le
arne
d ab
out f
ract
ions
in G
rade
4. T
his
is d
escr
ibed
bel
ow, b
ut
lear
ners
can
als
o co
unt i
n fra
ctio
ns.
78 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Cou
ntin
g in
frac
tions
can
hap
pen
• as
lear
ners
pla
ce d
own
fract
ion
piec
es
• on
the
num
ber l
ine
• or
in n
umbe
r cha
ins
like
the
one
show
n be
low.
+
1 2
+1 2
+1 2
+ 1 2
+1 2
+1 2
+
1 2 Eq
uiva
lenc
e, c
ompa
ring
and
orde
ring
Equi
vale
nce
shou
ld b
e ap
proa
ched
usi
ng a
ppar
atus
, dia
gram
s or
pro
blem
con
text
s. L
earn
ers
are
not e
xpec
ted
to b
e ab
le to
giv
e eq
uiva
lent
frac
tions
in s
ymbo
lic (n
umbe
r) fo
rm w
ithou
t hav
ing
diag
ram
s to
whi
ch th
ey c
an re
fer o
r a p
robl
em c
onte
xt in
whi
ch to
m
ake
sens
e of
the
equ
ival
ence
. O
nce
lear
ners
are
com
forta
ble
with
equ
ival
ence
, it
is e
asy
for
them
to
com
pare
and
ord
er
fract
ions
. C
alcu
latio
ns w
ith fr
actio
ns:
Cal
cula
tions
with
frac
tions
in th
e fir
st te
rm c
an fo
cus
on:
• m
akin
g fra
ctio
ns th
roug
h gr
oupi
ng o
r sh
arin
g w
hich
is li
nked
with
und
erst
andi
ng th
e re
latio
nshi
p be
twee
n di
visi
on a
nd
fract
ions
e.g
. If c
hild
ren
shar
e sw
eets
equ
ally,
they
will
each
get
1 5 o
f the
sw
eets
•
addi
ng fr
actio
ns w
ith th
e sa
me
deno
min
ator
s C
alcu
latio
ns a
s w
ith o
ther
asp
ects
of
fract
ions
sho
uld
be d
evel
oped
eith
er t
hrou
gh p
robl
em c
onte
xts
or w
ith t
he u
se o
f ap
para
tus
or d
iagr
ams.
Lea
rner
s sh
ould
be
give
n pr
oble
m c
onte
xts
in w
hich
they
nee
d to
add
frac
tion
parts
. Lea
rner
s sh
ould
al
so b
e gi
ven
eith
er f
ract
ion
piec
es t
o co
unt
e.g.
3 8 + 4 8
can
be
done
by
coun
ting
out
and
coun
ting
on i
n ei
ghth
s w
ith
appa
ratu
s or
by
colo
ring
in d
iagr
ams
or b
y “h
oppi
ng” i
n ei
ghth
s on
a n
umbe
r lin
e.
Gra
de 6
It
is u
sefu
l to
prac
tice
equi
vale
nce
betw
een
the
com
mon
frac
tion,
dec
imal
frac
tions
and
per
cent
age
form
s of
the
sam
e nu
mbe
r. D
ecim
al fr
actio
n is
a n
ew to
pic
for G
rade
6 le
arne
rs.
Lear
ners
sho
uld
alre
ady
have
wor
ked
with
tent
hs a
nd h
undr
edth
s in
com
mon
frac
tion
form
. The
y sh
ould
sta
rt by
rew
ritin
g an
d co
nver
ting
tent
hs a
nd h
undr
edth
s in
com
mon
fra
ctio
n fo
rm t
o de
cim
al f
ract
ions
. Whe
re d
enom
inat
ors
of o
ther
fra
ctio
ns a
re
fact
ors
of 1
0 e.
g. 2
, 5 o
r fac
tors
of 1
00 e
.g. 2
, 4, 2
5, 2
0, 5
0 le
arne
rs c
an c
onve
rt th
ese
to h
undr
edth
s us
ing
wha
t the
y kn
ow a
bout
3
79MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
equi
vale
nce.
D
ivid
ing
who
le n
umbe
rs b
y 10
, 100
, 1 0
00, e
tc. h
elps
to b
uild
lear
ners
’ und
erst
andi
ng o
f the
pla
ce v
alue
of t
he d
igits
in d
ecim
al
fract
ions
. Cal
cula
tors
can
be
usef
ul to
ols
for
lear
ners
to le
arn
abou
t pat
tern
s w
hen
mul
tiply
ing
or d
ivid
ing
deci
mal
frac
tions
by
10, 1
00, e
tc.
Cou
ntin
g in
dec
imal
s Le
arne
rs s
houl
d no
t spe
nd a
lot o
f tim
e do
ing
verb
al c
ount
ing
in d
ecim
als.
A m
ore
usef
ul e
xerc
ise
is u
sing
num
ber c
hain
s lik
e th
e on
e be
low
: The
se c
ount
ing
or “a
ddin
g on
” exe
rcis
es o
ften
help
lear
ners
to in
crea
se th
eir u
nder
stan
ding
of p
lace
val
ue.
Exer
cise
s lik
e th
e on
e ab
ove
can
be c
heck
ed u
sing
cal
cula
tors
and
lear
ners
can
exp
lain
any
diff
eren
ces
betw
een
thei
r ans
wer
s an
d th
ose
show
n by
the
calc
ulat
or.
Equi
vale
nce
betw
een
com
mon
frac
tions
and
dec
imal
frac
tion
form
s Le
arne
rs a
re n
ot e
xpec
ted
to b
e ab
le to
con
vert
all c
omm
on fr
actio
n in
to it
s de
cim
al fr
actio
n fo
rm, m
erel
y to
see
the
rela
tions
hip
betw
een
tent
hs a
nd h
undr
edth
s in
thei
r dec
imal
form
s.
Cal
cula
ting
usin
g de
cim
als
Lear
ners
add
and
sub
tract
dec
imal
frac
tions
. Lea
rner
sho
uld
estim
ate
thei
r ans
wer
s be
fore
cal
cula
ting.
The
y sh
ould
be
able
to
judg
e th
e re
ason
able
ness
of a
nsw
ers
and
also
che
ck th
eir
own
answ
ers.
Und
erst
andi
ng p
lace
val
ue o
f dig
its in
dec
imal
s w
ill he
lp le
arne
rs w
hen
addi
ng a
nd s
ubtra
ctin
g. L
earn
ers
can
use
the
colu
mn
met
hod
as th
ey d
o w
ith w
hole
num
bers
. All
prob
lem
ty
pes
that
are
use
d fo
r who
le n
umbe
rs c
an b
e us
ed fo
r dec
imal
frac
tions
. D
urin
g le
sson
s on
mea
sure
men
t, le
arne
rs c
an p
ract
ise
wha
t th
ey k
now
abo
ut d
ecim
als.
LT
SM
Res
ourc
es
Num
ber l
ines
: Stru
ctur
ed -,
sem
i- st
ruct
ured
- , u
nstru
ctur
ed n
umbe
r lin
es; C
ount
ers,
Pic
ture
s, a
rrays
/ dia
gram
s, fr
actio
n w
alls
, fra
ctio
n ci
rcle
s, d
iffer
ent m
odel
s of
frac
tions
, fra
ctio
n st
rips,
Gra
de 4
G
rade
5
Gra
de 6
W
orkb
ook
refe
renc
e
WB
1 p
p. 9
8 -
108
Ac
tiviti
es 3
4 - 3
9
WB
1 p
p. 1
04 –
114
Ac
tiviti
es 3
4 - 3
9
WB
1 p
p. 2
6 –
40, 4
2 ,4
4 A
ctiv
ities
9a
&b; 1
0a-c
; 11-
13; 1
4, 1
5 pp
. 128
– 1
38 A
ctiv
itite
s 48
, 49;
50
a&b;
51a
&b
DB
E Te
xtbo
ok re
fere
nce
Term
2: U
nit 3
: Com
mon
Fra
ctio
ns, p
. 13
6
Term
2: U
nit 3
: Com
mon
Fra
ctio
ns, p
. 12
9
Term
1: U
nit 4
: Com
mon
Fra
ctio
ns, p
. 55
Te
rm 2
: Uni
t 7: D
ecim
als,
p. 1
77
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
Test
80 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
81MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
6
TER
M 2
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
..to
……
.…
Tim
e: 2
HO
UR
S G
RAD
E 4
CAP
S p.
119
5
CAP
S p.
208
6
CAP
S p.
249
TO
PIC
Sy
mm
etry
C
once
pts,
Ski
lls a
nd
know
ledg
e Sy
mm
etry
Rec
ogni
ze, d
raw
and
des
crib
e lin
e(s)
of
sym
met
ry in
2-D
sha
pes.
Sym
met
ry
R
ecog
nize
, dra
w a
nd d
escr
ibe
line(
s)
of s
ymm
etry
in 2
-D s
hape
s.
Sym
met
ry
R
ecog
nize
, dra
w a
nd d
escr
ibe
line(
s) o
f sym
met
ry in
2-D
sha
pes.
SUG
GES
TED
M
ETH
OD
OLO
GY
Gra
de 4
– 6
Th
is s
houl
d in
clud
e sh
apes
in w
hich
ther
e is
mor
e th
an o
ne li
ne o
f sym
met
ry.
Dra
win
gs o
f 2-D
sha
pes
shou
ld in
clud
e th
ose
whe
re th
e lin
e of
sym
met
ry is
not
nec
essa
rily
verti
cal.
LTSM
Res
ourc
es
Varie
ty o
f 2D
sha
pes/
3D
obj
ects
, cha
rts w
ith le
tters
, sym
bols
Gra
de 4
G
rade
5
Gra
de 6
W
orkb
ook
refe
renc
e
W
B 1
pp.
140
– 1
42
Activ
ities
52,
54
WB
1 p
p 15
8 –
160
Ac
tiviti
es 5
8a&b
W
B 1
pp.
104
– 1
06
Activ
ities
38,
39
DB
E Te
xtbo
ok re
fere
nce
Term
2: U
nit 8
: Sym
met
ry, p
. 189
Term
2: U
nit 8
: Sym
met
ry, p
. 181
Term
2: U
nit 5
: Sym
met
ry, p
. 161
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al
asse
ssm
ent –
Tes
t
82 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
7
TER
M:
2
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E: fr
om
……
… to
……
…
Tim
e: 5
HO
UR
S G
RAD
E 4
CAP
S pp
. 73
- 75
5 C
APS
pp. 1
63 -
165
6 C
APS
pp. 2
72 -
274
TOPI
C
Leng
th
Con
cept
s, S
kills
and
kn
owle
dge
Prac
tical
mea
surin
g of
2-d
sh
apes
and
3-d
obj
ects
by:
•
estim
atin
g •
mea
surin
g •
reco
rdin
g •
com
parin
g an
d or
derin
g M
easu
ring
inst
rum
ents
ru
lers
, met
re s
ticks
, tap
e m
easu
res,
trun
dle
whe
els
Uni
ts:
milli
met
res
(mm
), ce
ntim
etre
s (c
m),
met
res
(m),
kilo
met
res
(km
) C
alcu
latio
ns a
nd p
robl
em-
solv
ing
rela
ted
to le
ngth
So
lve
prob
lem
s in
con
text
s re
late
d to
le
ngth
C
onve
rsio
ns in
clud
e co
nver
ting
betw
een
Prac
tical
mea
surin
g of
2-d
sh
apes
and
3-d
obj
ects
by:
•
estim
atin
g •
mea
surin
g •
reco
rdin
g •
com
parin
g an
d or
derin
g M
easu
ring
inst
rum
ents
ru
lers
, met
re s
ticks
, tap
e m
easu
res,
trun
dle
whe
els
Uni
ts:
milli
met
res
(mm
), ce
ntim
etre
s (c
m),
met
res
(m),
kilo
met
res
(km
) C
alcu
latio
ns a
nd p
robl
em-
solv
ing
rela
ted
to le
ngth
So
lve
prob
lem
s in
con
text
rela
ted
to
leng
th
Con
vers
ions
incl
ude
conv
ertin
g be
twee
n an
y of
the
follo
win
g
Prac
tical
mea
surin
g of
2-d
sh
apes
and
3-d
obj
ects
by:
•
estim
atin
g •
mea
surin
g •
reco
rdin
g •
com
parin
g an
d or
derin
g M
easu
ring
inst
rum
ents
ru
lers
, met
re s
ticks
, tap
e m
easu
res,
trun
dle
whe
els
Uni
ts:
milli
met
res
(mm
), ce
ntim
etre
s (c
m),
met
res
(m),
kilo
met
res
(km
) C
alcu
latio
ns a
nd p
robl
em-
solv
ing
rela
ted
to le
ngth
So
lve
prob
lem
s in
con
text
s re
late
d to
le
ngth
C
onve
rsio
ns in
clud
e co
nver
ting
betw
een
any
of th
e fo
llow
ing
units
:
83MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• m
illim
etre
s (m
m),
and
cent
imet
res
(cm
) •
cent
imet
res
(cm
) and
met
res
(m)
• m
etre
s (m
) and
kilo
met
res
(km
) C
onve
rsio
ns a
re li
mite
d to
who
le
num
bers
and
frac
tions
units
:
milli
met
res
(mm
), ce
ntim
etre
s (c
m),
met
res
(m) a
nd
kilo
met
res
(km
) C
onve
rsio
ns li
mite
d to
who
le n
umbe
rs
and
fract
ions
m
illim
etre
s (m
m),
cent
imet
res
(cm
), m
etre
s (m
) and
ki
lom
etre
s (k
m)
Con
vers
ions
sho
uld
incl
ude
fract
ion
and
deci
mal
form
s (to
2 d
ecim
al p
lace
s)
SUG
GES
TED
M
ETH
OD
OLO
GY
All l
earn
ers
can
star
t off
with
the
easi
er p
robl
ems.
Gra
de 4
lear
ners
are
trea
ting
the
wor
k as
new
whi
le th
e G
rade
5 an
d G
rade
6 le
arne
rs c
an m
ove
on to
mor
e co
mpl
ex p
robl
ems
as in
dica
ted
in th
e C
APS
polic
y do
cum
ent.
All g
rade
s:
In G
rade
3 le
arne
rs w
ork
with
non
-sta
ndar
d or
info
rmal
uni
ts w
hen
mea
surin
g. T
hey
are
intro
duce
d to
met
res
and
cent
imet
res.
The
y us
e ru
lers
to m
easu
re in
cen
timet
res
only.
In G
rade
3 le
arne
rs u
se m
etre
stic
ks o
r len
gths
of s
tring
to
mea
sure
in m
etre
s. T
hey
do n
ot le
arn
that
ther
e ar
e 10
0 cm
in 1
m. T
hey
do n
ot d
o co
nver
sion
s be
twee
n un
its. I
n G
rade
4
lear
ners
wor
k w
ith n
ew m
easu
ring
inst
rum
ents
. Milli
met
res
and
kilo
met
res
are
intro
duce
d an
d le
arne
rs d
o co
nver
sion
s
betw
een
units
. Gra
de 4
lear
ners
nee
d to
und
erst
and
and
lear
n th
e re
latio
nshi
p be
twee
n m
etre
s an
d ce
ntim
etre
s,
cent
imet
res
and
milli
met
res,
met
res
and
kilo
met
res.
Rea
ding
inst
rum
ents
for m
easu
ring
leng
ths
Lear
ners
sho
uld
mea
sure
leng
ths
usin
g
• ru
lers
(mm
, cm
)
• m
etre
stic
ks (m
)
• ta
pe m
easu
res
(m, c
m, m
m)
• tru
ndle
whe
els
(m)
84 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Lear
ners
find
rule
rs e
asy
to u
se fo
r mea
surin
g be
caus
e:
• ce
ntim
etre
s ar
e al
way
s nu
mbe
red
• th
ere
are
alw
ays
10m
m d
ivis
ions
in a
cen
timet
re
In G
rade
4 le
arne
rs n
orm
ally
reco
rd th
eir m
easu
rem
ents
with
rule
rs a
s m
illim
etre
s or
cen
timet
res
or m
illim
etre
s an
d
cent
imet
res
e.g.
the
penc
il is
11
cent
imet
res
and
3 m
illim
etre
s lo
ng.
Lear
ners
can
som
etim
es r
ecor
d th
eir
mea
sure
men
ts in
cen
timet
res
and
fract
ions
of
cent
imet
ers
e.g.
the
eras
er is
2 1 2 c
m
long
. Thi
s is
eas
y to
do
beca
use
on a
rule
r, th
e 5t
h m
illim
etre
gra
datio
n lin
e is
nor
mal
ly lo
nger
. Onc
e le
arne
rs h
ave
lear
ned,
from
read
ing
com
mer
cial
mas
s an
d ca
paci
ty p
acka
ging
, tha
t is
the
sam
e as
2,5
, the
y w
ill al
so b
e ab
le to
use
the
deci
mal
5 in
thei
r rec
ordi
ng i.
e. 2
,5 c
m lo
ng.
Che
ck th
at le
arne
rs k
now
to s
tart
mea
surin
g fro
m z
ero,
or t
o su
btra
ct th
e in
itial
mea
sure
men
t fro
m th
e fin
al
mea
sure
men
t. Th
is is
illu
stra
ted
belo
w.
Exa
mpl
e:
Th
e er
aser
is 2
cm +
7m
m o
r 20
mm
+ 7
mm
or 2
7mm
long
85MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
The
eras
er is
(3cm
–1c
m )
+ 7m
m =
2cm
+ 7
mm
or 2
0mm
+ 7
mm
or 2
7mm
long
Onc
e le
arne
rs h
ave
som
e ex
perie
nce
of m
easu
ring
in e
ach
unit,
they
sho
uld
estim
ate
befo
re e
very
mea
sure
men
t. It
is
usef
ul to
hav
e ev
eryd
ay re
fere
nts
as c
ompa
rison
s e.
g. th
e w
idth
of a
doo
r and
hei
ght o
f a w
indo
w a
re o
ften
1 m
, the
wid
th
of a
mat
ch is
ofte
n 1
mm
.
Tape
mea
sure
s th
at a
re lo
nger
than
1 m
and
2 m
sho
uld
also
be
used
e.g
. bui
lder
tape
s or
sur
veyo
r tap
es c
an b
e m
ore
than
10 m
etre
s. T
he lo
nger
mea
surin
g ta
pes
are
mor
e di
fficu
lt to
use
. Lea
rner
s ca
nnot
onl
y re
ad o
ff th
e nu
mbe
r cor
resp
ondi
ng w
ith
the
final
mea
sure
men
t. Th
ey a
lso
need
to k
now
for h
ow m
any
met
res
they
hav
e un
rolle
d th
e ta
pe, e
.g, t
he d
ista
nce
may
be
4
m a
nd 7
8 cm
, but
the
tape
may
onl
y sh
ow th
e nu
mbe
r 78.
Whe
n us
ing
the
long
er m
easu
ring
tape
s, e
stim
atio
n be
com
es e
ven
mor
e im
porta
nt.
Com
pare
and
ord
er le
ngth
s up
to 4
dig
its in
mm
, cm
, m, k
m
In G
rade
s R
to 2
lear
ners
pla
ce o
bjec
ts n
ext t
o ea
ch o
ther
and
dis
cuss
whi
ch is
long
er o
r sho
rter.
In th
e In
term
edia
te P
hase
lear
ners
nee
d to
com
pare
leng
ths
and
heig
hts
whe
n gi
ven
draw
ings
of o
bjec
ts w
ith s
peci
fied
leng
ths,
or w
ritte
n de
scrip
tions
of o
bjec
ts w
ith s
peci
fied
leng
ths.
At f
irst l
earn
ers
can
com
pare
leng
th g
iven
in th
e sa
me
units
, but
onc
e th
ey k
now
how
to
conv
ert b
etw
een
units
, the
y ca
n co
mpa
re le
ngth
s an
d he
ight
s of
obj
ects
whi
ch a
re s
peci
fied
in d
iffer
ent u
nits
.
Cal
cula
tions
(inc
ludi
ng c
onve
rsio
ns) a
nd p
robl
em –
solv
ing
Mea
sure
men
t pro
vide
s a
cont
ext i
n w
hich
to p
ract
ise
skills
acq
uire
d in
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
. The
ski
lls,
oper
atio
ns a
nd n
umbe
r ran
ges
that
lear
ners
hav
e w
orke
d w
ith s
o fa
r in
the
year
, are
giv
en b
elow
:
86 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Estim
ate
and
calc
ulat
e us
ing
mm
, cm
, m, k
m
• ro
undi
ng n
umbe
rs u
p or
dow
n to
the
appr
opria
te u
nit o
f len
gth
• ro
undi
ng o
ff to
10,
100
, 1 0
00
• ad
ditio
n an
d su
btra
ctio
n of
up
to 4
-dig
it nu
mbe
rs
• m
ultip
licat
ion
of 2
-dig
it by
1-d
igit
num
bers
• di
visi
on o
f 2-d
igit
by 1
-dig
it nu
mbe
rs
• ad
d fra
ctio
ns in
mea
sure
men
t con
text
s (u
sing
onl
y ha
lves
, thi
rds,
qua
rters
, fift
hs, s
ixth
s, s
even
ths
and
eigh
ths)
By th
e en
d of
the
year
the
num
ber r
ange
s an
d op
erat
ions
can
be
incr
ease
d to
incl
ude
ever
ythi
ng th
at is
cov
ered
und
er
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
.
Solv
e pr
oble
ms
rela
ting
to d
ista
nce
and
leng
th
Incl
ude
rate
and
ratio
pro
blem
s
Con
vers
ions
bet
wee
n un
its: m
m ↔
cm
; cm
↔ m
; m ↔
km
Con
verti
ng b
etw
een
the
units
of m
easu
rem
ent a
bove
pro
vide
s a
cont
ext f
or p
ract
isin
g m
ultip
lyin
g an
d di
vidi
ng b
y 10
; 100
and
1
000.
Con
vers
ions
sho
uld
be li
mite
d to
who
le n
umbe
rs a
nd fr
actio
ns g
iven
onl
y as
hal
ves,
third
s, q
uarte
rs, f
ifths
, six
ths,
sev
enth
s,
eigh
ths.
In G
rade
4 le
arne
rs d
o no
t cal
cula
te u
sing
dec
imal
s. W
hen
doin
g di
visi
on th
ey s
omet
imes
hav
e a
rem
aind
er e
.g. 3
7 ÷
4 =
9
rem
aind
er 1
. Sim
ilarly
whe
n co
nver
ting
betw
een
units
, the
y m
ay g
ive
thei
r ans
wer
s in
a c
ombi
natio
n of
uni
ts e
.g.
• 35
mm
= 3
cm a
nd 5
mm
or 3
1 2 cm
• 52
6cm
= 5
m a
nd 2
6cm
• 2
500m
= 2
m a
nd 5
00cm
• 4
1 2 km
= 4
500
m
87MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Gra
de 5
and
6:
In G
rade
5 le
arne
rs w
ork
with
the
sam
e un
its o
f len
gth
that
they
wor
ked
with
in G
rade
4. T
hey
also
wor
k w
ith th
e sa
me
mea
surin
g in
stru
men
ts. C
heck
whe
ther
lear
ners
hav
e a
sens
e of
whi
ch u
nits
and
inst
rum
ents
are
app
ropr
iate
for
mea
surin
g va
rious
leng
ths,
hei
ghts
and
dis
tanc
es
Lear
ners
sho
uld
have
a s
ense
of w
hich
uni
ts a
re a
ppro
pria
te fo
r mea
surin
g di
ffere
nt le
ngth
s. F
or e
xam
ple,
they
nee
d to
kno
w
whi
ch u
nits
to u
se to
sta
te
• th
e le
ngth
and
wid
th o
f a d
esk
• th
e di
stan
ce to
the
next
tow
n
• th
e le
ngth
of a
nai
l
Lear
ners
sho
uld
have
a s
ense
of w
hich
inst
rum
ents
are
app
ropr
iate
for m
easu
ring
diffe
rent
leng
ths.
For
exa
mpl
e, th
ey n
eed
to k
now
whi
ch in
stru
men
ts to
use
to m
easu
re:
• th
e le
ngth
and
wid
th o
f a d
esk
• th
e le
ngth
of t
he c
lass
room
• th
e le
ngth
of a
rugb
y fie
ld
Rea
ding
inst
rum
ents
for m
easu
ring
leng
ths
Lear
ners
sho
uld
mea
sure
leng
ths
usin
g
• ru
lers
(mm
, cm
)
• m
etre
stic
ks (m
)
• ta
pe m
easu
res
(m, c
m, m
m)
• tru
ndle
whe
els
(m)
88 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Lear
ners
find
rule
rs e
asy
to u
se fo
r mea
surin
g. T
his
is b
ecau
se
• ce
ntim
etre
s ar
e al
way
s nu
mbe
red
• th
ere
are
alw
ays
10m
m d
ivis
ions
in a
cen
timet
re.
Stat
ing
and
reco
rdin
g le
ngth
mea
sure
men
ts
In G
rade
5 le
arne
rs c
ontin
ue to
reco
rd th
eir m
easu
rem
ents
usi
ng ru
lers
, as
milli
met
res
or c
entim
etre
s or
milli
met
res
and
cent
imet
res
e.g.
the
penc
il is
11
cent
imet
res
and
3 m
illim
etre
s lo
ng. T
hey
can
som
etim
es re
cord
thei
r mea
sure
men
ts in
cent
imet
res
and
fract
ions
of c
entim
etre
s e.
g. th
e er
aser
is 2
1 2 cm
long
. Thi
s is
eas
y to
do
beca
use
on a
rule
r, th
e 5t
h m
illim
etre
grad
atio
n lin
e is
nor
mal
ly lo
nger
. Onc
e le
arne
rs h
ave
lear
ned,
from
read
ing
com
mer
cial
mas
s an
d ca
paci
ty p
acka
ging
, tha
t 2 1 2
is th
e sa
me
as 2
,5 ,
they
will
also
be
able
to u
se th
e de
cim
al ',
5' in
thei
r rec
ordi
ng i.
e. 2
,5cm
long
.
Tape
mea
sure
s th
at a
re lo
nger
than
1m
and
2m
sho
uld
also
be
used
e.g
. bui
lder
tape
s or
sur
veyo
r tap
es c
an b
e m
ore
than
10
met
res.
The
long
er m
easu
ring
tape
s ar
e m
ore
diffi
cult
to u
se. L
earn
ers
cann
ot o
nly
read
off
the
num
ber c
orre
spon
ding
with
the
final
mea
sure
men
t. Th
ey a
lso
need
to k
now
for h
ow m
any
met
res
they
hav
e un
rolle
d th
e ta
pe, e
.g, t
he d
ista
nce
may
be
4m a
nd 7
8cm
, but
the
tape
may
onl
y sh
ow th
e nu
mbe
r 78.
Whe
n us
ing
the
long
er lo
nger
mea
surin
g ta
pes,
est
imat
ion
beco
mes
eve
n m
ore
impo
rtant
.
Com
pare
and
ord
er le
ngth
s up
to 6
dig
its in
mm
, cm
, m, k
m
In th
e In
term
edia
te P
hase
lear
ners
nee
d to
wor
k w
ith d
raw
ings
of o
bjec
ts w
ith s
peci
fied
leng
ths,
or w
ritte
n de
scrip
tions
of
obje
cts
with
spe
cifie
d le
ngth
s. A
t firs
t lea
rner
s ca
n co
mpa
re le
ngth
giv
en in
the
sam
e un
its, b
ut o
nce
they
kno
w h
ow to
con
vert
betw
een
units
, the
y ca
n co
mpa
re le
ngth
s an
d he
ight
s of
obj
ects
whi
ch a
re s
peci
fied
in d
iffer
ent u
nits
89MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Cal
cula
tions
(inc
ludi
ng c
onve
rsio
ns) a
nd p
robl
em-s
olvi
ng
Mea
sure
men
t pro
vide
s a
cont
ext i
n w
hich
to p
ract
ise
skills
acq
uire
d in
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
. The
ski
lls,
oper
atio
ns a
nd n
umbe
r ran
ges
requ
ired
are
give
n be
low.
Estim
ate
and
calc
ulat
e us
ing
• R
ound
num
bers
up
or d
own
to th
e ap
prop
riate
uni
t of l
engt
h
• R
ound
ing
off t
o 5,
10,
100
and
1 00
0
• Ad
ditio
n an
d su
btra
ctio
n up
to 5
-dig
it nu
mbe
rs
• M
ultip
licat
ion:
3-d
igit
num
ber b
y 2-
digi
t num
ber
• D
ivis
ion:
3-d
igit
num
ber b
y 2-
digi
t num
ber
• Ad
d co
mm
on fr
actio
ns in
the
cont
ext o
f mea
sure
men
t (us
ing
only
hal
ves,
third
s, q
uarte
rs, f
ifths
, six
ths,
sev
enth
s an
d
eigh
ths)
By th
e en
d of
the
year
the
num
ber r
ange
s an
d op
erat
ions
can
be
incr
ease
d to
incl
ude
ever
ythi
ng th
at is
cov
ered
und
er
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
.
Solv
e pr
oble
ms
rela
ting
to d
ista
nce
and
leng
th in
clud
ing
rate
and
ratio
pro
blem
s.
Con
vers
ions
bet
wee
n un
its: m
m
↔
cm
; cm
↔
m;
m ↔
km
Con
verti
ng b
etw
een
the
units
of m
easu
rem
ent a
bove
pro
vide
s a
cont
ext f
or p
ract
isin
g m
ultip
licat
ion
and
divi
sion
by
10, 1
00, 1
000
Con
vers
ions
sho
uld
be li
mite
d to
who
le n
umbe
rs a
nd fr
actio
ns g
iven
onl
y as
hal
ves
/ thi
rds
/ qua
rters
/ fif
ths
/ six
ths
/ sev
enth
s /
eigh
ths.
90 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
In G
rade
5 le
arne
rs d
o no
t cal
cula
te u
sing
dec
imal
s. W
hen
doin
g di
visi
on th
ere
will
som
etim
es b
e a
rem
aind
er in
the
answ
er,
e.g.
37
÷ 4
= 9
rem
aind
er 1
. Sim
ilarly
whe
n co
nver
ting
betw
een
units
, ans
wer
s m
ay b
e st
ated
in a
com
bina
tion
of u
nits
e.g
.
• 35
cm =
3cm
and
5m
m o
r 3 1 2
cm
• 52
6cm
= 5
m a
nd 2
6cm
• 2
500m
= 2
m a
nd 5
00cm
• 4
1 2 km
= 4
500
m
Gra
de 6
: D
ecim
als
are
intr
oduc
ed.
This
allo
ws
lear
ners
to e
xpre
ss c
onve
rsio
ns a
nd p
arts
of m
easu
res
in d
ecim
al fr
actio
n fo
rm to
one
or t
wo
deci
mal
pla
ces.
Use
the
cont
exts
of l
engt
h m
easu
rem
ent t
o pr
actis
e th
e re
adin
g, w
ritin
g an
d un
ders
tand
ing
of d
ecim
al fr
actio
ns, a
nd fo
r
roun
ding
off,
con
verti
ng, a
ddin
g an
d su
btra
ctin
g w
ith d
ecim
al fr
actio
ns.
Rea
ding
inst
rum
ents
for m
easu
ring
leng
ths
Lear
ners
sho
uld
mea
sure
leng
ths
usin
g
• ru
lers
(mm
, cm
)
• m
etre
stic
ks (m
)
• ta
pe m
easu
res
(m, c
m, m
m)
• tru
ndle
whe
els
(in m
)
Lear
ners
find
rule
rs e
asy
to u
se fo
r mea
surin
g be
caus
e
• ce
ntim
etre
s ar
e al
way
s nu
mbe
red
• th
ere
are
alw
ays
10m
m d
ivis
ions
in a
cen
timet
er
•
91MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Stat
ing
and
reco
rdin
g le
ngth
mea
sure
men
ts
In G
rade
6 le
arne
rs s
houl
d be
giv
en o
ppor
tuni
ties
to re
cord
thei
r mea
sure
men
ts u
sing
rule
rs, i
n de
cim
al fr
actio
n fro
m e
.g.
e.g.
the
eras
er is
2,5
cm lo
ng.
Tape
mea
sure
s th
at a
re lo
nger
than
1m
and
2m
sho
uld
also
be
used
e.g
. bui
lder
tape
s or
sur
veyo
r tap
es c
an b
e m
ore
than
10 m
etre
s. T
he lo
nger
mea
surin
g ta
pes
are
mor
e di
fficu
lt to
use
. Lea
rner
s ca
n’t o
nly
read
off
the
num
ber a
t the
end
of t
he
dist
ance
. The
y al
so n
eed
to k
now
how
man
y m
etre
s th
ey h
ave
unro
lled
the
tape
. For
exa
mpl
e, th
e di
stan
ce m
ay b
e 4m
and
78cm
, but
at t
he e
nd o
f the
obj
ect /
dis
tanc
e th
e ta
pe m
ay o
nly
show
the
num
ber 7
8. W
ith th
ese
long
er ta
pe m
easu
res
estim
atio
n be
com
es e
ven
mor
e im
porta
nt. R
ecor
ding
this
in o
ne u
nit o
f mea
sure
men
t can
als
o be
com
e m
ore
com
plex
: in
this
exa
mpl
e 4,
78m
or 4
78cm
. But
if th
e m
easu
rem
ent i
s 4m
and
7cm
, lea
rner
s ne
ed to
rem
embe
r to
conv
ert c
orre
ctly
into
4,07
m o
r 407
cm
Com
pare
and
ord
er le
ngth
s up
to 9
dig
its in
mm
, cm
, m, k
m
In th
e In
term
edia
te P
hase
lear
ners
nee
d to
wor
k w
ith d
raw
ings
of o
bjec
ts w
ith s
peci
fied
leng
ths,
or w
ritte
n de
scrip
tions
of
obje
cts
with
spe
cifie
d le
ngth
s. In
Gra
de 6
the
focu
s is
on
com
parin
g le
ngth
s gi
ven
in d
ecim
al fo
rm
Cal
cula
tions
(inc
ludi
ng c
onve
rsio
ns) a
nd p
robl
em-s
olvi
ng
Mea
sure
men
t pro
vide
s a
cont
ext i
n w
hich
to p
ract
ise
skills
acq
uire
d in
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
. The
ski
lls,
oper
atio
ns a
nd n
umbe
r ran
ges
requ
ired
are
give
n be
low.
Estim
ate
and
calc
ulat
e us
ing
mm
, cm
, m, k
m
• ro
und
num
bers
up
or d
own
to th
e ap
prop
riate
uni
t of l
engt
h
• ro
undi
ng o
ff to
5, 1
0, 1
00, 1
000
(rea
ding
mea
sure
men
ts fr
om ru
lers
and
tape
mea
sure
s ca
n he
lp le
arne
rs to
und
erst
and
the
mea
ning
beh
ind
roun
ding
up
or d
own)
92 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• ad
ditio
n an
d su
btra
ctio
n ca
lcul
atio
ns c
an in
clud
e ca
lcul
atio
ns w
ith c
omm
on fr
actio
ns a
nd d
ecim
al fr
actio
ns to
2 d
ecim
al
plac
es
• m
ultip
licat
ion
of 4
-dig
it by
3-d
igit
num
bers
• di
visi
on o
f 4-d
igit
by 3
-dig
it nu
mbe
rs
• fin
d pe
rcen
tage
s of
who
le n
umbe
rs
• m
ultip
le o
pera
tions
with
or w
ithou
t bra
cket
s
Solv
e pr
oble
ms
rela
ting
to d
ista
nce
and
leng
th
• In
clud
e ra
te a
nd ra
tio p
robl
ems.
• Pr
oble
ms
with
dec
imal
s sh
ould
be
limite
d to
add
ing
and
subt
ract
ing
the
num
bers
.
Con
vers
ions
bet
wee
n un
its
• m
m ↔
cm
• cm
↔ m
• m
↔ k
m
• m
m ↔
m
• m
m ↔
km
• cm
↔ k
m ,
usin
g w
hole
num
bers
, com
mon
frac
tions
and
dec
imal
frac
tions
. Thi
s pr
ovid
es a
con
text
for l
earn
ers
to p
ract
ise
mul
tiply
ing
and
divi
ding
by
10, 1
00 a
nd 1
000
.
If co
nver
sion
s re
quire
mor
e th
an 2
dec
imal
pla
ces
e.g.
3 2
45m
con
verte
d to
kilo
met
res,
lear
ners
can
con
tinue
to w
rite
this
as
3km
and
245
m a
s th
ey h
ave
in p
revi
ous
grad
es. O
n th
e w
hole
thou
gh e
xam
ples
sho
uld
be c
hose
n to
avo
id th
is p
robl
em.
LTSM
Res
ourc
es
Mea
surin
g ta
pe, r
uler
s, s
trin
g, tr
undl
e w
heel
G
rade
4
Gra
de 5
G
rade
6
93MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Wor
book
refe
renc
e
WB
1 p
p. 1
10 –
114
Ac
tiviti
es 4
0; 4
1; 4
2
WB
1 p
p. 1
16 –
126
Ac
tiviti
es
40; 4
1a&b
; 42a
&b; 4
3
WB
1 p
p. 9
6 –
106
Activ
ities
10
0a&b
, 101
- 10
4
DB
E Te
xtbo
ok re
fere
nce
Term
2: U
nit 4
: Len
gth,
p. 1
47
Term
2: U
nit 4
: Len
gth,
p. 1
43
Term
3: U
nit 1
1: L
engt
h, p
. 285
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– te
st
94 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
8
TER
M:
2
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E: fr
om
……
… to
……
…
Tim
e: 5
HO
UR
S G
RAD
E 4
CAP
S pp
. 108
- 11
0 5
CAP
S pp
. 178
- 18
0 6
CAP
S pp
. 259
- 26
1 TO
PIC
M
ass
Con
cept
s, S
kills
and
kn
owle
dge
Prac
tical
mea
surin
g of
3-D
ob
ject
s by
•
estim
atin
g •
mea
surin
g, re
cord
ing
• co
mpa
ring
and
orde
ring
• 3-
D o
bjec
ts u
sing
mas
s M
easu
ring
inst
rum
ents
ba
thro
om s
cale
s, k
itche
n sc
ales
an
d ba
lanc
es
Uni
ts
gra
ms
(g) a
nd k
ilogr
ams
(kg)
Cal
cula
tions
and
pro
blem
-so
lvin
g w
ith m
ass
incl
ude
Solv
e pr
oble
ms
in c
onte
xts
with
mas
s co
nver
ting
betw
een
gram
s an
d ki
logr
ams
limite
d to
exa
mpl
es w
ith w
hole
num
bers
an
d fra
ctio
ns
Prac
tical
mea
surin
g of
3-D
ob
ject
s by
•
estim
atin
g •
mea
surin
g, re
cord
ing
• co
mpa
ring
and
orde
ring
Mea
surin
g in
stru
men
ts
bath
room
sca
les,
kitc
hen
scal
es
and
bala
nces
U
nits
gr
ams
(g) a
nd k
ilogr
ams
(kg)
; C
alcu
latio
ns a
nd p
robl
em-
solv
ing
rela
ted
to m
ass
incl
ude
Solv
e pr
oble
ms
in c
onte
xts
rela
ted
to
mas
s co
nver
ting
betw
een
gram
s an
d ki
logr
ams
limite
d to
exa
mpl
es w
ith
who
le n
umbe
rs a
nd fr
actio
n
Prac
tical
mea
surin
g of
3-D
ob
ject
s by
•
estim
atin
g •
mea
surin
g, re
cord
ing
• co
mpa
ring
and
orde
ring
Mea
surin
g in
stru
men
ts
bath
room
sca
les
(ana
logu
e an
d di
gita
l), k
itche
n sc
ales
(ana
logu
e an
d di
gita
l) an
d ba
lanc
es
Uni
ts
gram
s (g
) and
kilo
gram
s (k
g)
Cal
cula
tions
and
pro
blem
-so
lvin
g re
late
d to
mas
s in
clud
e So
lve
prob
lem
s in
con
text
usi
ng m
ass
conv
ertin
g be
twee
n gr
ams
and
kilo
gram
s co
nver
sion
s sh
ould
incl
ude
fract
ion
and
deci
mal
form
s (to
2 d
ecim
al p
lace
s).
95MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
SUG
GES
TED
M
ETH
OD
OLO
GY
All l
earn
ers
can
star
t off
with
the
easi
er p
robl
ems.
Gra
de 4
lear
ners
are
trea
ting
the
wor
k as
new
whi
le th
e G
rade
5
and
Gra
de 6
lear
ners
can
mov
e on
to m
ore
com
plex
pro
blem
s as
indi
cate
d in
the
CAP
S po
licy
docu
men
t. Al
l gra
des:
In
Gra
de 3
lear
ners
wor
k w
ith n
on-s
tand
ard
or in
form
al u
nits
whe
n m
easu
ring
mas
s. T
hey
also
wor
k w
ith k
ilogr
ams
and
gram
s. T
hey
read
bat
hroo
m s
cale
s bu
t onl
y re
ad th
e m
ass
at th
e nu
mbe
red
calib
ratio
n lin
es. T
hey
do n
ot le
arn
that
ther
e ar
e 1
000g
in 1
kg. T
hey
do n
ot c
onve
rt be
twee
n un
its. T
he G
rade
4 le
arne
rs m
ust l
earn
the
rela
tions
hip
betw
een
the
two
units
. G
rade
4 le
arne
rs n
eed
to:
co
nsol
idat
e th
eir s
ense
of h
ow m
uch
1kg
is
fu
rther
dev
elop
a s
ense
of h
ow m
uch
1g is
unde
rsta
nd a
nd k
now
the
rela
tions
hip
betw
een
gram
s an
d ki
logr
am
co
nver
t bet
wee
n gr
ams
and
kilo
gram
s
read
mea
sure
men
ts o
n sc
ales
indi
cate
d on
bot
h nu
mbe
red
and
unnu
mbe
red
calib
ratio
n lin
es.
Rea
ding
inst
rum
ents
and
mea
surin
g m
ass
Lear
ners
nee
d to
: •
estim
ate
mas
s in
gra
ms
and
kilo
gram
s •
read
the
mas
ses
stip
ulat
ed o
n pa
ckag
ing
• re
ad th
e m
ass
on p
ictu
res
of k
itche
n sc
ales
(in
g &
kg) a
nd b
athr
oom
sca
les
(in k
g) a
nd b
alan
ce s
cale
s (in
g &
kg)
•
read
the
mas
s on
real
kitc
hen
scal
es in
(g &
kg)
and
bat
hroo
m s
cale
s (in
kg)
and
bal
ance
sca
les
(in g
& k
g).
Rea
ding
the
mas
s on
kitc
hen
and
bath
room
sca
les
invo
lves
: •
know
ing
whe
re to
sta
nd to
read
the
scal
e co
rrect
ly
• kn
owin
g ho
w to
rea
d th
e nu
mbe
red
grad
atio
n lin
es a
nd to
cal
cula
te w
hat t
he u
n-nu
mbe
red
grad
atio
n lin
es m
ean.
Lea
rner
s ne
ed to
read
:
◊ di
ffere
nt k
inds
of m
ass
met
ers
◊ m
ass
met
ers
on w
hich
the
num
bere
d in
terv
als/
gra
datio
n lin
es /
calib
ratio
n re
pres
ent d
iffer
ent i
nter
vals
/mas
ses
◊ ap
para
tus
whi
ch h
ave
diffe
rent
num
bers
of u
n-nu
mbe
red
inte
rval
s w
ithin
eac
h nu
mbe
red
inte
rval
.
96 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Lea
rner
s ne
ed to
pra
ctic
e w
ith e
xam
ples
in w
hich
the
num
bere
d in
terv
als
are
divi
ded
into
:
- 2
un-n
umbe
red
inte
rval
s
- 4
un-n
umbe
red
inte
rval
s
- 5
un-n
umbe
red
inte
rval
s
- 10
un-
num
bere
d in
terv
als
Exa
mpl
e:
Her
e th
e nu
mbe
red
lines
sho
w 1
00g
inte
rval
s: 1
00g,
200
g, 3
00g,
400
g, 5
00g,
600
g, 7
00g,
800
g, 9
00g,
1 0
00g
It
is s
omet
imes
use
ful t
o co
nver
t the
circ
ular
dia
l int
o a
num
ber l
ine
for l
earn
ers
600
g
70
0 g
Ther
e ar
e 10
spa
ces
betw
een
each
100
g.
Each
100
g in
terv
al h
as b
een
divi
ded
into
10
smal
ler s
pace
s.
This
mea
ns th
at e
ach
un-n
umbe
red
inte
rval
sho
ws
100g
÷ 1
0 =
10g
97MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Com
pare
mas
ses
with
up
to 4
dig
its in
gra
ms
and
kilo
gram
s
Lear
ners
sho
uld
sequ
ence
con
tain
ers
mar
ked
in g
ram
s an
d/ki
logr
ams.
Her
e le
arne
rs n
eed
to b
e ab
le to
tran
slat
e th
e de
cim
al
num
bers
on
som
e pa
ckag
ing
into
frac
tions
e.g
. 2,5
kg o
f flo
ur is
the
sam
e as
2 1 2
kg o
f flo
ur. O
ne s
houl
d al
so c
hoos
e ex
ampl
es
that
allo
w le
arne
rs to
real
ize
that
the
size
of a
con
tain
er o
r the
vol
ume
it co
ntai
ns is
not
dire
ctly
pro
porti
onal
to th
e m
ass:
som
e su
bsta
nces
hav
e a
grea
ter d
ensi
ty th
an o
ther
s.
Cal
cula
tions
(inc
ludi
ng c
onve
rsio
ns) a
nd p
robl
em-s
olvi
ng
Mea
sure
men
t pro
vide
s a
cont
ext i
n w
hich
to p
ract
ice
skills
acq
uire
d in
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
. The
ski
lls,
op
erat
ions
and
num
ber r
ange
s re
quire
d ar
e gi
ven
belo
w.
Cal
cula
te a
nd e
stim
ate
(usi
ng g
ram
s an
d ki
logr
ams)
•
roun
d nu
mbe
rs u
p or
dow
n to
the
appr
opria
te u
nit o
f mas
s •
roun
ding
to 1
0, 1
00, 1
000
•
addi
tion
and
subt
ract
ion
of u
p to
4-d
igit
num
bers
•
mul
tiplic
atio
n 2-
digi
t by
2-di
git n
umbe
rs
• di
visi
on: 3
-dig
it by
1-d
igit
num
bers
•
add
fract
ions
in c
onte
xt (u
sing
onl
y ha
lves
, thi
rds,
qua
rters
, fift
hs, s
ixth
s, s
even
ths
and
eigh
ths)
So
lve
prob
lem
s re
latin
g to
mas
s:
• in
clud
e ra
te e
spec
ially
rand
s pe
r kilo
gram
s an
d ra
tio p
robl
ems
e.g.
incr
easi
ng o
r dec
reas
ing
the
mas
s of
ingr
edie
nts
in a
re
cipe
by
a se
t rat
io
• w
rite
num
ber s
ente
nces
to d
escr
ibe
prob
lem
s C
onve
rt b
etw
een
units
: g ↔
kg
Con
verti
ng b
etw
een
the
units
of m
easu
rem
ent a
bove
pro
vide
s a
cont
ext f
or p
ract
isin
g m
ultip
lyin
g an
d di
vidi
ng b
y
1
00
0.
Con
vers
ions
sho
uld
be li
mite
d to
who
le n
umbe
rs a
nd fr
actio
ns g
iven
onl
y as
hal
ves
/ thi
rds
/ qua
rters
/ fif
ths
/ six
ths
/ se
vent
hs /
eigh
ths.
Con
vers
ions
can
als
o in
clud
e co
nver
ting
the
deci
mal
hal
f to
the
com
mon
frac
tion
form
of h
alf.
Whe
n le
arne
rs d
o di
visi
on in
Gra
de 4
the
answ
ers
may
hav
e re
mai
nder
s e.
g.11
5 ÷
25 =
4 re
mai
nder
15.
Sim
ilarly
whe
n co
nver
ting
gram
s to
kilo
gram
s, le
arne
rs m
ay g
et p
art o
f the
ans
wer
in k
ilogr
ams
and
stat
e th
e re
mai
ning
par
t in
gram
s e.
g.
4 25
0g =
4kg
and
250
g
98 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Rec
ordi
ng m
asse
s Be
caus
e le
arne
rs w
ill on
ly w
ork
with
dec
imal
frac
tions
in G
rade
6, t
hey
shou
ld re
cord
mas
ses
in:
• ki
logr
ams
only
e.g
. 5kg
•
gram
s on
ly e
.g. 2
50g
Sinc
e le
arne
rs w
ill be
read
ing
half
kilo
gram
s in
dec
imal
form
on
som
e pa
ckag
ing,
they
can
als
o w
rite
half
kilo
gram
s in
the
deci
mal
form
. How
ever
this
is n
ot a
requ
irem
ent i
n th
is g
rade
. G
rade
5:
Let t
he G
rade
4, 5
and
6 le
arne
rs d
o th
e sa
me
wor
k w
ith th
e di
ffere
nces
as
indi
cate
d be
low
. R
eadi
ng in
stru
men
ts a
nd m
easu
ring
mas
s Le
arne
rs n
eed
to:
• es
timat
e m
ass
in g
ram
s an
d ki
logr
ams,
incl
udin
g be
ing
able
to m
atch
obj
ects
to th
e ap
prop
riate
uni
t of m
easu
rem
ent
befo
re m
easu
ring
them
. •
choo
se, w
ith re
ason
s, th
e m
ost a
ppro
pria
te s
cale
to u
se fo
r par
ticul
ar o
bjec
ts fr
om a
rang
e of
sca
les
prov
ided
E
xam
ple
Her
e th
e nu
mbe
red
lines
sho
w 1
00g
inte
rval
s: 1
00g;
200
g; 3
00g;
400
g; 5
00g;
600
g; 7
00g;
It
is s
omet
imes
use
ful t
o co
nver
t a c
ircul
ar d
ial i
nto
a nu
mbe
r lin
e fo
r lea
rner
s
100
2
00
300
4
00
500
6
00
700
Th
ere
are
10 s
pace
s be
twee
n ea
ch 1
00g.
Ea
ch 1
00g
inte
rval
has
bee
n di
vide
d in
to 1
0 sm
alle
r spa
ces.
Th
is m
eans
that
eac
h un
-num
bere
d in
terv
al s
how
s 10
0g ÷
10
= 10
g C
ompa
re m
asse
s w
ith u
p to
6-d
igits
in g
ram
s an
d ki
logr
ams.
99MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Gra
de 6
: It
mak
es s
ense
to le
t lea
rner
s w
ork
with
dig
ital s
cale
s, p
artic
ular
ly o
nes
that
giv
e re
adin
gs u
p to
one
or t
wo
deci
mal
pla
ces.
Pr
oble
ms,
cal
cula
tions
and
con
vers
ions
aro
und
mas
s pr
ovid
e a
cont
ext f
or p
ract
isin
g ca
lcul
atin
g w
ith d
ecim
al fr
actio
ns.
Supe
rmar
kets
with
ele
ctro
nic
scal
es o
ften
prin
t the
mas
s la
bels
incl
udin
g de
cim
al p
lace
s e.
g. 2
,25k
g po
tato
es. T
hese
co
ntex
ts c
an b
e us
ed to
pra
ctis
e th
e re
adin
g, w
ritin
g an
d un
ders
tand
ing
of d
ecim
al fr
actio
ns, a
nd fo
r rou
ndin
g of
f, co
nver
ting,
ad
ding
and
sub
tract
ing
deci
mal
frac
tions
. In
Gra
de 6
lear
ners
wor
k w
ith th
e sa
me
units
of m
ass
they
wor
ked
with
in G
rade
s 4
and
5. T
hey
also
wor
k w
ith th
e sa
me
mea
surin
g in
stru
men
ts.
Lear
ners
nee
d to
: •
cons
olid
ate
thei
r sen
se o
f how
muc
h is
1kg
•
cons
olid
ate
thei
r sen
se o
f how
muc
h is
1g
• to
und
erst
and
and
know
the
rela
tions
hip
betw
een
kilo
gram
s an
d gr
ams.
Le
arne
rs s
houl
d ha
ve a
sen
se o
f whi
ch u
nits
are
app
ropr
iate
for m
easu
ring
whi
ch d
iffer
ent m
asse
s. F
or e
xam
ple,
they
nee
d to
kno
w w
hich
uni
ts to
use
to s
tate
the
mas
s of
: •
a co
w
• a
baby
•
flour
for b
akin
g a
cake
•
thei
r ow
n m
ass
Rea
ding
sca
les
and
bala
nces
Le
arne
rs n
eed
to:
• es
timat
e m
ass
in g
ram
s an
d ki
logr
ams
• re
ad k
itche
n sc
ales
(gra
ms
and
kilo
gram
s) b
athr
oom
sca
les
(kilo
gram
s) a
nd b
alan
ces
scal
es (g
ram
s an
d ki
logr
ams)
Th
is in
clud
es re
adin
g th
e m
ass
on:
• re
al d
igita
l sca
les
• pi
ctur
es o
f dec
imal
sca
les
• re
al a
nalo
gue
scal
es
• pi
ctur
es o
f ana
logu
e sc
ales
100 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
The
skills
invo
lved
in re
adin
g an
alog
ue s
cale
s in
clud
e:
• kn
owin
g w
here
to s
tand
to re
ad th
e sc
ales
cor
rect
ly
• K
now
ing
how
to re
ad th
e nu
mbe
red
grad
atio
n lin
es a
nd to
cal
cula
te w
hat t
he u
n-nu
mbe
red
grad
atio
n lin
es in
dica
te.
Lear
ners
nee
d to
read
: •
diffe
rent
kin
ds o
f mea
surin
g ap
para
tus
• ap
para
tus
in w
hich
the
num
bere
d in
terv
als,
gra
datio
n lin
es o
r cal
ibra
tion
repr
esen
t diff
eren
t int
erva
ls
• A
ppar
atus
in w
hich
ther
e ar
e a
diffe
rent
num
ber o
f un-
num
bere
d in
terv
als
with
in e
ach
num
bere
d in
terv
al. L
earn
ers
need
pr
actic
e w
ith e
xam
ples
in w
hich
the
num
bere
d in
terv
als
are
divi
ded
into
:
- 2
un-n
umbe
red
inte
rval
s -
4 un
-num
bere
d in
terv
als
- 5
un-n
umbe
red
inte
rval
s -
10 u
n-nu
mbe
red
inte
rval
s
Exa
mpl
e:
H
ere
the
num
bere
d lin
es s
how
100
g in
terv
als:
100
g; 2
00g;
300
g; 4
00g;
500
g; 6
00g;
700
g.
It is
som
etim
es u
sefu
l to
conv
ert t
he c
ircul
ar d
ial i
nto
a nu
mbe
r lin
e Th
ere
are
10 s
pace
s be
twee
n ea
ch 1
00g.
Eac
h 10
0g in
terv
al h
as b
een
divi
ded
into
10
smal
ler s
pace
s. T
his
mea
ns th
at e
ach
un-n
umbe
red
inte
rval
sho
ws
100g
÷ 1
0 =
10g
101MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Com
pare
, ord
er, s
eque
nce
mas
ses
of u
p to
9 d
igits
in g
ram
s an
d ki
logr
ams
If le
arne
rs h
ave
not i
n pr
evio
us g
rade
s se
quen
ced
cont
aine
rs m
arke
d in
gra
ms
and
kilo
gram
s, it
is w
orth
doi
ng. C
hoos
e ex
ampl
es th
at a
llow
lear
ners
to re
aliz
e th
at th
e si
ze o
f a c
onta
iner
or t
he v
olum
e it
cont
ains
is n
ot d
irect
ly p
ropo
rtion
al to
the
mas
s be
caus
e so
me
subs
tanc
es h
ave
a gr
eate
r den
sity
than
oth
ers.
Lea
rner
s sh
ould
do
exer
cise
s fro
m th
eir t
extb
ook
that
as
k th
em to
ord
er a
nd c
ompa
re th
e m
ass
of o
bjec
ts in
clud
ing
groc
ery
item
s la
belle
d in
gra
ms
and
kilo
gram
s.
Lear
ners
sho
uld
also
com
pare
, ord
er, s
eque
nce
mas
ses
stat
ed in
diff
eren
t uni
ts.
Cal
cula
tions
(inc
ludi
ng c
onve
rsio
ns) a
nd p
robl
em-s
olvi
ng
Mea
sure
men
t pro
vide
s a
cont
ext i
n w
hich
to p
ract
ise
skills
acq
uire
d in
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
. The
ski
lls,
oper
atio
ns a
nd n
umbe
r ran
ges
usin
g gr
ams
and
kilo
gram
s re
quire
d ar
e gi
ven
belo
w.
• R
ound
ing
num
bers
up
or d
own
to th
e m
ost a
ppro
pria
te u
nit o
f mas
s
• R
ound
ing
off t
o 5,
10,
100
and
1 0
00 M
easu
rem
ent e
spec
ially
whe
n fo
cusi
ng o
n re
adin
g an
alog
ue m
easu
ring
inst
rum
ents
can
help
lear
ners
to u
nder
stan
d th
e m
eani
ng b
ehin
d ro
undi
ng u
p or
dow
n
• Ad
ditio
n an
d su
btra
ctio
n C
alcu
latio
ns a
nd p
robl
ems
shou
ld in
clud
e fra
ctio
nal p
arts
of k
ilogr
ams
expr
esse
d ei
ther
as
com
mon
frac
tions
or d
ecim
al fr
actio
ns- u
p to
2 d
ecim
al p
lace
s
• M
ultip
licat
ion
of u
p to
4-d
igit
by 3
-dig
it w
hole
num
bers
• D
ivis
ion
of u
p to
4-d
igit
by 3
-dig
it w
hole
num
bers
• Fi
nd p
erce
ntag
es o
f who
le n
umbe
rs
• m
ultip
le o
pera
tions
with
or w
ithou
t bra
cket
s
Solv
e pr
oble
ms
rela
ting
to m
ass
incl
udin
g:
• ra
te e
.g. p
rice
per k
ilogr
am a
nd ra
tio p
robl
ems
• pr
oble
ms
with
dec
imal
s sh
ould
be
limite
d to
add
ition
and
sub
tract
ion
C
onve
rt b
etw
een
units
: g↔
kg
Con
vers
ions
sho
uld
be g
iven
in th
e fo
llow
ing
form
s: w
hole
num
bers
, com
mon
frac
tions
, dec
imal
frac
tions
up
to 2
dec
imal
pl
aces
Thi
s pr
ovid
es a
con
text
for l
earn
ers
to p
ract
ise
mul
tiply
ing
and
divi
ding
by
1 00
0.
102 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
If co
nver
sion
s re
quire
mor
e th
an 2
dec
imal
pla
ces
e.g.
3 2
45 g
ram
s co
nver
ted
to k
ilogr
ams
lear
ners
can
con
tinue
to w
rite
this
as
3kg
and
245
g as
in p
revi
ous
grad
es. O
n th
e w
hole
thou
gh e
xam
ples
sho
uld
be c
hose
n to
avo
id th
is p
robl
em.
LT
SM
Res
ourc
es
Kitc
hen
scal
e, b
athr
oom
sca
le, b
alan
ce
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
W
B 2
pp.
112
– 1
22
Activ
ities
11
1, 1
12, 1
13a&
b, 1
14, 1
15)
WB
1 p
p. 2
0 –
26
Activ
ities
74a
&b, 7
5, 7
6
WB
2 p
p. 2
– 9
Act
iviti
es 6
5, 6
6a&b
, 67
DB
E Te
xtbo
ok re
fere
nce
Term
4: U
nit 3
: Mas
s, p
. 297
Term
3: U
nit 2
: Mas
s, p
. 211
Term
3: U
nit 1
: Mas
s, p
. 215
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
Test
103MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
9
TER
M:
2
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E: fr
om
……
… to
……
…
Tim
e: 5
HO
UR
S G
RAD
E 4
CAP
S pp
. 88
- 90
5 C
APS
pp. 1
50 -
153
6 C
APS
pp. 2
53 -
256
TOPI
C
Cap
acity
and
Vol
ume
Con
cept
s, S
kills
and
kn
owle
dge
Prac
tical
mea
surin
g of
3-D
ob
ject
s by
• es
timat
ing
•
mea
surin
g
• re
cord
ing
•
com
parin
g an
d or
derin
g M
easu
ring
inst
rum
ents
m
easu
ring
spoo
n, m
easu
ring
cups
, mea
surin
g ju
gs
Uni
ts
milli
litre
(ml)
, litr
es (l
) C
alcu
latio
ns a
nd p
robl
em-s
olvi
ng
rela
ted
to c
apac
ity/v
olum
e in
clud
e:
Prac
tical
mea
surin
g of
3-D
obj
ects
by
• es
timat
ing
•
mea
surin
g
• re
cord
ing
•
com
parin
g an
d or
derin
g
• Mea
surin
g in
stru
men
ts
mea
surin
g sp
oons
, mea
surin
g cu
ps,
mea
surin
g ju
gs
Uni
ts
milli
litre
(ml)
litre
(l)
Cal
cula
tions
and
pro
blem
-sol
ving
re
late
d to
cap
acity
/ vo
lum
e in
clud
e
Prac
tical
mea
surin
g of
3-D
ob
ject
s by
• es
timat
ing
•
mea
surin
g
• re
cord
ing
•
com
parin
g an
d or
derin
g M
easu
ring
inst
rum
ents
m
easu
ring
jugs
U
nits
m
illilit
re (m
l); li
tres
(l) a
nd k
ilolit
res
(kl)
Cal
cula
tions
and
pro
blem
-sol
ving
re
late
d to
cap
acity
/vol
ume
incl
ude:
104 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• So
lve
prob
lem
s in
con
text
s us
ing
capa
city
• C
onve
rt be
twee
n lit
res
and
milli
litre
s, li
mite
d to
exa
mpl
es o
f w
hole
num
bers
and
frac
tions
• so
lvin
g pr
oble
ms
in c
onte
xts
usin
g ca
paci
ty/v
olum
e
• co
nver
ting
betw
een
litre
s an
d m
illilit
res
limite
d to
exa
mpl
es w
ith
who
le n
umbe
rs a
nd fr
actio
ns
• so
lvin
g pr
oble
ms
in c
onte
xt w
ith
capa
city
• co
nver
ting
betw
een
kilo
litre
s,
litre
s an
d m
illilit
res
•
conv
ersi
ons
shou
ld in
clud
e fra
ctio
n an
d de
cim
al fo
rms
to 2
de
cim
al p
lace
s LT
SM
Res
ourc
es
Mea
surin
g ju
gs, b
ottle
s, v
arie
ty o
f con
tain
ers
from
lear
ner’s
con
text
, cub
es
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
WB
2 p
p. 2
– 1
2 Ac
tiviti
es 6
5; 6
6a&b
; 67
a&b;
68
pp. 1
52 –
156
Act
iviti
es 1
30, 1
31, 1
32
WB
2 p
p. 7
4 –
76 A
ctiv
ities
24a
&b
pp. 1
60 -1
64
Activ
ities
130
, - 1
32.
WB
1 p
p. 1
60 –
162
Ac
tiviti
es 6
2; 6
3 W
B 2
pp.
158
Ac
tivity
124
DB
E Te
xtbo
ok re
fere
nce
Term
3: U
nit 2
: Cap
acity
and
vol
ume,
p.
225
Term
1: U
nit 9
: Cap
acity
and
vol
ume,
p.
104
Term
2: U
nit 8
: Cap
acity
and
vol
ume,
p.
200
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
Test
105MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
10
TER
M:
2
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E: fr
om
……
… to
……
…
Tim
e: 5
HO
UR
S G
RAD
E 4
CAP
S pp
. 78
- 79
5 C
APS
pp. 1
67 -
168
6 C
APS
pp. 2
44 -
246
TOPI
C
3D O
bjec
ts
Con
cept
s, S
kills
and
kn
owle
dge
Obj
ects
lear
ners
nee
d to
kno
w
and
nam
e •
rect
angu
lar p
rism
s •
sphe
res
• cy
linde
rs
• co
nes
• sq
uare
-bas
ed p
yram
ids
Cha
ract
eris
tics
whi
ch le
arne
rs u
se
to d
istin
guis
h, d
escr
ibe,
sor
t and
co
mpa
re o
bjec
ts
• sh
apes
of f
aces
•
flat a
nd c
urve
d su
rface
s Fu
rthe
r act
iviti
es to
focu
s le
arne
rs
on c
hara
cter
istic
s of
obj
ects
C
reat
e 3-
D m
odel
s us
ing
cut-o
ut
Pol
ygon
s
Obj
ects
lear
ners
nee
d to
kno
w
and
nam
e •
rect
angu
lar p
rism
s an
d ot
her p
rism
s •
cube
s •
cylin
ders
•
cone
s •
pyra
mid
s •
sim
ilarit
ies
and
diffe
renc
es
betw
een
cube
s an
d re
ctan
gula
r pr
ism
s C
hara
cter
istic
s le
arne
rs u
se to
di
stin
guis
h, d
escr
ibe,
sor
t and
co
mpa
re s
hape
s •
shap
e of
face
s •
num
ber o
f fac
es
• fla
t and
cur
ved
surfa
ces
Furt
her a
ctiv
ities
to fo
cus
lear
ners
on
cha
ract
eris
tics
of o
bjec
ts
• M
ake
3-D
mod
els
usin
g cu
t out
po
lygo
ns
• C
uttin
g op
en b
oxes
to tr
ace
and
de
scrib
e th
eir n
ets
Obj
ects
lear
ners
nee
d to
kno
w
and
nam
e •
rect
angu
lar p
rism
s •
cube
s •
tetra
hedr
ons
and
othe
r pyr
amid
s •
sim
ilarit
ies
and
diffe
renc
es
betw
een
tetra
hedr
ons
and
othe
r py
ram
ids
Feat
ures
lear
ners
use
to
dist
ingu
ish,
des
crib
e, s
ort a
nd
com
pare
obj
ects
D
escr
ibe,
sor
t and
com
pare
2-D
sh
apes
and
3-D
obj
ects
in te
rms
of:
• nu
mbe
r and
sha
pe o
f fac
es
• nu
mbe
r of v
ertic
es
• nu
mbe
r of e
dges
Fu
rthe
r act
iviti
es to
focu
s le
arne
rs
on c
hara
cter
istic
s of
obj
ects
M
ake
3-D
mod
els
usin
g:
• dr
inki
ng s
traw
s/to
othp
icks
, etc
. to
form
a s
kele
ton
• ne
ts
106 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
SUG
GES
TED
M
ETH
OD
OLO
GY
Com
plex
ity c
hang
es fr
om g
rade
to g
rade
as
is s
tipul
ated
in th
e C
APS
docu
men
t. Al
l gra
des:
W
hat i
s di
ffere
nt to
Gra
de 3
? Le
arne
rs fo
cus
on th
e sa
me
3-D
geo
met
rical
obj
ects
, but
in G
rade
3 th
ey s
poke
of
bo
xes,
and
in G
rade
4 th
ey c
all t
hese
rect
angu
lar p
rism
s
• ba
ll sh
apes
and
in G
rade
4 th
ey c
all t
hese
sph
eres
Obj
ects
and
thei
r dis
tingu
ishi
ng c
hara
cter
istic
s Th
ere
are
two
way
s in
whi
ch le
arne
rs d
istin
guis
h 3-
D o
bjec
ts in
Gra
de 4
. 1.
C
heck
whe
ther
they
hav
e fla
t or c
urve
d su
rface
s. T
hree
dim
ensi
onal
obj
ects
can
be
grou
ped
as fo
llow
s:
• O
bjec
ts w
ith a
cur
ved
surfa
ce o
nly:
Exam
ple:
a s
pher
e
•
Obj
ects
with
flat
and
cur
ved
surfa
ces
C
ones
Cyl
inde
rs
107MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• O
bjec
ts w
ith o
nly
flat s
urfa
ces.
In G
rade
4 le
arne
rs o
nly
iden
tify
and
nam
e th
em.
E
xam
ples
rect
angu
lar p
rism
s.
pyr
amid
s: s
quar
e- b
ase
pyra
mid
2.
W
hen
look
ing
at th
e gr
oup
of o
bjec
ts w
ith fl
at s
urfa
ces,
lear
ners
sho
uld
know
that
the
flat s
urfa
ces
of a
3-D
obj
ect a
re
calle
d fa
ces.
The
y de
scrib
e th
ese
obje
cts
acco
rdin
g to
the
kind
s of
2-D
sha
pes
that
mak
e up
the
flat s
urfa
ces
e.g.
the
face
s of
a re
ctan
gula
r pris
m c
an a
ll be
rect
angl
es o
r som
e ca
n be
squ
ares
. Squ
are-
base
d py
ram
ids
have
one
squ
are
face
and
the
othe
r fac
es a
re tr
iang
les
Gra
de 5
and
6:
Wha
t is
diffe
rent
?
• cu
bes
are
intro
duce
d
• le
arne
rs w
ork
with
pris
ms
as a
gro
up fo
r the
firs
t tim
e
• in
the
sam
e w
ay th
at le
arne
rs d
istin
guis
h be
twee
n re
ctan
gles
and
squ
ares
, usi
ng th
e le
ngth
s of
thei
r sid
es, s
o th
ey
dist
ingu
ish
betw
een
cube
s an
d re
ctan
gula
r pris
ms
usin
g th
e sh
apes
of t
heir
face
s
• le
arne
rs c
ount
the
num
ber o
f fac
es o
n 3-
D o
bjec
ts a
nd u
se th
is a
s pa
rt of
thei
r des
crip
tions
of o
bjec
ts
Obj
ects
and
thei
r dis
tingu
ishi
ng c
hara
cter
istic
s
Ther
e ar
e th
ree
way
s in
whi
ch le
arne
rs d
istin
guis
h 3-
D o
bjec
ts in
Gra
de 5
1.
By c
heck
ing
whe
ther
they
hav
e fla
t or c
urve
d su
rface
s. T
hree
dim
ensi
onal
obj
ects
can
be
grou
ped
as fo
llow
s:
• O
bjec
ts w
ith a
cur
ved
surfa
ce o
nly:
108 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Exam
ple:
sph
ere
•
Obj
ects
with
flat
and
curv
ed s
urfa
ces
E
xam
ples
:
•
Obj
ects
with
onl
y fla
t sur
face
s. In
Gra
de 5
lear
ners
onl
y id
entif
y an
d na
me
Rec
tang
ular
pris
ms
Cub
es
109MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
2.
W
hen
look
ing
at th
e gr
oup
of o
bjec
ts w
ith fl
at s
urfa
ces,
lear
ners
sho
uld
know
that
the
flat s
urfa
ces
of a
3-D
obj
ect a
re
calle
d fa
ces.
The
y de
scrib
e th
ese
obje
cts
acco
rdin
g to
the
kind
s of
2-D
sha
pes
that
mak
e up
the
flat s
urfa
ces
e.g.
the
face
s of
a re
ctan
gula
r pris
m c
an a
ll be
rect
angl
es o
r som
e ca
n be
squ
ares
. Squ
are-
base
d py
ram
ids
have
one
squ
are
face
and
the
othe
r fac
es a
re tr
iang
les.
3.
Lear
ners
can
als
o lo
ok fo
r rig
ht a
ngle
s on
the
face
s of
obj
ects
. If t
he o
bjec
t tha
t the
y ar
e ex
amin
ing
has
face
s w
ith o
nly
right
ang
les,
then
it w
ill be
eith
er a
cub
e or
a re
ctan
gula
r pris
m.
Furt
her a
ctiv
ities
to fo
cus
lear
ners
on
char
acte
ristic
s of
obj
ects
:
• Le
arne
rs c
reat
e 3-
D o
bjec
ts b
y pu
tting
toge
ther
cut
-out
pol
ygon
s, w
hich
hel
ps to
focu
s at
tent
ion
on th
e sh
apes
of t
he
face
s of
the
3-D
obj
ects
.
• Le
arne
rs c
ut o
pen
boxe
s to
mak
e ne
ts. T
hey
desc
ribe
the
nets
of t
he b
oxes
. Int
erpr
etin
g dr
awin
gs o
f 3-D
obj
ects
and
writ
ten
exer
cise
s
Lear
ners
nee
d to
wor
k w
ith re
al o
bjec
ts. H
owev
er th
ey a
lso
need
to d
o w
ritte
n ex
erci
ses
on 3
-D o
bjec
ts. I
nter
pret
ing
pict
ures
of 3
-D o
bjec
ts is
mor
e di
fficu
lt th
an w
orki
ng w
ith th
e re
al o
bjec
ts. L
earn
ers
shou
ld p
ract
ice
inte
rpre
ting
draw
ings
of 3
-D
obje
cts.
The
y sh
ould
iden
tify
and
nam
e 3-
D o
bjec
ts in
dra
win
gs a
nd id
entif
y ev
eryd
ay o
bjec
ts th
at lo
ok li
ke g
eom
etric
obj
ects
e.g.
a m
ilk c
arto
n lo
oks
like
a re
ctan
gula
r pris
ms.
Des
crib
e th
e su
rface
s of
obj
ects
whe
n sh
own
draw
ing
of 3
-D o
bjec
ts, m
atch
110 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
the
2-D
sha
pes
that
hav
e th
e sa
me
shap
e as
the
face
s of
3-D
obj
ects
, mat
ch n
ets
of re
ctan
gula
r pris
ms
to th
e ap
prop
riate
draw
ing
of re
ctan
gula
r pris
ms
and
com
pare
3-D
obj
ects
from
dra
win
gs.
Gra
de 6
: W
hat i
s di
ffere
nt?
• Te
trahe
dron
s ar
e ne
w o
bjec
ts
• O
ther
pyr
amid
s ar
e ne
w o
bjec
ts
• Le
arne
rs d
istin
guis
h be
twee
n te
trahe
dron
s an
d ot
her p
yram
ids
by lo
okin
g at
the
shap
es o
f the
ir ba
ses,
• Le
arne
rs u
se n
ets
to b
uild
obj
ects
• Le
arne
rs m
atch
net
s w
ith d
raw
ings
of o
bjec
ts
• Le
arne
rs c
ount
the
num
ber o
f edg
es o
f 3-D
obj
ects
• Le
arne
rs b
uild
ske
leto
n ob
ject
s us
ing
drin
king
stra
ws
• Le
arne
rs c
ount
the
num
ber o
f ver
tices
of o
bjec
ts.
Obj
ects
and
thei
r dis
tingu
ishi
ng c
hara
cter
istic
s Th
ere
are
thre
e w
ays
in w
hich
lear
ners
dis
tingu
ish
3-D
obj
ects
in G
rade
6.
1.
Che
ckin
g w
heth
er th
ey h
ave
flat o
r cur
ved
surfa
ces.
Obj
ects
with
onl
y fla
t sur
face
s. In
Gra
de 6
lear
ners
onl
y id
entif
y an
d na
me
the
obje
cts.
Pris
ms
Rec
tang
ular
pris
ms
111MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Cub
es
O
ther
pris
ms
Pyra
mid
s 2.
W
hen
look
ing
at th
e gr
oup
of o
bjec
ts w
ith fl
at
surfa
ces,
lear
ners
sho
uld
know
that
the
flat s
urfa
ces
of 3
-D o
bjec
ts a
re c
alle
d fa
ces.
The
y de
scrib
e th
ese
obje
cts
acco
rdin
g to
• th
e ki
nds
and
num
bers
of 2
-D s
hape
s th
at m
ake
up th
e fla
t sur
face
s e.
g. a
rect
angu
lar p
rism
can
hav
e 6
face
s th
at a
re
rect
angl
es o
r 4 th
at a
re re
ctan
gles
and
2 th
at a
re s
quar
es.
• th
e nu
mbe
r of e
dges
• th
e nu
mbe
r of v
ertic
es
112 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
3.
Lear
ners
can
als
o lo
ok fo
r rig
ht a
ngle
s on
the
face
s of
obj
ects
. If t
he o
bjec
t tha
t the
y ar
e ex
amin
ing
has
face
s w
ith o
nly
right
ang
les,
then
it w
ill be
eith
er a
cub
e or
a re
ctan
gula
r pris
m.
Furt
her a
ctiv
ities
: mak
ing
mod
els
of 3
-d o
bjec
ts
• Le
arne
rs c
reat
e 3-
D o
bjec
ts fr
om n
ets
• Le
arne
rs c
reat
e sk
elet
ons
of 3
-D o
bjec
ts w
ith s
traw
s / t
ooth
pick
s, e
tc.
Inte
rpre
ting
draw
ings
of 3
-D o
bjec
ts a
nd w
ritte
n ex
erci
ses
Lear
ners
nee
d to
wor
k w
ith re
al o
bjec
ts. H
owev
er th
ey a
lso
need
to d
o w
ritte
n ex
erci
ses
on 3
-D o
bjec
ts. I
nter
pret
ing
pict
ures
of 3
-D o
bjec
ts is
mor
e di
fficu
lt th
an w
orki
ng w
ith th
e re
al o
bjec
ts. L
earn
ers
shou
ld p
ract
ise
inte
rpre
ting
draw
ings
of 3
-D o
bjec
ts. T
hey
shou
ld id
entif
y an
d na
me
3-D
obj
ects
in d
raw
ings
iden
tify
ever
yday
obj
ects
that
look
like
geo
met
ric
obje
cts
e.g.
a m
ilk c
arto
n lo
oks
like
a re
ctan
gula
r pris
m, m
atch
net
s of
obj
ects
to d
raw
ing
of o
bjec
ts, d
escr
ibe
3-D
obj
ects
by s
tatin
g th
e nu
mbe
r of f
lat a
nd c
urve
d su
rface
s, c
ount
the
num
ber o
f ver
tices
, edg
es, a
nd n
umbe
r and
sha
pe o
f fac
es
whe
n sh
own
draw
ings
of 3
-D o
bjec
ts.
In T
erm
2 le
arne
rs fo
cus
on th
e ki
nd o
f sur
face
, the
sha
pe a
nd th
e nu
mbe
r of f
aces
of a
3-D
obj
ect.
They
als
o bu
ild o
bjec
ts
usin
g ne
ts.
In T
erm
4 th
ey c
an c
onso
lidat
e w
hat t
hey
have
lear
ned
in T
erm
1 a
nd b
uild
ske
leto
n sh
apes
with
stra
ws
or to
othp
icks
. The
y w
ill
then
focu
s on
the
edge
s an
d ve
rtice
s of
the
obje
cts.
Thi
s m
eans
that
by
the
end
of th
e ye
ar th
ey w
ill be
abl
e to
des
crib
e
3-D
geo
met
ric o
bjec
ts a
ccor
ding
to s
urfa
ces,
face
s, e
dges
and
ver
tices
.
LTSM
Res
ourc
es
Varie
ty o
f 3D
obj
ects
from
lear
ner’s
con
text
, geo
solid
s
Gra
de 4
G
rade
5
Gra
de 6
113MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Wor
kboo
k re
fere
nce
WB
1 p
p 13
0 -1
34
Act
iviti
es 4
8, 4
9, 5
0 W
B 1
pp.
142
– 1
50 A
ctiv
ities
50
; 51;
52;
53;
54
WB
1 p
p 94
– 9
6 Ac
tiviti
es 3
3; 3
4
DB
E Te
xtbo
ok re
fere
nce
Term
2: U
nit 6
: Pro
pert
ies
of th
ree
dim
ensi
onal
obj
ects
, p. 1
73
Term
2: U
nit 6
: Pro
pert
ies
of th
ree
dim
ensi
onal
obj
ects
, p. 1
67
Term
2: U
nit 3
: Pro
pert
ies
of th
ree
dim
ensi
onal
obj
ects
, p. 1
42
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
as
sess
men
t – te
st
114 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LESS
ON
PLA
NS:
TER
M 3
115MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
1
TER
M 3
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
….
Tim
e: 3
HO
UR
S G
RAD
E 4
CAP
S p.
92 (m
etho
dolo
gy e
xpla
ined
on
pp. 3
7 - 3
8)
5 C
APS
p.81
(met
hodo
logy
exp
lain
ed o
n pp
. 125
-126
)
6 C
APS
p. 2
62 (m
etho
dolo
gy e
xpla
ined
on
pp.
215
– 2
16)
TOPI
C
Who
le n
umbe
rs
Con
cept
s, S
kills
and
kn
owle
dge
C
ount
forw
ards
and
bac
kwar
ds in
2s,
3s
, 5s,
10s
, 25s
, 50s
, 100
s be
twee
n 0
and
at le
ast 1
0 00
0
O
rder
, com
pare
and
repr
esen
t
nu
mbe
rs to
at l
east
4 d
igit
num
bers
.
Rep
rese
nt o
dd a
nd e
ven
num
bers
to
at le
ast 1
000
Rec
ogni
ze th
e pl
ace
valu
e of
dig
its in
w
hole
num
bers
to a
t lea
st 4
-dig
it nu
mbe
rs
R
ound
off
to th
e ne
ares
t 10,
100
, 10
00.
C
ount
forw
ards
and
bac
kwar
ds in
w
hole
num
ber i
nter
vals
up
to a
t lea
st
10 0
00
O
rder
, com
pare
and
repr
esen
t nu
mbe
rs to
at l
east
6-d
igit
num
bers
Rep
rese
nt o
dd a
nd e
ven
num
bers
to
at le
ast 1
000
.
Rec
ogni
ze th
e pl
ace
valu
e of
dig
its in
w
hole
num
bers
to a
t lea
st 6
dig
it nu
mbe
rs.
R
ound
off
to th
e ne
ares
t 5, 1
0, 1
00 ,
1 00
0 an
d 10
000
C
ount
forw
ards
and
bac
kwar
ds in
w
hole
num
ber i
nter
vals
up
to a
t lea
st
10 0
00
O
rder
, com
pare
and
repr
esen
t nu
mbe
rs to
at l
east
9-d
igit
num
bers
Rep
rese
nt p
rime
num
bers
to a
t lea
st
100
R
ecog
nizi
ng th
e pl
ace
valu
e of
dig
its
in w
hole
num
bers
to a
t lea
st 9
-dig
it nu
mbe
rs
R
ound
off
to th
e ne
ares
t 5, 1
0, 1
00,
1 00
0, 1
0 00
0, 1
00 0
00, a
nd
1 00
0 00
0
116 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
SUG
GES
TED
M
ETH
OD
OLO
GY
Ref
er b
ack
to T
erm
1
Expl
ain
from
kno
wn
(low
num
ber r
ange
) to
unkn
own
(hig
her r
ange
of n
umbe
rs);
wor
k w
ith c
oncr
ete
LTSM
C
ount
ing,
ord
erin
g, c
ompa
ring,
repr
esen
ting
of d
igits
N
ote
:Acc
ordi
ng to
CA
PS n
umbe
r ran
ge p
er g
rade
per
term
as
in c
onte
nt c
larif
icat
ion
Rea
d, s
ay a
nd w
rite
up to
at l
east
4-d
igit
num
bers
(Gr4
), 6-
digi
t (G
r5) a
nd 9
-dig
it (G
r6)
(Lea
rner
s ca
n w
rite
num
bers
with
fing
ers
in th
e ai
r whi
le th
ey a
re re
adin
g / s
ayin
g th
e w
ords
.) e.
g.,
One
hun
dred
and
tw
enty
-nin
e.
C
onve
rt fro
m w
ords
to n
umbe
rs a
nd n
umbe
rs to
wor
ds
Ar
rang
e th
e nu
mbe
rs b
elow
from
the
smal
lest
to th
e bi
gges
t:
Exam
ple:
10
111
; 1 1
01; 1
110
; 1 0
11
M
ake
the
bigg
est/s
mal
lest
num
ber y
ou c
an w
ith th
ese
digi
ts: 3
, 2, 5
, 4, 9
. O
dd a
nd e
ven
num
bers
: Ex
plor
e pr
actic
ally
by
wor
king
with
num
bers
to b
e ab
le to
des
crib
e th
e pa
ttern
e.g
. all
odd
num
bers
end
in 1
, 3, 5
, 7 o
r 9
ther
efor
e 2
201
, 2 2
03, 2
205
, 2 2
07, 2
209
are
all
odd
num
bers
. Pr
ime
num
bers
for G
rade
6
Iden
tify
prim
e nu
mbe
rs a
nd c
ompo
site
num
bers
up
to a
t lea
st 1
00
Mul
tiple
s:
I cou
nt in
mul
tiple
s of
3, u
p to
100
.
Will
I cou
nt th
e nu
mbe
r 12?
Why
?
Will
I cou
nt th
e nu
mbe
r 42?
Why
? Pl
ace
valu
e:
D
istin
guis
h be
twee
n th
e nu
mer
ic v
alue
and
the
plac
e va
lue.
Use
pla
ce v
alue
car
ds to
bui
ld u
p an
d br
eak
dow
n nu
mbe
rs
Rou
ndin
g of
f:
Rou
nd o
ff as
indi
cate
d pe
r gra
de (u
se b
ase
ten
bloc
ks, n
umbe
r lin
es, p
lace
val
ue ta
ble)
Use
con
cept
of r
ound
ing
off,
in p
robl
em s
olvi
ng c
onte
xt
117MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LTSM
R
esou
rces
N
umbe
r lin
es: 0
– 1
20, S
truct
ured
-, s
emi-
stru
ctur
ed -
, uns
truct
ured
num
ber l
ines
; Cou
nter
s, P
ictu
res,
arra
ys/ d
iagr
ams,
Fla
sh
card
s, B
ase
10 b
lock
s, 1
00 c
harts
, aba
cus,
bea
ds
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
ferr
ence
W
B 2
pp
28 -
30 A
ctiv
ities
76,
77
WB
2 p
p 32
Act
ivity
79
WB
2 p
p 10
8 –
110
Ac
tivity
105
a&b
DB
E Te
xtbo
ok re
fere
nce
Term
3: U
nit 3
: Who
le N
umbe
rs p
. 238
Te
rm 3
: Uni
t 3: W
hole
Num
bers
p.
218
Term
3: U
nit 2
: Who
le N
umbe
rs p
. 22
1 H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
118 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
2
TER
M 3
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
……
T
ime:
8 H
OU
RS
GR
ADE
4 C
APS
p.93
(met
hodo
logy
exp
lain
ed o
n pp
. 43
- 45)
5 C
APS
p 18
2- 1
83 (m
etho
dolo
gy
expl
aine
d on
pp.
132
– 1
35)
6 C
APS
p.26
2-26
3 (m
etho
dolo
gy
expl
aine
d on
pp.
222
– 2
25)
TOPI
C
Addi
tion
and
subt
ract
ion
of w
hole
num
bers
C
once
pts,
Ski
lls a
nd
know
ledg
e N
umbe
r ran
ge fo
r cal
cula
tions
•
Addi
tion
and
subt
ract
ion
of w
hole
nu
mbe
rs o
f at l
east
4 d
igits
Cal
cula
tion
tech
niqu
es
Use
a ra
nge
of te
chni
ques
to p
erfo
rm
and
chec
k w
ritte
n an
d m
enta
l ca
lcul
atio
ns o
f who
le n
umbe
rs
incl
udin
g •
estim
atio
n •
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
• ro
undi
ng o
ff an
d co
mpe
nsat
ing
• do
ublin
g an
d ha
lvin
g •
usin
g a
num
ber l
ine
• us
ing
addi
tion
and
subt
ract
ion
as in
vers
e op
erat
ions
Num
ber r
ange
for c
alcu
latio
ns
Ad
ditio
n an
d su
btra
ctio
n of
who
le
num
bers
of a
t lea
st 5
dig
its
Cal
cula
tion
tech
niqu
es
Usi
ng a
rang
e of
tech
niqu
es to
pe
rform
and
che
ck w
ritte
n an
d m
enta
l ca
lcul
atio
ns w
ith w
hole
num
bers
in
clud
ing
• es
timat
ion
• ad
ding
and
sub
tract
ing
in c
olum
ns
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
usin
g a
num
ber l
ine
• ro
undi
ng o
ff an
d co
mpe
nsat
ing
• do
ublin
g an
d ha
lvin
g •
usin
g ad
ditio
n an
d su
btra
ctio
n as
inve
rse
oper
atio
ns
Num
ber
rang
e fo
r cal
cula
tions
•
Addi
tion
and
subt
ract
ion
of w
hole
nu
mbe
rs w
ith a
t lea
st 6
-dig
it nu
mbe
r •
Mul
tiple
ope
ratio
ns o
n w
hole
nu
mbe
rs w
ith o
r with
out
brac
kets
C
alcu
latio
n te
chni
ques
U
sing
a ra
nge
of te
chni
ques
to
perfo
rm a
nd c
heck
writ
ten
and
men
tal c
alcu
latio
ns w
ith w
hole
nu
mbe
rs in
clud
ing
• es
timat
ion
• ad
ding
, sub
tract
ing
in c
olum
ns
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
roun
ding
off
and
com
pens
atin
g •
usin
g ad
ditio
n an
d su
btra
ctio
n as
inve
rse
oper
atio
ns
• us
ing
a ca
lcul
ator
119MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e an
d as
soci
ativ
e pr
oper
ties
with
who
le n
umbe
rs
Solv
ing
prob
lem
s
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g w
hole
num
bers
, inc
ludi
ng fi
nanc
ial
cont
exts
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e pr
oper
ties
with
w
hole
num
bers
•
0 in
term
s of
its
addi
tive
prop
erty
•
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
num
bers
, inc
ludi
ng
o fin
anci
al c
onte
xts
o m
easu
rem
ent c
onte
xts
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
•
0 in
term
s of
its
addi
tive
prop
erty
So
lvin
g pr
oble
ms
• So
lve
prob
lem
s in
volv
ing
who
le n
umbe
rs a
nd d
ecim
al
fract
ions
, inc
ludi
ng
o fin
anci
al c
onte
xts
o m
easu
rem
ent c
onte
xts
• So
lve
prob
lem
s in
volv
ing
who
le
num
bers
, inc
ludi
ng c
ompa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd
(ratio
) LT
SM
R
esou
rces
N
umbe
r lin
es: 0
– 1
20, S
truct
ured
-, s
emi-
stru
ctur
ed -
, uns
truct
ured
num
ber l
ines
; Cou
nter
s, P
ictu
res,
arra
ys/ d
iagr
ams,
Fla
sh
card
s, B
ase
10 b
lock
s, 1
00 c
harts
, cou
nter
s, m
aths
vid
eo c
lips,
E le
arni
ng re
sour
ces
onlin
e, M
aths
gam
es
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
WB
2 p
p. 3
2 -4
0 ; p
p 70
– 7
6 Ac
tiviti
es
(78a
&b; 7
9-81
; 95a
&b; 9
6)
WB
2 p
p. 4
0 –
48 A
ctiv
ities
82
a&b;
83-
85
WB
2 p
p. 2
0 –
44 A
ctiv
ities
71
a&b;
72a
&b; 7
3-78
D
BE
Text
book
refe
renc
e Te
rm 2
: Uni
t 9: W
hole
Num
bers
: Ad
ditio
n an
d su
btra
ctio
n, p
. 193
Te
rm 3
: Uni
t 4: W
hole
Num
bers
: Ad
ditio
n an
d su
btra
ctio
n, p
. 243
Term
3: U
nit 4
: Who
le N
umbe
rs:
Addi
tion
and
subt
ract
ion,
p. 2
23
Term
3: U
nit 3
: Who
le N
umbe
rs:
Addi
tion
and
subt
ract
ion,
p. 2
24
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
Test
120 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
3
TER
M 3
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to
…
T
ime:
3 H
OU
RS
GR
ADE
4 M
ultip
licat
ion
- CAP
S pp
.101
5 M
ultip
licat
ion
- CAP
S p.
192
(Ref
er to
p.1
66
for m
etho
dolo
gy.)
6 M
ultip
licat
ion
- CAP
S p.
241-
243
TOPI
C
Mul
tiplic
atio
n of
who
le n
umbe
rs
Con
cept
s, S
kills
and
kn
owle
dge
Num
ber
rang
e fo
r cal
cula
tions
•
Mul
tiplic
atio
n of
at l
east
who
le 2
-di
git b
y 2-
digi
t num
bers
Num
ber
rang
e fo
r cal
cula
tions
•
Mul
tiplic
atio
n of
at l
east
who
le 3
-dig
it by
2-
digi
t num
bers
Num
ber
rang
e fo
r cou
ntin
g,
orde
ring,
com
parin
g an
d re
pres
entin
g, a
nd p
lace
val
ue
of d
igits
•
Ord
er, c
ompa
re a
nd re
pres
ent
num
bers
to a
t lea
st 9
-dig
it nu
mbe
rs
• R
epre
sent
prim
e nu
mbe
rs to
at
leas
t 100
•
Rec
ogni
ze t
he p
lace
val
ue o
f di
gits
in
who
le n
umbe
rs t
o at
le
ast 9
-dig
it nu
mbe
rs
• R
ound
off
to th
e ne
ares
t 5, 1
0,
100
or 1
000
Num
ber
rang
e fo
r cal
cula
tions
•
Mul
tiplic
atio
n of
at l
east
who
le 4
-di
git b
y 3-
digi
t num
bers
•
Mul
tiple
ope
ratio
ns o
n w
hole
nu
mbe
rs w
ith o
r with
out
brac
kets
121MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Cal
cula
tion
tech
niqu
es
Use
a ra
nge
of te
chni
ques
to
perfo
rm a
nd c
heck
writ
ten
and
men
tal c
alcu
latio
ns w
ith w
hole
nu
mbe
rs in
clud
ing
• es
timat
ion
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
roun
ding
off
and
com
pens
atin
g •
doub
ling
and
halv
ing
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s M
ultip
les
of 1
-dig
it nu
mbe
rs to
at l
east
10
0 Pr
oper
ties
of w
hole
num
bers
Rec
ogni
ze a
nd u
se th
e co
mm
utat
ive;
ass
ocia
tive;
and
di
strib
utiv
e pr
oper
ties
of w
hole
nu
mbe
rs
So
lvin
g pr
oble
ms
• So
lve
prob
lem
s in
con
text
s in
volv
ing
who
le n
umbe
rs,
incl
udin
g fin
anci
al c
onte
xts
Cal
cula
tion
tech
niqu
es
Usi
ng a
rang
e of
tech
niqu
es to
pe
rform
and
che
ck w
ritte
n an
d m
enta
l cal
cula
tions
of w
hole
num
bers
in
clud
ing:
•
estim
atio
n •
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
• us
ing
a nu
mbe
r lin
e •
roun
ding
off
and
com
pens
atin
g •
doub
ling
and
halv
ing
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
2-d
igits
who
le n
umbe
rs to
at
leas
t 100
•
Fact
ors
of 2
-dig
it w
hole
num
bers
to a
t le
ast 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e;
asso
ciat
ive
and
dist
ribut
ive
prop
ertie
s w
ith w
hole
num
bers
•
0 in
term
s of
its
addi
tive
prop
erty
•
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
Cal
cula
tion
tech
niqu
es in
clud
e •
estim
atio
n •
mul
tiply
ing
in c
olum
ns
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
roun
ding
off
and
com
pens
atin
g •
usin
g a
calc
ulat
or
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
2-d
igit
and
3-di
git
num
bers
•
Fact
ors
of 2
-dig
it an
d 3-
digi
t who
le
num
bers
•
Prim
e fa
ctor
s of
num
bers
to a
t le
ast 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
w
hole
num
bers
•
0 in
term
s of
its
addi
tive
prop
erty
•
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
num
bers
and
dec
imal
fra
ctio
ns, i
nclu
ding
122 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
•
Solv
e pr
oble
ms
invo
lvin
g w
hole
num
bers
, inc
ludi
ng
o co
mpa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd
(ratio
) o
com
parin
g tw
o qu
antit
ies
of
diffe
rent
kin
ds (r
ate)
o fin
anci
al c
onte
xts
o m
easu
rem
ent
cont
exts
•
Solv
e pr
oble
ms
invo
lvin
g w
hole
num
bers
, in
clud
ing
com
parin
g tw
o or
mor
e qu
antit
ies
of
the
sam
e ki
nd (r
atio
)
- fin
anci
al c
onte
xts
- m
easu
rem
ent c
onte
xts
• So
lve
prob
lem
s in
volv
ing
who
le n
umbe
rs, i
nclu
ding
o
com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(ra
tio)
o co
mpa
ring
two
quan
titie
s of
di
ffere
nt k
inds
(rat
e)
SUG
GES
TED
M
ETH
OD
OLO
GY
Ref
er to
Ter
m1
and
Term
2 le
sson
Pla
ns
Expl
ain
from
kno
wn
(low
num
ber r
ange
); w
ork
with
con
cret
e LT
SM.
Lear
ners
sho
uld
do c
onte
xt fr
ee c
alcu
latio
ns a
nd s
olve
pro
blem
s in
con
text
s
Lear
ners
sho
uld
cont
inue
to
• ch
eck
thei
r sol
utio
ns b
y us
ing
mul
tiplic
atio
n w
hen
doin
g di
visi
on a
nd v
ice
vers
a •
judg
e th
e re
ason
able
ness
of t
heir
solu
tions
, by
estim
atin
g be
fore
cal
cula
ting
Mul
tiplic
atio
n (K
now
tim
es ta
bles
– p
ract
ice
regu
larly
up
to 1
0 x
10 fo
r Gra
des
4 an
d 5
and
12 x
12
for G
rade
6).
Follo
w th
ese
step
s in
teac
hing
mul
tiplic
atio
n:
• So
lve
prob
lem
s in
con
text
. U
nder
stan
d th
at: 8
6 +
86 +
86
is e
quiv
alen
t to
86 x
3 o
r 3 x
86
(repe
ated
add
ition
) •
mul
tiplic
atio
n by
1 le
aves
a n
umbe
r unc
hang
ed e
.g. 5
x 1
= 5
; 99
x 1
= 99
•
mul
tiplic
atio
n of
zer
o re
sults
in z
ero
e.g.
7 x
0 =
0; 3
1 x
0 =
0 U
nder
stan
d th
at m
ultip
licat
ion
is th
e in
vers
e of
div
isio
n (m
ultip
licat
ion
reve
rses
div
isio
n an
d vi
ce v
ersa
) and
use
this
to c
heck
re
sults
. e.g
. 15
x 35
= 5
25
525
÷ 2
5 =
15 o
r 525
÷ 1
5 =
25
Not
e: In
Gra
de 5
Ter
m 3
lear
ners
are
intro
duce
d to
col
umn
met
hods
of m
ultip
licat
ion
123MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
DIV
ISIO
N
Men
tal d
ivis
ion
: Tur
ning
the
tabl
es –
pra
ctic
e re
gula
rly (e
.g. 5
x 8
= 4
0 4
0 ÷
8 =
5 / 4
0 ÷
5 =
8) (A
lso
calle
d in
vers
e op
erat
ion
or
reci
proc
al o
pera
tion.
) M
ake
lear
ners
aw
are
that
div
isio
n is
non
-com
mut
ativ
e i.e
. 81
÷ 9
is n
ot th
e sa
me
as 9
÷ 8
1.
With
the
conc
ept g
rasp
ed, t
each
ing
divi
sion
will
beco
me
mor
e ab
out g
uide
d pr
actic
e to
hel
p th
e le
arne
rs to
bec
ome
fam
iliar w
ith
the
divi
sion
ope
ratio
n (a
lthou
gh it
’s re
ally
goi
ng to
be
a di
ffere
nt ty
pe o
f mul
tiplic
atio
n pr
actic
e.) S
tart
by p
ract
isin
g di
visi
on b
y 1,
2
and
3 an
d th
en g
radu
ally
mov
e up
to 9
. N
ote:
Gra
de 4
and
5 fo
cus
is o
n us
ing
the
clue
boa
rd –
met
hod
ON
LY! G
rade
6 is
the
intro
duct
ion
of lo
ng d
ivis
ion
in th
e th
ird
term
LT
SM
Res
ourc
es
Num
ber l
ines
: 0 –
120
, Stru
ctur
ed -,
sem
i- st
ruct
ured
- , u
nstru
ctur
ed n
umbe
r lin
es; C
ount
ers,
Pic
ture
s, a
rrays
/ dia
gram
s, F
lash
ca
rds,
Bas
e 10
blo
cks,
100
cha
rts, m
ultip
licat
ion
tabl
e m
aths
vid
eo c
lips,
E le
arni
ng re
sour
ces
onlin
e, M
aths
gam
es, c
ount
ers
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
W
B 2
pp.
78
– 90
Act
iviti
es
98 a
&b, 9
9a&b
; 100
-101
W
B 2
pp.
90
– 94
Act
iviti
es
103a
&b; 1
04
WB
2 p
p. 1
22 –
130
Act
iviti
es
110a
&b; 1
11; 1
12a&
b D
BE
refe
renc
e Te
rm 3
: Uni
t 10
Who
le N
umbe
rs:
Mul
ti[pl
icat
ion,
p. 2
75
Term
3: U
nit 1
1: W
hole
Num
bers
: M
ulti[
plic
atio
n, p
. 269
Te
rm 4
: Uni
t 2: W
hole
Num
bers
: M
ulti[
plic
atio
n, p
. 300
5 H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
as
sess
men
t – T
est
124 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
4
TER
M 3
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
…..…
T
ime:
4 H
OU
RS
GR
ADE
4 D
ivis
ion
- CAP
S p.
84-8
5 (M
etho
dolo
gy
refe
r to
pp. 8
4 - 8
5
5 D
ivis
ion
- CAP
S p.
200
(Met
hodo
logy
refe
r to
pp.1
72)
6 D
ivis
ion
- CAP
S p.
250
– 2
51
(Met
hodo
logy
refe
r to
pp.1
72)
TOPI
C
Div
isio
n of
who
le n
umbe
rs
Con
cept
s, S
kills
and
kn
owle
dge
Num
ber
rang
e fo
r cal
cula
tions
D
ivis
ion
of a
t lea
st w
hole
3-d
igit
by
1-di
git n
umbe
rs.
Cal
cula
tion
tech
niqu
es
Use
a ra
nge
of te
chni
ques
to p
erfo
rm
and
chec
k w
ritte
n an
d m
enta
l ca
lcul
atio
ns o
f who
le n
umbe
rs
incl
udin
g -
estim
atio
n -
build
ing
up
and
br
eaki
ng
dow
n nu
mbe
rs
- ro
undi
ng o
ff an
d co
mpe
nsat
ing
- do
ublin
g an
d ha
lvin
g -
usin
g m
ultip
licat
ion
and
divi
sion
as
inve
rse
oper
atio
ns
Num
ber
rang
e fo
r cal
cula
tions
D
ivis
ion
of a
t lea
st w
hole
3-d
igit
by
2-di
git n
umbe
rs
Cal
cula
tion
tech
niqu
es
Use
a ra
nge
of te
chni
ques
to p
erfo
rm
and
chec
k w
ritte
n an
d m
enta
l ca
lcul
atio
ns w
ith w
hole
num
bers
in
clud
ing
• es
timat
ion
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
usin
g m
ultip
licat
ion
and
divi
sion
as
inve
rse
oper
atio
ns
Num
ber
rang
e fo
r cal
cula
tions
D
ivis
ion
of a
t lea
st w
hole
4-d
igit
by
3-di
git n
umbe
rs: m
ultip
le o
pera
tions
on
who
le n
umbe
rs w
ith o
r with
out b
rack
ets
Cal
cula
tion
tech
niqu
es
• es
timat
ion
• us
ing
the
reci
proc
al re
latio
nshi
p be
twee
n m
ultip
licat
ion
and
divi
sion
•
long
div
isio
n •
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
• ro
undi
ng o
ff an
d co
mpe
nsat
ing
• us
ing
a ca
lcul
ator
125MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
1-d
igit
num
bers
to a
t le
ast 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e;
asso
ciat
ive;
and
dis
tribu
tive
prop
ertie
s of
who
le n
umbe
rs
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g w
hole
num
bers
-
finan
cial
con
text
s -
mea
sure
men
t con
text
s
• So
lve
prob
lem
s in
volv
ing
who
le
num
bers
, inc
ludi
ng
- gr
oupi
ng a
nd e
qual
sha
ring
w
ith re
mai
nder
s -
com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(rat
io)
- co
mpa
ring
two
quan
titie
s of
di
ffere
nt k
inds
(rat
e)
Num
ber
rang
e fo
r cou
ntin
g,
orde
ring
and
repr
esen
ting,
and
pl
ace
valu
e of
dig
its
• Rec
ogni
ze th
e pl
ace
valu
e of
dig
its
in w
hole
num
bers
to a
t lea
st 6
-dig
it nu
mbe
rs.
• R
ound
off
to th
e ne
ares
t 10,
100
, 1
000
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
2-d
igit
num
bers
to a
t le
ast 1
00
• Fa
ctor
s of
2-d
igit
who
le n
umbe
rs
to a
t lea
st 1
00
Mul
tiplic
atio
n fa
cts
• U
nits
by
mul
tiple
s of
10
• U
nits
by
mul
tiple
s of
100
Pr
oper
ties
of w
hole
num
bers
•
Rec
ogni
ze a
nd u
se th
e co
mm
utat
ive;
as
soci
ativ
e; a
nd d
istri
butiv
e pr
oper
ties
of w
hole
num
bers
•
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g w
hole
num
bers
, inc
ludi
ng fi
nanc
ial
cont
exts
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
2-d
igit
and
3-di
git
num
bers
•
Fact
ors
of 2
-dig
it an
d 3-
digi
t who
le
num
bers
•
Prim
e fa
ctor
s of
num
bers
up
to a
t le
ast 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
•
0 in
term
s of
its
addi
tive
prop
erty
•
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs a
nd d
ecim
al fr
actio
ns,
incl
udin
g -
finan
cial
con
text
s -
mea
sure
men
t con
text
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
-
com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(rat
io)
- co
mpa
ring
two
quan
titie
s of
-
diffe
rent
kin
ds (r
ate)
-
grou
ping
and
equ
al s
harin
g w
ith
rem
aind
ers
126 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• So
lve
prob
lem
s in
volv
ing
who
le
num
bers
, inc
ludi
ng
- co
mpa
ring
two
or m
ore
quan
titie
s of
th
e sa
me
kind
(rat
io)
- co
mpa
ring
two
quan
titie
s of
di
ffere
nt k
inds
(rat
e)
- gr
oupi
ng a
nd e
qual
sha
ring
with
re
mai
nder
s SU
GG
ESTE
D
MET
HO
DO
LOG
Y R
efer
to T
erm
1 a
nd T
erm
2 l
esso
n pl
ans
for c
larif
icat
ion
Expl
ain
from
kno
wn
(low
num
ber r
ange
); w
ork
with
con
cret
e LT
SM.
Lear
ners
sho
uld
do c
onte
xt fr
ee c
alcu
latio
ns a
nd s
olve
pro
blem
s in
con
text
s.
Lear
ners
sho
uld
cont
inue
to
• ch
eck
thei
r sol
utio
ns th
emse
lves
, by
usin
g m
ultip
licat
ion
whe
n do
ing
divi
sion
and
vic
e ve
rsa
• ju
dge
the
reas
onab
lene
ss o
f the
ir so
lutio
ns, b
y es
timat
ing
befo
re c
alcu
latin
g
Mul
tiplic
atio
n (K
now
tim
es ta
bles
– p
ract
ice
regu
larly
up
to 1
0 x
10 fo
r Gra
de 4
and
5 a
nd 1
2 x
12 fo
r Gra
de 6
).
Follo
w th
ese
step
s in
teac
hing
mul
tiplic
atio
n:
- So
lve
prob
lem
s in
con
text
.
Und
erst
and
that
: 86
+ 86
+ 8
6 is
equ
ival
ent t
o 86
x 3
or 3
x 8
6 (re
peat
ed a
dditi
on)
- m
ultip
licat
ion
by 1
leav
es a
num
ber u
ncha
nged
e.g
. 5 x
1 =
5; 9
9 x
1 =
99
- m
ultip
licat
ion
of z
ero
resu
lts in
zer
o e.
g. 7
x 0
= 0
; 31
x 0
= 0
127MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Und
erst
and
that
mul
tiplic
atio
n is
the
inve
rse
of d
ivis
ion
(mul
tiplic
atio
n re
vers
es d
ivis
ion
and
vice
ver
sa) a
nd u
se th
is to
che
ck
resu
lts. e
.g. 1
5 x
35 =
525
5
25 ÷
25
= 15
or 5
25 ÷
15
= 25
Not
e: In
Gra
de 5
Ter
m 3
lear
ners
are
intro
duce
d to
col
umn
met
hods
of m
ultip
licat
ion
DIV
ISIO
N
Men
tal d
ivis
ion
: Tur
ning
the
tabl
es –
pra
ctic
e re
gula
rly (e
.g. 5
x 8
= 4
0 4
0 ÷
8 =
5 / 4
0 ÷
5 =
8)
(
Also
cal
led
inve
rse
oper
atio
n or
reci
proc
al o
pera
tion.
)
Mak
e le
arne
rs a
war
e th
at d
ivis
ion
is n
on-c
omm
utat
ive
i.e. 8
1 ÷
9 is
not
the
sam
e as
9 ÷
81.
With
the
conc
ept g
rasp
ed, t
each
ing
divi
sion
will
beco
me
mor
e ab
out g
uide
d pr
actic
e to
hel
p yo
ur le
arne
rs to
bec
ome
fam
iliar
with
the
divi
sion
ope
ratio
n (a
lthou
gh it
’s re
ally
goi
ng to
be
a di
ffere
nt ty
pe o
f mul
tiplic
atio
n pr
actic
e.) S
tart
by p
ract
isin
g di
visi
on
by 1
, 2 a
nd 3
and
then
gra
dual
ly m
ove
up to
9.
Not
e: G
rade
s 4
and
5 fo
cus
is o
n us
ing
the
clue
boa
rd –
met
hod
ON
LY! I
n G
rade
6 th
e lo
ng d
ivis
ion
is in
trodu
ced
in th
e th
ird
term
LTSM
Res
ourc
es
Te
xt b
ooks
; Int
erne
t Web
site
s; N
umbe
r boa
rd; F
lard
car
ds; B
ase
10 b
lock
s / D
iene
s bl
ocks
; Con
cret
e m
ater
ial,
e.g.
cou
nter
s;
Num
ber l
ines
+ e
mpt
y on
es; H
undr
ed c
hart,
mul
tiplic
atio
n ta
ble,
mat
hs v
ideo
clip
s, E
lear
ning
reso
urce
s on
line,
Mat
hs g
ames
Gra
de 4
G
rade
5
Gra
de 6
W
orkb
oo re
fere
nce
WB
2 p
. 142
Act
iviti
es 1
25
WB
2 p
p. 1
38 –
144
Ac
tiviti
es 1
20 -
123
WB
2 p
p. 1
64 –
174
Act
iviti
es
126;
127
a7b;
128
; 129
a&b
DB
E Te
xtbo
ok re
fere
nce
Term
4: U
nit 6
: Who
le N
umbe
rs:
Div
isio
n, p
. 313
Te
rm 3
: Uni
t 5: W
hole
Num
bers
: D
ivis
ion,
p. 3
10
Term
4: U
nit 7
: Who
le N
umbe
rs:
Div
isio
n, p
. 336
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
128 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
129MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
5
TER
M 3
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
……
T
ime:
6 H
OU
RS
GR
ADE
4
Num
eric
pat
tern
s: p
p. 9
7 - 9
9
Geo
met
ric p
atte
rns:
pp.
117
m
etho
d ex
plai
ned
on p
p. 8
0 -8
2
5
Num
eric
pat
tern
s: p
p. 1
89 –
191
,
Geo
met
ric p
atte
rns:
p. 2
06,
met
hod
expl
aine
d on
p. 1
69
6
Num
eric
pat
tern
s: p
p. 2
70 -
272
G
eom
etric
pat
tern
s: p
p. 2
47 -
249
TOPI
C
Geo
met
ric a
nd N
umer
ic p
atte
rns
N
ote:
Geo
met
ric p
atte
rns
are
bein
g do
ne a
s ex
tend
ed c
onso
lidat
ion
in th
is c
ycle
. C
once
pts,
Ski
lls a
nd
know
ledg
e N
umer
ic p
atte
rns:
•
Inve
stig
ate
and
exte
nd n
umer
ic
patte
rns
look
ing
for r
elat
ions
hips
or
rule
s of
pat
tern
s:
o se
quen
ces
invo
lvin
g a
cons
tant
diff
eren
ce o
r rat
io
o of
lear
ner’s
ow
n cr
eatio
n o
repr
esen
ted
in ta
bles
•
Des
crib
e th
e ge
nera
l rul
es fo
r the
ob
serv
ed re
latio
nshi
ps
Inpu
t and
out
put v
alue
s •
Det
erm
ine
inpu
t val
ues,
out
put
valu
es a
nd ru
les
for t
he p
atte
rns
and
rela
tions
hips
usi
ng:
o flo
w d
iagr
ams
o ta
bles
Equi
vale
nt fo
rms
Det
erm
ine
equi
vale
nce
of d
iffer
ent
desc
riptio
ns o
f the
sam
e re
latio
nshi
p or
ru
le p
rese
nted
Num
eric
pat
tern
s:
• In
vest
igat
e an
d ex
tend
num
eric
pa
ttern
s lo
okin
g fo
r rel
atio
nshi
ps o
r ru
les
of p
atte
rns:
o
sequ
ence
s no
t lim
ited
to a
co
nsta
nt d
iffer
ence
or r
atio
o
of le
arne
r’s o
wn
crea
tion
•
Des
crib
e th
e ge
nera
l rul
es fo
r the
ob
serv
ed re
latio
nshi
ps
Inpu
t and
out
put v
alue
s •
Det
erm
ine
inpu
t val
ues,
out
put
valu
es a
nd ru
les
for t
he p
atte
rns
and
rela
tions
hips
usi
ng:
o flo
w d
iagr
ams
o ta
bles
Equi
vale
nt fo
rms
Det
erm
ine
equi
vale
nce
of d
iffer
ent
desc
riptio
ns o
f the
sam
e re
latio
nshi
p or
ru
le p
rese
nted
Num
eric
pat
tern
s :
• In
vest
igat
e an
d ex
tend
num
eric
pa
ttern
s lo
okin
g fo
r rel
atio
nshi
ps o
r ru
les
of p
atte
rns:
o
sequ
ence
s no
t lim
ited
to a
co
nsta
nt d
iffer
ence
or r
atio
o
of le
arne
r’s o
wn
crea
tion
o re
pres
ente
d in
tabl
es
• D
escr
ibe
the
gene
ral r
ules
for t
he
obse
rved
rela
tions
hips
In
put a
nd o
utpu
t val
ues
• D
eter
min
e in
put v
alue
s, o
utpu
t va
lues
and
rule
s fo
r the
pat
tern
s an
d re
latio
nshi
ps u
sing
: o
flow
dia
gram
s o
tabl
es
Equi
vale
nt fo
rms
Det
erm
ine
equi
vale
nce
of d
iffer
ent
desc
riptio
ns o
f the
sam
e re
latio
nshi
p or
ru
le p
rese
nted
130 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• ve
rbal
ly
• in
a fl
ow d
iagr
am
• in
a ta
ble
• by
a n
umbe
r sen
tenc
e G
eom
etric
pat
tern
s •
Inve
stig
ate
and
exte
nd g
eom
etric
pa
ttern
s lo
okin
g fo
r rel
atio
nshi
ps o
r ru
les
of p
atte
rns
o re
pres
ente
d in
phy
sica
l or
diag
ram
form
o
sequ
ence
s no
t lim
ited
to a
co
nsta
nt d
iffer
ence
or r
atio
o
of le
arne
r’s o
wn
crea
tion
• D
escr
ibe
obse
rved
rela
tions
hips
or
rule
s in
lear
ners
’ ow
n w
ords
Inpu
t and
out
put v
alue
s •
Det
erm
ine
inpu
t val
ues,
out
put
valu
es a
nd ru
les
for t
he p
atte
rns
and
rela
tions
hips
usi
ng
flow
dia
gram
s Eq
uiva
lent
form
s •
Det
erm
ine
equi
vale
nce
of d
iffer
ent
desc
riptio
ns o
f the
sam
e re
latio
nshi
p or
rule
pre
sent
ed
o ve
rbal
ly
o in
a fl
ow d
iagr
am
o by
a n
umbe
r sen
tenc
e
• ve
rbal
ly
• in
a fl
ow d
iagr
am
• in
a ta
ble
• by
a n
umbe
r sen
tenc
e G
eom
etric
pat
tern
s •
Inve
stig
ate
and
exte
nd g
eom
etric
pa
ttern
s lo
okin
g fo
r rel
atio
nshi
ps o
r ru
les
of p
atte
rns
o re
pres
ente
d in
phy
sica
l or
diag
ram
form
o
sequ
ence
s no
t lim
ited
to a
co
nsta
nt d
iffer
ence
or r
atio
o
of le
arne
r’s o
wn
crea
tion
• D
escr
ibe
obse
rved
rela
tions
hips
or
rule
s in
lear
ners
’ ow
n w
ords
In
put a
nd o
utpu
t val
ues
• D
eter
min
e in
put v
alue
s, o
utpu
t va
lues
and
rule
s fo
r the
pat
tern
s an
d re
latio
nshi
ps u
sing
flo
w d
iagr
ams
Equi
vale
nt fo
rms
• D
eter
min
e eq
uiva
lenc
e of
diff
eren
t de
scrip
tions
of t
he s
ame
rela
tions
hip
or ru
le p
rese
nted
o
verb
ally
o
in a
flow
dia
gram
o
by a
num
ber s
ente
nce
• ve
rbal
ly
• in
a fl
ow d
iagr
am
• in
a ta
ble
• by
a n
umbe
r sen
tenc
e
G
eom
etric
pat
tern
s •
Inve
stig
ate
and
exte
nd g
eom
etric
pa
ttern
s lo
okin
g fo
r rel
atio
nshi
ps o
r ru
les
of p
atte
rns
o re
pres
ente
d in
phy
sica
l or
diag
ram
form
o
sequ
ence
s no
t lim
ited
to a
co
nsta
nt d
iffer
ence
or r
atio
o
of le
arne
r’s o
wn
crea
tion
o re
pres
ente
d in
tabl
es
•
Des
crib
e th
e ge
nera
l rul
es fo
r the
ob
serv
ed re
latio
nshi
ps
Inpu
t and
out
put v
alue
s •
Det
erm
ine
inpu
t val
ues,
out
put
valu
es a
nd ru
les
for t
he p
atte
rns
and
rela
tions
hips
usi
ng
o flo
w d
iagr
ams
o ta
bles
Eq
uiva
lent
form
s •
Det
erm
ine
equi
vale
nce
of d
iffer
ent
desc
riptio
ns o
f the
sam
e re
latio
nshi
p or
rule
pre
sent
ed
o ve
rbal
ly
o in
a fl
ow d
iagr
am
o in
a ta
ble
o by
a n
umbe
r sen
tenc
e
131MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
SUG
GES
TED
M
ETH
OD
OLO
GY
Ref
er b
ack
to th
e le
sson
pla
n fo
r Ter
m 1
on
Num
eric
Pat
tern
s fo
r rev
isio
n N
umer
ic P
atte
rns:
Th
e fo
cus
shou
ld b
e on
inpu
t-out
put f
low
dia
gram
s th
at h
elp
lear
ners
to u
nder
stan
d an
d le
arn
abou
t:
• th
e in
vers
e op
erat
ion
betw
een
mul
tiplic
atio
n an
d di
visi
on
• th
e m
ultip
licat
ion
of u
nits
by
mul
tiple
s of
ten
in G
rade
4; a
nd 1
0, 1
00 a
nd 1
000
in G
rade
5 a
nd G
rade
6
• th
e as
soci
ativ
e pr
oper
ty w
ith w
hole
num
bers
and
how
we
can
use
this
pro
perty
whe
n w
e m
ultip
ly b
y m
ultip
les
of 1
0.
Usi
ng fl
ow d
iagr
ams
help
lear
ners
to u
nder
stan
d an
d us
e th
e fa
ct th
at m
ultip
licat
ion
and
divi
sion
are
inve
rse
oper
atio
ns
Lear
ners
are
not
exp
ecte
d to
use
the
expr
essi
on “i
nver
se o
pera
tions
”. Th
ey a
re e
xpec
ted
to k
now
that
:
• th
ey c
an u
se m
ultip
licat
ion
to c
heck
div
isio
n ca
lcul
atio
ns
• th
ey c
an u
se d
ivis
ion
to c
heck
mul
tiplic
atio
n ca
lcul
atio
ns
Then
they
can
wor
k w
ith e
xam
ples
whi
ch h
ave
a tw
o st
age
rule
e.g
. mul
tiply
and
then
add
, whe
re o
ne s
tage
is le
ft ou
t.
Sequ
ence
s of
num
bers
: In
the
Inte
rmed
iate
Pha
se le
arne
rs e
xten
d se
quen
ces
of n
umbe
rs. I
n G
rade
4 th
ey w
ork
with
two
kind
s of
seq
uenc
es.
1.
Sequ
ence
s in
volv
ing
a co
nsta
nt d
iffer
ence
Ex
ampl
es
a)
2; 4
; 6; 8
…
b)
18; 1
6; 1
4; 1
2…
In th
e ex
ampl
es a
bove
lear
ners
are
add
ing
2 or
sub
tract
ing
2 to
mak
e th
e pa
ttern
.
Lear
ners
may
des
crib
e it
as a
pat
tern
of c
ount
ing
on o
r cou
ntin
g ba
ck in
twos
.
Lear
ners
sho
uld
also
be
give
n ex
ampl
es w
hich
do
not s
tart
on a
mul
tiple
of t
he n
umbe
r the
y ar
e ad
ding
or s
ubtra
ctin
g.
132 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Exam
ples
a)
1;
4; 7
; 10…
….
b)
87; 6
6; 4
5; …
…..
2.
Sequ
ence
s in
volv
ing
a co
nsta
nt ra
tio
Exam
ple
1 60
0; 8
00; 4
00; .
..
In th
e ab
ove
exam
ple
lear
ners
are
div
idin
g by
2. A
ll th
e nu
mbe
rs in
the
sequ
ence
are
mul
tiple
s of
2.
Lear
ners
sho
uld
also
be
give
n ex
ampl
es in
whi
ch th
e nu
mbe
rs in
the
sequ
ence
are
not
mul
tiple
s of
the
num
ber b
y w
hich
they
are
mul
tiply
ing
or d
ivid
ing.
Exam
ples
a)
3;
6; 1
2; 2
4; ..
.
b)
10; 3
0; 9
0; 2
70; .
..
NB:
Tow
ards
the
end
of G
rade
6, t
he fo
cus
shou
ld b
e on
“fin
ding
the
rule
”
Geo
met
ric P
atte
rns
NB:
1.
Patte
rns
inve
stig
ated
sho
uld
incl
ude
shap
es a
s pe
r Gra
de, r
equi
red
in C
onte
nt A
rea
3. In
Gra
de 6
ther
e is
an
incr
ease
in
com
plex
ity o
f exa
mpl
es.
2.
Educ
ator
s m
ay p
refe
r to
teac
h G
eom
etric
pat
tern
s fir
st a
nd li
nk it
with
num
eric
pat
tern
s.
Lear
ners
sho
w th
e sa
me
patte
rns
in d
iffer
ent w
ays:
in a
dia
gram
, as
a ve
rbal
des
crip
tion,
as
a flo
w d
iagr
am a
nd in
a n
umbe
r
sent
ence
. Som
etim
es le
arne
rs a
re a
ble
to s
ee d
iffer
ent a
spec
ts o
f a p
atte
rn w
hen
they
cha
nge
the
form
in w
hich
the
patte
rn
is p
rese
nted
. Lea
rner
s w
ork
with
pat
tern
s th
at a
re m
ade
from
2-D
sha
pes
and
3-D
obj
ects
or f
rom
dra
win
gs/d
iagr
ams
of
133MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
thes
e sh
apes
and
obj
ects
. In
Patte
rns,
Fun
ctio
ns a
nd A
lgeb
ra w
e ch
oose
geo
met
ric p
atte
rns
that
can
be
re-d
escr
ibed
usi
ng a
num
ber p
atte
rn (t
his
does
not
mea
n th
at it
can
’t be
des
crib
ed in
wor
ds, i
n fa
ct th
e de
scrip
tion
in w
ords
is u
sual
ly th
e st
artin
g
poin
t). In
Sha
pe a
nd S
pace
lear
ners
als
o w
ork
with
vis
ual p
atte
rns
that
are
geo
met
ric. H
owev
er, i
n Sh
ape
and
Spac
e th
ey
are
only
requ
ired
to d
escr
ibe
the
patte
rns
usin
g th
e la
ngua
ge o
f geo
met
ry a
nd to
cop
y th
e pa
ttern
s. W
hile
man
y of
thes
e
patte
rns
can
be d
escr
ibed
usi
ng a
lgeb
raic
exp
ress
ions
, thi
s is
bey
ond
the
scop
e of
Inte
rmed
iate
Pha
se le
arne
rs.
Gra
de 4
,5 a
nd 6
Wha
t is
diffe
rent
to G
rade
3?
In G
rade
3 le
arne
rs c
opy,
ext
end
and
desc
ribe
patte
rns
mad
e w
ith n
umbe
rs, o
bjec
ts o
r dra
win
gs T
he d
escr
iptio
ns a
re o
nly
verb
al. T
hey
also
cre
ate
thei
r ow
n pa
ttern
s.
The
kind
s of
pat
tern
s be
com
e m
ore
com
plex
in G
rade
4.
In G
rade
4 le
arne
rs a
re in
trodu
ced
to a
new
way
to re
pres
ent p
atte
rns:
the
inpu
t- ou
tput
flow
dia
gram
(som
e le
arne
rs m
ay
have
use
d th
is in
Fou
ndat
ion
Phas
e, b
ut it
is n
ot a
spe
cific
atio
n).
Lear
ners
sho
w th
e sa
me
patte
rns
in d
iffer
ent w
ays:
in a
dia
gram
, as
a ve
rbal
des
crip
tion,
as
a flo
w d
iagr
am a
nd in
a n
umbe
r se
nten
ce. S
omet
imes
lear
ners
are
abl
e to
see
diff
eren
t asp
ects
of a
pat
tern
whe
n th
ey c
hang
e th
e fo
rm in
whi
ch th
e pa
ttern
is
pres
ente
d.
Lear
ners
wor
k w
ith p
atte
rns
that
are
mad
e fro
m 2
-D s
hape
s an
d 3-
D o
bjec
ts o
r fro
m d
raw
ings
/dia
gram
s of
thes
e sh
apes
an
d ob
ject
s. In
Pat
tern
s, F
unct
ions
and
Alg
ebra
we
choo
se g
eom
etric
pat
tern
s th
at c
an b
e re
-des
crib
ed u
sing
a n
umbe
r pa
ttern
(thi
s do
es n
ot m
ean
that
it c
an’t
be d
escr
ibed
in w
ords
, in
fact
the
desc
riptio
n in
wor
ds is
usu
ally
the
star
ting
poin
t).
In S
hape
and
Spa
ce le
arne
rs a
lso
wor
k w
ith v
isua
l pat
tern
s th
at a
re g
eom
etric
. How
ever
, in
Shap
e an
d Sp
ace
they
are
on
ly re
quire
d to
des
crib
e th
e pa
ttern
s us
ing
the
lang
uage
of g
eom
etry
and
to c
opy
the
patte
rns.
Whi
le m
any
of th
ese
patte
rns
can
be d
escr
ibed
usi
ng a
lgeb
raic
exp
ress
ions
, thi
s is
bey
ond
the
scop
e of
Inte
rmed
iate
Pha
se le
arne
rs.
Wha
t kin
ds o
f geo
met
ric p
atte
rns
shou
ld le
arne
rs w
ork
with
? •
Sim
ple
repe
atin
g pa
ttern
s –
but t
his
is re
ally
mor
e of
a fo
cus
in th
e Fo
unda
tion
Phas
e
134 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Exam
ple:
Com
plet
e th
e pa
ttern
•
Patt
erns
in w
hich
the
shap
es g
row
or d
ecre
ase
in d
iffer
ent w
ays.
We
can
desc
ribe
thes
e pa
ttern
s by
the
way
th
ey lo
ok.
patte
rns
in w
hich
the
shap
e ke
eps
its fo
rm, b
ut g
ets
larg
er (o
r sm
alle
r) in
eac
h st
age.
patte
rns
in w
hich
a s
hape
or p
art o
f a s
hape
is a
dded
at e
ach
stag
e
In
eac
h of
the
exam
ples
abo
ve th
e pa
ttern
s ar
e m
ade
by a
ddin
g on
the
sam
e nu
mbe
r of m
atch
es in
eac
h su
cces
sive
sha
pe.
In th
e to
p pa
ttern
3 m
atch
es a
re a
dded
eac
h tim
e. In
the
seco
nd p
atte
rn tw
o m
atch
es a
re a
dded
eac
h tim
e. B
oth
patte
rns
show
num
ber p
atte
rns
with
a c
onst
ant d
iffer
ence
. M
ost g
eom
etric
pat
tern
s le
arne
rs s
ee in
Gra
de 4
, will
be p
atte
rns
with
a c
onst
ant d
iffer
ence
. The
y ar
e m
ore
likel
y to
get
pa
ttern
s w
ith a
con
stan
t rat
io w
hen
wor
king
onl
y w
ith n
umbe
r seq
uenc
es.
• P
atte
rns
with
nei
ther
a c
onst
ant d
iffer
ence
nor
a c
onst
ant r
atio
.
Exa
mpl
e
135MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Wha
t sho
uld
lear
ners
do?
•
Cop
y an
d ex
tend
the
patte
rn. T
his
help
s th
em to
und
erst
and
how
the
patte
rn is
form
ed.
• D
escr
ibe
the
patte
rn in
wor
ds.
-
Diff
eren
t lea
rner
s w
ill de
scrib
e di
ffere
nt a
spec
ts o
f the
pat
tern
.
- Y
ou w
ant l
earn
ers
to d
escr
ibe
the
rela
tions
hip
betw
een
shap
es in
the
sequ
ence
or
rule
s in
thei
r ow
n w
ords
. To
do th
is,
lear
ners
nee
d to
dis
cuss
how
they
mad
e th
e pa
ttern
or t
o an
swer
the
ques
tion
“How
do
I get
from
one
sta
ge in
the
patte
rn
to th
e ne
xt?”
Le
arne
rs n
eed
to h
ave
oppo
rtuni
ties
to s
ee th
at s
omet
imes
cha
ngin
g th
e fo
rm o
f rep
rese
ntat
ion
(geo
met
ric to
ver
bal o
r to
a flo
w d
iagr
am o
r to
a ta
ble)
can
hel
p th
em to
und
erst
and
the
patte
rn in
diff
eren
t way
s. L
earn
ers
shou
ld “t
rans
late
” the
se
geom
etric
seq
uenc
es in
to o
ther
form
s of
exp
ress
ion
or re
pres
enta
tion,
nam
ely
• ve
rbal
ly d
escr
ibe
the
patte
rn
• nu
mbe
r seq
uenc
es w
hich
can
als
o be
reco
rded
in a
tabl
e fo
rm.
Exa
mpl
e:
Exte
ndin
g th
e pa
ttern
:
Des
crib
ing
the
patte
rn in
ow
n w
ords
“It
is
a p
atte
rn o
f tria
ngle
s”
“ Eac
h tri
angl
e is
big
ger t
han
the
one
befo
re”
Des
crib
ing
how
they
mad
e th
e pa
ttern
or a
nsw
erin
g th
e qu
estio
n “h
ow to
I ge
t fro
m o
ne s
tage
to th
e ne
xt?”
“I
adde
d on
e m
ore
mat
chst
ick
to e
ach
side
of e
ach
trian
gle”
“E
ach
trian
gle
has
one
mor
e m
atch
stic
k in
eac
h si
de th
an th
e tri
angl
e on
its
left”
136 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Rec
ordi
ng th
e nu
mbe
r pat
tern
in a
tabl
e.
Whe
n le
arne
rs fi
ll in
the
tabl
e lik
e th
e on
e sh
own
belo
w, th
ey w
ill se
e th
at th
e nu
mbe
r of m
atch
stic
ks u
sed
for e
ach
trian
gle
is 3
tim
es th
e po
sitio
n of
the
trian
gle
in th
e se
quen
ce. T
hey
will
see
that
the
rule
is tr
iang
le n
umbe
r tim
es 3
. Lea
rner
s ca
n th
en b
e as
ked
to p
redi
ct h
ow m
any
mat
ches
they
will
use
for t
riang
les
they
hav
e no
t bui
lt, e
.g. 1
0th,
100
th e
tc.
G
rade
6:
Wha
t is
diffe
rent
? •
Ther
e is
mor
e em
phas
is o
n pr
esen
ting
patte
rns
in ta
bles
. •
Ther
e is
mor
e em
phas
is o
n st
atin
g th
e ge
nera
l rul
e of
the
patte
rn.
Wha
t kin
ds o
f geo
met
ric p
atte
rns
shou
ld le
arne
rs w
ork
with
? Le
arne
rs c
an w
ork
with
pat
tern
s w
hich
are
mad
e fro
m re
al s
hape
s, o
r obj
ects
con
cret
e ap
para
tus.
W
hat k
inds
of p
atte
rns
shou
ld le
arne
rs w
ork
with
? Pa
ttern
s in
whi
ch th
e sh
apes
gro
w o
r dec
reas
e in
diff
eren
t way
s.
LT
SM
R
esou
rces
N
umbe
r lin
es: 0
– 1
20, S
truct
ured
-, s
emi-
stru
ctur
ed -
, uns
truct
ured
num
ber l
ines
; Cou
nter
s, P
ictu
res,
arra
ys/ d
iagr
ams,
Fla
sh
card
s, B
ase
10 b
lock
s, 1
00 c
harts
, mat
hs v
ideo
clip
s, E
lear
ning
reso
urce
s on
line,
Mat
hs g
ames
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
W
B 2
pp.
168
– 1
70
Activ
ities
138
-139
WB
2 p
p. 1
80 –
184
Act
iviti
es
140;
141
a&b;
101;
102
) W
B 2
pp.
98
– 10
2 Ac
tiviti
es 3
5,36
,37
DB
E Te
xtbo
ok re
fere
nce
Term
4: U
nit 1
0: G
eom
etric
Pat
tern
s, p
. 33
9 Te
rm 4
: Uni
t 9: G
eom
etric
Pat
tern
s,
p. 3
38
Term
2: U
nit 4
: Geo
met
ric P
atte
rns,
p.
152
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
137MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
138 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
6
TER
M 3
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
……
T
ime:
8 H
OU
RS
GR
ADE
4
CAP
S p.
93,
115
and
116
5
CAP
S p.
184
- 18
5 6
CAP
S p.
263
- 26
5 TO
PIC
Pr
oper
ties
of 2
-D s
hape
s.
Tran
sfor
mat
ions
; Pos
ition
and
vie
ws;
Loc
atio
n an
d di
rect
ions
Con
cept
s, S
kills
and
kn
owle
dge
2 - D
sha
pes,
R
ecog
nize
, vis
ualiz
e an
d na
me
2-D
sh
apes
in
re
gula
r and
irre
gula
r pol
ygon
s –
trian
gles
, squ
ares
, rec
tang
les,
oth
er
quad
rilat
eral
s, p
enta
gons
, hex
agon
s an
d ci
rcle
s
Cha
ract
eris
tics
of s
hape
s
stra
ight
sid
es
cu
rved
sid
es
nu
mbe
r of s
ides
2 -
D s
hape
s,
Rec
ogni
ze, v
isua
lize
and
nam
e 2-
D
shap
es in
regu
lar a
nd ir
regu
lar p
olyg
ons
– tri
angl
es, s
quar
es, r
ecta
ngle
s, o
ther
qu
adril
ater
als,
pen
tago
ns, h
exag
ons,
he
ptag
ons
and
circ
les
si
mila
ritie
s an
d di
ffere
nces
bet
wee
n sq
uare
s an
d re
ctan
gles
C
hara
cter
istic
s of
sha
pes
st
raig
ht s
ides
curv
ed s
ides
num
ber o
f sid
es
an
gles
in s
hape
D
raw
2-D
sha
pes
on g
rid p
aper
In
volv
ing
angl
es
2 - D
sha
pes,
R
ecog
nize
, vis
ualiz
e an
d na
me
2-D
sh
apes
in
re
gula
r and
irre
gula
r pol
ygon
s -
trian
gles
, sq
uare
s, re
ctan
gles
, par
alle
logr
ams,
ot
her
quad
rilat
eral
s, p
enta
gons
, hex
agon
s,
hept
agon
s, o
ctag
ons
si
mila
ritie
s an
d di
ffere
nces
bet
wee
n re
ctan
gles
and
par
alle
logr
ams
C
hara
cter
istic
s of
sha
pes
nu
mbe
r of s
ides
leng
ths
in s
ides
size
s of
ang
les
Dra
w 2
-D s
hape
s on
grid
pap
er
Invo
lvin
g an
gles
139MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Tran
sfor
mat
ions
Build
com
posi
te s
hape
s
Tess
ella
tions
Des
crib
e pa
ttern
s Po
sitio
n an
d vi
ews
Loca
tion
and
dire
ctio
ns
Rec
ogni
ze a
nd d
escr
ibe
angl
es in
2-D
sh
apes
Tr
ansf
orm
atio
ns
U
se tr
ansf
orm
atio
ns to
mak
e co
mpo
site
sha
pes
U
se tr
ansf
orm
atio
ns to
mak
e te
ssel
latio
ns
D
escr
ibe
patte
rns
Posi
tion
and
view
s Lo
catio
n an
d di
rect
ions
Rec
ogni
ze a
nd d
escr
ibe
angl
es in
2-D
sh
apes
Tr
ansf
orm
atio
ns
U
se tr
ansf
orm
atio
ns to
mak
e co
mpo
site
sha
pes
E
nlar
gem
ent a
nd re
duct
ions
Des
crib
e pa
ttern
s Po
sitio
n an
d vi
ews
Loca
tion
and
dire
ctio
ns
SU
GG
ESTE
D
MET
HO
DO
LOG
Y Pr
oper
ties
of 2
D s
hape
s Se
e Te
rm 1
for s
ugge
sted
teac
hing
met
hodo
logy
. Le
arne
rs re
vise
and
con
solid
ate
wha
t the
y le
arne
d in
Ter
m 1
. Gra
de 6
lear
ners
dra
w c
ircle
s an
d pa
ttern
s w
ith c
ircle
s us
ing
a pa
ir of
pai
r of c
ompa
sses
. Vi
ewin
g ob
ject
s Le
arne
rs w
ork
with
sid
e vi
ews,
pla
n vi
ews
and
top
view
s of
sim
ple
sing
le o
bjec
ts s
uch
as a
cup
, hat
, sho
e, b
ox o
r app
le. T
hey
also
wor
k w
ith s
ide
view
s an
d pl
an v
iew
s of
a c
lass
room
, sim
ple
build
ings
, and
sch
ool f
ield
s.
Posi
tion
/ Loc
atio
n an
d di
rect
ion
This
link
s w
ith th
e w
ork
done
in G
eogr
aphy
in M
ap S
kills
. Cel
ls in
a g
rid a
re o
ften
labe
lled
with
a le
tter a
nd a
num
ber e
.g. D
4;
A3; E
7. T
his
is c
alle
d al
pha-
num
eric
refe
renc
ing.
The
ski
lls o
f ide
ntify
ing
ever
yday
obj
ects
and
col
lect
ions
of o
bjec
ts, a
nd th
e sk
ills d
escr
ibed
bel
ow c
an b
e de
velo
ped
in th
e G
eogr
aphy
less
on a
nd p
ract
ised
in th
e M
athe
mat
ics
less
on.
Le
arne
rs w
ork
with
alp
ha-n
umer
ic g
rid re
fere
nces
on
grid
s an
d m
aps.
Loc
ate
obje
cts
usin
g th
e gr
id re
fere
nces
. W
hen
lear
ners
wor
k w
ith g
rid re
fere
nces
they
nee
d to
lear
n
to fi
nd th
e ce
ll i.e
. to
answ
er q
uest
ions
like
“Wha
t is
in c
ell B
3?”
in
whi
ch c
ell a
n ob
ject
is i.
e. to
ans
wer
que
stio
ns li
ke “W
here
is th
e co
w?”
Tr
ansf
orm
atio
ns
Gra
de 4
lear
ners
sho
uld
focu
s on
:
build
ing
com
posi
te s
hape
s in
clud
ing
som
e sh
apes
with
line
sym
met
ry.
140 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
te
ssel
latio
ns a
nd d
escr
ibin
g pa
ttern
s in
real
life
. Te
ssel
latio
ns
Le
arne
rs u
se 2
-D s
hape
s to
cre
ate
tess
ella
tion
patte
rns.
Tilin
g pa
ttern
s ca
n be
mad
e by
pac
king
out
the
tiles
.
Le
arne
rs n
eed
to id
entif
y an
d de
scrib
e te
ssel
latio
n pa
ttern
s.
Gra
de 4
lear
ners
are
not
requ
ired
to c
reat
e th
e pa
ttern
s by
rota
ting,
tran
slat
ing
or re
flect
ing
a si
ngle
sha
pe.
Des
crib
e pa
ttern
s Le
arne
rs d
escr
ibe
patte
rns
by ta
lkin
g ab
out t
he s
hape
s th
ey s
ee in
the
patte
rn. e
.g.
th
e pa
ttern
I se
e on
the
cran
e is
mad
e of
stra
ight
line
s
the
patte
rn w
e se
e on
the
hone
ycom
b lo
oks
like
a te
ssel
latio
n pa
ttern
of h
exag
ons
th
e pa
ttern
I se
e on
the
bead
bra
cele
t loo
ks li
ke a
tess
ella
tion
patte
rn o
f tria
ngle
s Le
arne
rs d
escr
ibe
patte
rns
by d
iscu
ssin
g th
e sy
mm
etry
of s
hape
s e.
g. th
e bu
tterfl
y’s
win
gs m
ake
a sy
mm
etric
al p
atte
rn.
Lear
ners
ofte
n fin
d pa
ttern
s ea
sier
to d
escr
ibe,
onc
e th
ey h
ave
copi
ed o
r mad
e th
e pa
ttern
s. It
is u
sefu
l to
link
the
proc
ess
of
mak
ing
or c
opyi
ng p
atte
rns
with
the
desc
riptio
ns o
f pat
tern
s fro
m n
atur
e, m
oder
n ev
eryd
ay li
fe a
nd o
ur c
ultu
ral h
erita
ge. O
ften
the
geom
etric
al p
roce
ss y
ou u
se to
mak
e a
copy
of t
he p
atte
rn is
not
the
sam
e as
the
orig
inal
pro
cess
use
d to
mak
e th
e pa
ttern
. In
Gra
de 5
lear
ners
wor
k w
ith v
iew
s of
sin
gle
ever
yday
obj
ects
or c
olle
ctio
ns o
f eve
ryda
y ob
ject
s. T
hey
mat
ch v
iew
s of
the
obje
ct o
r obj
ects
with
the
posi
tion
of th
e vi
ewer
. Lea
rner
s ar
e pr
esen
ted
with
mul
tiple
vie
ws
of a
n ev
eryd
ay o
bjec
t or c
olle
ctio
n of
ev
eryd
ay o
bjec
ts o
r sce
nes
from
eve
ryda
y lif
e, a
s w
ell a
s po
sitio
ns o
f vie
wer
s in
rela
tion
to th
e ob
ject
or o
bjec
ts. T
hey
mat
ch
each
vie
w w
ith a
vie
wer
or v
iew
poin
t. Ev
eryd
ay o
bjec
ts o
ften
have
mor
e irr
egul
ar s
urfa
ces
than
geo
met
ric o
bjec
ts e
.g. c
ompa
re
a te
apot
to a
sph
ere
or a
per
son
to a
cub
e. T
his
mak
es it
eas
ier t
o id
entif
y vi
ews
and
view
poin
ts o
f eve
ryda
y ob
ject
s.
In G
rade
4 le
arne
rs c
reat
e co
mpo
site
sha
pes
by p
laci
ng 2
-D s
hape
s ne
xt to
eac
h ot
her.
In G
rade
5 le
arne
rs tr
ace
and
mov
e a
2-D
sha
pe u
sing
refle
ctio
ns, r
otat
ions
and
tran
slat
ions
to d
raw
com
posi
te s
hape
s.
In
Gra
de 4
lear
ners
cre
ate
tess
ella
tions
by
pack
ing
out s
hape
s. In
Gra
de 5
lear
ners
trac
e an
d m
ove
a 2-
D s
hape
usi
ng
refle
ctio
ns, r
otat
ions
and
tran
slat
ions
to d
raw
tess
ella
tions
. Le
arne
rs u
se a
2-D
sha
pe a
s a
tem
plat
e w
hich
they
trac
e an
d m
ove
by re
flect
ing,
tran
slat
ing
and
rota
ting
to c
reat
e co
mpo
site
sh
apes
. Som
e of
the
new
sha
pes
draw
n sh
ould
hav
e lin
es o
f sym
met
ry. L
earn
ers
desc
ribe
how
they
mov
ed th
e sh
ape
to c
reat
e th
e pa
ttern
usi
ng th
e w
ords
“rot
atio
n, tr
ansl
atio
n an
d re
flect
ion”
In
Gra
de 6
vie
win
g an
d po
sitio
n is
ext
ende
d to
geo
met
ric o
bjec
ts o
r col
lect
ions
of g
eom
etric
obj
ects
or c
ompo
site
geo
met
ric
obje
cts.
Lea
rner
s ar
e pr
esen
ted
with
mul
tiple
vie
ws
of a
n ev
eryd
ay o
r geo
met
ric o
bjec
t or c
olle
ctio
ns o
f obj
ects
or c
ompo
site
141MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
geom
etric
obj
ects
, as
wel
l as
posi
tions
of v
iew
ers
in re
latio
n to
the
obje
ct o
r obj
ects
. The
y m
atch
eac
h vi
ew w
ith a
vie
wer
or
view
poin
t. In
Gra
de 6
, lea
rner
s ar
e on
ly re
quire
d to
use
the
trans
form
atio
n co
ncep
ts in
des
crib
ing
patte
rns.
Lea
rner
s de
scrib
e pa
ttern
s by
di
scus
sing
the
shap
es th
ey s
ee in
the
patte
rn a
nd h
ow th
ey w
ould
tran
sfor
m th
at s
hape
if th
ey w
ante
d to
ext
end
the
patte
rn
Th
e pa
ttern
I se
e on
the
hone
ycom
b lo
oks
like
a te
ssel
latio
n pa
ttern
of h
exag
ons.
I ca
n m
ake
this
pat
tern
by
trans
latin
g th
e he
xago
n.
Th
e pa
ttern
I se
e on
the
bead
bra
cele
t loo
ks li
ke a
tess
ella
tion
patte
rn o
f tria
ngle
s. I
can
mak
e th
is p
atte
rn b
y re
flect
ing
the
trian
gle.
I can
mak
e a
patte
rn li
ke th
e on
e I s
ee o
n th
e do
ily b
y tra
nsla
ting
the
para
llelo
gram
. Le
arne
rs id
entif
y sy
mm
etry
in p
atte
rns.
Alth
ough
lear
ners
are
not
requ
ired
to d
raw
the
patte
rns
in G
rade
6, t
hey
ofte
n fin
d pa
ttern
s ea
sier
to d
escr
ibe,
onc
e th
ey h
ave
copi
ed o
r mad
e th
e pa
ttern
s. It
is u
sefu
l to
link
the
proc
ess
of m
akin
g or
cop
ying
pa
ttern
s w
ith th
e de
scrip
tions
of p
atte
rns
from
nat
ure,
mod
ern
ever
yday
life
and
our
cul
tura
l her
itage
. Ofte
n th
e ge
omet
rical
pr
oces
s yo
u us
e to
mak
e a
copy
of t
he p
atte
rn is
not
the
sam
e as
the
orig
inal
pro
cess
use
d to
mak
e th
e pa
ttern
. Bee
s do
not
te
ssel
late
with
hex
agon
s to
mak
e a
hone
ycom
b, b
ut if
lear
ners
tess
ella
te w
ith a
hex
agon
, the
y ca
n m
ake
a pa
ttern
that
look
s si
mila
r to
the
patte
rn th
ey s
ee in
the
hone
ycom
b.
Gra
de 6
lear
ners
als
o do
enl
arge
men
ts a
nd re
duct
ions
.
LTSM
R
esou
rces
Va
riety
of r
egul
ar a
nd ir
regu
lar p
olyg
ons:
( To
cut
out
) - t
riang
les,
squ
ares
, rec
tang
les,
par
alle
logr
ams,
oth
er q
uadr
ilate
rals
, pen
tago
ns, h
exag
ons,
hep
tago
ns, o
ctag
ons
- Tan
gram
s pa
ir of
com
pass
es, g
eobo
ards
Gra
de 4
G
rade
5
Gra
de 6
WB
2 p
p. 4
2 –
50 A
ctiv
ities
82
-85b
pp
. 158
– 1
62
Activ
ities
133
-135
)
WB
2 p
p. 5
0 –
66
Activ
ities
86-
93;
pp. 1
66 –
178
Ac
tiviti
es 1
33-1
39
WB
2 p
p. 4
6 –
48 A
ctiv
ities
79
a&b;
83;
84a
&b
DB
E Te
xtbo
ok re
fere
nce
Term
3: U
nit 6
: Pro
pert
ies
of tw
o di
men
sion
al s
hape
s, p
. 355
Te
rm 3
: Uni
t 12:
Tra
nsfo
rmat
ion,
p. 2
86
Term
4: U
nit 9
: Tra
nsfo
rmat
ion,
p. 3
33
Term
3: U
nit 5
: Vie
win
g ob
ject
s, p
. 250
Te
rm 4
: Uni
t 8: P
ositi
on a
nd m
ovem
ent,
p.
329
Term
3: U
nit 6
: Pro
pert
ies
of tw
o di
men
sion
al s
hape
s, p
. 236
Te
rm 3
: Uni
t 7: T
rans
form
atio
n, p
. 24
2 Te
rm 4
: Uni
t 8: T
rans
form
atio
n, p
. 33
3 Te
rm 3
: Uni
t 5: V
iew
ing
obje
cts,
p.
233
Term
3: U
nit 5
: Pro
pert
ies
of tw
o di
men
sion
al s
hape
s, p
. 237
Te
rm 3
: Uni
t 6: T
rans
form
atio
n, p
. 24
7 Te
rm 4
: Uni
t 9: T
rans
form
atio
n, p
. 35
0 Te
rm 3
: Uni
t 4: V
iew
ing
obje
cts,
p.
231
142 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Term
4: U
nit 7
: Pos
ition
and
m
ovem
ent,
p. 3
31
Term
4: U
nit 1
0: P
ositi
on a
nd
mov
emen
t, p
. 358
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –T
est
143MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
7
TER
M 3
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
….…
T
ime:
4 H
OU
RS
GR
ADE
4 M
ake
use
of le
sson
pla
ns o
f Ter
m 2
5
M
ake
use
of le
sson
pla
ns o
f Ter
m 2
6
M
ake
use
of le
sson
pla
ns o
f Ter
m 2
TO
PIC
Le
ngth
, Mas
s, C
apac
ity a
nd V
olum
e C
once
pts,
Ski
lls a
nd
know
ledg
e Le
ngth
Prac
tical
mea
surin
g of
2-D
sha
pes
and
3-D
obj
ects
Mea
surin
g in
stru
men
ts
U
nits
Cal
cula
tions
and
pro
blem
sol
ving
in
volv
ing
leng
th
Leng
th
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D o
bjec
ts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng
invo
lvin
g le
ngth
Leng
th
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D o
bjec
ts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng
invo
lvin
g le
ngth
C
once
pts,
Ski
lls a
nd
know
ledg
e M
ass
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D o
bjec
ts
M
easu
ring
inst
rum
ents
Uni
ts ((
milli
litre
s, li
tres)
Cal
cula
tions
and
pro
blem
sol
ving
in
volv
ing
mas
s
Mas
s
Prac
tical
mea
surin
g of
2-D
sha
pes
and
3-D
obj
ects
Mea
surin
g in
stru
men
ts
U
nits
(milli
litre
s, li
tres)
Cal
cula
tions
and
pro
blem
sol
ving
in
volv
ing
mas
s
Mas
s
Prac
tical
mea
surin
g of
2-D
sha
pes
and
3-D
obj
ects
Mea
surin
g in
stru
men
ts
U
nits
(milli
litre
s, li
tres,
kilo
litre
s)
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng
invo
lvin
g m
ass
(incl
ude
fract
ion
and
deci
mal
form
s to
2 d
ecim
al p
lace
s)
Con
cept
s, S
kills
and
kn
owle
dge
Cap
acity
/Vol
ume
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D o
bjec
ts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng
invo
lvin
g ca
paci
ty/v
olum
e
Cap
acity
/Vol
ume
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D o
bjec
ts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng
invo
lvin
g ca
paci
ty/v
olum
e
Cap
acity
/Vol
ume
Pr
actic
al m
easu
ring
of 2
-D s
hape
s an
d 3-
D o
bjec
ts
M
easu
ring
inst
rum
ents
Uni
ts
C
alcu
latio
ns a
nd p
robl
em s
olvi
ng
invo
lvin
g ca
paci
ty/v
olum
e
144 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LTSM
Res
ourc
es
Mea
surin
g ta
pe, r
uler
s, s
trin
g, tr
undl
e w
heel
, Kitc
hen
scal
e, b
athr
oom
sca
le, b
alan
ce, M
easu
ring
jugs
, bot
tles,
var
iety
of
con
tain
ers
from
lear
ner’s
con
text
, cub
es
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
W
B 1
pp.
110
– 1
14
Activ
ities
40
– 42
M
ass
WB
2 p
p. 1
12 -
122
Ac
tiviti
es
111-
115
Volu
me/
Cap
acity
WB
2 p
p. 1
52 –
156
Ac
tiviti
es 1
30-1
32
WB
1 p
p 11
6 - 1
26
Activ
ities
40
– 43
M
ass
WB
2 p
p. 2
0 - 2
6 W
B 2
Act
iviti
es
74 -
76; 7
8 Vo
lum
e/ca
paci
ty W
B 2
pp.
160
– 1
64
Activ
ities
130
- 13
2
Leng
th W
B 1
pp.
102
- 10
6 Ac
tiviti
es
102
- 104
M
ass
WB
1 p
p. 1
0 –
12 A
ctiv
ities
68
a&b
Volu
me/
cap
acity
WB
1 p
p. 1
64 –
166
Ac
tiviti
es 6
4a&b
DB
E Te
xtbo
ok re
fere
nce
Term
2: U
nit 4
: Len
gth,
p. 1
47
Term
4: U
nit 3
: Mas
s, p
. 297
Te
rm 3
: Uni
t 2: C
apac
ity a
nd v
olum
e,
p. 2
25
Term
2: U
nit 4
: Len
gth,
p. 1
43
Term
3: U
nit 2
: Mas
s, p
. 211
Te
rm 1
: Uni
t 9: C
apac
ity a
nd v
olum
e,
p. 1
04
Term
3: U
nit 1
1: L
engt
h, p
. 285
Te
rm 3
: Uni
t 1: M
ass,
p. 2
15
Term
2: U
nit 8
: Cap
acity
and
vol
ume,
p.
200
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent –
Te
st
145MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
8
TER
M 3
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
….…
T
ime:
12
HO
UR
S G
RAD
E 4
Com
mon
Fra
ctio
ns
CAP
S p.
91
5 C
omm
on fr
actio
ns
CAP
S p.
160-
162,
176
-177
& 1
99
6 C
omm
on fr
actio
ns
CAP
S p.
226
-227
, 280
D
ecim
al fr
actio
ns -
CAP
S p.
252
, Pe
rcen
tage
s -
CAP
S p.
267
TO
PIC
C
omm
on fr
actio
ns, d
ecim
al fr
actio
ns a
nd p
erce
ntag
es
146 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Con
cept
s, S
kills
and
kn
owle
dge
Des
crib
ing
and
orde
ring
frac
tions
Com
pare
and
ord
er c
omm
on
fract
ions
with
diff
eren
t den
omin
ator
s (h
alve
s; th
irds,
qua
rters
; fift
hs;
sixt
hs; s
even
ths;
eig
hths
)
Des
crib
e an
d co
mpa
re c
omm
on
fract
ions
in d
iagr
am fo
rm
Cal
cula
tions
with
frac
tions
:
Addi
tion
of c
omm
on fr
actio
ns w
ith
the
sam
e de
nom
inat
ors
Rec
ogni
ze, d
escr
ibe
and
use
the
equi
vale
nce
of d
ivis
ion
and
fract
ions
So
lvin
g pr
oble
ms
•
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g fra
ctio
ns, i
nclu
ding
gr
oupi
ng a
nd e
qual
sha
ring
Equi
vale
nt fo
rms:
R
ecog
nize
and
use
equ
ival
ent f
orm
s of
co
mm
on fr
actio
ns (f
ract
ions
in w
hich
one
de
nom
inat
or is
a m
ultip
le o
f ano
ther
)
Des
crib
ing
and
orde
ring
frac
tions
:
Cou
nt fo
rwar
ds a
nd b
ackw
ards
in
fract
ions
Com
pare
and
ord
er c
omm
on
fract
ions
to a
t lea
st tw
elfth
s C
alcu
latio
ns w
ith fr
actio
ns:
•
Addi
tion
and
subt
ract
ion
of c
omm
on
fract
ions
with
the
sam
e de
nom
inat
ors
•
Addi
tion
and
subt
ract
ion
of m
ixed
nu
mbe
rs
•
Frac
tions
of w
hole
num
bers
whi
ch
resu
lt in
who
le n
umbe
rs
•
Rec
ogni
ze, d
escr
ibe
and
use
the
equi
vale
nce
of d
ivis
ion
and
fract
ions
So
lvin
g pr
oble
ms
•
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g co
mm
on fr
actio
ns, i
nclu
ding
gr
oupi
ng a
nd s
harin
g Eq
uiva
lent
form
s:
Rec
ogni
ze a
nd u
se e
quiv
alen
t for
ms
of
com
mon
frac
tions
(fra
ctio
ns in
whi
ch o
ne
deno
min
ator
is a
mul
tiple
of a
noth
er)
Des
crib
ing
and
orde
ring
frac
tions
: •
Com
pare
and
ord
er c
omm
on
fract
ions
, inc
ludi
ng te
nths
and
hu
ndre
dths
C
alcu
latio
ns w
ith fr
actio
ns:
•
Addi
tion
and
subt
ract
ion
of c
omm
on
fract
ions
in w
hich
one
den
omin
ator
is
a m
ultip
le o
f ano
ther
•
Addi
tion
and
subt
ract
ion
of m
ixed
nu
mbe
rs
•
Frac
tions
of w
hole
num
bers
So
lvin
g pr
oble
ms
•
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g co
mm
on fr
actio
ns, i
nclu
ding
gr
oupi
ng a
nd s
harin
g Pe
rcen
tage
s •
Find
per
cent
ages
of w
hole
num
bers
Eq
uiva
lent
form
s:
•
Rec
ogni
ze a
nd u
se e
quiv
alen
t for
ms
of c
omm
on fr
actio
ns w
ith 1
-dig
it or
2-
digi
t den
omin
ator
s (fr
actio
ns in
whi
ch
one
deno
min
ator
is a
mul
tiple
of
anot
her)
•
Rec
ogni
ze e
quiv
alen
ce b
etw
een
147MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
com
mon
frac
tion
and
deci
mal
fra
ctio
n fo
rms
of th
e sa
me
num
ber
•
Rec
ogni
ze e
quiv
alen
ce b
etw
een
com
mon
frac
tion,
dec
imal
frac
tion
and
perc
enta
ge fo
rms
of th
e sa
me
num
ber
Rec
ogni
zing
, ord
erin
g an
d pl
ace
valu
e of
dec
imal
frac
tions
•
Cou
nt fo
rwar
ds a
nd b
ackw
ards
in
deci
mal
frac
tions
to a
t lea
st tw
o de
cim
al p
lace
s •
Com
pare
and
ord
er d
ecim
al fr
actio
ns
to a
t lea
st tw
o de
cim
al p
lace
s •
Plac
e va
lue
of d
igits
to a
t lea
st tw
o de
cim
al p
lace
s C
alcu
latio
ns w
ith d
ecim
al fr
actio
ns
•
Addi
tion
and
subt
ract
ion
of d
ecim
al
fract
ions
with
at l
east
two
deci
mal
pl
aces
•
Mul
tiply
dec
imal
frac
tions
by
10 a
nd
100
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
in c
onte
xt in
volv
ing
deci
mal
frac
tions
C
alcu
latio
ns
•
Find
per
cent
ages
of w
hole
num
bers
. SU
GG
ESTE
D
MET
HO
DO
LOG
Y R
efer
to th
e Le
sson
pla
ns in
Ter
m 2
148 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
In G
rade
4 th
is is
revi
sion
and
con
solid
atio
n of
the
conc
epts
dev
elop
ed in
Ter
m 3
. (Se
e Te
rm 3
not
es)
In T
erm
4 le
ngth
, cap
acity
and
mas
s ca
n be
use
d as
con
text
s fo
r fra
ctio
ns.
Teac
hing
frac
tions
in d
iagr
am fo
rms
shou
ld in
clud
e: re
gion
mod
els
, len
gth
mod
els
(incl
udin
g nu
mbe
r lin
es) a
nd s
et m
odel
s.
Lear
ners
sho
uld
solv
e pr
oble
ms
as w
ell a
s w
ork
with
app
arat
us to
und
erst
and
the
rela
tions
hip
betw
een
fract
ions
and
div
isio
n i.e
. if
you
shar
e 1
amon
gst 3
lear
ners
you
will
be m
akin
g th
irds.
Le
arne
rs m
ust a
ble
to n
ame
fract
ions
. Ter
min
olog
y lik
e “3
ove
r 4” s
houl
d be
avo
ided
as
it te
nds
to e
ncou
rage
lear
ners
to th
ink
abou
t eac
h fra
ctio
n as
two
diffe
rent
num
bers
, rat
her t
han
3 4 bei
ng a
num
ber w
hich
is g
reat
er 1 2 t
han
but l
ess
than
1.
Whe
n na
min
g fra
ctio
n pa
rts it
is u
sefu
l for
lear
ners
to ra
ther
use
the
form
“3 q
uarte
rs”.
Lear
ners
sho
uld,
thro
ugh
wor
k w
ith a
ppar
atus
, dia
gram
s an
d so
lvin
g pr
oble
ms,
lear
n th
e ne
w fr
actio
ns th
at th
ey w
ill de
al w
ith in
G
rade
4
Teac
h fr
actio
ns a
s eq
ual p
arts
of a
who
le
Exam
ple
1 •
Div
ide
a ba
nana
une
venl
y an
d as
k tw
o le
arne
rs w
heth
er th
ey w
ould
be
satis
fied
with
this
div
isio
n. W
hy n
ot?
• Ex
plai
n th
at fr
actio
ns a
re fo
rmed
with
the
divi
ding
of a
who
le in
to E
QU
AL P
ARTS
. Ex
ampl
e 2
Giv
e di
ffere
nt m
athe
mat
ical
sha
pes
to le
arne
rs –
circ
les
/ rec
tang
les
/ squ
ares
/ et
c.
• W
ork
prac
tical
ly –
div
ide
one
(circ
le) e
qual
ly b
etw
een
2 –
then
4 –
then
8 le
arne
rs
• Ex
plai
n w
hat w
e ca
ll th
ese
fract
ions
and
wha
t the
not
atio
n lo
oks
like
1 2 ; 1 4 (
at fi
rst o
nly)
Ex
ampl
e 3
Div
ide
a ch
ocol
ate
(rect
angl
e) e
qual
ly b
etw
een
3 –
then
6 le
arne
rs.
Exam
ple
4 D
ivid
e a
cake
(squ
are)
equ
ally
bet
wee
n 5
– th
en 1
0 le
arne
rs.
Expl
ain
the
nota
tion
ever
y tim
e in
the
abov
e ex
ampl
es.
A w
ritte
n or
ora
l exe
rcis
e ca
n be
don
e at
this
poi
nt. T
he fo
llow
ing
can
be u
sed:
Th
e te
ache
r sho
uld
take
the
lead
and
ask
que
stio
ns. A
sk th
e le
arne
rs to
writ
e th
e fra
ctio
n no
tatio
n on
the
boar
d fo
r the
who
le
clas
s to
see
.
149MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Addi
tion
of fr
actio
ns:
•
Wor
k w
ith c
oncr
ete
obje
cts:
•
Wor
k w
ith d
iagr
ams.
Sha
de o
ne p
art i
n on
e co
lour
. Sha
de a
noth
er p
art i
n a
diffe
rent
col
our.
Whi
ch fr
actio
n is
sha
ded
in
tota
l?
•
Wor
k w
ith fr
actio
n w
all:
(Sta
rt w
ith s
impl
e fra
ctio
ns)
Star
t with
the
sam
e de
nom
inat
or, e
.g.,
1 4 + 1 4
If le
arne
rs c
an d
o th
e ad
ditio
n us
ing
conc
rete
exa
mpl
es, t
hey
can
then
pro
gres
s to
writ
ing
the
fract
ion
nota
tion
belo
w th
e co
ncre
te e
xam
ple.
F
ollo
w th
ese
step
s, e
.g.
Step
1: M
ake
sure
the
botto
m n
umbe
rs (t
he d
enom
inat
ors)
are
the
sam
e St
ep 2
: Add
the
top
num
bers
(the
num
erat
ors)
. Put
the
answ
er o
ver t
he s
ame
deno
min
ator
as
in s
tep
1 St
ep 3
: Sim
plify
the
fract
ion
(if n
eede
d).
DEC
IMAL
S
Impo
rtan
t: R
efer
to th
e Le
sson
Pla
ns o
n D
ecim
al F
ract
ions
in T
erm
2
Con
vert
from
frac
tions
to d
ecim
al fr
actio
ns a
nd to
per
cent
ages
. Onl
y ta
ught
in G
rade
6.
PER
CEN
TAG
ES
Perc
enta
ges
are
a ne
w to
pic
for G
rade
6 le
arne
rs.
Lear
ners
hav
e al
read
y w
orke
d w
ith t
enth
s an
d hu
ndre
dths
in
com
mon
fra
ctio
n fo
rm.
They
sho
uld
star
t by
rew
ritin
g an
d co
nver
ting
tent
hs a
nd h
undr
edth
s in
com
mon
frac
tion
form
to p
erce
ntag
es. W
here
den
omin
ator
s of
oth
er fr
actio
ns a
re fa
ctor
s of
10,
e.g
., 2,
5 o
r fac
tors
of 1
00 e
.g. 2
, 4, 5
, 20,
25,
50
lear
ners
can
con
vert
thes
e to
hun
dred
ths
usin
g w
hat t
hey
know
abo
ut
equi
vale
nce.
Eq
uiva
lenc
e be
twee
n co
mm
on fr
actio
ns a
nd p
erce
ntag
e Le
arne
rs a
re n
ot e
xpec
ted
to b
e ab
le to
con
vert
any
com
mon
frac
tion
into
its
perc
enta
ge fo
rm, m
erel
y to
see
the
rela
tions
hip
betw
een
tent
hs a
nd h
undr
edth
s in
thei
r per
cent
age
form
. Lea
rner
s sh
ould
be
able
to c
onve
rt an
y de
cim
al fr
actio
n in
tent
hs o
r hu
ndre
dths
into
a p
erce
ntag
e.
150 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Cal
cula
tions
Le
arne
rs s
houl
d be
abl
e to
find
per
cent
ages
of w
hole
num
ber,s
e.g
., W
hat i
s 25
% o
f R30
0? H
ere
lear
ners
use
wha
t the
y kn
ow
abou
t bot
h co
nver
ting
betw
een
perc
enta
ge a
nd c
omm
on fr
actio
n fo
rm a
nd a
lso
wha
t the
y kn
ow a
bout
find
ing
fract
ions
of w
hole
nu
mbe
rs e
.g. 2
5% o
f R30
= 1 4
of R
300
= R
75.
LTSM
R
esou
rces
N
umbe
r lin
es: S
truct
ured
-, s
emi-
stru
ctur
ed -
, uns
truct
ured
num
ber l
ines
; Cou
nter
s, P
ictu
res,
arra
ys/ d
iagr
ams,
frac
tion
wal
ls,
fract
ion
circ
les,
diff
eren
t mod
els
of fr
actio
ns, f
ract
ion
strip
s,
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
W
B 1
pp.
34
– 39
Act
iviti
es 9
8 - 1
08
WB
2 p
p. 1
28 –
138
Act
iviti
es 1
18 -
123
WB
2 p
p. 1
16 –
132
Ac
tiviti
es 1
12 -
118
WB
2 p
p 13
6 –
148
Activ
ities
115
-120
a&b
DB
E Te
xtbo
ok re
fere
nce
Term
3: U
nit 1
: Com
mon
Fra
ctio
ns, p
. 21
1
Term
3: U
nit 1
: Com
mon
Fra
ctio
ns, p
. 19
9
Term
4: U
nit 3
: Com
mon
Fra
ctio
ns, p
. 30
6 Te
rm 2
: Uni
t 7: D
ecim
als,
p. 1
77
Term
3: U
nit 8
: Per
cent
ages
, p. 2
62
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
Test
151MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LESS
ON
PLA
NS:
TER
M 4
152 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
MU
LTI G
RAD
E LE
SSO
N P
LAN
1
TER
M 4
EDU
CAT
OR
: ……
……
……
……
……
DAT
E: fr
om
……
…to
……
.
T
ime:
3 H
OU
RS
GR
ADE
4 C
APS
p.10
4 (m
etho
dolo
gy e
xpla
ined
on
pp.
37
- 38)
5 C
APS
p.19
4 (m
etho
dolo
gy e
xpla
ined
on
pp.
125
-126
)
6 C
APS
p. 2
76 (m
etho
dolo
gy e
xpla
ined
on
pp.
215
– 2
16)
TOPI
C
Who
le n
umbe
rs
Con
cept
s, S
kills
and
kn
owle
dge
C
ount
forw
ards
and
bac
kwar
ds in
2s,
3s
, 5s,
10s
, 25s
, 50s
, 100
s be
twee
n 0
and
at le
ast 1
0 00
0
O
rder
, com
pare
and
repr
esen
t
nu
mbe
rs to
at l
east
4 d
igit
num
bers
.
Rep
rese
nt o
dd a
nd e
ven
num
bers
to
at le
ast 1
000
Rec
ogni
ze th
e pl
ace
valu
e of
dig
its in
w
hole
num
bers
to a
t lea
st 4
-dig
it nu
mbe
rs
R
ound
off
to th
e ne
ares
t 10,
100
, 10
00.
C
ount
forw
ards
and
bac
kwar
ds in
w
hole
num
ber i
nter
vals
up
to a
t lea
st
10 0
00
O
rder
, com
pare
and
repr
esen
t nu
mbe
rs to
at l
east
6-d
igit
num
bers
Rep
rese
nt o
dd a
nd e
ven
num
bers
to
at le
ast 1
000
.
Rec
ogni
ze th
e pl
ace
valu
e of
dig
its in
w
hole
num
bers
to a
t lea
st 6
dig
it nu
mbe
rs.
R
ound
off
to th
e ne
ares
t 5, 1
0, 1
00 ,
1 00
0 an
d 10
000
C
ount
forw
ards
and
bac
kwar
ds in
w
hole
num
ber i
nter
vals
up
to a
t lea
st
10 0
00
O
rder
, com
pare
and
repr
esen
t nu
mbe
rs to
at l
east
9-d
igit
num
bers
Rep
rese
nt p
rime
num
bers
to a
t lea
st
100
R
ecog
nizi
ng th
e pl
ace
valu
e of
dig
its
in w
hole
num
bers
to a
t lea
st 9
-dig
it nu
mbe
rs
R
ound
off
to th
e ne
ares
t 5, 1
0, 1
00,
1 00
0, 1
0 00
0, 1
00 0
00, a
nd
1 00
0 00
0 SU
GG
ESTE
D
MET
HO
DO
LOG
Y R
efer
bac
k to
Ter
m 1
Ex
plai
n fr
om k
now
n (lo
w n
umbe
r ran
ge) t
o un
know
n (h
ighe
r ran
ge o
f num
bers
); w
ork
with
con
cret
e LT
SM
Cou
ntin
g, o
rder
ing,
com
parin
g, re
pres
entin
g of
dig
its
Not
e: A
ccor
ding
to C
APS
num
ber r
ange
per
gra
de p
er te
rm a
s in
con
tent
cla
rific
atio
n
R
ead,
say
and
writ
e up
to a
t lea
st 4
-dig
it nu
mbe
rs (G
rade
4) ,
6-d
igit
(Gra
de 5
) and
9-d
igit
(Gra
de 6
)
153MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
(Lea
rner
s ca
n w
rite
num
bers
with
fing
ers
in th
e ai
r whi
le th
ey a
re re
adin
g / s
ayin
g th
e w
ords
.) e.
g. O
ne h
undr
ed a
nd
twen
ty-n
ine
C
onve
rt fro
m w
ords
to n
umbe
rs a
nd n
umbe
rs to
wor
ds
Ar
rang
e th
e nu
mbe
rs b
elow
from
the
smal
lest
to th
e bi
gges
t:
Exam
ple:
10
111
; 1 1
01; 1
110
; 1 0
11
M
ake
the
bigg
est/s
mal
lest
num
ber y
ou c
an w
ith th
ese
digi
ts: 3
, 2, 5
, 4, 9
. O
dd a
nd e
ven
num
bers
: Ex
plor
e pr
actic
ally
by
wor
king
with
num
bers
to b
e ab
le to
des
crib
e th
e pa
ttern
e.g
. all
odd
num
bers
end
in 1
, 3, 5
, 7 o
r 9
ther
efor
e 2
201
, 2 2
03, 2
205
, 2 2
07, 2
209
are
all
odd
num
bers
.
Prim
e nu
mbe
rs fo
r Gra
de 6
Id
entif
y pr
ime
num
bers
and
com
posi
te n
umbe
rs u
p to
at l
east
100
M
ultip
les:
I c
ount
in m
ultip
les
of 3
, up
to 1
00.
W
ill I c
ount
the
num
ber 1
2? W
hy?
W
ill I c
ount
the
num
ber 4
2? W
hy?
Plac
e va
lue:
Dis
tingu
ish
betw
een
the
num
eric
val
ue a
nd th
e pl
ace
valu
e.
U
se p
lace
val
ue c
ards
to b
uild
up
and
brea
k do
wn
num
bers
R
ound
ing
off:
R
ound
off
as in
dica
ted
per g
rade
(use
bas
e te
n bl
ocks
, num
ber l
ines
, pla
ce v
alue
tabl
e)
154 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
U
se c
once
pt o
f rou
ndin
g of
f, in
pro
blem
sol
ving
con
text
LTSM
R
esou
rces
N
umbe
r lin
es: 0
– 1
20, S
truct
ured
-, s
emi-
stru
ctur
ed -
, uns
truct
ured
num
ber l
ines
; Cou
nter
s, P
ictu
res,
arra
ys/ d
iagr
ams,
Fla
sh
card
s, B
ase
10 b
lock
s, 1
00 c
harts
, mul
tiplic
atio
n ta
ble
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
WB
2 p
. 100
Act
iviti
es 1
05
WB
2 p
. 32
– 38
; p. 9
6 Ac
tiviti
es 7
9 - 8
1; 1
05)
WB
2 p
p. 1
08 –
110
Ac
tiviti
es 1
05a&
b
DB
E Te
xtbo
ok re
fere
nce
Term
4: U
nit 1
: Who
le N
umbe
rs, p
. 291
Term
4: U
nit 1
: Who
le N
umbe
rs, p
. 28
3
Term
4: U
nit 1
: Who
le N
umbe
rs, p
. 29
7
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
test
155MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
M
ULT
I GR
ADE
LESS
ON
PLA
N 2
TE
RM
4
EDU
CAT
OR
: ……
……
……
……
……
DAT
E : f
rom
…
……
to …
……
T
ime:
6 H
OU
RS
GR
ADE
4 C
APS
p.93
(met
hodo
logy
exp
lain
ed o
n pp
. 43
- 45)
5 C
APS
pp 1
82- 1
83 (m
etho
dolo
gy
expl
aine
d on
pp.
132
– 1
35)
6 C
APS
pp.2
62-2
63 (m
etho
dolo
gy
expl
aine
d on
pp.
222
– 2
25)
TOPI
C
Addi
tion
and
subt
ract
ion
of w
hole
num
bers
C
once
pts,
Ski
lls a
nd
know
ledg
e N
umbe
r ran
ge fo
r cal
cula
tions
Ad
ditio
n an
d su
btra
ctio
n of
who
le
num
bers
of a
t lea
st 4
dig
its
Cal
cula
tion
tech
niqu
es
Use
a ra
nge
of te
chni
ques
to p
erfo
rm
and
chec
k w
ritte
n an
d m
enta
l ca
lcul
atio
ns o
f who
le n
umbe
rs in
clud
ing
es
timat
ion
bu
ildin
g up
and
bre
akin
g do
wn
num
bers
roun
ding
off
and
com
pens
atin
g
doub
ling
and
halv
ing
us
ing
a nu
mbe
r lin
e
usin
g ad
ditio
n an
d su
btra
ctio
n as
in
vers
e op
erat
ions
Num
ber r
ange
for c
alcu
latio
ns
• Add
ition
and
sub
tract
ion
of w
hole
nu
mbe
rs o
f at l
east
5 d
igits
Cal
cula
tion
tech
niqu
es
Usi
ng a
rang
e of
tech
niqu
es to
per
form
an
d ch
eck
writ
ten
and
men
tal
calc
ulat
ions
with
who
le n
umbe
rs
incl
udin
g
estim
atio
n
addi
ng a
nd s
ubtra
ctin
g in
col
umns
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
us
ing
a nu
mbe
r lin
e
roun
ding
off
and
com
pens
atin
g
• do
ublin
g an
d ha
lvin
g
usin
g ad
ditio
n an
d su
btra
ctio
n as
in
vers
e op
erat
ions
Num
ber
rang
e fo
r cal
cula
tions
•
Addi
tion
and
subt
ract
ion
of w
hole
nu
mbe
rs w
ith a
t lea
st 6
-dig
it nu
mbe
r •
Mul
tiple
ope
ratio
ns o
n w
hole
nu
mbe
rs w
ith o
r with
out
brac
kets
C
alcu
latio
n te
chni
ques
U
sing
a ra
nge
of te
chni
ques
to
perfo
rm a
nd c
heck
writ
ten
and
men
tal
calc
ulat
ions
with
who
le n
umbe
rs
incl
udin
g
estim
atio
n
addi
ng, s
ubtra
ctin
g in
col
umns
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
ro
undi
ng o
ff an
d co
mpe
nsat
ing
us
ing
addi
tion
and
subt
ract
ion
as
inve
rse
oper
atio
ns
us
ing
a ca
lcul
ator
156 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Prop
ertie
s of
who
le n
umbe
rs
Rec
ogni
ze a
nd u
se th
e co
mm
utat
ive
and
asso
ciat
ive
prop
ertie
s w
ith
who
le n
umbe
rs
Solv
ing
prob
lem
s So
lve
prob
lem
s in
con
text
s in
volv
ing
who
le n
umbe
rs, i
nclu
ding
fina
ncia
l co
ntex
ts
Prop
ertie
s of
who
le n
umbe
rs
R
ecog
nize
and
use
the
com
mut
ativ
e,
asso
ciat
ive
and
dist
ribut
ive
prop
ertie
s w
ith w
hole
num
bers
-
0 in
term
s of
its
addi
tive
prop
erty
-
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s So
lve
prob
lem
s in
volv
ing
who
le
num
bers
, inc
ludi
ng:
- fin
anci
al c
onte
xts
- m
easu
rem
ent c
onte
xts
Prop
ertie
s of
who
le n
umbe
rs
R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
-
0 in
term
s of
its
addi
tive
prop
erty
-
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs a
nd d
ecim
al fr
actio
ns,
incl
udin
g -
finan
cial
con
text
s -
mea
sure
men
t con
text
s
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(ra
tio)
LTSM
R
esou
rces
N
umbe
r lin
es: 0
– 1
20, S
truct
ured
-, s
emi-
stru
ctur
ed -
, uns
truct
ured
num
ber l
ines
; Cou
nter
s, P
ictu
res,
arra
ys/ d
iagr
ams,
Fla
sh
card
s, B
ase
10 b
lock
s, 1
00 c
harts
, mul
tiplic
atio
n ta
ble
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
W
B 2
pp.
102
– 1
10; p
.176
Ac
tiviti
es 1
07 –
110
; 142
W
B 2
pp.
98
– 10
8; p
. 186
Ac
tiviti
es
106a
&b -
110;
142
WB
2 p
p. 2
0 –
44
Activ
ities
71a
&b -
78
DB
E Te
xtbo
ok re
fere
nce
Term
3: U
nit 9
: Who
le N
umbe
rs: A
dditi
on
and
subt
ract
ion,
p. 2
68
Term
4: U
nit 2
: Who
le N
umbe
rs: A
dditi
on
and
subt
ract
ion,
p. 2
93
Term
4: U
nit 1
1: W
hole
Num
bers
: Add
ition
an
d su
btra
ctio
n, p
. 343
Term
4: U
nit 2
: Who
le N
umbe
rs:
Addi
tion
and
subt
ract
ion,
p. 2
86
Term
3: U
nit 3
: Who
le N
umbe
rs:
Addi
tion
and
subt
ract
ion,
p. 2
24
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t
157MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
– Te
st
158 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
M
ULT
I GR
ADE
LESS
ON
PLA
N 3
TE
RM
4
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to
…
T
ime:
3 H
OU
RS
GR
ADE
4 M
ultip
licat
ion
- CAP
S pp
.101
5 M
ultip
licat
ion
- CAP
S p.
192
(Ref
er to
p.
166
for m
etho
dolo
gy.)
6 M
ultip
licat
ion
- CAP
S p.
241-
243
TOPI
C
Mul
tiplic
atio
n of
who
le n
umbe
rs
Con
cept
s, S
kills
and
kn
owle
dge
Num
ber
rang
e fo
r cal
cula
tions
•
Mul
tiplic
atio
n of
at l
east
who
le 2
-di
git b
y 2-
digi
t num
bers
C
alcu
latio
n te
chni
ques
U
se a
rang
e of
tech
niqu
es to
per
form
an
d ch
eck
writ
ten
and
men
tal
Num
ber
rang
e fo
r cal
cula
tions
•
Mul
tiplic
atio
n of
at l
east
who
le 3
-di
git b
y 2-
digi
t num
bers
C
alcu
latio
n te
chni
ques
U
sing
a ra
nge
of te
chni
ques
to
perfo
rm a
nd c
heck
writ
ten
and
Num
ber
rang
e fo
r cou
ntin
g,
orde
ring,
com
parin
g an
d re
pres
entin
g, a
nd p
lace
val
ue o
f di
gits
•
Ord
er, c
ompa
re a
nd re
pres
ent
num
bers
to a
t lea
st 9
-dig
it nu
mbe
rs
• R
epre
sent
prim
e nu
mbe
rs to
at
leas
t 100
•
Rec
ogni
ze
the
plac
e va
lue
of
digi
ts i
n w
hole
num
bers
to
at
leas
t 9-d
igit
num
bers
•
Rou
nd o
ff to
the
near
est 5
, 10,
10
0 or
1 0
00
Num
ber
rang
e fo
r cal
cula
tions
•
Mul
tiplic
atio
n of
at l
east
who
le 4
-di
git b
y 3-
digi
t num
bers
•
Mul
tiple
ope
ratio
ns o
n w
hole
nu
mbe
rs w
ith o
r with
out
brac
kets
C
alcu
latio
n te
chni
ques
incl
ude
• es
timat
ion
• m
ultip
lyin
g in
col
umns
159MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
calc
ulat
ions
with
who
le n
umbe
rs
incl
udin
g •
estim
atio
n •
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
• ro
undi
ng o
ff an
d co
mpe
nsat
ing
• do
ublin
g an
d ha
lvin
g N
umbe
r ra
nge
for m
ultip
les
and
fact
ors
Mul
tiple
s of
1-d
igit
num
bers
to a
t lea
st
100
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e; a
nd
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g w
hole
num
bers
, in
clud
ing
finan
cial
con
text
s
men
tal c
alcu
latio
ns o
f who
le
num
bers
incl
udin
g:
• es
timat
ion
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
usin
g a
num
ber l
ine
• ro
undi
ng o
ff an
d co
mpe
nsat
ing
• do
ublin
g an
d ha
lvin
g N
umbe
r ra
nge
for m
ultip
les
and
fact
ors
• M
ultip
les
of 2
-dig
its w
hole
nu
mbe
rs to
at l
east
100
•
Fact
ors
of 2
-dig
it w
hole
num
bers
to
at l
east
100
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e an
d di
strib
utiv
e pr
oper
ties
with
who
le
num
bers
o
0 in
term
s of
its
addi
tive
prop
erty
o
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
num
bers
, inc
ludi
ng
o fin
anci
al
cont
exts
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
roun
ding
off
and
com
pens
atin
g •
usin
g a
calc
ulat
or
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
2-d
igit
and
3-di
git
num
bers
•
Fact
ors
of 2
-dig
it an
d 3-
digi
t who
le
num
bers
•
Prim
e fa
ctor
s of
num
bers
to a
t le
ast 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
w
hole
num
bers
o 0
in te
rms
of it
s ad
ditiv
e pr
oper
ty
o 1
in te
rms
of it
s m
ultip
licat
ive
prop
erty
So
lvin
g pr
oble
ms
• So
lve
prob
lem
s in
volv
ing
who
le n
umbe
rs a
nd d
ecim
al
fract
ions
, inc
ludi
ng
o fin
anci
al c
onte
xts
160 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• So
lve
prob
lem
s in
volv
ing
who
le n
umbe
rs, i
nclu
ding
o
com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(ra
tio)
o co
mpa
ring
two
quan
titie
s of
di
ffere
nt k
inds
(rat
e)
o m
easu
rem
ent
cont
exts
•
Solv
e pr
oble
ms
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
o
com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(ra
tio)
o m
easu
rem
ent c
onte
xts
• So
lve
prob
lem
s in
volv
ing
who
le n
umbe
rs, i
nclu
ding
o
com
parin
g tw
o or
mor
e qu
antit
ies
o of
the
sam
e ki
nd (r
atio
) co
mpa
ring
two
quan
titie
s of
di
ffere
nt k
inds
(rat
e)
Topi
c
Div
isio
n of
who
le n
umbe
rs
N
umbe
r ra
nge
for c
alcu
latio
ns
• D
ivis
ion
of a
t lea
st w
hole
3-d
igit
by
1-di
git n
umbe
rs.
Cal
cula
tion
tech
niqu
es
• U
se a
rang
e of
tech
niqu
es to
pe
rform
and
che
ck w
ritte
n an
d m
enta
l cal
cula
tions
of w
hole
nu
mbe
rs in
clud
ing
• es
timat
ion
• bu
ildin
g u
p a
nd
brea
king
do
wn
num
bers
•
roun
ding
off
and
com
pens
atin
g •
doub
ling
and
halv
ing
• us
ing
mul
tiplic
atio
n an
d di
visi
on a
s in
vers
e op
erat
ions
Num
ber
rang
e fo
r cal
cula
tions
D
ivis
ion
of a
t lea
st w
hole
3-d
igit
by
2-di
git n
umbe
rs
Cal
cula
tion
tech
niqu
es
Use
a ra
nge
of te
chni
ques
to
perfo
rm a
nd c
heck
writ
ten
and
men
tal c
alcu
latio
ns w
ith w
hole
nu
mbe
rs in
clud
ing
• es
timat
ion
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
•
usin
g m
ultip
licat
ion
and
divi
sion
as
inve
rse
oper
atio
ns
Num
ber
rang
e fo
r cal
cula
tions
•
Div
isio
n of
at l
east
who
le 4
-dig
it by
3-
digi
t num
bers
•
mul
tiple
ope
ratio
ns o
n w
hole
nu
mbe
rs w
ith o
r with
out
brac
kets
Cal
cula
tion
tech
niqu
es
• es
timat
ion
• us
ing
the
reci
proc
al re
latio
nshi
p be
twee
n m
ultip
licat
ion
and
divi
sion
•
long
div
isio
n •
build
ing
up a
nd b
reak
ing
dow
n nu
mbe
rs
• ro
undi
ng o
ff an
d co
mpe
nsat
ing
• us
ing
a ca
lcul
ator
161MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
1-d
igit
num
bers
to
at le
ast 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e; a
nd
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
So
lvin
g pr
oble
ms
• So
lve
prob
lem
s in
con
text
s in
volv
ing
who
le n
umbe
rs
o fin
anci
al c
onte
xts
o m
easu
rem
ent c
onte
xts
Num
ber
rang
e fo
r cou
ntin
g,
orde
ring
and
repr
esen
ting,
and
pl
ace
valu
e of
dig
its
• Rec
ogni
ze th
e pl
ace
valu
e of
dig
its
in w
hole
num
bers
to
at l
east
6-
digi
t num
bers
. •
Rou
nd o
ff to
the
near
est 1
0, 1
00,
1 00
0 N
umbe
r ra
nge
for m
ultip
les
and
fact
ors
• M
ultip
les
of 2
-dig
it nu
mbe
rs to
at
leas
t 100
•
Fact
ors
of 2
-dig
it w
hole
nu
mbe
rs to
at l
east
100
M
ultip
licat
ion
fact
s •
Uni
ts b
y m
ultip
les
of 1
0 •
Uni
ts b
y m
ultip
les
of 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e; a
nd
dist
ribut
ive
prop
ertie
s of
who
le
num
bers
o
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
in c
onte
xts
invo
lvin
g w
hole
num
bers
, in
clud
ing
finan
cial
con
text
s
Num
ber
rang
e fo
r mul
tiple
s an
d fa
ctor
s •
Mul
tiple
s of
2-d
igit
and
3-di
git
num
bers
•
Fact
ors
of 2
-dig
it an
d 3-
digi
t who
le
num
bers
•
Prim
e fa
ctor
s of
num
bers
up
to a
t le
ast 1
00
Prop
ertie
s of
who
le n
umbe
rs
• R
ecog
nize
and
use
the
com
mut
ativ
e; a
ssoc
iativ
e;
dist
ribut
ive
prop
ertie
s of
w
hole
num
bers
o
0 in
term
s of
its
addi
tive
prop
erty
o
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty
Solv
ing
prob
lem
s •
Solv
e pr
oble
ms
invo
lvin
g w
hole
num
bers
and
dec
imal
fra
ctio
ns, i
nclu
ding
o
finan
cial
con
text
s
162 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
• So
lve
prob
lem
s in
volv
ing
who
le n
umbe
rs, i
nclu
ding
o
grou
ping
and
equ
al s
harin
g
with
rem
aind
ers
o co
mpa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd
(ratio
) o
com
parin
g tw
o qu
antit
ies
of
diffe
rent
kin
ds (r
ate)
•
Solv
e pr
oble
ms
invo
lvin
g w
hole
num
bers
, inc
ludi
ng
o co
mpa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd
(ratio
) o
com
parin
g tw
o qu
antit
ies
of
diffe
rent
kin
ds (r
ate)
o
grou
ping
and
equ
al s
harin
g w
ith
rem
aind
ers
o m
easu
rem
ent c
onte
xts
• So
lve
prob
lem
s in
volv
ing
who
le n
umbe
rs, i
nclu
ding
o
com
parin
g tw
o or
mor
e qu
antit
ies
of th
e sa
me
kind
(ra
tio)
o co
mpa
ring
two
quan
titie
s of
di
ffere
nt k
inds
(rat
e)
o gr
oupi
ng a
nd e
qual
sha
ring
with
rem
aind
ers
SUG
GES
TED
M
ETH
OD
OLO
GY
Ref
er to
Ter
m1
and
Term
2 le
sson
Pla
ns
Expl
ain
from
kno
wn
(low
num
ber r
ange
); w
ork
with
con
cret
e LT
SM.
Lear
ners
sho
uld
do c
onte
xt fr
ee c
alcu
latio
ns a
nd s
olve
pro
blem
s in
con
text
s
Lear
ners
sho
uld
cont
inue
to
• ch
eck
thei
r sol
utio
ns b
y us
ing
mul
tiplic
atio
n w
hen
doin
g di
visi
on a
nd v
ice
vers
a •
judg
e th
e re
ason
able
ness
of t
heir
solu
tions
, by
estim
atin
g be
fore
cal
cula
ting
Mul
tiplic
atio
n (K
now
tim
es ta
bles
– p
ract
ice
regu
larly
up
to 1
0 x
10 fo
r Gra
des
4 an
d 5
and
12 x
12
for G
rade
6).
Follo
w th
ese
step
s in
teac
hing
mul
tiplic
atio
n:
• So
lve
prob
lem
s in
con
text
. U
nder
stan
d th
at: 8
6 +
86 +
86
is e
quiv
alen
t to
86 x
3 o
r 3 x
86
(repe
ated
add
ition
) •
mul
tiplic
atio
n by
1 le
aves
a n
umbe
r unc
hang
ed e
.g. 5
x 1
= 5
; 99
x 1
= 99
•
mul
tiplic
atio
n of
zer
o re
sults
in z
ero
e.g.
7 x
0 =
0; 3
1 x
0 =
0 U
nder
stan
d th
at m
ultip
licat
ion
is th
e in
vers
e of
div
isio
n (m
ultip
licat
ion
reve
rses
div
isio
n an
d vi
ce v
ersa
) and
use
this
to c
heck
re
sults
. e.g
. 15
x 35
= 5
25
525
÷ 2
5 =
15 o
r 525
÷ 1
5 =
25
Not
e: In
Gra
de 5
Ter
m 3
lear
ners
are
intro
duce
d to
col
umn
met
hods
of m
ultip
licat
ion
163MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
DIV
ISIO
N
Men
tal d
ivis
ion
: Tur
ning
the
tabl
es –
pra
ctic
e re
gula
rly (e
.g. 5
x 8
= 4
0 4
0 ÷
8 =
5 / 4
0 ÷
5 =
8) (A
lso
calle
d in
vers
e op
erat
ion
or re
cipr
ocal
ope
ratio
n.)
Mak
e le
arne
rs a
war
e th
at d
ivis
ion
is n
on-c
omm
utat
ive
i.e. 8
1 ÷
9 is
not
the
sam
e as
9 ÷
81.
W
ith th
e co
ncep
t gra
sped
, tea
chin
g di
visi
on w
ill be
com
e m
ore
abou
t gui
ded
prac
tice
to h
elp
the
lear
ners
to b
ecom
e fa
milia
r with
th
e di
visi
on o
pera
tion
(alth
ough
it’s
real
ly g
oing
to b
e a
diffe
rent
type
of m
ultip
licat
ion
prac
tice.
) Sta
rt by
pra
ctis
ing
divi
sion
by
1, 2
an
d 3
and
then
gra
dual
ly m
ove
up to
9.
Not
e: G
rade
4 a
nd 5
focu
s is
on
usin
g th
e cl
ue b
oard
– m
etho
d O
NLY
! Gra
de 6
is th
e in
trodu
ctio
n of
long
div
isio
n in
the
third
te
rm
LTSM
R
esou
rces
N
umbe
r lin
es: 0
– 1
20, S
truct
ured
-, s
emi-
stru
ctur
ed -
, uns
truct
ured
num
ber l
ines
; Cou
nter
s, P
ictu
res,
arra
ys/ d
iagr
ams,
Fla
sh
card
s, B
ase
10 b
lock
s, 1
00 c
harts
, mul
tiplic
atio
n ta
ble
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
W
B 2
pp.
78
– 90
Ac
tiviti
es 9
8a-c
, 99a
&b; 1
00-1
01
pp. 1
42 –
144
Ac
tiviti
es 1
24 -
125
WB
2 p
p. 9
0 –
94
Activ
ities
103
a&b;
104
; pp.
138
– 1
52
Activ
ities
120
- 126
a&b
WB
2 p
p. 1
12 –
130
Ac
tiviti
es
106a
&b-1
12a&
b pp
.164
– 1
74
Activ
ities
; 126
-129
a&b
DB
E Te
xtbo
ok re
fere
nce
Term
3: U
nit 1
0: W
hole
Num
bers
: M
ultip
licat
ion,
p. 2
75
Term
4: U
nit 6
: Who
le N
umbe
rs:
Div
isio
n, p
. 313
Term
3: U
nit 1
1: W
hole
Num
bers
: M
ultip
licat
ion,
p. 2
69
Term
4: U
nit 5
: Who
le N
umbe
rs:
Div
isio
n, p
. 310
Term
4: U
nit 2
: Who
le N
umbe
rs:
Mul
tiplic
atio
n, p
. 300
Te
rm 4
: Uni
t 7: W
hole
Num
bers
: D
ivis
ion,
p. 3
36
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
Test
164 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
M
ULT
I GR
ADE
LESS
ON
PLA
N 4
TE
RM
4
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to …
……
T
ime:
6 H
OU
RS
GR
ADE
4 C
APS
pp. 1
11
5 C
APS
pp. 1
98
6 C
APS
pp. 2
81
TOPI
C
Prop
ertie
s of
3-D
sha
pes
Con
cept
s, S
kills
and
kn
owle
dge
Prop
ertie
s of
3-D
obj
ects
R
ange
of O
bjec
ts:
re
ctan
gula
r pris
ms,
sphe
res
cy
linde
rs
py
ram
ids
Cha
ract
eris
tics
of o
bjec
ts
sh
apes
of f
aces
flat a
nd c
urve
d su
rface
s Fu
rthe
r act
iviti
es
M
ake
3-D
mod
els
usin
g cu
t out
po
lygo
ns
Prop
ertie
s of
3-D
obj
ects
R
ange
of O
bjec
ts:
re
ctan
gula
r pris
ms
and
othe
r pr
ism
s
cube
s
cylin
ders
cone
s
pyra
mid
s
sim
ilarit
ies
and
diffe
renc
es
betw
een
cube
s an
d re
ctan
gula
r pr
ism
s C
hara
cter
istic
s of
obj
ects
shap
e of
face
s
num
ber o
f fac
es
fla
t and
cur
ved
surfa
ces
Furt
her a
ctiv
ities
Mak
e 3-
D m
odel
s us
ing
cut o
ut p
olyg
ons
ne
ts
Prop
ertie
s of
3-D
obj
ects
R
ange
of O
bjec
ts:
re
ctan
gula
r pris
ms
cu
bes
te
trahe
dron
s
pyra
mid
s
sim
ilarit
ies
and
diffe
renc
es
betw
een
tetra
hedr
ons
and
othe
r py
ram
ids
Cha
ract
eris
tics
of o
bjec
ts
nu
mbe
r and
sha
pe o
f fac
es
nu
mbe
r of v
ertic
es
nu
mbe
r of e
dges
Fu
rthe
r act
iviti
es
M
ake
3-D
mod
els
usin
g:
dr
inki
ng s
traw
s, to
othp
icks
etc
nets
165MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
SUG
GES
TED
M
ETH
OD
OLO
GY
Ref
er to
Ter
m 2
not
es fo
r rev
isio
n an
d co
nsol
idat
ion.
In T
erm
4 le
arne
rs s
houl
d co
nsol
idat
e w
hat t
hey
lear
nt a
bout
3-D
obj
ects
ear
lier i
n th
e ye
ar. T
his
incl
udes
:
w
orki
ng w
ith a
ll of
the
obje
cts
pres
crib
ed fo
r Gra
de 4
, 5 a
nd 6
.
fo
cusi
ng o
n th
e ki
nd o
f sur
face
and
the
shap
e an
d nu
mbe
r of f
aces
.
bu
ildin
g ob
ject
s us
ing
nets
.
In T
erm
4 le
arne
rs c
an b
uild
ske
leto
n sh
apes
with
stra
ws
or to
othp
icks
. The
y w
ill th
en fo
cus
on th
e ed
ges
and
verti
ces
of th
e
obje
cts.
Thi
s m
eans
that
by
the
end
of th
e ye
ar th
ey w
ill be
abl
e to
des
crib
e 3-
D g
eom
etric
obj
ects
acc
ordi
ng to
the
num
ber
and
shap
e of
face
s an
d th
e nu
mbe
r of e
dges
and
ver
tices
of 3
-D O
bjec
ts. L
earn
ers
need
to w
ork
with
real
obj
ects
. How
ever
,
they
als
o ne
ed to
do
writ
ten
exer
cise
s on
3-D
obj
ects
. Int
erpr
etin
g pi
ctur
es a
bout
3-D
obj
ects
is m
ore
diffi
cult
than
wor
king
with
the
real
obj
ects
. Lea
rner
s sh
ould
pra
ctis
e in
terp
retin
g dr
awin
gs o
f 3-D
obj
ects
. The
y sh
ould
iden
tify
and
nam
e 3-
D
obje
cts
in d
raw
ings
; ide
ntify
eve
ryda
y ob
ject
s th
at lo
ok li
ke g
eom
etric
obj
ects
(e.g
. a m
ilk c
arto
n lo
oks
like
a re
ctan
gula
r
pris
m),
mat
ch n
ets
of o
bjec
ts to
dra
win
g of
obj
ects
, des
crib
e 3-
D o
bjec
ts b
y st
atin
g th
e nu
mbe
r of f
lat a
nd/o
r cur
ved
surfa
ces,
the
num
ber o
f ver
tices
, edg
es, a
nd n
umbe
r and
sha
pe o
f fac
es w
hen
show
n dr
awin
gs o
f 3-D
obj
ects
.
LTSM
R
esou
rces
Va
riety
of 3
D o
bjec
ts fr
om le
arne
r’s c
onte
xt, g
eoso
lids
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
W
B 2
pp.
124
– 1
26
Act
iviti
es 1
16 -
117
WB
1 p
p. 1
50 A
ctiv
ity 5
4 W
B 2
pp.
152
Ac
tivity
122
D
BE
Text
book
refe
renc
e Te
rm 4
: Uni
t 4: P
rope
rtie
s of
thre
e di
men
sion
al o
bjec
ts, p
. 306
Te
rm 4
: Uni
t 3: P
rope
rtie
s of
thre
e di
men
sion
al o
bjec
ts, p
. 292
Te
rm 4
: Uni
t 4: P
rope
rtie
s of
thre
e di
men
sion
al o
bjec
ts, p
. 315
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent –
Te
st
166 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
M
ULT
I GR
ADE
LESS
ON
PLA
N 5
TE
RM
4
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to…
……
.…
Tim
e: 8
HO
UR
S G
RAD
E 4
C
APS
p. 1
14
5 C
APS
p. 2
02
6 C
APS
p. 2
82
TOPI
C
Perim
eter
, Are
a an
d Vo
lum
e C
once
pts,
Ski
lls a
nd
know
ledg
e Pe
rimet
er
Mea
sure
per
imet
er u
sing
rule
rs o
r m
easu
ring
tape
s M
easu
rem
ent o
f are
a Fi
nd a
reas
of r
egul
ar a
nd ir
regu
lar
shap
es b
y co
untin
g sq
uare
s on
grid
s in
or
der t
o de
velo
p an
und
erst
andi
ng o
f sq
uare
uni
ts
Mea
sure
men
t of v
olum
e Fi
nd v
olum
e/ca
paci
ty o
f obj
ects
(by
pack
ing
or fi
lling
them
in o
rder
to d
evel
op
an u
nder
stan
ding
of c
ubic
uni
ts
Perim
eter
M
easu
re p
erim
eter
usi
ng ru
lers
or
mea
surin
g ta
pes
Mea
sure
men
t of a
rea
Find
are
as o
f reg
ular
and
irre
gula
r sh
apes
by
coun
ting
squa
res
on g
rids
in
orde
r to
deve
lop
an u
nder
stan
ding
of
squa
re u
nits
M
easu
rem
ent o
f vol
ume
Find
vol
ume/
capa
city
of o
bjec
ts b
y pa
ckin
g or
fillin
g th
em in
ord
er to
de
velo
p an
und
erst
andi
ng o
f cub
ic u
nits
Perim
eter
M
easu
re p
erim
eter
usi
ng ru
lers
or
mea
surin
g ta
pes
Mea
sure
men
t of a
rea
• C
ontin
ue to
find
are
as o
f reg
ular
and
irr
egul
ar s
hape
s by
cou
ntin
g sq
uare
s on
grid
s •
Dev
elop
an
unde
rsta
ndin
g of
why
th
e ar
ea o
f rec
tang
les
can
be
desc
ribed
as
thei
r len
gth
mul
tiplie
d by
thei
r wid
th
Mea
sure
men
t of v
olum
e •
Con
tinue
to fi
nd v
olum
e/ca
paci
ty o
f ob
ject
s (b
y pa
ckin
g or
fillin
g th
em.
• D
evel
op a
n un
ders
tand
ing
of w
hy
the
volu
me
of re
ctan
gula
r pris
ms
can
be d
escr
ibed
as
thei
r len
gth
mul
tiplie
d by
thei
r wid
th m
ultip
lied
by
thei
r hei
ght
Inve
stig
ate
the:
•
rela
tions
hip
betw
een
perim
eter
and
ar
ea o
f rec
tang
les
and
squa
res
• re
latio
nshi
p be
twee
n su
rface
are
a an
d vo
lum
e of
rect
angu
lar p
rism
s
167MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
SUG
GES
TED
M
ETH
OD
OLO
GY
Wha
t is
capa
city
? W
hat i
s vo
lum
e?
Cap
acity
is th
e am
ount
of s
ubst
ance
that
an
obje
ct c
an h
old
or th
e am
ount
of s
pace
insi
de th
e ob
ject
. Vo
lum
e is
the
amou
nt o
f spa
ce th
at a
n ob
ject
occ
upie
s.
A bo
ttle
can
have
a 1
litre
cap
acity
, but
it m
ay n
ot b
e fil
led
to it
s fu
ll ca
paci
ty, i
t cou
ld fo
r exa
mpl
e, o
nly
cont
ain
a vo
lum
e of
25
0ml.
Con
tent
Area
and
vol
ume
are
only
mea
sure
d in
form
ally
in th
e In
term
edia
te P
hase
. Lea
rner
s ar
e no
t req
uire
d to
kno
w o
r app
ly
form
ulae
for t
he p
erim
eter
, are
a or
vol
ume
of a
ny s
hape
or o
bjec
ts.
In
Gra
de 3
lear
ners
onl
y m
easu
red
perim
eter
info
rmal
ly b
y fin
ding
the
dist
ance
aro
und
two-
dim
ensi
onal
sha
pes
usin
g st
ring.
Lea
rner
s in
Gra
de 3
are
not
requ
ired
to s
tate
or w
rite
how
long
a p
erim
eter
is. T
hey
only
sho
w th
e st
ring
leng
th o
r co
mpa
re d
iffer
ent p
erim
eter
s by
com
parin
g st
ring
leng
ths.
In G
rade
4 le
arne
rs m
easu
re th
e pe
rimet
ers
of s
hape
s an
d sp
aces
with
rule
rs a
nd m
easu
ring
tape
s. T
hey
are
requ
ired
to s
tate
and
reco
rd th
is m
easu
rem
ent i
n st
anda
rd u
nits
: mm
, cm
, m. L
earn
ers
are
also
requ
ired
to w
ork
from
dra
win
gs in
whi
ch s
ide
leng
ths
are
spec
ified
in m
m, c
m, m
, km
. Her
e th
ey
add
the
leng
ths.
In G
rade
4 th
ey w
ill al
so c
ount
the
leng
ths
of th
e pe
rimet
ers
by c
ount
ing
the
num
ber o
f sid
es o
f squ
are
grid
s on
whi
ch s
hape
s ar
e dr
awn.
Her
e le
arne
rs n
eed
to k
now
that
the
diag
onal
dis
tanc
es b
etw
een
corn
ers
of a
grid
squ
are
are
long
er th
an th
e ve
rtica
l or h
oriz
onta
l dis
tanc
es b
etw
een
corn
ers
of a
grid
squ
are.
In G
rade
3 le
arne
rs o
nly
inve
stig
ate
area
s us
ing
tilin
g. In
Gra
de 4
are
a m
easu
rem
ents
con
tinue
to b
e in
form
al, b
ut n
ow
lear
ners
use
bot
h til
ing
and
squa
re g
rids.
Lea
rner
s co
unt h
ow m
any
grid
squ
ares
the
shap
e co
vers
. The
are
a is
sta
ted
in
num
ber o
f grid
squ
ares
. Sha
pes
shou
ld in
clud
e re
gula
r sha
pes,
irre
gula
r sha
pes
and
shap
es w
ith c
urve
d si
des.
Lear
ners
do
not w
ork
with
vol
ume
in G
rade
3. I
n G
rade
4 le
arne
rs c
ount
how
man
y cu
bes
or re
ctan
gula
r pris
ms
are
used
to
fill a
con
tain
er. T
he v
olum
e of
the
cont
aine
r is
stat
ed in
num
ber o
f cub
es o
r rec
tang
ular
pris
ms
such
as
boxe
s or
blo
cks.
Le
arne
rs m
ake
stac
ks w
ith c
ubes
or r
ecta
ngul
ar p
rism
s. T
he v
olum
e of
the
stac
k is
sta
ted
in n
umbe
r of c
ubes
or
rect
angu
lar p
rism
s su
ch a
s bo
xes
or b
lock
s.
In
Gra
de 4
, lea
rner
s in
terp
ret p
ictu
res
of s
tack
s m
ade
of c
ubes
or r
ecta
ngul
ar p
rism
s in
ord
er to
sta
te th
e vo
lum
e in
term
s of
the
num
ber o
f cub
es o
r rec
tang
ular
pris
ms.
The
y in
terp
ret p
ictu
res
of c
onta
iner
s fil
led
with
cub
es o
r rec
tang
ular
pris
ms
in
orde
r to
stat
e th
e vo
lum
e in
term
s of
the
num
ber o
f cub
es o
r rec
tang
ular
pris
ms.
In G
rade
5 a
nd 6
lear
ners
pra
ctis
e an
d co
nsol
idat
e w
hat t
hey
have
lear
ned
abou
t per
imet
er, a
rea
and
volu
me
in G
rade
4.
168 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
In
Gra
de 6
they
sho
uld
inve
stig
ate
why
the
area
of a
rect
angl
e ca
n be
sta
ted
as it
s le
ngth
mul
tiplie
d by
its
wid
th. T
hey
are
not r
equi
red
to k
now
this
form
ula
off b
y he
art,
nor a
re th
ey re
quire
d to
app
ly th
is fo
rmul
a in
are
a ca
lcul
atio
ns.
G
rade
6 le
arne
rs in
vest
igat
e th
e re
latio
nshi
p be
twee
n th
e ar
ea a
nd p
erim
eter
of r
ecta
ngle
s an
d sq
uare
s. T
his
inve
stig
atio
n ca
n be
don
e as
an
Asse
ssm
ent T
ask.
The
re a
re tw
o di
ffere
nt in
vest
igat
ions
that
lear
ners
can
do.
1.
If
lear
ners
are
giv
en th
e pe
rimet
er o
f a re
ctan
gle,
they
can
dra
w a
num
ber o
f rec
tang
les
of d
iffer
ing
area
s. D
oes
this
al
so w
ork
with
squ
ares
?
2.
Sim
ilarly
if th
ey a
re g
iven
the
area
of a
squ
are,
ther
e w
ill on
ly b
e on
e po
ssib
ility
for t
he le
ngth
of t
he s
ides
. Is
this
the
sam
e fo
r rec
tang
les?
In
vest
igat
ing
the
rela
tions
hip
betw
een
the
area
s an
d pe
rimet
ers
of s
quar
es a
nd re
ctan
gles
can
be
com
bine
d w
ith th
e sh
ape
and
spac
e re
quire
men
t.
G
rade
6 le
arne
rs a
lso
draw
enl
arge
men
ts a
nd re
duct
ions
of 2
-D s
hape
s us
ing
grid
pap
er to
com
pare
thei
r siz
e an
d sh
ape.
H
ere
lear
ners
can
dra
w a
squ
are
or re
ctan
gle
with
spe
cifie
d si
de le
ngth
s. T
hen
they
can
inve
stig
ate
wha
t hap
pens
to th
e ar
ea o
f the
sha
pe, i
f the
leng
th o
f one
pai
r of o
ppos
ite s
ides
of t
he s
hape
are
dou
bled
or h
alve
d L
TSM
R
esou
rces
Va
riety
of 2
D s
hape
s. R
uler
s, m
easu
ring
tape
s, s
quar
blo
ck p
aper
Gra
de 4
G
rade
5
Gra
de 6
W
orkb
ook
refe
renc
e
WB
2 p
p. 1
46 -
156
Ac
tiviti
es 1
27 -
132
WB
2 p
p. 1
54 -
164
Activ
ities
127
- 13
0
WB
2 p
p. 1
54 –
162
Ac
tiviti
es
123a
&b;1
24;1
25a&
b D
BE
Text
book
refe
renc
e Te
rm 4
: Uni
t 7: P
erim
eter
, are
a an
d vo
lum
e, p
. 318
Te
rm 4
: Uni
t 6: P
erim
eter
, are
a an
d vo
lum
e, p
. 318
Te
rm 4
: Uni
t 5: P
erim
eter
, are
a an
d vo
lum
e, p
. 322
H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
169MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
M
ULT
I GR
ADE
LESS
ON
PLA
N 6
TE
RM
4
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to…
….…
T
ime:
4 H
OU
RS
GR
ADE
4 C
APS
p. 9
5
5 C
APS
p. 1
87 -
188
6 C
APS
p. 2
68 -
269
TOPI
C
Dat
a H
andl
ing
Con
cept
s, S
kills
and
kn
owle
dge
Dat
a ha
ndlin
g
Col
lect
ing
and
orga
nizi
ng d
ata
R
epre
sent
ing
data
Anal
ysin
g, in
terp
retin
g an
d re
porti
ng
data
Dat
a ha
ndlin
g
Col
lect
ing
and
orga
nizi
ng d
ata
R
epre
sent
ing
data
Anal
ysin
g, in
terp
retin
g an
d re
porti
ng
data
Ung
roup
ed d
ata
Dat
a ha
ndlin
g
Col
lect
ing
and
orga
nizi
ng d
ata
R
epre
sent
ing
data
Anal
ysin
g, in
terp
retin
g an
d re
porti
ng
data
incl
udin
g do
uble
bar
gra
phs
ce
ntra
l ten
denc
ies
– (m
ode
and
med
ian)
Ung
roup
ed d
ata
SUG
GES
TED
M
ETH
OD
OLO
GY
Teac
hers
in th
is p
hase
sho
uld
ensu
re th
at d
iffer
ent t
opic
s ar
e ch
osen
for d
ata
colle
ctio
n in
eac
h of
the
grad
es. T
he fo
llow
ing
are
new
in G
rade
4
Le
arne
rs re
ad, i
nter
pret
, ana
lyse
and
sum
mar
ise
pie
char
ts, w
here
the
info
rmat
ion
is p
rese
nted
in fr
actio
ns o
nly
Le
arne
rs re
ad, a
naly
se d
ata
repr
esen
ted
in w
ords
i.e.
sho
rt pa
ragr
aphs
– th
e da
ta p
rese
nted
in w
ords
sho
uld
be
repr
esen
ted
in o
ther
form
s an
d th
en a
naly
sed
Anal
ysin
g gr
aphs
An
alys
e gr
aphs
on
envi
ronm
enta
l or s
ocio
-eco
nom
ic c
onte
xts
and
answ
er q
uest
ions
on
grap
hs. B
oth
grap
hs a
nd q
uest
ions
to b
e pr
ovid
ed b
y te
ache
r or t
extb
ook.
Lea
rner
s sh
ould
wor
k w
ith a
t lea
st
1
pie
grap
h w
here
the
info
rmat
ion
is g
iven
in c
omm
on fr
actio
ns a
nd n
ot p
erce
ntag
es
1
bar g
raph
Su
itabl
e to
pics
incl
ude:
quan
titie
s of
mat
eria
ls re
cycl
ed in
the
tow
n, p
rovi
nce,
cou
ntry
quan
titie
s of
recy
clin
g m
ater
ials
col
lect
ed b
y sc
hool
s ar
ound
the
coun
try
so
urce
s of
ligh
ting
and
heat
ing
in S
A
ki
nds
of to
ilets
in S
A ho
mes
kind
s of
hom
es in
SA
170 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
The
follo
win
g ar
e ne
w in
Gra
de 5
orde
ring
data
set
s
anal
yzin
g da
ta n
ot o
nly
acco
rdin
g to
cat
egor
ies
but a
lso
taki
ng in
to a
ccou
nt c
onte
xts
and
sour
ces
of d
ata
an
alyz
ing
ungr
oupe
d nu
mer
ical
dat
a se
ts to
find
the
mod
e
pict
ogra
phs
whi
ch s
how
man
y-to
-one
cor
resp
onde
nce
co
nclu
sion
s an
d pr
edic
tions
whe
n an
alys
ing
and
sum
mar
isin
g da
ta
Dev
elop
crit
ical
ana
lysi
s sk
ills
Lear
ners
com
pare
gra
phs
on th
e sa
me
topi
c, b
ut w
here
dat
a ha
s be
en c
olle
cted
from
diff
eren
t gro
ups
of p
eopl
e, a
t diff
eren
t tim
es, i
n di
ffere
nt p
lace
s or
in d
iffer
ent w
ays.
Her
e le
arne
rs w
ill be
abl
e to
dis
cuss
the
diffe
renc
es b
etw
een
the
grap
hs. T
he a
im
is a
lso
for l
earn
ers
to b
ecom
e aw
are
of fa
ctor
s th
at c
an im
pact
on
the
data
. Lea
rner
s ca
n su
mm
ariz
e th
e fin
ding
s of
thei
r co
mpa
rison
in a
par
agra
ph.
Exam
ples
cou
ld in
clud
e:
co
mpa
ring
data
abo
ut c
ars
that
pas
s th
e sc
hool
at d
iffer
ent t
imes
or c
ompa
ring
data
abo
ut c
ars
that
pas
s di
ffere
nt
venu
es (b
usy
and
quie
t are
as, p
oore
r and
rich
er a
reas
etc
)
com
parin
g da
ta c
olle
cted
at y
our s
choo
l to
natio
nal d
ata
from
‘Cen
sus
At S
choo
l e.g
. fav
ourit
e sp
orts
; fav
ourit
e su
bjec
ts;
trans
port
to s
choo
l; tim
e ta
ken
to g
et to
sch
ool;
type
of d
wel
ling;
acc
ess
to g
oods
and
ser
vice
s at
hom
e
com
parin
g da
ta c
olle
cted
from
girl
s an
d bo
ys e
.g. f
avou
rite
spor
ts, f
avou
rite
mov
ies,
favo
urite
sch
ool s
ubje
cts
co
mpa
ring
rain
fall
each
mon
th fo
r a to
wn
in s
umm
er a
nd w
inte
r rai
nfal
l are
as
Lear
ners
sho
uld
do a
t lea
st 1
exa
mpl
e in
whi
ch th
ey c
ompa
re g
raph
s.
Com
plet
e da
ta c
ycle
: con
text
per
sona
l dat
a Th
e co
mpl
ete
data
cyc
le in
clud
es a
skin
g a
ques
tion,
col
lect
ion,
org
anis
ing,
repr
esen
ting,
ana
lyzi
ng a
nd in
terp
retin
g da
ta a
nd
repo
rting
on
the
data
. Cho
ose
a di
ffere
nt to
pic
to T
erm
1. W
ork
thro
ugh
the
who
le d
ata
cycl
e to
mak
e an
indi
vidu
al b
ar g
raph
us
ing
cont
exts
that
rela
te to
them
selv
es, t
heir
clas
s, th
eir s
choo
l or t
heir
fam
ily.
Suita
ble
topi
cs in
clud
e:
fa
vour
ite s
ports
/ fa
vour
ite m
ovie
s / f
avou
rite
mus
ic /
favo
urite
TV
prog
ram
mes
/ fo
ods
or c
ool d
rinks
/ fav
ourit
e co
lour
s,
etc.
heig
hts
of le
arne
rs in
cla
ss
m
ass
of le
arne
rs in
cla
ss
sh
oe s
ize
of le
arne
rs in
cla
ss
av
erag
e tim
e ta
ken
to g
et fr
om h
ome
to s
choo
l
num
ber o
f peo
ple
stay
ing
in h
omes
of l
earn
ers
in th
e cl
ass
171MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Anal
yse
ungr
oupe
d nu
mer
ical
dat
a us
ing
mea
sure
s of
cen
tral
tend
ency
Le
arne
rs d
eter
min
e th
e m
ode
of u
ngro
uped
num
eric
al d
ata
sets
. Su
itabl
e to
pics
incl
ude:
heig
hts
of le
arne
rs in
the
clas
s
mas
s of
lear
ners
in th
e cl
ass
sh
oe s
ize
of le
arne
rs in
the
clas
s
aver
age
time
take
n to
get
from
hom
e to
sch
ool
nu
mbe
r of p
eopl
e st
ayin
g in
the
hom
es o
f lea
rner
s in
the
clas
s
tem
pera
ture
s fo
r a m
onth
Th
e fo
llow
ing
are
new
in G
rade
6
gr
aphs
can
incl
ude
data
exp
ress
ed in
per
cent
ages
. Thi
s is
impo
rtant
in p
ie c
harts
, but
per
cent
ages
can
als
o be
use
d in
ba
r gra
phs
or d
oubl
e ba
r gra
phs
co
llect
ing
data
by
usin
g si
mpl
e qu
estio
nnai
res
do
uble
bar
gra
phs
th
e m
edia
n of
a d
ata
set
Com
plet
e a
data
cyc
le in
clud
ing
draw
ing
a do
uble
bar
gra
ph: c
onte
xt p
erso
nal d
ata
This
is re
com
men
ded
as th
e M
athe
mat
ics
proj
ect i
n G
rade
6
The
com
plet
e da
ta c
ycle
incl
udes
pos
ing
a qu
estio
n, c
olle
ctin
g, o
rgan
isin
g, re
pres
entin
g, a
naly
zing
, int
erpr
etin
g da
ta a
nd
repo
rting
on
the
data
. Lea
rner
s w
ork
thro
ugh
the
who
le d
ata
cycl
e to
mak
e an
indi
vidu
al d
oubl
e ba
r gra
ph u
sing
con
text
s th
at
rela
te to
them
selv
es, t
heir
clas
s, th
eir s
choo
l or t
heir
fam
ily.
Suita
ble
topi
cs in
clud
e:
fa
vour
ite s
ports
/ fa
vour
ite m
ovie
s / f
avou
rite
mus
ic /
favo
urite
TV
prog
ram
mes
/ fo
ods
or c
ool d
rinks
/ fav
ourit
e co
lour
s,
etc.
Incl
ude
boys
ver
sus
girls
heig
hts
of le
arne
rs in
cla
ss. I
nclu
de b
oys
vers
us g
irls
m
ass
of le
arne
rs in
cla
ss. I
nclu
de b
oys
vers
us g
irls
sh
oe s
ize
of le
arne
rs in
cla
ss. I
nclu
de b
oys
vers
us g
irls
Anal
ysin
g un
grou
ped
num
eric
al d
ata
usin
g m
easu
res
of c
entr
al te
nden
cy
Lear
ners
find
the
mod
e an
d m
edia
n of
ung
roup
ed n
umer
ical
dat
a se
ts. S
uita
ble
topi
cs s
ame
as fo
r Gra
de 5
.
Teac
hers
in th
is p
hase
sho
uld
ensu
re th
at d
iffer
ent t
opic
s ar
e ch
osen
for d
ata
colle
ctio
n an
d an
alys
is in
eac
h of
the
grad
es.
172 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LTSM
R
esou
rces
Ex
empl
ers
of p
icto
grap
hs, b
ar g
raph
s, p
ie c
harts
– (c
onte
xt s
ensi
tive)
, IC
T –
Exce
l wor
kshe
ets
with
gra
phs,
vi
deo
clip
s, E
lear
ning
onl
ine
reso
urce
s, M
aths
gam
es,
G
rade
4
Gra
de 5
G
rade
6
Wor
kboo
k re
fere
nce
W
B 2
pp.
52
– 62
Ac
tiviti
es 8
6 - 9
1 W
B 2
pp.
68
– 84
A
ctiv
ities
94
- 100
W
B 2
pp.
76
– 88
Ac
tiviti
es 9
1 - 9
6 D
BE
Text
book
refe
renc
e Te
rm 3
: Uni
t 7: D
ata
Han
dlin
g, p
. 258
Te
rm 4
: Uni
t 12:
Pro
babi
lity,
p. 3
47
Term
3: U
nit 9
: Dat
a H
andl
ing,
p. 2
57
Term
4: U
nit 1
1: P
roba
bilit
y, p
. 346
Te
rm 3
: Uni
t 9: D
ata
Han
dlin
g, p
. 268
Te
rm 4
: Uni
t 11:
Pro
babi
lity,
p. 3
63
HO
MEW
OR
K
AS
SESS
MEN
T E.
g. In
form
al a
sses
smen
t –
Test
173MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
M
ULT
I GR
ADE
LESS
ON
PLA
N 7
TE
RM
4
EDU
CAT
OR
: ……
……
……
……
……
DAT
E : f
rom
…
……
to …
….…
T
ime:
12
HO
UR
S G
RAD
E 4
Com
mon
Fra
ctio
ns
CAP
S p.
91
5 C
omm
on fr
actio
ns
CAP
S pp
.160
-162
, 176
-177
& 1
99
6 C
omm
on fr
actio
ns
C
APS
pp. 2
26-2
27, 2
80
Dec
imal
frac
tions
- C
APS
p. 2
52,
Perc
enta
ges
- CAP
S p.
267
TO
PIC
C
omm
on fr
actio
ns, d
ecim
al fr
actio
ns a
nd p
erce
ntag
es
Con
cept
s, S
kills
and
kn
owle
dge
Des
crib
ing
and
orde
ring
frac
tions
:•
C
ompa
re a
nd o
rder
com
mon
fra
ctio
ns w
ith d
iffer
ent d
enom
inat
ors
(hal
ves;
third
s, q
uarte
rs; f
ifths
; si
xths
; sev
enth
s; e
ight
hs)
D
escr
ibe
and
com
pare
com
mon
fra
ctio
ns in
dia
gram
form
Cal
cula
tions
with
frac
tions
:
Addi
tion
of c
omm
on fr
actio
ns w
ith
the
sam
e de
nom
inat
ors
Rec
ogni
ze, d
escr
ibe
and
use
the
equi
vale
nce
of d
ivis
ion
and
fract
ions
Des
crib
ing
and
orde
ring
frac
tions
: • C
ount
forw
ards
and
bac
kwar
ds in
fra
ctio
ns
• Com
pare
and
ord
er c
omm
on fr
actio
ns
to a
t lea
st tw
elfth
s C
alcu
latio
ns w
ith fr
actio
ns:
Ad
ditio
n an
d su
btra
ctio
n of
com
mon
fra
ctio
ns w
ith th
e sa
me
deno
min
ator
s
Addi
tion
and
subt
ract
ion
of m
ixed
nu
mbe
rs
Fr
actio
ns o
f who
le n
umbe
rs w
hich
re
sult
in w
hole
num
bers
Rec
ogni
ze, d
escr
ibe
and
use
the
equi
vale
nce
of d
ivis
ion
and
fract
ions
Des
crib
ing
and
orde
ring
frac
tions
: • C
ompa
re a
nd o
rder
com
mon
frac
tions
, in
clud
ing
tent
hs a
nd h
undr
edth
s C
alcu
latio
ns w
ith fr
actio
ns:
Ad
ditio
n an
d su
btra
ctio
n of
com
mon
fra
ctio
ns in
whi
ch o
ne d
enom
inat
or
is a
mul
tiple
of a
noth
er
Ad
ditio
n an
d su
btra
ctio
n of
mix
ed
num
bers
Frac
tions
of w
hole
num
bers
174 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Solv
ing
prob
lem
s So
lve
prob
lem
s in
con
text
s in
volv
ing
fract
ions
, inc
ludi
ng g
roup
ing
and
equa
l sh
arin
g Eq
uiva
lent
form
s:
Rec
ogni
ze a
nd u
se e
quiv
alen
t for
ms
of
com
mon
frac
tions
(fra
ctio
ns in
whi
ch
one
deno
min
ator
is a
m
ultip
le o
f ano
ther
)
Solv
ing
prob
lem
s So
lve
prob
lem
s in
con
text
s in
volv
ing
com
mon
frac
tions
, inc
ludi
ng g
roup
ing
and
shar
ing
Equi
vale
nt fo
rms:
R
ecog
nize
and
use
equ
ival
ent f
orm
s of
co
mm
on fr
actio
ns (f
ract
ions
in w
hich
one
de
nom
inat
or is
a
mul
tiple
of a
noth
er)
Solv
ing
prob
lem
s So
lve
prob
lem
s in
con
text
s in
volv
ing
com
mon
frac
tions
, inc
ludi
ng g
roup
ing
and
shar
ing
Perc
enta
ges
• Fin
d pe
rcen
tage
s of
who
le n
umbe
rs
Equi
vale
nt fo
rms:
Rec
ogni
ze a
nd u
se e
quiv
alen
t for
ms
of c
omm
on fr
actio
ns w
ith 1
-dig
it or
2-
digi
t den
omin
ator
s (fr
actio
ns in
w
hich
one
den
omin
ator
is a
mul
tiple
of
ano
ther
)
Rec
ogni
ze e
quiv
alen
ce b
etw
een
com
mon
frac
tion
and
deci
mal
fra
ctio
n fo
rms
of th
e sa
me
num
ber
R
ecog
nize
equ
ival
ence
bet
wee
n co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r R
ecog
nizi
ng, o
rder
ing
and
plac
e va
lue
of d
ecim
al fr
actio
ns
C
ount
forw
ards
and
bac
kwar
ds in
de
cim
al fr
actio
ns to
at l
east
two
deci
mal
pla
ces
C
ompa
re a
nd o
rder
dec
imal
fra
ctio
ns to
at l
east
two
deci
mal
pl
aces
Plac
e va
lue
of d
igits
to a
t lea
st tw
o de
cim
al p
lace
s
175MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Cal
cula
tions
with
dec
imal
frac
tions
Addi
tion
and
subt
ract
ion
of d
ecim
al
fract
ions
with
at l
east
two
deci
mal
pl
aces
Mul
tiply
dec
imal
frac
tions
by
10 a
nd
100
Solv
ing
prob
lem
s So
lve
prob
lem
s in
con
text
invo
lvin
g de
cim
al fr
actio
ns
Cal
cula
tions
Fi
nd p
erce
ntag
es o
f who
le n
umbe
rs.
Equi
vale
nt fo
rms:
Rec
ogni
ze e
quiv
alen
ce b
etw
een
com
mon
frac
tion
and
deci
mal
fra
ctio
n fo
rms
of th
e sa
me
num
ber
R
ecog
nize
equ
ival
ence
bet
wee
n co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
176 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
SUG
GES
TED
M
ETH
OD
OLO
GY
Ref
er to
the
Less
on p
lans
in T
erm
2
In G
rade
4 th
is is
revi
sion
and
con
solid
atio
n of
the
conc
epts
dev
elop
ed in
Ter
m 3
. (Se
e Te
rm 3
not
es)
In T
erm
4 le
ngth
, cap
acity
and
mas
s ca
n be
use
d as
con
text
s fo
r fra
ctio
ns.
Teac
hing
frac
tions
in d
iagr
am fo
rms
shou
ld in
clud
e: re
gion
mod
els
, len
gth
mod
els
(incl
udin
g nu
mbe
r lin
es) a
nd s
et m
odel
s.
Lear
ners
sho
uld
solv
e pr
oble
ms
as w
ell a
s w
ork
with
app
arat
us to
und
erst
and
the
rela
tions
hip
betw
een
fract
ions
and
div
isio
n i.e
. if
you
shar
e 1
amon
gst 3
lear
ners
you
will
be m
akin
g th
irds.
Le
arne
rs m
ust a
ble
to n
ame
fract
ions
. Ter
min
olog
y lik
e “3
ove
r 4” s
houl
d be
avo
ided
as
it te
nds
to e
ncou
rage
lear
ners
to th
ink
abou
t eac
h fra
ctio
n as
two
diffe
rent
num
bers
, rat
her t
han
3 4 bei
ng a
num
ber w
hich
is g
reat
er 1 2 t
han
but l
ess
than
1.
Whe
n na
min
g fra
ctio
n pa
rts it
is u
sefu
l for
lear
ners
to ra
ther
use
the
form
“3 q
uarte
rs”.
Lear
ners
sho
uld,
thro
ugh
wor
k w
ith a
ppar
atus
, dia
gram
s an
d so
lvin
g pr
oble
ms,
lear
n th
e ne
w fr
actio
ns th
at th
ey w
ill de
al w
ith in
G
rade
4
Teac
h fr
actio
ns a
s eq
ual p
arts
of a
who
le
Exam
ple
1 - D
ivid
e a
bana
na u
neve
nly
and
ask
two
lear
ners
whe
ther
they
wou
ld b
e sa
tisfie
d w
ith th
is d
ivis
ion.
Why
not
? - E
xpla
in th
at fr
actio
ns a
re fo
rmed
with
the
divi
ding
of a
who
le in
to E
QU
AL P
ARTS
. Ex
ampl
e 2
Giv
e di
ffere
nt m
athe
mat
ical
sha
pes
to le
arne
rs –
circ
les
/ rec
tang
les
/ squ
ares
/ et
c.
- Wor
k pr
actic
ally
– d
ivid
e on
e (c
ircle
) equ
ally
bet
wee
n 2
– th
en 4
– th
en 8
lear
ners
- E
xpla
in w
hat w
e ca
ll th
ese
fract
ions
and
wha
t the
not
atio
n lo
oks
like
1 2 ; 1 4 (
at fi
rst o
nly)
Ex
ampl
e 3
Div
ide
a ch
ocol
ate
(rect
angl
e) e
qual
ly b
etw
een
3 –
then
6 le
arne
rs.
177MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Exam
ple
4 D
ivid
e a
cake
(squ
are)
equ
ally
bet
wee
n 5
– th
en 1
0 le
arne
rs.
Exp
lain
the
nota
tion
ever
y tim
e in
the
abov
e ex
ampl
es.
A w
ritte
n or
ora
l exe
rcis
e ca
n be
don
e at
this
poi
nt. T
he fo
llow
ing
can
be u
sed:
Th
e te
ache
r sho
uld
take
the
lead
and
ask
que
stio
ns. A
sk th
e le
arne
rs to
writ
e th
e fra
ctio
n no
tatio
n on
the
boar
d fo
r the
who
le
clas
s to
see
. Ad
ditio
n of
frac
tions
: W
ork
with
con
cret
e ob
ject
s:
Wor
k w
ith d
iagr
ams.
Sha
de o
ne p
art i
n on
e co
lour
. Sha
de a
noth
er p
art i
n a
diffe
rent
col
our.
Whi
ch fr
actio
n is
sha
ded
in to
tal?
W
ork
with
frac
tion
wal
l: (S
tart
with
sim
ple
fract
ions
) St
art w
ith th
e sa
me
deno
min
ator
, e.g
., 1 4 +
1 4 If
lear
ners
can
do
the
addi
tion
usin
g co
ncre
te e
xam
ples
, the
y ca
n th
en p
rogr
ess
to w
ritin
g th
e fra
ctio
n no
tatio
n be
low
the
conc
rete
exa
mpl
e.
Fol
low
thes
e st
eps,
e.g
. St
ep 1
: Mak
e su
re th
e bo
ttom
num
bers
(the
den
omin
ator
s) a
re th
e sa
me
Step
2: A
dd th
e to
p nu
mbe
rs (t
he n
umer
ator
s). P
ut th
e an
swer
ove
r the
sam
e de
nom
inat
or a
s in
ste
p 1
Step
3: S
impl
ify th
e fra
ctio
n (if
nee
ded)
. D
ECIM
ALS
Im
port
ant:
Ref
er to
the
Less
on P
lans
on
Dec
imal
Fra
ctio
ns in
Ter
m 2
Con
vert
from
frac
tions
to d
ecim
al fr
actio
ns a
nd to
per
cent
ages
. Onl
y ta
ught
in G
rade
6.
178 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
PER
CEN
TAG
ES
Perc
enta
ges
are
a ne
w to
pic
for G
rade
6 le
arne
rs.
Lear
ners
hav
e al
read
y w
orke
d w
ith t
enth
s an
d hu
ndre
dths
in
com
mon
fra
ctio
n fo
rm.
They
sho
uld
star
t by
rew
ritin
g an
d co
nver
ting
tent
hs a
nd h
undr
edth
s in
com
mon
frac
tion
form
to p
erce
ntag
es. W
here
den
omin
ator
s of
oth
er fr
actio
ns a
re fa
ctor
s of
10,
e.g
., 2,
5 o
r fac
tors
of 1
00 e
.g. 2
, 4, 5
, 20,
25,
50
lear
ners
can
con
vert
thes
e to
hun
dred
ths
usin
g w
hat t
hey
know
abo
ut
equi
vale
nce.
Eq
uiva
lenc
e be
twee
n co
mm
on fr
actio
ns a
nd p
erce
ntag
e Le
arne
rs a
re n
ot e
xpec
ted
to b
e ab
le to
con
vert
any
com
mon
frac
tion
into
its
perc
enta
ge fo
rm, m
erel
y to
see
the
rela
tions
hip
betw
een
tent
hs a
nd h
undr
edth
s in
thei
r per
cent
age
form
. Lea
rner
s sh
ould
be
able
to c
onve
rt an
y de
cim
al fr
actio
n in
tent
hs o
r hu
ndre
dths
into
a p
erce
ntag
e.
Cal
cula
tions
Le
arne
rs s
houl
d be
abl
e to
find
per
cent
ages
of w
hole
num
ber,s
e.g
., W
hat i
s 25
% o
f R30
0? H
ere
lear
ners
use
wha
t the
y kn
ow
abou
t bot
h co
nver
ting
betw
een
perc
enta
ge a
nd c
omm
on fr
actio
n fo
rm a
nd a
lso
wha
t the
y kn
ow a
bout
find
ing
fract
ions
of w
hole
nu
mbe
rs e
.g. 2
5% o
f R30
= 1 4
of R
300
= R
75.
LTSM
R
esou
rces
G
r 4 T
ext b
ooks
, Int
erne
t Web
site
s, N
umbe
r boa
rd,,
Cui
senn
arie
rods
/num
ber r
ods,
Fra
ctio
n ci
rcle
s, 2
D re
latio
nal s
hape
s, B
ase
10 b
lock
s/D
iene
s bl
ocks
, Con
cret
e m
ater
ial,
e.g.
cou
nter
s, N
umbe
r lin
es, F
ract
ion
wal
l cou
nter
s; N
umbe
r lin
es +
em
pty
ones
; H
undr
ed c
hart
G
rade
4
Gra
de 5
G
rdad
e 6
Wor
kboo
k re
fere
nce
W
B 2
pp.
128
– 1
38
Activ
ities
118
- 12
3
WB
2 p
p. 2
– 1
8; 2
8; 1
16
Activ
ities
65
– 7
3, 7
7, 1
12
WB
2 p
p. 1
32 –
148
Ac
tiviti
es 1
13 -
120
DB
E Te
xtbo
ok re
fere
nce
Term
4: U
nit 5
: Com
mon
Fra
ctio
ns, p
. 31
2 Te
rm 4
: Uni
t 4: C
omm
on F
ract
ions
, p.
301
Term
4: U
nit 3
: Com
mon
Fra
ctio
ns, p
. 30
6 H
OM
EWO
RK
ASSE
SSM
ENT
E.g.
Info
rmal
ass
essm
ent
– Te
st
179MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
MAT
HEM
ATIC
S IN
TER
MED
IATE
PH
ASE
M
ULT
I GR
ADE
LESS
ON
PLA
N 8
TE
RM
4
ED
UC
ATO
R: …
……
……
……
……
…
DAT
E : f
rom
…
……
to
……
…
Tim
e: 3
HO
UR
S G
RAD
E 4
CAP
S pp
. 39
– 42
5
CAP
S pp
. 127
-131
6
CAP
S pp
. 217
– 2
22
This
less
on a
cts
as c
onso
lidat
ion
for t
he to
pic
of n
umbe
r sen
tenc
es
TOPI
C
Num
ber s
ente
nces
C
once
pts,
Ski
lls a
nd
know
ledg
e •
Writ
e nu
mbe
r sen
tenc
es to
de
scrib
e pr
oble
m s
ituat
ions
•
Solv
e an
d co
mpl
ete
num
ber
sent
ence
s by
-
insp
ectio
n -
trial
and
impr
ovem
ent
• C
heck
sol
utio
n by
sub
stitu
tion
• W
rite
num
ber s
ente
nces
to
desc
ribe
prob
lem
situ
atio
ns
• So
lve
and
com
plet
e nu
mbe
r se
nten
ces
by
- in
spec
tion
- tri
al a
nd im
prov
emen
t •
Che
ck s
olut
ion
by s
ubst
itutio
n
• W
rite
num
ber s
ente
nces
to
desc
ribe
prob
lem
situ
atio
ns
• So
lve
and
com
plet
e nu
mbe
r se
nten
ces
by
- in
spec
tion
- tri
al a
nd im
prov
emen
t •
Che
ck s
olut
ion
by s
ubst
itutio
n
SUG
GES
TED
M
ETH
OD
OLO
GY
U
se n
umbe
r sen
tenc
es to
des
crib
e pr
oble
m s
ituat
ions
. Ex
ampl
e: P
robl
em s
ituat
ion:
I bo
ught
750
g of
sw
eets
and
div
ided
them
am
ong
25 c
hild
ren.
Num
ber s
ente
nce:
750
÷25
U
se n
umbe
r sen
tenc
es a
s eq
uiva
lent
form
of e
xpre
ssio
n to
sec
tions
of f
low
dia
gram
or t
able
s.
Exam
ple:
Tab
le
1 2
3 4
×3
180 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
Flo
w d
iagr
am
E
quiv
alen
t rep
rese
ntat
ion
of th
e ta
ble
and
the
flow
dia
gram
: ×
3
• U
sing
num
ber
sent
ence
s to
hel
p le
arne
rs u
nder
stan
d an
d us
e th
e fa
ct t
hat
addi
tion
and
subt
ract
ion
are
inve
rse
oper
atio
ns
Exa
mpl
e: 3
7 –
4 +
4 =
∆ •
Use
num
ber s
ente
nces
hel
ps le
arne
rs d
evel
op a
dditi
on a
nd s
ubtra
ctio
n te
chni
ques
Exa
mpl
e: 3
6+13
= th
eref
ore
49 –
13
=
•
Com
mut
ativ
e pr
oper
ty o
f add
ition
Num
bers
can
be
adde
d in
any
ord
er.
Exam
ple:
29
+ 19
= 1
9 +
26
T
here
fore
13
+ 49
= o
r 49
+ 1
3 =
•
Ass
ocia
tive
prop
erty
of a
dditi
on
Th
e as
soci
ativ
e pr
oper
ty a
llow
s nu
mbe
rs t
o be
gro
uped
in
diffe
rent
way
s w
hen
addi
ng m
ore
than
wo
num
bers
, with
out i
t af
fect
ing
the
answ
er.
Exa
mpl
e: (3
1 +
26) +
19=
i
s th
e sa
me
as 3
1 +(
26+
19)
•
Use
num
ber s
ente
nces
to h
elp
lear
ners
see
and
use
pat
tern
s in
add
ition
and
sub
tract
ion
num
ber b
onds
for:
181MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
-
10
-
mul
tiple
s of
10
-
mul
tiple
s of
100
Exa
mpl
es:
-
Ten
3 +
7=
4
+ 6
= 2
+ 8
=
5 +
5 =
- M
ultip
les
of 1
0
1
3 +
7 =
14
+ 6
=
12
+ 8=
15 +
5 =
- M
ultip
les
of 1
00
Sim
ilar e
xam
ples
can
be
give
n fo
r mul
tiple
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182 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TASKS & MEMORANDA
183MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
EXEMPLAR INVESTIGATION: GRADE 4
TERM 4 Investigating the relationship between perimeter and area 15 marks
1. The side of each square in the grid below is 1unit. Determine the perimeter and the area of each of the shape. Write your answers in the table provided.
B D
C
A
E
Shape A B C D E
Perimeter
Area in number of squares
(10)
2. Does the shape with the longest perimeter also have the greatest area? (1)
3. Which shapes have equal perimeter? (2)
4. Do shapes of equal perimeter have equal area? (1)
5. Does the perimeter tell something about the area of a shape? (1)
184 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
EXEMPLAR INVESTIGATION MEMO: GRADE 4 TERM 4
Investigating the relationship between perimeter and area 15 marks
1. The side of each square in the grid below is 1unit. Determine the perimeter and the area of each of the shape. Write your answers in the table provided.
B D
C
A
E
Shape A B C D E
Perimeter 12 12 14 14
12
Area in number of squares 9 5 6 6 8
(10)
2. Does the shape with the longest perimeter also have the greatest area?
No (1)
3. Which shapes have equal perimeter?
A, B and E C and D (2)
4. Do shapes of equal perimeter have equal area?
No (1)
5. Does the perimeter tell something about the area of a shape?
No (1)
185MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
GRADE 4 EXEMPLAR TEST – TERM 2
INSTRUCTIONS TO LEARNERS:
1. Answer all questions in the spaces provided. 2. The use of calculators is NOT allowed. 3. The test duration is 40 minutes
QUESTION 1 Circle the letter next to the correct answer.
1.1 The multiple of 5 in the following is
A 58
B 90
C 59
B 09 (1)
1.2 The number 967 rounded off to the nearest 10 is
A 900
B 960
C 970
D 1 000 (1)
1.3 Complete: 40 + 35 = 30 + ___
A 35
B 40
C 75
D 45 (1)
(3) QUESTION 2 2.1 Write the following numbers in order from the smallest to the largest.
4 910 9 410 4 190 9 140
_________________________________________________________________
(1)
2.2 What is the biggest number you can make using the digits
7 1 4 8 ?
_________________________________________________________________
(1)
2.3 What is the value of the underlined digit?
8 367
_________________________________________________________________
(1)
2.4 Fill in the missing numbers in the following:
2.4.1 930; 933; 936; __________. (1)
186 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
2.4.2 7 050; 7 000; 6 950; __________. (1)
2.5 Which number is written in expanded notation as
(4 × 1 000) + (5 × 100) + (8 × 10) + (2 × 1)?
_________________________________________________________________
(1)
2.6 Write 6 427 in words.
______________________________________________________________________
____________________________________________________________
(1)
2.7 Draw a circle around all the odd numbers in the group below.
(2)
2.8 Say whether each of the following is TRUE or FALSE.
2.8.1 67 − 45 is equal to 45 − 67 (1)
2.8.2 54 + 29 is equal to 29 + 54 (1)
(11) QUESTION 3 Calculate each of the following.
3.1 3 679 + 3 124 (2)
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
____________________________________________
3.2 5 635 – 4 334 (2)
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
3.3 65 × 24
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
710 477 804 415 502 655 312 666 971
187MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
_____________________________________________ (3)
3.4 584 ÷ 8
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(3)
(10) QUESTION 4 4.1 If 3 153 people live in Phambili and 5 244 peolple live in Sinamuva. How many
people live in Phambili and Sinamuva altogether?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(3)
4.2 Rajen changes his R100 note for R5 coins only. How many coins does he get.
Rajen gets ____________________________ coins.
(3)
4.3 Betty wants to buy a book for R46,99 and a poster for R25,89.
4.3.1 How much will this cost altogether?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(3)
4.3.2 Betty only has R60,00 in her wallet. How much more money does she need?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(3)
4.4 Tshepo planted 11 rows of tomatoes with 6 plants in each row. How many tomato plants
did he plant altogether?
______________________________________________________________________
______________________________________________________________________
188 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(2)
4.5 Calculate the difference between the value of the underlined digits in the numbers 9 008
and 8 190.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
(3)
(18)
189MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
GRADE 4 EXEMPLAR TEST – MEMORANDUM
QUESTION EXPECTED ANSWER MARKS TOTAL
1.1 B (1) 3 1.2 C (1)
1.3 D (1) 2.1 4 190 4 910 9 140 9 410 (1)
11
2.2 8 741 (1) 2.3 8 000 (1) 2.4.1 939 (1) 2.4.2 6 900 (1) 2.5 4 582 (1) 2.6 Six thousand four hundred and twenty seven (1) 2.7
(2)
2.8.1 False (1) 2.8.2 True (1) 3.1 3 659 + 3 124
= 3 000 + 600 + 50 + 9 + 3 000 + 100 + 20 + 4 = 3 000 + 3 000 + 600 + 100 + 50 + 20 + 9 + 4 = 6 000 + 700 + 70 + 13 = 6 783
(2)
10
3.2 5 635 – 4 334 = 5 000 + 600 + 30 + 5 – (4 000 + 300 + 30 + 4) = (5 000 – 4 000) + (600 – 300) + (30 –30) + (5 – 4) = 1 000 + 300 + 0 + 1 = 1 301
(2) 3.3 65 × 24
= (60 + 5) × (20 + 4) = (60 × 20) + (60 × 4) + (5 × 20) + (5 × 4) = 1 200 + 240 + 100 + 20 = 1 440 + 100 + 20 = 1 540 + 20 = 1 560
(3) 3.4 586 ÷ 8 = 70 + 3 = 73 remainder 2
Multiply Subtract CLUE BOARD 70 × 8 = 560 3 × 8 = 24
586 − 560 = 26 26 – 24 = 2 rem
10 × 8 = 80 20 × 8 = 160 30 × 8 = 240 40 × 8 = 320 50 × 8 = 400 60 × 8 = 480 70 × 8 = 560 80 × 8 = 640
8 × 1 = 8 8 × 2 = 16 8 × 3 = 24
(3) 4.1 3 153 + 5 244
= 3 100 + (5 244 + 53) [Rounding off and compensating] = 3 100 + 5 297 = 8 398 8 398 live in Phambili and Sinamuva,
(3)
18
710 477 804 415 502 655 312 666 971
190 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
4.2 Rajen gets 20 coins.
(3) 4.3.1 R46,99 + R25,89
= R47,00 + R25,88 [Rounding off and compensating] = R40,00 + R32,88 =R72,88 The book and poster cost R72,88
(3)
4.3.2 She needs R72,88 – R60,00 = R 12,88
(3)
4.4 Tshepo planted 11 rows of tomatoes with 6 plants in each row. How many tomato plants did he plant altogether? Tshepo planted 11 × 6 = 66 rows
(3)
4.5 The difference is 9 000 – 90 = 8 910 (3)
GRAND TOTAL 40 MARKS
191MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
EXEMPLAR INVESTIGATION: GRADE 5 TERM 4
Investigating the relationship between perimeter and area 20 marks
QUESTION 1
1.1 Draw the following shapes in the grid provided. Label you’re the shapes. a) A square S1 with a perimeter of 16 units. b) Two different rectangles R1 and R2 also having a perimeter of 16 units
c)
(3)
1.2 Use the shapes that you have drawn to complete the table.
Shape S1 R1 R2 Perimeter Area
(3)
1.3 Is the area of the square greater, smaller or equal to that of the triangles? (1) 1.4 Do the shapes have equal area? (1) 1.5 Is it correct to say that, “quadrilaterals with equal perimeter have equal area”? (1)
192 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
QUESTION 2
2.1 Draw the following shapes in the grid provided; three different rectangles R1, R2, and R3 each with an area of 24 squares. Label your diagrams.
d)
(3)
2.2 Use the shapes that you have drawn to complete the table.
Shape R1 R2 R3 Perimeter Area
(3)
2.3 Do the shapes have equal perimeter? (1) 2.4 Does the shape with a larger perimeter have the biggest area? (1) 2.4 Is it correct to say that, “quadrilaterals with equal area have equal perimeter”? (1) 2.5 Does perimeter of a shape tell us anything about the area of that shape? (1) 2.6 Does area of a shape tell us anything about the perimeter of the shape? (1)
193MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
EXEMPLAR INVESTIGATION MEMO: GRADE 5 TERM 4
Investigating the relationship between perimeter and area 20 marks
QUESTION 1
1.2 Draw the following shapes in the grid provided. Label you’re the shapes. e) A square S1 with a perimeter of 16 units. f) Two different rectangles R1 and R2 also having a perimeter of 16 units
S1
R1
R2
(3)
1.3 Use the shapes that you have drawn to complete the table.
Shape S1 R1 R2 Perimeter 16 16 16 Area 16 15 12
(3)
1.3 Is the area of the square greater, smaller or equal to that of the triangles? Greater
(1) 1.4 Do the shapes have equal area?
No (1) 1.5 Is it correct to say that, “quadrilaterals with equal perimeter have equal area”?
It is incorrect (1)
194 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
QUESTION 2
2.3 Draw the following shapes in the grid provided; three different rectangles R1, R2, and R3 each with an area of 24 squares. Label your diagrams.
g)
R1
R2
R3
[Accept any correct diagrams] (3)
2.4 Use the shapes that you have drawn to complete the table.
Shape R1 R2 R3 Perimeter 20 22 28 Area 24 24 24
(3)
2.3 Do the shapes have equal perimeter? No (1)
2.4 Does the shape with a larger perimeter have the biggest area? No (1)
2.4 Is it correct to say that, “quadrilaterals with equal area have equal perimeter”? No (1) 2.5 Does perimeter of a shape tell us anything about the area of that shape?
It tells us nothing (1) 2.6 Does area of a shape tell us anything about the perimeter of the shape?
It does not tell us anything (1)
195MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
GRADE 5 EXEMPLAR TEST – TERM 2
INSTRUCTIONS TO LEARNERS:
1. Answer all questions in the space provided. 2. The use of calculators is NOT allowed. 3. The test duration is 60 minutes
QUESTION 1 Circle the letter next to the correct answer.
1.1 Which number is 2 000 more than 957 467?
A 972 467
B 959 467
C 957 667
B 977 467 (1)
1.2 The third multiple of 9 is
A 3
B 9
C 18
D 27 (1)
1.3 Which number consists of the following:
6H + 4Th + 8Tth + 7U + 5T
A 64 875
B 57 864
C 75 684
D 84 657 (1)
1.4 A number divided by 5 is 12. What is the number?
A 55
B 60
C 65
D 70 (1)
1.5 The number 33 756 rounded off to the nearest 5 is ____
A 33 750
B 33 755
C 33 760
D 33 765 (1)
[5]
196 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
QUESTION 2 2.1 Write the following numbers in order from the smallest to the largest.
4 910 9 410 4 190 9 140
________________________________________________________________
(1)
2.2 What is the biggest number you can make using the digits
7 1 4 8 5?
________________________________________________________________
(1)
2.3 What is the value of the underlined digit?
128 367
________________________________________________________________
(1)
2.4 Fill in the missing numbers in the following:
2.4.1 5 930 ; 5 933 ; 5 936 ; __________. (1)
2.4.2 27 050 ; 27 000 ; 26 950 ; __________. (1)
2.5 Which number is written in expanded notation as
(6 × 10 000) + (4 × 1 000) + (5 × 100) + (8 × 10) + (2 × 1)?
________________________________________________________________
(1)
2.6 Write 86 427 in words.
_____________________________________________________________________
___________________________________________________________
(1)
2.7 Draw a triangle around all the odd numbers in the group below.
(2)
[9]
QUESTION 3
3.1 Say whether the following are True or False?
3.1.1 51 + 32 = 32 + 51 (1)
3.1.2 34 ÷ 5 = 5 ÷ 34 (1)
3.1.3 3(4 + 5) = (3 × 4) + (3 × 5) (1)
3.1.4 63 ÷ 7 × 7 = 63 (1)
3.1.5 (251 + 27) + 49 has the same answer as 251 + (27 + 49) (1)
1710 3 477 804 6 415 3 502 655 312 666 2 971
197MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
3.2 Write down all the multiples 9 between 40 and 60.
________________________________________________________________
(1)
3.3 3.3.1 Is 21 758 closer to 21 700 or 21 800?
________________________________________________________________
(1)
3.3.2 R214,76 ≈ _________________________ rounded off to the nearest rand. (1)
3.4 3.4.1 Insert the missing factor of 12:
2, _____, 12, 3, 6, 4
(1)
3.4.2 Which 2 whole numbers can I multiply to get 99?
__________ and __________
(2)
[11]
QUESTION 4 Calculate
4.1 73 679 + 25 184
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
__________________________________________________
(2)
4.2 65 635 – 64 384
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(2)
4.3 365 × 24
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(3)
4.4 928 ÷ 12
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(3)
[10]
198 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
QUESTION 5 5.1 There were 41 295 spectators at a soccer match, 23 985 were men,11 378 were women
and the remainder were children.
5.1.1 How many adults attended the soccer match?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(3)
5.2 How many children attended the soccer match?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
__________________________________________________
(3)
5.3 Mr Brown buys a muffin for R2,50 and sells it for R5,50.
5.3.1 How much profit does he make?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(3)
5.3.2 How much profit will he make if he sells 35 muffins?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(3)
5.5 375 learners will use buses during a school excursion. How many buses will they hire if
each bus transposts 95 learners?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_____________________________________________
(3)
[15]
199MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
GRADE 5 MATHEMATICS TEST MEMORANDUM – TERM 2
General marking notes:
1. Give full marks for answers only, unless otherwise stated. 2. Accept any alternative correct solution that is not included in the memorandum. 3. Apply consistency accuracy [CA], where necessary.
QUESTION
EXPECTED ANSWER MARKS
TOTAL
1.1 B (1)
5
1.2 D (1)
1.3 D (1)
1.4 B (1)
1.5 B (1)
2.1 4 190 4 910 9 140 9 410 (1)
9
2.2 87 541 (1)
2.3 Twenty thousand or 20 000 or (2 × 10 000) (1)
2.4.1 5 930; 5 933; 5 936; 5 939 (1)
2.4.2 27 050; 27 000; 26 950; 26 900 (1)
2.5 64 582 (1)
2.6 Eighty six thousand four hundred and twenty seven (1)
2.7
numbers are 655, 2 971, 3 477 and 6 415
(2)
3.1.1 True (1)
11
3.1.2 False (1)
3.1.3 True (1)
3.1.4 True (1)
3.1.5 True (1)
3.2 45 and 54 (1)
3.3.1 21 758 is closer to 21 800 (1)
3.3.1 R214,76 ≈ R215,00 rounded off to the nearest rand. (1)
3.4.1 1 (1)
3.4.2 9 and 11 (2)
4.1 73 679 + 25 184 98 863
70 000 + 3 000 + 600 + 70 + 9 +20 000 + 5 000 + 100 + 80 + 4 90 000 + 8 000 + 800 + 60 + 3
= 98 863
[Accept any method]
1 mark for 863 and 1
mark for 98.
A mark for correct
hundreds, tens & units
and another mark for
thousands and ten
thousands
(2)
10
4.2 65 635 – 64 384
Any suitable method [1 mark for 251 and 1 (2)
200 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
1 251 mark for 1.
A mark for correct
hundreds, tens & units
and another mark for
thousands]
4.3 365 × 24 = (300 + 60 + 5) × (20 + 4) = (300 × 20) + (60 × 20) + (5 × 20) + (300 × 4) + (60
× 4) + (5 × 4) = 6 000 + 1 200 + 100 + 1 200 + 240 + 20 = 8 400 + 340 + 20 = 8 740 + 20 = 8 760
[Accept any method]
[2 marks for method
1 mark for correct
answer]
(3)
4.4
928 ÷ 12 = 77 rem 4
MULTIPLY SUBTRACT CLUE BOARD 12 × 70 = 840 12 × 7 = 84
928 − 840 = 88 88 − 84 = 4 rem
12 × 10 = 120 12 × 20 = 240 12 × 30 = 360 12 × 40 = 480 12 × 50 = 600 12 × 60 = 720 12 × 70 = 840 12 × 80 = 960
[Accept any method]
[2 marks for metho
1 mark for correct
answer]
(3)
5.1.1 23 985 + 11 378 = 35 363 ∴ 35 363 adults attended the soccer match.
[Accept any method]
[2 marks for method
1 mark for correct
answer]
(3)
15
5.1.2 41 295 + 35 663 5 932 ∴ 5 932 children attended the soccer match.
[Accept any method]
[Apply consistency
accuracy]
[2 marks for method
1 mark for correct
answer]
(3)
5.2.1 R5,50 −R2,50 R3,00 ∴ He makes R3,00 profit.
[Accept any method]
[2 marks for method
1 mark for correct
answer]
(3)
5.2.2 He will make R3,00 × 35 = R105,00 profit. (R3,00 × 30) + (R3,00 × 5) = R90,00 + R15,00 = R105,00
[Accept any method]
[Apply consistency
accuracy]
[2 marks for method
1 mark for correct
answer]
(3)
201MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
5.3 CALCULATION CLUE BOARD [Accept any method]
[Apply consistency
accuracy]
[2 marks for method
1 mark for correct
answer]
(3) 380 is bigger than 375 , so we choose 285. So we can say 3 groups of 95 is 285. We then subtract : 375 – 285 = 90 375 ÷ 95 = 3 rem 90 ∴ The school will hire 4 buses for an
excursion.
1 × 95 = 95 2 × 95 = 190 3 × 95 = 285 4 × 95 = 380
GRAND TOTAL 40
202 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
EXEMPLAR INVESTIGATION: GRADE 6 TERM 4
Investigating the relationship between surface area and volume 15 marks
QUESTION 1
1.1 Determine the Surface area and the volume of each stack of boxes below. Give the surface area in number of squares and the volume in number of cubes.
STACK A B C D E
Surface area in number of squares
VOLUME in number of cubes
(12)
1.2 Which stacks have the same volume? (2)
203MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
1.3 Is the surface area of the stack A equal to that of stack B? (1) 1.4 Is the surface area of the stack D equal to that of stack F? (1) 1.5 Do stacks of equal volume also have equal surface area? (1) 1.6 Which stacks have equal surface area? (1) 1.5 Do stacks of equal surface area have equal volume? (1) 1.6 Does knowing volume of a stack tell us the surface area of the stack? (1) 1.7 What conclusion can be drawn from the above observations? (2)
204 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
EXEMPLAR INVESTIGATION MEMO: GRADE 6 TERM 4
Investigating the relationship between surface area and volume 15 marks
QUESTION 1
1.1 Determine the Surface area and the volume of each stack of boxes below. Give the surface area in number of squares and the volume in number of cubes.
1.2
STACK A B C D E
Surface area in number of squares
26
22
22
28
24
VOLUME in number of cubes
6 6 6 8 8
(10)
205MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
1.2 Which stacks have the same volume? A, B and C D and E (2)
1.3 Is the surface area of the stack A equal to that of stack B?
No (1) 1.4 Is the surface area of the stack D equal to that of stack F?
No (1) 1.5 Do stacks of equal volume also have equal surface area?
Sometimes (1) 1.6 Which stacks have equal surface area?
B and C (1) 1.5 Do stacks of equal surface area have equal volume?
Sometimes (1) 1.6 Does knowing volume of a stack tell us the surface area of the stack?
No (1) 1.7 What conclusion can be drawn from the above observations?
Stacks of equal volume do not necessarily have equal surface area Stacks of equal surface area have equal volume (2)
206 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
GRADE 6 EXEMPLAR TEST – TERM 2
INSTRUCTIONS TO LEARNERS:
1. Answer all questions in the space provided. 2. The use of calculators is NOT allowed. 3. The test duration is 60 minutes
QUESTION 1 Circle the letter next to the correct answer.
1.1 The number, three hunderd and fifty nine thousand eight hundred and three can be
written as
A 359 308
B 395 803
C 359 803
B 359 083 (1)
1.2 Which number is represented by (3 × 100 000) + (40 × 1 000) + (9 000) + (15 tens) +
(7 × 1)?
A 349 570
B 350 507
C 349 082
D 349 157 (1)
1.3 Which number is 3 000 000 more than 567 432 957 ?
A 570 432 957
B 567 732 957
C 597 432 957
D 867 432 957 (1)
1.4 The value of the underlined digit in 65 359 468 is
A 5 × 10 000 000
B 5 × 1 000 000
C 5 × 100 000
D 50 000 000 (1)
1.5 Which is the best estimation of the number of South African soccer fans?
A 50 000
B 1 800
C 1 208 400
D 160 000
(1)
207MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
1.6 The number 133 756 rounded off to the nearest 5 is ____
A 133 750
B 133 755
C 133 760
D 133 765 (1)
1.7 What is the value of B if 51 − 6 = 𝑩𝑩 − 51
A 45
B 67
C 81
D 96 (1)
1.8 Which sum does not give an answer of 49?
A 8 × 5 + 9
B (8 × 5) + 9
C 8 × (5 + 9)
D (8 × 5 + 9) (1)
1.9 Which number is not a factor of 36?
A 3
B 4
C 8
D 18 (1)
10 Which number between 12 and 144 is a multiple of 12?
A 6
B 12
C 240
D 96 (1)
(10) QUESTION 2 2.1 Write the following numbers in descending order.
134 910 139 410 143 190 139 140
_______________________________________________________________________
________
(1)
2.2 What is the biggest number you can make using the digits
7 1 4 8 5 9 4?
_______________________________________________________________________
________
(1)
2.3 What is the value of the underlined digit?
657 128 367
208 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
_______________________________________________________________________
________
(1)
2.4 Fill in the missing numbers in the following:
2.4.1 135 930 ; 135 933 ; 135 936 ; _______________. (1)
2.4.2 1 227 050 ; 1 227 000 ; 1 226 950 ; _______________. (1)
2.5 Write the number 5 103 467 in expanded notation
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
___________________________
(3)
2.6 Write 35 386 427 in words.
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
___________________________
(1)
2.7 57; 27; 72; 36; 61; 81; 45
From the numbers above, choose:
2.7.1 a prime number
_______________________________________________________________________
_________
(1)
2.7.2 A number which is the product of two prime numbers
_______________________________________________________________________
________
(1)
(11) QUESTION 3
3.1 Say whether the following statements are True or False?
3.1.1 247 889 > 247 898 ____________________ (1)
3.1.2 25 × 27 ≈ (20 + 5) × (20 + 7) ______________________ (1)
3.1.3 (18 × 4) × 5 = 18 × (5 × 4) ____________________ (1)
3.1.4 When I multiply a number by 1, the answer is always equal to the original number.
____________________
(1)
3.1.5 When we add zero (0) to a number, the number is doubled.
____________________
(1)
209MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
3.2 What is the Lowest Common Multiple (LCM) of 12 and 36.
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
____________________________________
(2)
3.3 3.3.1 Is 821 758 closer to 821 700 or 821 800?
_______________________________________________________________________
_________
(1)
3.3.2 R6 214,76 ≈ _________________________ rounded off to the nearest rand. (1)
3.4 3.4.1 Insert the missing factor of 12: 2 , _____ , 12 , 3 , 6 , 4
(1) 3.4.2 List all the factors of 225.
_______________________________________________________________________
_________
(1)
3.4.2 Which 2 whole numbers can I multiply to get to 125?
_______________________________________________________________________
_________ (12)
(1)
QUESTION 4 Calculate
4.1 Add using columns: 3 473 679 ; 725 184 𝑎𝑎𝑎𝑎𝑎𝑎 2 378 487
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_____________________________________________
(3)
4.2 Subtract 1 764 384 from 3 065 635
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_____________________________________________
(3)
210 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
4.3 Multiply 7 365 and 25
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_____________________________________________
(3)
4.4 Calculate the remainder, using long division, if 2 836 is divided by 450
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_
(3)
4.5 Calculate:
4.5.1 (58 + 12) − (33 − 19)
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
___________________________
(3)
4.5.2 2 + 3 × 4 − 6
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
___________________________
(17)
(2)
211MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
QUESTION 5 5.1 A lady buys a specific brand of DVD players for all her stores. She buys 126 789 black,
341 567 white and 344 532 silver DVD players. How many DVD players did she buy
altogether?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
________________________________________
(3)
5.2 Farm workers picked 342 345 pears during the morning. After lunch they picked some
more. By the end of the day, they had 866 589 pears. How many pears did they pick
after lunch?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
________________________________________
(3)
5.3 156 pairs of shoes cost R7 020.
How much will one pair of the same shoes cost?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
________________________________________
(3)
5.4 A company gave 536 boxes of soccer balls to multigrade schools. Each box contained
3 126 soccer balls. How many soccer balls did the company give away?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
________________________________________
(3)
(12)
212 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
GRADE 6 EXEMPLAR TEST MEMORANDUM – TERM 2
General marking notes:
1. Give full marks for answers only, unless otherwise stated. 2. Accept any alternative correct solution that is not included in the memorandum. 3. Apply consistency accuracy [CA], where necessary.
QUESTION EXPECTED ANSWER MARKS
TOTAL
1.1 B (1)
10
1.2 D (1) 1.3 A (1) 1.4 B (1) 1.5 C (1) 1.6 B (1) 1.7 D (1) 1.8 C (1) 1.9 C (1) 1.10 D (1) 2.1 143 190 139 410 139 140 134 910 (1)
8
2.2 9 875 441 (1)
2.3 7 000 000 or 7 million or (7 × 1 000 000) (1)
2.4.1 135 930; 135 933; 135 936; 135 939. (1)
2.4.2 1 227 050; 1 227 000; 1 226 950; 1 226 900. (1)
2.5 Thirty five million three hundred and eighty six thousand four hundred and
twenty seven
(1)
2.6.1 61 (1)
2.6.2 57 [a product of 3 and 19] (1)
3.1.1 False (1)
13
3.1.2 True (1)
3.1.3 True (1)
3.1.4 True (1)
3.1.5 False (1)
3.2 Multiples of 12 = 12; 24; 36; 48; …
Multiples of 36 = 36; 72; 108; …
Lowest Common Multiple = 36
(3)
3.3.1 821 758 is closer to 821 800. (1)
3.3.2 R6 214,76 ≈ R6 215 rounded off to the nearest rand. (1)
3.4.1 The missing factor is 1. (1)
3.4.2 Factors of 225 are: 1; 3; 5; 9;15; 45; 225. (1)
3.4.3 1 and 125 or 5 and 25 (1)
4.1 3 476 679 725 184 + 2 378 487 6 580 350
[2 marks for method 1 mark for correct answer] Correct answer –3 marks
(3) 17
213MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
4.2 3 065 635 −1 764 384 1 301 251
[2 marks for method 1 mark for correct answer] Correct answer –3 marks
(3)
4.3 Calculate the product of 7 365 and 25
7 365 × 25 36 825 + 147 200 184 125
2 marks for method
1 mark for correct answer Correct answer –3 marks
(3)
4.4 2 836 ÷ 255 = 11 remainder 31
11
255 2 836 − 255 286 −255 31 rem
2 marks for method
1 mark for correct answer Correct answer –3 marks
(3)
4.5.1 (58 + 12) − (33 − 19) = 70 − 12 = 58
2 marks for method
1 mark for correct answer
(3)
4.5.2 2 + 3 × 4 − 6 = 2 + 12 − 6 = 14 − 6 = 8
2 marks for method
1 mark for correct answer
(2)
5.1 126 789 341 567 + 344 532 812 888 She bought 812 888 DVD players.
[Accept any
method]
[2 marks for
method
1 mark for correct answer]
(3)
12
5.2 866 589 − 342 345 524 244
Farm workers picked 524 244 pears after lunch.
[Accept any
method]
[2 marks for
method
1 mark for correct answer]
(3)
5.3 7 020 ÷ 156 = 45
∴ Each shoe costs R45
[Accept any
method]
[2 marks for
method
1 mark for correct answer]
(3)
MULTIPLY SUBTRACT CLUE BOARD 156 × 40= 6 240 156 × 5= 780
7 020 − 6 240= 780 780 − 780 = 0
156 × 10 = 1 560 156 × 20 = 3 120 156 × 30 = 4 680 156 × 40 = 6 240 156 × 5 = 780
5.4 3 126 × 536 18 756 93 780
[Accept any
method]
[2 marks for
214 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
+ 1 563 000 1 675 536 The company gave 1 675 536 balls away.
method
1 mark for correct answer]
(3)
GRAND TOTAL 60
215MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LESS
ON
PLA
NS:
AFR
IKA
AN
S
216 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
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TER
MED
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E FA
SE
MU
LTIG
RAA
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KW
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……
……
……
……
……
……
..
DAT
UM
: W
EEK
3 2
8 /0
1 –
01 /0
2 2
013
TYD
: 5 D
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6
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WER
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217MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
218 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
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TER
MED
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E FA
SE
MU
LTIG
RAA
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KW
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……
……
……
……
…..
DAT
UM
: W
EEK
4
4 –
8 F
EBR
UAR
IE
2013
TYD
: 5 D
AE
6
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RAA
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4 5
6 O
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B
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Get
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etal
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kom
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ensk
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van
hee
lget
alle
: Ko
mm
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iew
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As
sosi
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kapp
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loss
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Los
pr
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me
in k
onte
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p;
insl
uite
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ëlek
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kste
Get
alge
bied
: 5-s
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get
alle
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katti
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pbou
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afbr
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van
geta
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Verd
ubbe
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skap
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op
tellin
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kap
Prob
leem
oplo
ssin
g: L
os p
robl
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in
kont
eks
op;
insl
uite
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ëlek
onte
kste
Ve
rgel
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of m
eerh
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de v
an
dies
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de s
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verh
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OM
:
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NAS
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ALE
WER
KB
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TUIS
WER
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OPD
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TE
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ING
219MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
220 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
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TER
MED
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E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
O
PVO
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: ……
……
……
..
DAT
UM
: W
EEK
5
11
– 15
FEB
RU
ARIE
201
3
TY
D: 4
DAE
5 U
RE
GR
AAD
4
5 6
ON
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WER
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Patr
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Dok
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EN
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Ky
kna
die
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tant
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skil/
verh
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Besk
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et g
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Be
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diag
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vloe
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get
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221MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
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TER
MED
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E FA
SE
MU
LTIG
RAA
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KW
ARTA
AL E
EN
O
PVO
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: ……
……
……
……
……
……
…..
DAT
UM
: W
EEK
6
– 7
18 F
EBR
UAR
IE -
01
MAA
RT
201
3
T
YD: 1
0 D
AE
12
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4 5
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Hee
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Verm
enig
vuld
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g&D
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l. 54
– 5
8 B
EGR
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EN
VA
ARD
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Get
alge
bied
: Le
erde
rson
twik
kel e
n le
erta
fels
[2x
– 10
x]
Verm
: 2-s
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met
1-s
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D
eel3
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er d
eur 1
-syf
er
Tegn
ieke
:
ska
t O
pbou
en
afbr
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halv
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van
‘n g
etal
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mge
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mut
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As
sosi
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tribu
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loss
ing:
In
kont
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rgel
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an
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t [ra
tio]V
erge
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kille
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verd
elin
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Get
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bied
: Lee
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sont
wik
kel
en le
erta
fels
[2x
– 10
x]
Verm
: 3-s
yfer
met
2-s
yfer
D
eel 3
-syf
er d
eur 2
-syf
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Tegn
ieke
: s
kat
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bree
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skap
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mm
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iew
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term
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Prob
leem
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ssin
g: In
kon
teks
Fi
nans
iële
Kont
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Verg
elyk
ings
van
die
selfd
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rt
[ratio
] Ve
rgel
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an
vers
kille
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oorte
G
roep
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g en
ver
delin
g m
et re
ste
Get
alge
bied
: Lee
rder
sont
wik
kel
en le
erta
fels
[11x
; 12x
; 13x
; 15x
; 20
x; 2
5x; 5
0x]
Verm
: 4-s
yfer
met
3-s
yfer
[met
of
sond
erha
kies
]Dee
l 4-s
yfer
deu
r 3-
syfe
r[ m
et o
f son
derh
akie
s]
Tegn
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:
ska
tOpb
ou e
n af
bree
kAfro
ndin
g en
ko
mpe
nser
ingG
ebru
iksa
krek
enaa
r Ko
lom
verm
enig
vuld
igin
g Ve
elvo
ude
en
Fak
tore
: 2-
syfe
r en
3-s
yfer
geta
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t Pr
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fakt
ore
van
geta
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t ten
m
inst
e 10
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ensk
appe
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etal
le:
Kom
mut
atie
we;
Ass
osia
tiew
e;
Dis
tribu
tiew
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n 1
in te
rme
van
syve
rmen
igvu
ldig
ings
eien
skap
Pr
oble
emop
loss
ing:
In k
onte
ks
Fina
nsië
leKo
ntek
s Ve
rgel
ykin
gs v
an d
iese
lfdes
oort
[ra
tio]
Verg
elyk
ings
van
ve
rski
llend
esoo
rte
Gro
eper
ing
en v
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met
rest
e
LOO
M:
HAN
DB
OEK
VE
RW
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GS.
NAS
ION
ALE
WER
KB
OEK
222 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TUIS
WER
K
OPD
RAG
TE
223MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
O
PVO
EDER
: ……
……
……
…..
DAT
UM
: W
EEK
8
4- 8
MAA
RT
2013
TYD
: 5 D
AE
6
UR
E G
RAA
D
4 5
6 O
ND
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ERP
TYD
KAB
V P.
57, 1
46, 2
34
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ber
eken
inge
m
et b
etre
kkin
g to
t tyd
Bere
kent
ydin
terv
alle
G
eski
eden
is v
an ty
d
Lees
, sê
en s
kryf
12-
uur
en
24 -
uurty
d op
dig
itale
en
anal
oogi
nstru
men
te in
Ure
, min
en
seko
ndes
Le
es v
an a
lman
akke
Pr
oble
emop
loss
ing
en
bere
keni
nge
met
bet
rekk
ing
tot
tyd
Bere
kent
ydin
terv
alle
G
eski
eden
is v
an ty
d
Lees
, sê
en s
kryf
12-
uur
en
24 -
uurty
d op
dig
itale
en
anal
oogi
nstru
men
te in
Ure
, min
en
seko
ndes
Le
es v
an a
lman
akke
Pr
oble
emop
loss
ing
en
bere
keni
nge
met
bet
rekk
ing
tot
tyd
Lees
tyds
ones
op
karte
Bere
kent
ydin
terv
alle
G
eski
eden
is v
an ty
d LO
OM
:
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
224 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
OPV
OED
ER: …
……
……
……
……
……
….
DAT
UM
: W
EEK
9
11
- 15
MAA
RT2
013
TYD
: 5 D
AE
6
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
DAT
AHAN
TER
ING
P.5
9, 1
48, 2
39
BEG
RIP
PE E
N
VAAR
DIG
HED
E Ve
rsam
el e
n or
gani
seer
da
ta
tellin
gsta
belle
] St
el d
ata
voor
Pikt
ogra
mm
e
Staa
fgra
fieke
An
alis
e; in
terp
reta
sie
en
vers
lagd
oeni
ng v
an d
ata
Pi
ktog
ram
me
St
aafg
rafie
ke
Vers
amel
en
orga
nise
er
data
[ te
llinst
abel
leas
ooko
rden
van
kl
eins
te to
t gro
otst
e]
Stel
dat
a vo
or
Pi
ktog
ram
me
St
aafg
rafie
ke
Anal
ise;
inte
rpre
tasi
e en
ve
rsla
gdoe
ning
van
dat
a
Pikt
ogra
mm
e
Staa
fgra
fieke
Sirk
eldi
agra
mm
e w
oord
elik
s
Vers
amel
en
orga
nise
er d
ata
te
llinst
abel
leas
ook
or
den
van
klei
nste
tot g
root
ste
vr
aely
ste
Stel
dat
a vo
or
Pi
ktog
ram
me
St
aafg
rafie
ke
Anal
ise;
inte
rpre
tasi
e en
ver
slag
doen
ing
van
data
Pikt
ogra
mm
e
Staa
fgra
fieke
asoo
kdub
bele
staa
fgra
fieke
Sirk
eldi
agra
mm
e
Woo
rdel
iks
m
odus
LO
OM
:
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
225MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
O
PVO
EDER
: ……
……
……
……
……
…..
DAT
UM
: W
EEK
2
18
- 22
MAA
RT
201
3
T
YD: 5
DAE
6 U
RE
GR
AAD
4
5 6
ON
DER
WER
P Ei
ensk
appe
van
2D
-Vor
m K
ABV
Bl.
61 -6
3
KAB
V B
l. 15
0-15
2KAB
V B
l. 23
5 –
238
B
EGR
IPPE
EN
VA
ARD
IGH
EDE
Beno
emvo
rms
dr
ieho
eke
vi
erka
nte
re
ghoe
ke
an
derv
ierh
oeke
pent
agon
e
heks
agon
e
sirk
els
Eien
skap
p va
n vo
rms
ge
boë
/regu
itsye
aant
alsy
e Te
ken
2D -V
orm
s
Beno
emvo
rms
dr
ieho
eke
vi
erka
nte
re
ghoe
ke
an
derv
ierh
oeke
pent
agon
e
heks
agon
e
hept
agon
e
sirk
els
Eien
skap
p va
n vo
rms
ge
boë
/regu
itsye
aant
alsy
e
leng
te v
an s
ye
ho
eke
[regt
ehoe
ke
en k
lein
er/g
rote
r as
regt
ehoe
ke]
Teke
n 2D
-Vor
ms
Ken
en
beno
emre
ëlm
atig
e en
on
reël
mat
igev
ierh
oeke
, dr
ieho
eke,
vie
rkan
te,
regh
oeke
en
para
llelo
gram
me;
pe
ntag
one;
hek
sogo
ne;
hept
agon
e en
okt
agon
e Ei
ensk
appe
van
Vor
ms:
aant
alsy
e
leng
te v
an s
ye
gr
ootte
van
hoe
ke
Teke
n 2D
Vor
ms
; geb
ruik
pa
sser
virs
irkel
s H
erke
n en
ben
oem
hoek
e
LOO
M:
H
AND
BO
EK
VER
WYS
ING
S.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
AS
SESS
ERIN
G
TOET
S 1
226 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
OPV
OED
ER: …
……
……
……
……
……
……
..
DAT
UM
: W
EEK
3 2
8 /0
1 –
01 /0
2 2
013
TYD
: 5 D
AE
6
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
Get
alle
sinn
eInl
eidi
ng to
t Alg
ebra
iiseu
itdru
kkin
gs
B
EGR
IPPE
EN
VA
ARD
IGH
EDE
Ek
wiv
alen
teui
tdru
kkin
gs /
geta
lsin
ne
Ko
mm
utat
iew
e-,
asso
siat
iew
e- e
n
Dis
tribu
tiew
eeie
nska
ppe
In
vers
e be
wer
king
s en
dieW
isku
ndig
ewaa
rded
aa
rvan
Ve
rmen
igvu
ldig
ings
eien
skap
van
1
O
ptel
lings
eien
skap
van
0
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ntw
ikke
lopt
el e
n
aftre
kteg
niek
ed.m
.vge
tals
inn
e
As
sosi
atie
wee
iens
kap
van
opte
lling
G
etal
sinn
e - M
aal e
n
Dee
l met
10,
100
en
1000
Vo
lgor
de b
y
aftre
kkin
g
L
os g
etal
lesi
nne
op
deur
In
spek
sie
Pr
obee
r en
verb
eter
Kont
role
er d
ie
oplo
ssin
gdeu
rver
vang
ing
LOO
M:
Patro
onka
arte
, vlo
eika
arte
,
227MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
228 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
OPV
OED
ER: …
……
……
……
……
…..
DAT
UM
: W
EEK
4
4 –
8 F
EBR
UAR
IE
2013
TYD
: 5 D
AE
6
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
Hee
lget
alle
Opt
ellin
g&Af
trekk
ing
B
EGR
IPPE
EN
VA
ARD
IGH
EDE
Get
alge
bied
: 3-s
yfer
get
alle
Te
gnie
ke:
Skat
ting
Opb
ou e
n af
bree
k va
n ge
talle
Ve
rdub
bel e
n ha
lvee
r G
etal
lely
ne
Afro
ndin
g en
kom
pens
erin
g Ei
ensk
appe
van
hee
lget
alle
: Ko
mm
utat
iew
e en
As
sosi
atie
wee
iens
kapp
e Pr
oble
emop
loss
ing:
Los
pr
oble
me
in k
onte
ks o
p;
insl
uite
ndfin
ansi
ëlek
onte
kste
Get
alge
bied
: 5-s
yfer
get
alle
Te
gnie
ke: S
katti
ngO
pbou
en
afbr
eek
van
geta
lle
Verd
ubbe
l en
halv
eeG
etal
lely
neAf
rond
ing
en k
ompe
nser
ing
Inve
rse
bew
erki
ngs
Eien
skap
pe v
an h
eelg
etal
le:
Kom
mut
atie
we;
As
sosi
atie
we
en
dist
rubi
tiew
eeie
nska
ppe
0 se
opt
ellin
gs- e
iens
kap
Prob
leem
oplo
ssin
g: L
os
prob
lem
e in
kon
teks
op;
in
slui
tend
finan
siël
ekon
teks
te
Get
alge
bied
: 6 –
syfe
rget
alle
Ve
elvu
ldig
ebew
erki
nge
met
/s
onde
rhak
ies
Tegn
ieke
: Ska
tting
O
pbou
en
afbr
eek
van
geta
lle
Verd
ubbe
l en
halv
eer
Get
alle
lyne
Af
rond
ing
en k
ompe
nser
in
Inve
rse
bew
erki
ngsS
akre
kena
ar
Eien
skap
pe v
an h
eelg
etal
le:
Kom
mut
atie
we;
Ass
osia
tiew
e en
di
stru
bitie
wee
iens
kapp
e
0 se
op
tellin
gs- e
iens
kap
Prob
leem
oplo
ssin
g: L
os p
robl
eme
in
kont
eks
op;
insl
uite
ndfin
ansi
ëlek
onte
kste
Ve
rgel
yk 2
of m
eerh
oeve
elhe
de v
an
dies
elfe
de s
ort [
verh
oudi
ng]
LO
OM
:
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K
OPD
RAG
TE
OPM
ERK
ING
229MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
230 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
O
PVO
EDER
: ……
……
……
..
DAT
UM
: W
EEK
5
11
– 15
FEB
RU
ARIE
201
3
TY
D: 4
DAE
5 U
RE
GR
AAD
4
5 6
ON
DER
WER
P N
umer
iese
Patr
oon
K
ABV
Dok
. B
EGR
IPPE
EN
VA
ARD
IGH
EDE
Ond
erso
ek e
n br
eipa
troon
uit
Ky
kna
die
reel
s
Ree
ks m
et
kons
tant
ever
skil/
verh
oudi
ngs
Besk
ryfre
ëls
in w
oord
e
Leer
der s
e ei
eske
ppin
g Be
paal
Inse
t- ;
uits
etw
aard
es e
n re
ëls
met
vlo
eidi
agra
mm
e Ek
wiv
alen
tevo
rms
Woo
rdel
iks
In
vlo
eidi
agra
mm
e M
et g
etal
lesi
nne
Ond
erso
ek e
n br
eipa
troon
uit
Ky
kna
die
reel
s
Ree
ks m
et
kons
tant
ever
skil/
verh
oud
ings
Besk
ryfre
ëls
in w
oord
e
Leer
der s
e ei
eske
ppin
g Be
paal
Inse
t- ;
uits
etw
aard
es e
n re
ëls
met
vlo
eidi
agra
mm
e Ek
wiv
alen
tevo
rms
W
oord
elik
s
Invl
oeid
iagr
amm
e M
et g
etal
lesi
nne
Ond
erso
ek e
n br
eipa
troon
uit
Ky
kna
die
reel
s
Ree
ks m
et
niek
onst
ante
vers
kil/v
erho
udin
gs
Be
skry
freël
s in
woo
rde
Le
erde
r se
eies
kepp
ing
Bepa
al In
set-
; ui
tset
waa
rdes
en
reël
s m
et v
loei
diag
ram
me
Ekw
ival
ente
vorm
s
Woo
rdel
iks
In
vloe
idia
gram
me
Met
get
alle
sinn
e
LOO
M:
H
AND
BO
EK
VER
WYS
ING
S.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K
OPD
RAG
TE
OPM
ERK
ING
231MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
O
PVO
EDER
: ……
……
……
……
……
……
…..
DAT
UM
: W
EEK
6
– 7
18 F
EBR
UAR
IE -
01
MAA
RT
201
3
T
YD: 1
0 D
AE
12
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
Hee
lget
alle
Verm
enig
vuld
igin
g&D
elin
g
K
ABV
Dok
B
l. 54
– 5
8 B
EGR
IPPE
EN
VA
ARD
IGH
EDE
Get
alge
bied
: Le
erde
rson
twik
kel e
n le
erta
fels
[2x
– 10
x]
Verm
: 2-s
yfer
met
1-s
yfer
D
eel3
-syf
er d
eur 1
-syf
er
Tegn
ieke
:
ska
t O
pbou
en
afbr
eek
Afro
ndin
g en
kom
pens
erin
g Ve
rdub
bel&
halv
eerG
ebru
ik
van
‘n g
etal
lely
n O
mge
keer
debe
wer
king
Ve
elvo
ude
en F
akto
re: 1
-sy
fer g
etal
le to
t 100
Ei
ensk
appe
venH
eelg
etal
le:
Kom
mut
atie
we;
As
sosi
atie
we;
Dis
tribu
tiew
e Pr
oble
emop
loss
ing:
In
kont
eks
Fina
nsië
leKo
ntek
s Ve
rgel
ykin
gs v
an
dies
efde
soor
t [ra
tio]V
erge
lyki
ngs
van
vers
kille
ndes
oorte
G
roep
erin
g en
ge
lyke
verd
elin
g
Get
alge
bied
: Lee
rder
sont
wik
kel
en le
erta
fels
[2x
– 10
x]
Verm
: 3-s
yfer
met
2-s
yfer
D
eel 3
-syf
er d
eur 2
-syf
er
Tegn
ieke
: s
kat
Opb
ou e
n af
bree
k Af
rond
ing
en k
ompe
nser
ing
Verd
ubbe
l&ha
lvee
r G
ebru
ik v
an ‘n
get
alle
lyn
Om
geke
erde
rbew
erki
ng
Veel
voud
e en
Fak
tore
: 2-s
yfer
ge
talle
tot 1
00
Eien
skap
peve
nHee
lget
alle
: Ko
mm
utat
iew
e; A
ssos
iatie
we;
D
istri
butie
we0
en
1 in
term
e va
n sy
verm
enig
vuld
igin
gsei
ensk
ap
Prob
leem
oplo
ssin
g: In
kon
teks
Fi
nans
iële
Kont
eks
Verg
elyk
ings
van
die
selfd
esoo
rt
[ratio
] Ve
rgel
ykin
gs v
an
vers
kille
ndes
oorte
G
roep
erin
g en
ver
delin
g m
et re
ste
Get
alge
bied
: Lee
rder
sont
wik
kel
en le
erta
fels
[11x
; 12x
; 13x
; 15x
; 20
x; 2
5x; 5
0x]
Verm
: 4-s
yfer
met
3-s
yfer
[met
of
sond
erha
kies
]Dee
l 4-s
yfer
deu
r 3-
syfe
r[ m
et o
f son
derh
akie
s]
Tegn
ieke
:
ska
tOpb
ou e
n af
bree
kAfro
ndin
g en
ko
mpe
nser
ingG
ebru
iksa
krek
enaa
r Ko
lom
verm
enig
vuld
igin
g Ve
elvo
ude
en
Fak
tore
: 2-
syfe
r en
3-s
yfer
geta
lle to
t Pr
iem
fakt
ore
van
geta
lle to
t ten
m
inst
e 10
0 Ei
ensk
appe
venH
eelg
etal
le:
Kom
mut
atie
we;
Ass
osia
tiew
e;
Dis
tribu
tiew
e0 e
n 1
in te
rme
van
syve
rmen
igvu
ldig
ings
eien
skap
Pr
oble
emop
loss
ing:
In k
onte
ks
Fina
nsië
leKo
ntek
s Ve
rgel
ykin
gs v
an d
iese
lfdes
oort
[ra
tio]
Verg
elyk
ings
van
ve
rski
llend
esoo
rte
Gro
eper
ing
en v
erde
ling
met
rest
e
LOO
M:
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
232 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
TUIS
WER
K
OPD
RAG
TE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
O
PVO
EDER
: ……
……
……
…..
DAT
UM
: W
EEK
8
4- 8
MAA
RT
2013
TYD
: 5 D
AE
6
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
TYD
KAB
V P.
57, 1
46, 2
34
BEG
RIP
PE E
N
VAAR
DIG
HED
E Le
es, s
ê en
skr
yf 1
2- u
ur e
n 24
- uu
rtyd
op d
igita
le e
n an
aloo
gins
trum
ente
in
U
re, m
in e
n se
kond
es
Lees
van
alm
anak
ke
Be
reke
naan
tald
aetu
ssen
2
datu
ms
Prob
leem
oplo
ssin
g en
ber
eken
inge
m
et b
etre
kkin
g to
t tyd
Bere
kent
ydin
terv
alle
G
eski
eden
is v
an ty
d
Lees
, sê
en s
kryf
12-
uur
en
24 -
uurty
d op
dig
itale
en
anal
oogi
nstru
men
te in
Ure
, min
en
seko
ndes
Le
es v
an a
lman
akke
Pr
oble
emop
loss
ing
en
bere
keni
nge
met
bet
rekk
ing
tot
tyd
Bere
kent
ydin
terv
alle
G
eski
eden
is v
an ty
d
Lees
, sê
en s
kryf
12-
uur
en
24 -
uurty
d op
dig
itale
en
anal
oogi
nstru
men
te in
Ure
, min
en
seko
ndes
Le
es v
an a
lman
akke
Pr
oble
emop
loss
ing
en
bere
keni
nge
met
bet
rekk
ing
tot
tyd
Lees
tyds
ones
op
karte
Bere
kent
ydin
terv
alle
G
eski
eden
is v
an ty
d
233MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
LOO
M:
H
AND
BO
EK
VER
WYS
ING
S.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
234 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
OPV
OED
ER: …
……
……
……
……
……
….
DAT
UM
: W
EEK
9
11
- 15
MAA
RT2
013
TYD
: 5 D
AE
6
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
DAT
AHAN
TER
ING
P.5
9, 1
48, 2
39
BEG
RIP
PE E
N
VAAR
DIG
HED
E Ve
rsam
el e
n or
gani
seer
da
ta
tellin
gsta
belle
] St
el d
ata
voor
Pikt
ogra
mm
e
Staa
fgra
fieke
An
alis
e; in
terp
reta
sie
en
vers
lagd
oeni
ng v
an d
ata
Pi
ktog
ram
me
St
aafg
rafie
ke
Vers
amel
en
orga
nise
er
data
[ te
llinst
abel
leas
ooko
rden
van
kl
eins
te to
t gro
otst
e]
Stel
dat
a vo
or
Pi
ktog
ram
me
St
aafg
rafie
ke
Anal
ise;
inte
rpre
tasi
e en
ve
rsla
gdoe
ning
van
dat
a
Pikt
ogra
mm
e
Staa
fgra
fieke
Sirk
eldi
agra
mm
e w
oord
elik
s
Vers
amel
en
orga
nise
er d
ata
te
llinst
abel
leas
ook
or
den
van
klei
nste
tot g
root
ste
vr
aely
ste
Stel
dat
a vo
or
Pi
ktog
ram
me
St
aafg
rafie
ke
Anal
ise;
inte
rpre
tasi
e en
ver
slag
doen
ing
van
data
Pikt
ogra
mm
e
Staa
fgra
fieke
asoo
kdub
bele
staa
fgra
fieke
Sirk
eldi
agra
mm
e
Woo
rdel
iks
m
odus
LO
OM
:
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
235MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
O
PVO
EDER
: ……
……
……
……
……
…..
DAT
UM
: W
EEK
2
18
- 22
MAA
RT
201
3
T
YD: 5
DAE
6 U
RE
GR
AAD
4
5 6
ON
DER
WER
P Ei
ensk
appe
van
2D
-Vor
m K
ABV
Bl.
61 -6
3
KAB
V B
l. 15
0-15
2KAB
V B
l. 23
5 –
238
BEG
RIP
PE E
N
VAAR
DIG
HED
E Be
noem
vorm
s
drie
hoek
e
vier
kant
e
regh
oeke
ande
rvie
rhoe
ke
pe
ntag
one
he
ksag
one
si
rkel
s Ei
ensk
app
van
vorm
s
gebo
ë /re
guits
ye
aa
ntal
sye
Teke
n 2D
-Vor
ms
Beno
emvo
rms
dr
ieho
eke
vi
erka
nte
re
ghoe
ke
an
derv
ierh
oeke
pent
agon
e
heks
agon
e
hept
agon
e
sirk
els
Eien
skap
p va
n vo
rms
ge
boë
/regu
itsye
aant
alsy
e
leng
te v
an s
ye
ho
eke
[regt
ehoe
ke
en k
lein
er/g
rote
r as
regt
ehoe
ke]
Teke
n 2D
-Vor
ms
Ken
en
beno
emre
ëlm
atig
e en
on
reël
mat
igev
ierh
oeke
, dr
ieho
eke,
vie
rkan
te,
regh
oeke
en
para
llelo
gram
me;
pe
ntag
one;
hek
sogo
ne;
hept
agon
e en
okt
agon
e Ei
ensk
appe
van
Vor
ms:
aant
alsy
e
leng
te v
an s
ye
gr
ootte
van
hoe
ke
Teke
n 2D
Vor
ms
; ge
brui
k pa
sser
virs
irkel
s H
erke
n en
ben
oem
hoek
e
LOO
M:
H
AND
BO
EK
VER
WYS
ING
S.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
AS
SESS
ERIN
G
TOET
S 1
236 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
OPV
OED
ER: …
……
……
……
……
……
……
..
DAT
UM
: W
EEK
3 2
8 /0
1 –
01 /0
2 2
013
TYD
: 5 D
AE
6
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
Get
alle
sinn
eInl
eidi
ng to
t Alg
ebra
iiseu
itdru
kkin
gs
B
EGR
IPPE
EN
VA
ARD
IGH
EDE
Ek
wiv
alen
teui
tdru
kkin
gs /
geta
lsin
ne
Ko
mm
utat
iew
e-,
asso
siat
iew
e- e
n
Dis
tribu
tiew
eeie
nska
ppe
In
vers
e be
wer
king
s en
dieW
isku
ndig
ewaa
rded
aa
rvan
Ve
rmen
igvu
ldig
ings
eien
skap
van
1
O
ptel
lings
eien
skap
van
0
O
ntw
ikke
lopt
el e
n
aftre
kteg
niek
ed.m
.vge
tals
inn
e
As
sosi
atie
wee
iens
kap
van
opte
lling
G
etal
sinn
e - M
aal e
n
Dee
l met
10,
100
en
1000
Vo
lgor
de b
y
aftre
kkin
g
L
os g
etal
lesi
nne
op
deur
In
spek
sie
Pr
obee
r en
verb
eter
Kont
role
er d
ie
oplo
ssin
gdeu
rver
vang
ing
LOO
M:
Patro
onka
arte
, vlo
eika
arte
,
237MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
238 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
OPV
OED
ER: …
……
……
……
……
…..
DAT
UM
: W
EEK
4
4 –
8 F
EBR
UAR
IE
2013
TYD
: 5 D
AE
6
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
Hee
lget
alle
Opt
ellin
g&Af
trekk
ing
B
EGR
IPPE
EN
VA
ARD
IGH
EDE
Get
alge
bied
: 3-s
yfer
get
alle
Te
gnie
ke:
Skat
ting
Opb
ou e
n af
bree
k va
n ge
talle
Ve
rdub
bel e
n ha
lvee
r G
etal
lely
ne
Afro
ndin
g en
kom
pens
erin
g Ei
ensk
appe
van
hee
lget
alle
: Ko
mm
utat
iew
e en
As
sosi
atie
wee
iens
kapp
e Pr
oble
emop
loss
ing:
Los
pr
oble
me
in k
onte
ks o
p;
insl
uite
ndfin
ansi
ëlek
onte
kste
Get
alge
bied
: 5-s
yfer
get
alle
Te
gnie
ke: S
katti
ngO
pbou
en
afbr
eek
van
geta
lle
Verd
ubbe
l en
halv
eeG
etal
lely
neAf
rond
ing
en k
ompe
nser
ing
Inve
rse
bew
erki
ngs
Eien
skap
pe v
an h
eelg
etal
le:
Kom
mut
atie
we;
As
sosi
atie
we
en
dist
rubi
tiew
eeie
nska
ppe
0 se
opt
ellin
gs- e
iens
kap
Prob
leem
oplo
ssin
g: L
os
prob
lem
e in
kon
teks
op;
in
slui
tend
finan
siël
ekon
teks
te
Get
alge
bied
: 6 –
syfe
rget
alle
Ve
elvu
ldig
ebew
erki
nge
met
/s
onde
rhak
ies
Tegn
ieke
: Ska
tting
O
pbou
en
afbr
eek
van
geta
lle
Verd
ubbe
l en
halv
eer
Get
alle
lyne
Af
rond
ing
en k
ompe
nser
in
Inve
rse
bew
erki
ngsS
akre
kena
ar
Eien
skap
pe v
an h
eelg
etal
le:
Kom
mut
atie
we;
Ass
osia
tiew
e en
di
stru
bitie
wee
iens
kapp
e
0 se
op
tellin
gs- e
iens
kap
Prob
leem
oplo
ssin
g: L
os p
robl
eme
in
kont
eks
op;
insl
uite
ndfin
ansi
ëlek
onte
kste
Ve
rgel
yk 2
of m
eerh
oeve
elhe
de v
an
dies
elfe
de s
ort [
verh
oudi
ng]
LO
OM
:
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K
OPD
RAG
TE
OPM
ERK
ING
239MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
O
PVO
EDER
: ……
……
……
..
WIS
KU
ND
E IN
TERM
EDIê
RE
FASE
M
ULT
IGR
AAD
KW
ARTA
AL E
EN
O
PVO
EDER
: …
……
……
……
……
……
……
..
DAT
UM
: W
EEK
6
– 7
18 F
EBR
UAR
IE -
01
MAA
RT
201
3
T
YD: 1
0 D
AE
12
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
Hee
lget
alle
Verm
enig
vuld
igin
g&D
elin
g
K
ABV
Dok
B
l. 54
– 5
8
DAT
UM
: W
EEK
5
11
– 15
FEB
RU
ARIE
201
3
TY
D: 4
DAE
5 U
RE
GR
AAD
4
5 6
ON
DER
WER
P N
umer
iese
Patr
oon
K
ABV
Dok
. B
EGR
IPPE
EN
VA
ARD
IGH
EDE
Ond
erso
ek e
n br
eipa
troon
uit
Ky
kna
die
reel
s
Ree
ks m
et
kons
tant
ever
skil/
verh
oudi
ngs
Besk
ryfre
ëls
in w
oord
e
Leer
der s
e ei
eske
ppin
g Be
paal
Inse
t- ;
uits
etw
aard
es e
n re
ëls
met
vlo
eidi
agra
mm
e Ek
wiv
alen
tevo
rms
Woo
rdel
iks
In
vlo
eidi
agra
mm
e M
et g
etal
lesi
nne
Ond
erso
ek e
n br
eipa
troon
uit
Ky
kna
die
reel
s
Ree
ks m
et
kons
tant
ever
skil/
verh
oud
ings
Besk
ryfre
ëls
in w
oord
e
Leer
der s
e ei
eske
ppin
g Be
paal
Inse
t- ;
uits
etw
aard
es e
n re
ëls
met
vlo
eidi
agra
mm
e Ek
wiv
alen
tevo
rms
W
oord
elik
s
Invl
oeid
iagr
amm
e M
et g
etal
lesi
nne
Ond
erso
ek e
n br
eipa
troon
uit
Ky
kna
die
reel
s
Ree
ks m
et
niek
onst
ante
vers
kil/v
erho
udin
gs
Be
skry
freël
s in
woo
rde
Le
erde
r se
eies
kepp
ing
Bepa
al In
set-
; ui
tset
waa
rdes
en
reël
s m
et v
loei
diag
ram
me
Ekw
ival
ente
vorm
s
Woo
rdel
iks
In
vloe
idia
gram
me
Met
get
alle
sinn
e
LOO
M:
H
AND
BO
EK
VER
WYS
ING
S.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K
OPD
RAG
TE
REM
IND
ERS
240 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
BEG
RIP
PE E
N
VAAR
DIG
HED
E G
etal
gebi
ed:
Leer
ders
ontw
ikke
l en
leer
tafe
ls [2
x –
10x]
Ve
rm: 2
-syf
er m
et 1
-syf
er
Dee
l3-s
yfer
deu
r 1-s
yfer
Te
gnie
ke:
s
kat
Opb
ou e
n af
bree
k Af
rond
ing
en k
ompe
nser
ing
Verd
ubbe
l&ha
lvee
rGeb
ruik
va
n ‘n
get
alle
lyn
Om
geke
erde
bew
erki
ng
Veel
voud
e en
Fak
tore
: 1-
syfe
r get
alle
tot 1
00
Eien
skap
peve
nHee
lget
alle
: Ko
mm
utat
iew
e;
Asso
siat
iew
e; D
istri
butie
we
Prob
leem
oplo
ssin
g: In
ko
ntek
s Fi
nans
iële
Kont
eks
Verg
elyk
ings
van
di
esef
deso
ort
[ratio
]Ver
gely
king
s va
n ve
rski
llend
esoo
rte
Gro
eper
ing
en
gely
keve
rdel
ing
Get
alge
bied
: Lee
rder
sont
wik
kel
en le
erta
fels
[2x
– 10
x]
Verm
: 3-s
yfer
met
2-s
yfer
D
eel 3
-syf
er d
eur 2
-syf
er
Tegn
ieke
: s
kat
Opb
ou e
n af
bree
k Af
rond
ing
en k
ompe
nser
ing
Verd
ubbe
l&ha
lvee
r G
ebru
ik v
an ‘n
get
alle
lyn
Om
geke
erde
rbew
erki
ng
Veel
voud
e en
Fak
tore
: 2-s
yfer
ge
talle
tot 1
00
Eien
skap
peve
nHee
lget
alle
: Ko
mm
utat
iew
e; A
ssos
iatie
we;
D
istri
butie
we0
en
1 in
term
e va
n sy
verm
enig
vuld
igin
gsei
ensk
ap
Prob
leem
oplo
ssin
g: In
kon
teks
Fi
nans
iële
Kont
eks
Verg
elyk
ings
van
die
selfd
esoo
rt
[ratio
] Ve
rgel
ykin
gs v
an
vers
kille
ndes
oorte
G
roep
erin
g en
ver
delin
g m
et re
ste
Get
alge
bied
: Lee
rder
sont
wik
kel
en le
erta
fels
[11x
; 12x
; 13x
; 15x
; 20
x; 2
5x; 5
0x]
Verm
: 4-s
yfer
met
3-s
yfer
[met
of
sond
erha
kies
]Dee
l 4-s
yfer
deu
r 3-
syfe
r[ m
et o
f son
derh
akie
s]
Tegn
ieke
:
ska
tOpb
ou e
n af
bree
kAfro
ndin
g en
ko
mpe
nser
ingG
ebru
iksa
krek
enaa
r Ko
lom
verm
enig
vuld
igin
g Ve
elvo
ude
en
Fak
tore
: 2-
syfe
r en
3-s
yfer
geta
lle to
t Pr
iem
fakt
ore
van
geta
lle to
t ten
m
inst
e 10
0 Ei
ensk
appe
venH
eelg
etal
le:
Kom
mut
atie
we;
Ass
osia
tiew
e;
Dis
tribu
tiew
e0 e
n 1
in te
rme
van
syve
rmen
igvu
ldig
ings
eien
skap
Pr
oble
emop
loss
ing:
In k
onte
ks
Fina
nsië
leKo
ntek
s Ve
rgel
ykin
gs v
an d
iese
lfdes
oort
[ra
tio]
Verg
elyk
ings
van
ve
rski
llend
esoo
rte
Gro
eper
ing
en v
erde
ling
met
rest
e
LOO
M:
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K
OPD
RAG
TE
241MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
O
PVO
EDER
: ……
……
……
…..
DAT
UM
: W
EEK
8
4- 8
MAA
RT
2013
TYD
: 5 D
AE
6
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
TYD
KAB
V P.
57, 1
46, 2
34
BEG
RIP
PE E
N
VAAR
DIG
HED
E Le
es, s
ê en
skr
yf 1
2- u
ur e
n 24
- uu
rtyd
op d
igita
le e
n an
aloo
gins
trum
ente
in
U
re, m
in e
n se
kond
es
Lees
van
alm
anak
ke
Be
reke
naan
tald
aetu
ssen
2
datu
ms
Prob
leem
oplo
ssin
g en
ber
eken
inge
m
et b
etre
kkin
g to
t tyd
Bere
kent
ydin
terv
alle
G
eski
eden
is v
an ty
d
Lees
, sê
en s
kryf
12-
uur
en
24 -
uurty
d op
dig
itale
en
anal
oogi
nstru
men
te in
Ure
, min
en
seko
ndes
Le
es v
an a
lman
akke
Pr
oble
emop
loss
ing
en
bere
keni
nge
met
bet
rekk
ing
tot
tyd
Bere
kent
ydin
terv
alle
G
eski
eden
is v
an ty
d
Lees
, sê
en s
kryf
12-
uur
en
24 -
uurty
d op
dig
itale
en
anal
oogi
nstru
men
te in
Ure
, min
en
seko
ndes
Le
es v
an a
lman
akke
Pr
oble
emop
loss
ing
en
bere
keni
nge
met
bet
rekk
ing
tot
tyd
Lees
tyds
ones
op
karte
Bere
kent
ydin
terv
alle
G
eski
eden
is v
an ty
d LO
OM
:
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
242 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
243MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
OPV
OED
ER: …
……
……
……
……
……
….
DAT
UM
: W
EEK
9
11
- 15
MAA
RT2
013
TYD
: 5 D
AE
6
UR
E G
RAA
D
4 5
6 O
ND
ERW
ERP
DAT
AHAN
TER
ING
P.5
9, 1
48, 2
39
BEG
RIP
PE E
N
VAAR
DIG
HED
E Ve
rsam
el e
n or
gani
seer
da
ta
tellin
gsta
belle
] St
el d
ata
voor
Pikt
ogra
mm
e
Staa
fgra
fieke
An
alis
e; in
terp
reta
sie
en
vers
lagd
oeni
ng v
an d
ata
Pi
ktog
ram
me
St
aafg
rafie
ke
Vers
amel
en
orga
nise
er
data
[ te
llinst
abel
leas
ooko
rden
van
kl
eins
te to
t gro
otst
e]
Stel
dat
a vo
or
Pi
ktog
ram
me
St
aafg
rafie
ke
Anal
ise;
inte
rpre
tasi
e en
ve
rsla
gdoe
ning
van
dat
a
Pikt
ogra
mm
e
Staa
fgra
fieke
Sirk
eldi
agra
mm
e w
oord
elik
s
Vers
amel
en
orga
nise
er d
ata
te
llinst
abel
leas
ook
or
den
van
klei
nste
tot g
root
ste
vr
aely
ste
Stel
dat
a vo
or
Pi
ktog
ram
me
St
aafg
rafie
ke
Anal
ise;
inte
rpre
tasi
e en
ver
slag
doen
ing
van
data
Pikt
ogra
mm
e
Staa
fgra
fieke
asoo
kdub
bele
staa
fgra
fieke
Sirk
eldi
agra
mm
e
Woo
rdel
iks
m
odus
LO
OM
:
HAN
DB
OEK
VE
RW
YSIN
GS.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
244 MULTIGRADE TOOLKIT MATHEMATICS INTERMEDIATE PHASE
WIS
KU
ND
E IN
TER
MED
IêR
E FA
SE
MU
LTIG
RAA
D
KW
ARTA
AL E
EN
O
PVO
EDER
: ……
……
……
……
……
…..
DAT
UM
: W
EEK
2
18
- 22
MAA
RT
201
3
T
YD: 5
DAE
6 U
RE
GR
AAD
4
5 6
ON
DER
WER
P Ei
ensk
appe
van
2D
-Vor
m K
ABV
Bl.
61 -6
3
KAB
V B
l. 15
0-15
2KAB
V B
l. 23
5 –
238
BEG
RIP
PE E
N
VAAR
DIG
HED
E Be
noem
vorm
s
drie
hoek
e
vier
kant
e
regh
oeke
ande
rvie
rhoe
ke
pe
ntag
one
he
ksag
one
si
rkel
s Ei
ensk
app
van
vorm
s
gebo
ë /re
guits
ye
aa
ntal
sye
Teke
n 2D
-Vor
ms
Beno
emvo
rms
dr
ieho
eke
vi
erka
nte
re
ghoe
ke
an
derv
ierh
oeke
pent
agon
e
heks
agon
e
hept
agon
e
sirk
els
Eien
skap
p va
n vo
rms
ge
boë
/regu
itsye
aant
alsy
e
leng
te v
an s
ye
ho
eke
[regt
ehoe
ke
en k
lein
er/g
rote
r as
regt
ehoe
ke]
Teke
n 2D
-Vor
ms
Ken
en
beno
emre
ëlm
atig
e en
on
reël
mat
igev
ierh
oeke
, dr
ieho
eke,
vie
rkan
te,
regh
oeke
en
para
llelo
gram
me;
pe
ntag
one;
hek
sogo
ne;
hept
agon
e en
okt
agon
e Ei
ensk
appe
van
Vor
ms:
aant
alsy
e
leng
te v
an s
ye
gr
ootte
van
hoe
ke
Teke
n 2D
Vor
ms
; ge
brui
k pa
sser
virs
irkel
s H
erke
n en
ben
oem
hoek
e
LOO
M:
H
AND
BO
EK
VER
WYS
ING
S.
NAS
ION
ALE
WER
KB
OEK
TUIS
WER
K O
PDR
AGTE
OPM
ERK
ING
AS
SESS
ERIN
G
TOET
S 1
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