plan 7: introduction to angles - project maths
TRANSCRIPT
Teaching & Learning PlansPlan 7: Introduction to Angles
Junior Certificate Syllabus
The Teaching & Learning Plans are structured as follows:
Aims outline what the lesson, or series of lessons, hopes to achieve.
Prior Knowledge points to relevant knowledge students may already have and also to knowledge which may be necessary in order to support them in accessing this new topic.
Learning Outcomes outline what a student will be able to do, know and understand having completed the topic.
Relationship to Syllabus refers to the relevant section of either the Junior and/or Leaving Certificate Syllabus.
Resources Required lists the resources which will be needed in the teaching and learning of a particular topic.
Introducing the topic (in some plans only) outlines an approach to introducing the topic.
Lesson Interaction is set out under four sub-headings:
i. Student Learning Tasks – Teacher Input: This section focuses on teacher input and gives details of the key student tasks and teacher questions which move the lesson forward.
ii. Student Activities – Possible and Expected Responses: Gives details of possible student reactions and responses and possible misconceptions students may have.
iii. Teacher’s Support and Actions: Gives details of teacher actions designed to support and scaffold student learning.
iv. Checking Understanding: Suggests questions a teacher might ask to evaluate whether the goals/learning outcomes are being/have been achieved. This evaluation will inform and direct the teaching and learning activities of the next class(es).
Student Activities linked to the lesson(s) are provided at the end of each plan.
© Project Maths Development Team 2009 www.projectmaths.ie 1
Teaching & Learning Plan 7: Introduction to Angles
AimsTo introduce students to the concept of an angle as a rotation and naming •an angle
To help students to learn about various angle types and the measurement •of angles (In degrees)
To help students to recall and/or deepen their understanding of the •concepts of parallel and perpendicular lines and horizontal and vertical lines
Prior Knowledge Students should understand and recall the concepts of planes, points, etc. introduced in Teaching and Learning Plan 6. They should be familiar with the circle as a shape.
Learning OutcomesAs a result of studying this topic, students will be able to
recognise angles in terms of rotation•
classify and describe angles•
describe the various angle types in terms of degrees•
relate angles to shape•
name an angle•
identify and name parallel and perpendicular lines, vertical and horizontal •lines
Relationship to Junior Certificate Syllabus
Sub-topics Ordinary Level2.1 Synthetic geometry
The geometrical results should be first encountered through discovery and investigation.
(Refer to the appendix on geometry)Terms: Angle; Rotate; acute, right angle, obtuse, straight angle, reflex angle, ordinary angle; circle, perpendicular linesConcepts (introduced as required)Constructions: 1, 2, 3, 4, 5, 6, 8, 9, 10, 11Theorems: non-rigorous treatment of theorems 1 – 6.
Teaching & Learning Plan 7: Introduction to Angles
© Project Maths Development Team 2009 www.projectmaths.ie 2
Resources RequiredGeostrips and geometry sets for each student
Introducing the TopicStudents may well have some misconceptions about angles, which will need to be explored and overcome:
the size of an angle varies with the length of the arms•
the size of an angle varies with the size of arc made with the angle vertex •as centre
different orientations of an angle as a source of confusion•
that a right angle only exists between vertical and horizontal lines•
Teac
hing
& L
earn
ing
Plan
7: I
ntro
duct
ion
to A
ngle
s
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t Tea
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stud
ent
answ
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espo
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3
Less
on
In
tera
ctio
nSt
uden
t Le
arni
ng T
asks
: Te
ache
r In
put
Stud
ent A
ctiv
itie
s: P
ossi
ble
and
Expe
cted
Res
pons
esTe
ache
r’s S
uppo
rt a
nd
Act
ions
Chec
king
Und
erst
andi
ng
Tod
ay’s
cla
ss is
all
abo
ut
»an
gle
s. Y
ou
mee
t an
gle
s ev
eryw
her
e yo
u g
o –
all
sort
s an
d s
izes
of
ang
les
in
bu
ildin
gs
and
ro
om
s an
d
even
in n
atu
ral t
hin
gs.
Let
u
s st
art
by
talk
ing
ab
ou
t h
ow
an
an
gle
is m
ade.
W
hen
we
hav
e tw
o r
ays
in
the
sam
e p
lace
in t
he
pla
ne
(“o
n t
op
of
each
oth
er”)
, an
d w
e ro
tate
(o
r tu
rn)
on
e ab
ou
t so
me
com
mo
n p
oin
t,
wh
ile t
he
oth
er s
tays
wh
ere
it is
, we
get
an
an
gle
, ju
st
like
thes
e tw
o g
eo-s
trip
s h
ere.
As
you
can
see
wh
en
we
rota
te o
ne
stri
p, w
e g
et
an a
ng
le. T
he
ang
le is
th
e am
ou
nt
of
rota
tio
n t
hat
is
do
ne.
Star
t a
“new
wo
rds”
»
sect
ion
on
th
e b
oar
d. I
nse
rt
the
wo
rd “
AN
GLE
S”.
Dem
on
stra
te t
he
con
cep
t »
of
ang
le b
y u
sin
g t
wo
(lo
ng
re
d)
Geo
stri
ps
fast
ened
to
get
her
at
on
e en
d. T
he
stri
ps
will
be
on
to
p o
f ea
ch
oth
er a
t fi
rst,
th
en t
he
top
o
ne
is s
low
ly r
ota
ted
to
re
veal
an
an
gle
. Pu
t m
ajo
r em
ph
asis
on
th
e R
OTA
TIO
N
par
t o
f th
is m
oti
on
.
Stu
den
ts f
aste
n G
eost
rip
s »
(of
sam
e co
lou
r an
d le
ng
th)
tog
eth
er a
nd
ro
tate
.
Giv
e ea
ch s
tud
ent
two
»
Geo
stri
ps:
tw
o o
f th
e sa
me
colo
ur
and
len
gth
an
d a
n
add
itio
nal
tw
o s
trip
s o
f a
dif
fere
nt
colo
ur
and
len
gth
to
th
e p
revi
ou
s tw
o.
Are
stu
den
ts m
ovi
ng
th
e »
Geo
stri
ps
in a
way
th
at
sho
ws
they
un
der
stan
d t
he
term
‘ro
tate
’?
Teac
hing
& L
earn
ing
Plan
7: I
ntro
duct
ion
to A
ngle
s
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roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
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ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
4
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
Do
yo
u u
nd
erst
and
th
e »
mea
nin
g o
f “r
ota
te”?
Can
yo
u g
ive
me
ano
ther
»
wo
rd m
ean
ing
th
e sa
me?
Turn
…tw
ist.
•W
rite
th
e w
ord
RO
TATE
»
on
th
e b
oar
d in
th
e “n
ew
wo
rds”
list
.
Can
yo
u g
ive
exam
ple
s o
f »
thin
gs
that
yo
u h
ave
seen
ro
tati
ng
?
Bo
ttle
to
p, s
teer
ing
wh
eel
•o
f ca
r…yo
ur
arm
…yo
ur
leg
.
Wh
at a
bo
ut
wh
en w
e o
pen
»
the
do
or?
Th
e d
oo
r ro
tate
s ar
ou
nd
th
e h
ing
es, d
oes
it
no
t? S
ee h
ow
th
e d
oo
r m
akes
an
an
gle
wit
h t
he
wal
l as
I ro
tate
it.
Go
to
th
e cl
assr
oo
m d
oo
r »
and
op
en it
. An
an
gle
fo
rms
bet
wee
n t
he
do
or
and
so
me
wal
l.
No
w le
t u
s ro
tate
th
e st
rip
»
furt
her
; we
get
a b
igg
er
ang
le. I
f w
e ro
tate
mo
re,
we
get
a b
igg
er a
ng
le s
till.
Stu
den
ts r
ota
te G
eost
rip
s. »
Ro
tate
th
e to
p G
eost
rip
»
furt
her
to
mak
e a
big
ger
an
gle
, th
en v
ary
the
amo
un
t o
f ro
tati
on
to
em
ph
asis
e th
e p
oin
t.
Are
stu
den
ts s
ure
wh
at it
»
mea
ns
for
som
eth
ing
to
ro
tate
?
The
key
thin
g h
ere
is t
hat
»
the
ang
le is
th
e ro
tati
on
of
on
e ra
y ab
ou
t an
oth
er r
ay
thro
ug
h a
co
mm
on
po
int.
Th
e an
gle
ch
ang
es a
s w
e ch
ang
e th
e am
ou
nt
of
rota
tio
n.
The
two
ray
s w
hic
h m
ake
»u
p t
he
ang
le a
re c
alle
d t
he
arm
s o
f th
e an
gle
.
Dra
w a
n a
ng
le o
n t
he
»b
oar
d a
nd
ind
icat
e th
e ra
ys
as a
rms
of
the
ang
le, a
nd
ad
ds
“AR
MS
of
the
AN
GLE
” to
th
e “n
ew w
ord
s” li
st.
Teac
hing
& L
earn
ing
Plan
7: I
ntro
duct
ion
to A
ngle
s
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roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
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ject
mat
hs.ie
KE
Y:
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ext
step
•
stud
ent
answ
er/r
espo
nse
5
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
Act
ions
Chec
king
Und
erst
andi
ng
No
w le
t u
s se
e w
hat
hap
pen
s »
if w
e ch
ang
e th
e le
ng
th o
f th
e st
rip
we
use
to
mak
e th
e an
gle
. Let
us
rota
te t
he
sho
rter
str
ip a
t th
e sa
me
tim
e as
th
e la
rger
. Do
es t
his
ch
ang
e th
e si
ze o
f th
e an
gle
?
No
•U
se t
wo
sh
ort
er (
yello
w
»fo
r co
ntr
ast)
str
ips.
Ro
tate
o
ne
of
thes
e an
d o
ne
of
the
lon
ger
red
str
ips
sim
ult
aneo
usl
y to
sh
ow
th
at t
he
amo
un
t o
f ro
tati
on
an
d t
her
efo
re a
ng
le s
ize,
is
un
affe
cted
by
the
len
gth
of
stri
p u
sed
.
Do
yo
u a
gre
e o
r d
isag
ree
wit
h
»th
is?
Invi
te s
tud
ents
to
ag
ree
or
»d
isag
ree,
bu
t ex
pla
in t
hey
m
ust
hav
e a
valid
rea
son
fo
r so
do
ing
.
Are
yo
u s
atis
fied
th
at
»th
e ex
pla
nat
ion
s st
ud
ents
giv
e yo
u, s
ho
w
that
th
e le
ng
th o
f th
e ar
ms
of
the
ang
le d
o
no
t d
icta
te t
he
size
of
the
ang
le?
Can
yo
u s
ee t
hat
th
e am
ou
nt
»o
f ro
tati
on
of
the
larg
er s
trip
is
th
e sa
me
as t
he
amo
un
t o
f ro
tati
on
of
the
lon
ger
str
ip?
Stu
den
ts m
irro
r w
ith
»
thei
r g
eost
rip
s w
hat
th
e te
ach
er h
as d
emo
nst
rate
d.
No
w h
ave
a lo
ok
at t
hes
e »
two
an
gle
s o
n t
he
bo
ard
. Th
ey h
ave
the
sam
e d
egre
e o
f ro
tati
on
, bu
t th
e ar
cs a
re
dif
fere
nt
size
s. A
re t
hes
e an
gle
s th
e sa
me
size
or
is o
ne
big
ger
th
an t
he
oth
er?
They
are
th
e sa
me
size
•
bec
ause
th
ey b
oth
hav
e th
e sa
me
deg
ree
of
rota
tio
n.
Dra
w t
wo
eq
ual
an
gle
s »
on
th
e b
oar
d, b
ut
inse
rt
dif
fere
nt
size
d a
rcs
on
eac
h.
Ask
th
e cl
ass
and
giv
e th
em
»a
mo
men
t to
th
ink
bef
ore
as
kin
g o
ne
stu
den
t.
Can
th
e st
ud
ents
exp
lain
»
clea
rly
wh
y th
e tw
o
ang
les
are
the
sam
e si
ze
even
th
ou
gh
th
e ar
cs
are
dif
fere
nt
size
s?
Teac
hing
& L
earn
ing
Plan
7: I
ntro
duct
ion
to A
ngle
s
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
6
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
No
w le
t u
s ro
tate
th
e st
rip
»
furt
her
.
Do
yo
u k
no
w w
hat
we
call
»th
is a
ng
le?
Stu
den
ts m
irro
r w
ith
th
eir
»g
eost
rip
s w
hat
th
e te
ach
er
has
dem
on
stra
ted
.
Acu
te a
ng
le.
•
Use
th
e re
d (
lon
ger
) st
rip
to
»
sho
w a
n a
cute
an
gle
.
Ask
th
e cl
ass
and
giv
e th
em
»a
mo
men
t to
th
ink
bef
ore
as
kin
g o
ne
stu
den
t.
Yes
. No
tice
ho
w s
har
p t
he
»p
oin
t o
f th
e an
gle
loo
ks.
“acu
te”
mea
ns
“sh
arp
”.
Wri
te t
he
wo
rds
AC
UTE
»
AN
GLE
on
th
e b
oar
d.
Hav
e yo
u m
et t
he
wo
rd
»“a
cute
” b
efo
re?
Wh
ere?
Acu
te a
pp
end
icit
is, a
cute
•
sho
rtag
e et
c…
Wh
ere
the
two
arm
s m
eet
»is
cal
led
th
e V
ERTE
X o
f th
e an
gle
.
Ind
icat
e o
n G
eost
rip
s »
wh
ere
the
vert
ex is
.
Wri
te t
he
wo
rd V
ERTE
X o
n
»th
e b
oar
d.
No
w le
t u
s ro
tate
th
e st
rip
»
furt
her
.M
ove
th
e st
rip
to
th
e »
vert
ical
po
siti
on
to
sh
ow
a
rig
ht
ang
le.
Do
yo
u k
no
w w
hat
we
call
»th
is a
ng
le?
A r
igh
t an
gle
(so
me
may
•
say
90°)
.A
sk t
he
clas
s an
d g
ive
them
»
a m
om
ent
to t
hin
k b
efo
re
aski
ng
on
e st
ud
ent.
Wh
y d
o y
ou
th
ink
this
is
»ca
lled
a r
igh
t an
gle
?St
ud
ents
may
say
bec
ause
it
•is
…”u
pri
gh
t”?
The
wo
rd “
rig
ht”
has
man
y »
mea
nin
gs
in E
ng
lish
.B
rief
cla
ss d
iscu
ssio
n o
f th
e »
mea
nin
g o
f th
e w
ord
rig
ht
in t
he
Eng
lish
lan
gu
age.
Wri
te t
he
wo
rds
“RIG
HT
»A
NG
LE”
on
th
e b
oar
d in
th
e “n
ew w
ord
s” li
st.
Are
stu
den
ts a
ctiv
ely
»p
arti
cip
atin
g in
th
e d
iscu
ssio
n?
Teac
hing
& L
earn
ing
Plan
7: I
ntro
duct
ion
to A
ngle
s
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
7
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
Act
ions
Chec
king
Und
erst
andi
ng
No
w if
I w
ere
to t
urn
th
e »
sam
e si
ze a
ng
le t
he
oth
er
way
, wo
uld
I ca
ll it
a “
left
an
gle
”?
No
•
Stu
den
ts m
irro
r w
ith
th
eir
»g
eost
rip
s w
hat
th
e te
ach
er
has
dem
on
stra
ted
.
Turn
th
e an
gle
ro
un
d s
o t
hat
»
the
rig
ht
ang
le is
on
th
e le
ft
as s
een
by
the
stu
den
ts.
Ask
th
e cl
ass
to e
xpla
in w
hy.
»
Are
an
y st
ud
ents
hav
ing
»
dif
ficu
lty
wit
h t
he
new
w
ord
s?
No
w le
t u
s ro
tate
th
e st
rip
»
even
fu
rth
er.
Mo
ve t
he
stri
p t
o t
he
»p
osi
tio
n t
o s
ho
w a
n o
btu
se
ang
le.
Do
yo
u k
no
w w
hat
we
call
»th
is a
ng
le?
An
ob
tuse
an
gle
.•
Ask
th
e cl
ass;
th
en s
elec
t an
»
ind
ivid
ual
stu
den
t to
an
swer
.
Wri
te t
he
wo
rds
OB
TUSE
»
AN
GLE
on
th
e b
oar
d.
No
tice
ho
w t
he
po
int
of
»th
e an
gle
loo
ks le
ss s
har
p.
“Ob
tuse
” m
ean
s “b
lun
t”.
Hav
e yo
u m
et t
he
wo
rd
“acu
te”
bef
ore
?
Stu
den
ts m
ay n
ot
hav
e m
et
»th
is w
ord
bef
ore
in o
ther
co
nve
rsat
ion
?
No
w le
t u
s ro
tate
th
e st
rip
»
furt
her
.St
ud
ents
mir
ror
wit
h t
hei
r »
geo
stri
ps
wh
at t
he
teac
her
h
as d
emo
nst
rate
d.
Mo
ve t
he
stri
p t
o t
he
»p
osi
tio
n t
o s
ho
w a
refl
ex
ang
le.
Do
yo
u k
no
w w
hat
we
call
»th
is a
ng
le?
A r
eflex
an
gle
»A
sk t
he
clas
s; t
hen
sel
ect
an
»in
div
idu
al s
tud
ent
to a
nsw
er.
Wri
te t
he
wo
rds
REF
LEX
»
AN
GLE
on
th
e b
oar
d.
Teac
hing
& L
earn
ing
Plan
7: I
ntro
duct
ion
to A
ngle
s
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
8
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
No
w le
t u
s ro
tate
th
e st
rip
»
furt
her
un
til w
e co
me
bac
k to
wh
ere
we
star
ted
.
Stu
den
ts m
irro
r w
ith
th
eir
»g
eost
rip
s w
hat
th
e te
ach
er
has
dem
on
stra
ted
.
Mo
ve t
he
stri
p t
o t
he
»p
osi
tio
n w
her
e it
sta
rted
.
No
w w
e ar
e b
ack
wh
ere
we
»st
arte
d a
nd
we
hav
e d
on
e a
full
revo
luti
on
wh
ich
mea
ns
that
th
e en
d o
f th
e st
rip
has
co
mp
lete
d a
fu
ll ci
rcle
.
Loo
k ar
ou
nd
th
e cl
assr
oo
m
»an
d id
enti
fy w
her
e an
gle
s ar
e fo
rmed
. Wh
at k
ind
of
ang
les
are
they
? W
hic
h is
th
e m
ost
co
mm
on
an
gle
an
d
wh
ich
is t
he
leas
t co
mm
on
an
gle
?
Stu
den
ts lo
ok
for
ang
les
»in
th
e ro
om
an
d w
rite
a
nu
mb
er o
f th
em in
to t
hei
r co
pie
s.
Wal
k ar
ou
nd
to
see
wh
at
»st
ud
ents
are
wri
tin
g d
ow
n.
Som
e st
ud
ents
may
hav
e d
iffi
cult
y. A
s yo
u w
alk
aro
un
d id
enti
fy a
nd
gu
ide
tho
se s
tud
ents
.
Has
eve
ryo
ne
com
ple
ted
»
the
task
?
No
w w
e m
ust
tal
k o
f »
mea
suri
ng
an
gle
s.
Do
es a
nyo
ne
kno
w w
hat
un
it
»w
e u
se t
o m
easu
re a
ng
les?
Deg
rees
•
Ask
th
e cl
ass;
th
en s
elec
t »
an in
div
idu
al s
tud
ent
to
answ
er.
Ho
w m
any
deg
rees
in a
fu
ll »
circ
le?
360
•°
Ask
th
e cl
ass;
th
en s
elec
t »
an in
div
idu
al s
tud
ent
to
answ
er.
This
is a
fu
nn
y n
um
ber
to
»
hav
e fo
r a
full
circ
le is
it
no
t? W
ell,
the
reas
on
fo
r th
is g
oes
bac
k to
th
e an
cien
t B
abyl
on
ian
s o
f 20
00 B
.C. a
nd
th
eir
way
of
mea
suri
ng
th
e ti
me
in a
day
.
Are
stu
den
ts a
ctiv
ely
»p
arti
cip
atin
g?
Teac
hing
& L
earn
ing
Plan
7: I
ntro
duct
ion
to A
ngle
s
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
9
Stud
ent
Lear
ning
Tas
ks: T
each
er In
put
Stud
ent A
ctiv
itie
s: P
ossi
ble
and
Expe
cted
Res
pons
esTe
ache
r’s S
uppo
rt a
nd
Act
ions
Chec
king
U
nder
stan
ding
Let
us
loo
k ag
ain
at
the
stri
ps
as w
e »
mak
e th
e va
rio
us
ang
les.
Prep
are
to d
emo
nst
rate
»
vari
ou
s an
gle
siz
es u
sin
g
bo
ard
an
d g
eo-s
trip
s. M
ove
th
e st
rip
to
th
e ve
rtic
al
po
siti
on
to
sh
ow
a r
igh
t an
gle
.
Ho
w m
any
deg
rees
in a
rig
ht
ang
le?
»90
•°
Ask
th
e cl
ass;
th
en s
elec
t »
an in
div
idu
al s
tud
ent
to
answ
er.
Wh
y? »
Bec
ause
at
this
po
int
we
•ar
e o
ne
qu
arte
r o
f th
e w
ay
to a
fu
ll ci
rcle
an
d 9
0° =
1/4
of
360°
.
Ho
w m
any
deg
rees
in a
str
aig
ht
ang
le?
»18
0•
°M
ove
th
e st
rip
to
th
e »
po
siti
on
to
sh
ow
a s
trai
gh
t an
gle
.
Wh
y? »
Bec
ause
at
this
po
int
we
•ar
e h
alf-
way
to
a f
ull
circ
le
and
180
°= ½
of
360°
.
Ask
th
e cl
ass;
th
en s
elec
t »
an in
div
idu
al s
tud
ent
to
answ
er.
Ther
e is
a n
ame
for
two
lin
es w
hic
h
»ar
e at
an
an
gle
of
90°
to e
ach
oth
er.
Do
yo
u k
no
w t
his
nam
e?
Stu
den
ts m
irro
r w
ith
th
eir
»g
eost
rip
s w
hat
th
e te
ach
er
has
dem
on
stra
ted
.
Perp
end
icu
lar
lines
•
Mo
ve t
he
stri
p t
o t
he
»p
osi
tio
n t
o s
ho
w a
str
aig
ht
ang
le.
Ask
th
e cl
ass;
th
en s
elec
t »
an in
div
idu
al s
tud
ent
to
answ
er.
Yes
th
ey a
re c
alle
d p
erp
end
icu
lar
lines
. »
Rem
emb
er y
ou
mu
st h
ave
at le
ast
two
»
lines
to
co
mp
are
if y
ou
wan
t to
use
th
e w
ord
“p
erp
end
icu
lar”
.
Wri
te t
he
wo
rds
»PE
RPE
ND
ICU
LAR
LIN
ES
on
th
e b
oar
d in
th
e “n
ew
wo
rds”
list
.
Teac
hing
& L
earn
ing
Plan
7: I
ntro
duct
ion
to A
ngle
s
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
10
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
Act
ions
Chec
king
Und
erst
andi
ng
Can
yo
u s
ee a
ny
lines
»
per
pen
dic
ula
r to
eac
h
oth
er in
th
is r
oo
m?
Stu
den
ts lo
ok
for
»p
erp
end
icu
lar
lines
in t
he
roo
m a
nd
wri
te a
nu
mb
er
of
them
into
th
eir
cop
ies.
Wal
k ar
ou
nd
to
see
wh
at
»st
ud
ents
are
wri
tin
g d
ow
n.
Som
e st
ud
ents
may
hav
e d
iffi
cult
y. A
s yo
u w
alk
aro
un
d
iden
tify
an
d g
uid
e th
ose
st
ud
ents
.
Has
eve
ryo
ne
»co
mp
lete
d t
he
task
?
Wh
at d
o y
ou
cal
l tw
o li
nes
»
wh
ich
are
alw
ays
the
sam
e d
ista
nce
ap
art?
Para
llel l
ines
.•
Mo
ve t
he
stri
ps
to t
he
po
siti
on
»
to s
ho
w p
aral
lel l
ines
.
Ask
th
e cl
ass;
th
en s
elec
t an
»
ind
ivid
ual
stu
den
t to
an
swer
.
Wri
te t
he
wo
rds
PAR
ALL
EL
»LI
NES
on
th
e b
oar
d in
th
e “n
ew w
ord
s” li
st.
Can
yo
u s
ee a
ny
lines
»
par
alle
l to
eac
h o
ther
in
this
ro
om
?
Stu
den
ts lo
ok
for
par
alle
l »
lines
in t
he
roo
m a
nd
wri
te
a n
um
ber
of
them
into
th
eir
cop
ies.
Wal
k ar
ou
nd
to
see
wh
at
»st
ud
ents
are
wri
tin
g d
ow
n.
Som
e st
ud
ents
may
hav
e d
iffi
cult
y. A
s yo
u w
alk
aro
un
d
you
iden
tify
an
d g
uid
e th
ose
st
ud
ents
.
Has
eve
ryo
ne
»co
mp
lete
d t
he
task
?
Wh
at is
th
e n
ame
for
a »
line
wh
ich
go
es s
trai
gh
t u
p
and
is p
erp
end
icu
lar
to t
he
gro
un
d?
A v
erti
cal l
ine
•A
sk t
he
clas
s; t
hen
sel
ect
an
»in
div
idu
al s
tud
ent
to a
nsw
er.
Wri
te t
he
wo
rd V
ERTI
CA
L o
n
»th
e b
oar
d in
th
e “n
ew w
ord
s”
list.
Wh
at is
th
e n
ame
for
a »
line
wh
ich
is le
vel a
nd
ru
ns
par
alle
l to
th
e g
rou
nd
?
A h
ori
zon
tal l
ine
•W
rite
th
e w
ord
HO
RIZ
ON
TAL
»o
n t
he
bo
ard
in t
he
“new
w
ord
s” li
st.
Do
stu
den
ts u
nd
erst
and
»
thes
e w
ord
s?
Teac
hing
& L
earn
ing
Plan
7: I
ntro
duct
ion
to A
ngle
s
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
11
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
Fin
ally
we
wan
t to
nam
e »
an a
ng
le. W
e n
ame
an
ang
le b
y th
e th
ree
lett
ers
wh
ich
giv
e th
e tw
o r
ays
that
mak
e u
p t
he
ang
le, s
o
that
th
e p
oin
t d
eno
tin
g t
he
vert
ex is
in t
he
mid
dle
.
Dem
on
stra
te n
amin
g a
n
»an
gle
on
th
e b
oar
d u
sin
g
thre
e le
tter
s in
tw
o w
ays,
fo
r ex
amp
le <
AB
C o
r <
CB
A.
Wo
rkin
g in
pai
rs, c
om
ple
te
»St
ud
ent
Act
ivit
y 1.
Stu
den
ts fi
ll o
ut
»St
ud
ent
Act
ivit
y 1.
Dis
trib
ute
»
Stu
den
t A
ctiv
ity
1.
Wal
k ar
ou
nd
to
see
wh
at
»st
ud
ents
are
wri
tin
g d
ow
n.
If a
nyo
ne
is s
tru
gg
ling
, ask
q
ues
tio
ns
wh
ich
will
giv
e th
em a
hin
t o
f an
exa
mp
le.
Did
stu
den
ts h
ave
lots
of
»d
iffe
ren
t su
gg
esti
on
s?
Stu
den
ts c
op
y d
iffe
ren
t id
eas
»to
th
eir
ow
n f
rom
th
e b
oar
d.
Take
sel
ecti
on
s fr
om
eac
h
»g
rou
p a
nd
rec
ord
th
em o
n
the
bo
ard
/flip
char
t/la
pto
p.
Co
mp
lete
»
Stu
den
t A
ctiv
ity
2 an
d 3
.St
ud
ents
fill
ou
t »
Stu
den
t A
ctiv
ity
2 an
d 3
.D
istr
ibu
te
»St
ud
ent
Act
ivit
y 2
and
3.
Cir
cula
te a
nd
su
pp
ort
»
stu
den
ts w
ho
hav
e d
iffi
cult
y w
ith
th
e ta
sk.
Do
stu
den
ts u
nd
erst
and
»
the
wo
rds,
ph
rase
s an
d
dia
gra
ms?
Teac
hing
& L
earn
ing
Plan
7: I
ntro
duct
ion
to A
ngle
s
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
12
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed
Resp
onse
sTe
ache
r’s S
uppo
rt a
nd
Act
ions
Chec
king
U
nder
stan
ding
Refl
ecti
on
Wri
te d
ow
n 3
item
s yo
u
»le
arn
ed a
bo
ut
ang
les
and
lin
es t
od
ay.
Wri
te d
ow
n a
nyt
hin
g y
ou
»
fou
nd
dif
ficu
lt.
Wri
te d
ow
n a
ny
qu
esti
on
»
you
may
hav
e.
Ther
e ar
e m
any
size
s o
f an
gle
s: a
cute
, 1.
ri
gh
t, o
btu
se, s
trai
gh
t an
d r
eflex
.
A f
ull
circ
le h
as 3
60 d
egre
es.
2.
Two
lin
es t
hat
mee
t at
90
deg
rees
to
eac
h
3.
oth
er a
re c
alle
d p
erp
end
icu
lar
lines
.
An
gle
s ar
e n
amed
usi
ng
th
ree
lett
ers
wit
h
4.
the
vert
ex in
th
e m
idd
le.
Lin
es w
hic
h a
re a
lway
s th
e sa
me
dis
tan
ce
5.
apar
t ar
e ca
lled
par
alle
l lin
es.
A li
ne
wh
ich
go
es s
trai
gh
t u
p a
nd
is
6.
par
alle
l to
th
e g
rou
nd
is c
alle
d a
ver
tica
l lin
e.
A li
ne
wh
ich
is le
vel a
nd
ru
ns
par
alle
l to
7.
th
e g
rou
nd
is c
alle
d a
ho
rizo
nta
l lin
e.
Cir
cula
te a
nd
tak
e »
no
te p
arti
cula
rly
of
any
qu
esti
on
s st
ud
ents
h
ave
and
hel
p t
hem
to
an
swer
th
ese.
Teaching & Learning Plan 7: Introduction to Angles
© Project Maths Development Team 2009 www.projectmaths.ie 13
Student Activity 1
Students work in pairs.
1. Find and list 5 surfaces in the classroom which are horizontal and 5 which are
vertical. ______________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
2. See if you can find lines or surfaces which are parallel. __________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
3. See if you can find lines or surfaces which are perpendicular to each other.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
4. Can you find perpendicular lines in the classroom where the lines are not vertical or
horizontal? __________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
5. What type of lines are used in the pages of your copy? __________________________
_____________________________________________________________________________
_____________________________________________________________________________
6. Why is it important to have walls vertical? _____________________________________
_____________________________________________________________________________
_____________________________________________________________________________
7. Is it important to have floors horizontal? Why? _________________________________
_____________________________________________________________________________
_____________________________________________________________________________
8. Do you know what a builder uses to ensure that he builds a wall vertically?
_____________________________________________________________________________
_____________________________________________________________________________
9. What building in Italy is famous for not being vertical? __________________________
_____________________________________________________________________________
_____________________________________________________________________________
Teaching & Learning Plan 7: Introduction to Angles
© Project Maths Development Team 2009 www.projectmaths.ie 14
Student Activity 2
Description Mathematical words/phrases
Diagram
Line going directly upwards Horizontal Line
Angle greater than 90° but less than 180°
Acute angle
Line parallel to the ground Right Angle
Angle of 180° Obtuse Angle
Angle greater than 180° Straight Angle
Angle of 90° Reflex Angle
Angle less than 180° Ordinary Angle (more than one diagram)
Lines which never meet Perpendicular Lines
Lines at an angle of 90° to each other
Parallel lines
Angle less than 90° Vertical line
Look at the mathematical words/phrases in the middle column below and rewrite each into the correct description box on the left and diagram box on the right.
Teaching & Learning Plan 7: Introduction to Angles
© Project Maths Development Team 2009 www.projectmaths.ie 15
Angle Name one Name two
1. Name each of these angles using three letters in two ways:
Student Activity 3
2. What is a wide-angle lens in a camera? What does it do? What type of picture does it
take? ________________________________________________________________________
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3. What does it mean when we say that in football that “the goalkeeper narrowed the
angle”? What angle did the goalkeeper narrow? ________________________________
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4. Draw out the last five letters of the alphabet in capitals. What kinds of angles are
formed in them? _____________________________________________________________
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5. What kinds of angle are formed by the hands of a clock?
(a) At 9.00p.m? _______________________________________________________________
(b) At 6.00 a.m.? ______________________________________________________________
(c) At 3.00 a.m.? ______________________________________________________________
6. Through how many degrees will the minute hand of a clock rotate in:
(a) 30 minutes? _______________________________________________________________
(b) 20 minutes? _______________________________________________________________
(c) 40 minutes? _______________________________________________________________
(d) 45 minutes? _______________________________________________________________