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Teaching & Learning Plans Plan 6: Planes and Points Junior Certificate Syllabus

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Page 1: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teaching & Learning PlansPlan 6: Planes and Points

Junior Certificate Syllabus

Page 2: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

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.

Page 3: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

© Project Maths Development Team 2009 www.projectmaths.ie 1

Teaching & Learning Plan 6: Planes and Points

AimsTo introduce students to the concepts: plane; points; lines; line segments; •rays and length of line segments

To enable them to develop an understanding of, and use, mathematical •instruments

Prior Knowledge No prior knowledge of geometry assumed. Students should however know metric units of distance and be able to measure lengths.

Learning OutcomesAs a result of studying this topic, students will be able to

recall the origins of geometry•

recognise and have an intuitive knowledge of the plane, points, lines, line •segments, rays and length of line segments

have an interest in the subject and a desire to learn more•

Relationship to Junior Certificate SyllabusSub-topics Ordinary Level2.1 Synthetic geometry The geometrical results should be first

encountered through discovery and investigation.

(Refer to the appendix on geometry)Concepts (introduced as required)Constructions: 1, 2, 3, 4, 5, 6, 8, 9, 10, 11Theorems: non-rigorous treatment of theorems 1 – 6.

Resources RequiredA geometry set and a sheet of drawing paper for each student

Page 4: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teaching & Learning Plan 6: Planes and Points

© Project Maths Development Team 2009 www.projectmaths.ie 2

Introducing the TopicGeometry is one of the oldest branches of mathematics, having arisen in response to such practical problems as those found in surveying, and its name comes from Greek words meaning “Earth measurement”. It is concerned with the shape of individual objects, the way that shapes relate to other objects and the properties of the surrounding space. So, we will be looking at lines, triangles, quadrilaterals and so on, which you may have already studied in Primary School.

The geometry which we will be doing is mostly concerned with FLAT surfaces. This is called PLANE GEOMETRY. We will look into work which is over 2000 years old and is called Euclidean Geometry, after a mathematician called Euclid (c. 300 B.C.) One of the first things you should do is to look up “Euclid” on the internet or in the library and see what you find. Other famous people who contributed to this before Euclid were Thales, Pythagoras, Plato and Aristotle.

Page 5: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teac

hing

& L

earn

ing

Plan

6: P

lane

s an

d Po

ints

© 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

3

Less

on

In

tera

ctio

nSt

uden

t Le

arni

ng T

asks

: Tea

cher

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

The

firs

t co

nce

pt

we

mee

t in

»

geo

met

ry is

a ‘p

lan

e’. T

his

is ju

st

a fl

at s

urf

ace

like

the

top

of

the

des

k, o

r th

e te

ach

er’s

bo

ard

, ex

cep

t th

at it

go

es o

n a

nd

on

fo

reve

r in

eve

ry d

irec

tio

n. I

f yo

u

cou

ld im

agin

e th

is, i

t w

ou

ld s

lice

rig

ht

thro

ug

h s

pac

e an

d c

ut

it

in t

wo

. It

is a

lso

a b

it li

ke t

he

vast

pla

ins

of

Afr

ica,

bu

t sp

elle

d

dif

fere

ntl

y.

Beg

in a

co

lum

n h

ead

ed

»“N

ew W

ord

s” o

n t

he

bo

ard

(R

HS)

an

d w

rite

in

the

wo

rd “

PLA

NE”

.

Try

to im

agin

e yo

ur

dra

win

g

»sh

eet

go

ing

on

fo

reve

r in

eve

ry

dir

ecti

on

: th

is is

wh

at a

pla

ne

is.

Just

imag

ine-

go

ing

on

fo

reve

r…

Do

es a

nyo

ne

kno

w a

wo

rd w

e »

use

fo

r “g

oin

g o

n f

ore

ver”

?

We

use

th

is s

ymb

ol f

or

infi

nit

y »

You

do

no

t n

eed

to

rem

emb

er

»th

is ju

st n

ow

, bu

t d

o g

et u

sed

to

sy

mb

ols

in m

ath

s an

d d

o n

ot

be

afra

id t

o u

se t

hem

.

Infi

nit

y.•

Giv

e a

shee

t o

f d

raw

ing

pap

er t

o e

ach

stu

den

t.

Wri

te t

he

wo

rd ‘i

nfi

nit

y’

•o

n t

he

bo

ard

in t

he

“New

W

ord

s” li

st.

Wri

te t

he

•∞

sym

bo

l on

th

e b

oar

d.

Loo

k ar

ou

nd

th

e ro

om

an

d s

ee

»if

yo

u c

an p

ick

ou

t ex

amp

les

of

a p

lan

e. W

hat

exa

mp

les

can

yo

u

see?

Stu

den

ts lo

ok

for

»ex

amp

les

of

a p

lan

e in

th

e ro

om

.

The

ceili

ng

, flo

or,

wal

l….

Page 6: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teac

hing

& L

earn

ing

Plan

6: P

lane

s an

d Po

ints

© 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

4

Stud

ent

Lear

ning

Tas

ks: T

each

er

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

This

dra

win

g s

hee

t is

th

e p

lan

e »

you

will

be

wo

rkin

g o

n.

Nex

t w

e w

ant

to t

alk

abo

ut

»th

e th

ing

s w

hic

h m

ake

up

th

e p

lan

e. T

hes

e ar

e ca

lled

‘po

ints

’.

A p

oin

t is

like

a d

ot

that

yo

u

»w

ou

ld m

ake

wit

h y

ou

r p

enci

l, o

nly

eve

n s

mal

ler.

Stu

den

ts s

pre

ad o

ut

»d

raw

ing

sh

eet

and

get

p

enci

l an

d r

ule

r re

ady

for

dra

win

g.

On

yo

ur

shee

t, m

ark

in 1

0 d

ots

»

anyw

her

e at

all

on

th

e p

age

(wel

l sp

read

ou

t).

Stu

den

ts m

ark

in 1

0 d

ots

»

on

th

eir

shee

ts.

Mo

ve a

rou

nd

ob

serv

ing

»

stu

den

ts’ p

rog

ress

on

th

e ta

sk.

Do

all

the

stu

den

ts k

no

w

»h

ow

to

pla

ce p

oin

ts o

n

the

pag

e?

We

will

cal

l th

ese

po

ints

, eve

n

»th

ou

gh

str

ictl

y sp

eaki

ng

a

po

int

has

on

ly g

ot

po

siti

on

; it

do

es n

ot

hav

e le

ng

th, w

idth

or

thic

knes

s.

Ad

d t

he

wo

rd “

Poin

ts”

to

»th

e “n

ew w

ord

s” c

olu

mn

o

n t

he

bo

ard

.

Hav

e yo

u h

eard

of

a w

ord

fo

r »

littl

e el

emen

ts w

hic

h m

ake

up

a

dig

ital

ph

oto

gra

ph

?

The

wo

rd P

IXEL

sta

nd

s fo

r »

“pic

ture

ele

men

ts”.

Ou

r p

oin

ts a

re a

bit

like

th

at; t

her

e ar

e m

illio

ns

and

mill

ion

s o

f th

em in

th

e p

lan

e. T

his

is n

ot

som

eth

ing

wh

ich

yo

u n

eed

to

b

e co

nce

rned

ab

ou

t, b

ut

just

re

mem

ber

th

at a

po

int

has

no

si

ze.

Pixe

ls.

No

w p

ut

10 p

oin

ts o

n t

he

»b

oar

d (

mai

n s

ecti

on

) fo

r ex

tra

clar

ity

and

fu

rth

er

dem

on

stra

tio

n.

Page 7: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teac

hing

& L

earn

ing

Plan

6: P

lane

s an

d Po

ints

© 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

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

A

ctio

nsCh

ecki

ng U

nder

stan

ding

We

den

ote

po

ints

by

»ca

pit

al le

tter

s A

, B, C

, etc

.

Put

“nam

es”

on

yo

ur

10

»p

oin

ts w

ith

cap

ital

lett

ers

(say

, th

e 1s

t 10

lett

ers

of

the

alp

hab

et).

Stu

den

ts d

eno

te t

hei

r 10

»

po

ints

by

cap

ital

lett

ers

(A

to J

).

Cir

cula

te o

bse

rvin

g

»st

ud

ents

’ pro

gre

ss o

n t

he

task

.

Are

stu

den

ts la

bel

ling

»

po

ints

co

rrec

tly

wit

h c

apit

al

lett

ers?

No

w, g

et y

ou

r ru

ler

and

»

join

up

po

ints

A a

nd

B, a

nd

le

t yo

ur

pen

cil g

o b

eyo

nd

th

e tw

o p

oin

ts a

t ea

ch e

nd

u

nti

l yo

u c

om

e to

th

e ed

ge

of

the

shee

t at

eac

h e

nd

. Th

is is

wh

at w

e ca

ll th

e lin

e A

B a

s yo

u m

igh

t h

ave

imag

ined

.

Stu

den

ts d

raw

th

e lin

e A

B.

»M

ove

ab

ou

t th

e ro

om

an

d

»o

bse

rve

the

stu

den

ts a

t w

ork

, all

the

tim

e ch

ecki

ng

fo

r u

nd

erst

and

ing

.

Are

stu

den

ts d

raw

ing

th

e »

line

corr

ectl

y?

Ho

w f

ar c

an t

his

lin

e g

o?

»It

can

go

on

fo

reve

r in

bo

th

•d

irec

tio

ns.

To

infi

nit

y b

oth

w

ays.

No

w w

rite

in “

line

AB

” o

n

»th

is li

ne.

No

tice

th

at t

he

nam

e o

f »

the

line

do

es n

ot

hav

e an

y b

rack

ets,

just

tw

o le

tter

s n

amin

g t

wo

po

ints

on

th

e lin

e. Y

ou

may

rev

erse

th

e o

rder

an

d c

all i

t lin

e B

A if

yo

u w

ish

.

Stu

den

ts m

ark

“lin

e A

B”

or

»“B

A”

on

th

eir

line.

Mo

ve a

bo

ut

the

roo

m

»ev

alu

atin

g t

he

wo

rk

visu

ally

.

Dra

w t

he

line

AB

on

th

e »

bo

ard

so

th

at t

he

pu

pils

ca

n c

om

par

e it

wit

h t

hei

r w

ork

.

Are

stu

den

ts u

sin

g c

apit

al

»le

tter

s?

Do

stu

den

ts u

nd

erst

and

»

that

lin

e A

B is

th

e sa

me

as

line

BA

?

Page 8: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teac

hing

& L

earn

ing

Plan

6: P

lane

s an

d Po

ints

© 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

The

line

can

be

exte

nd

ed

»in

eit

her

dir

ecti

on

fo

r as

fa

r as

we

wis

h. (

We

call

this

in

fin

ity)

. We

nam

e a

line

by

any

two

po

ints

th

rou

gh

w

hic

h it

pas

ses.

Co

uld

I d

raw

a d

iffe

ren

t »

line

thro

ug

h A

an

d B

?

No

.•

Mar

k “l

ine

AB

” o

n t

he

line

»o

n t

he

bo

ard

an

d a

dd

it

also

to

th

e n

ew w

ord

s lis

t.

Are

stu

den

ts a

ctiv

ely

»p

arti

cip

atin

g in

d

raw

ing

an

d s

ho

win

g

un

der

stan

din

g?

So t

his

is t

he

on

ly li

ne

»w

hic

h c

an b

e d

raw

n

thro

ug

h A

an

d B

.

No

w m

ark

in t

he

po

int

P »

anyw

her

e o

n t

his

lin

e. It

ca

n b

e b

etw

een

A a

nd

B o

r it

nee

d n

ot

be.

Stu

den

ts m

ark

in p

oin

t P

»o

n t

he

line

AB

.M

ove

ab

ou

t th

e ro

om

an

d

»o

bse

rve

the

stu

den

ts a

t w

ork

, all

the

tim

e ch

ecki

ng

fo

r u

nd

erst

and

ing

.

No

w it

is p

oss

ible

to

nam

e »

this

lin

e in

sev

eral

oth

er

way

s. C

an y

ou

nam

e th

em?

AP

or

PA.

BP

or

PB.

Mar

k in

po

int

P o

n t

he

line

»A

B o

n t

he

bo

ard

.

Sin

ce t

he

po

ints

A, P

»

and

B a

re in

th

e sa

me

(str

aig

ht)

lin

e, w

e ca

ll th

em

CO

LLIN

EAR

po

ints

.

Ad

d t

he

wo

rds

“CO

LLIN

EAR

»

POIN

TS”

to t

he

new

wo

rds

list

on

th

e b

oar

d.

Page 9: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teac

hing

& L

earn

ing

Plan

6: P

lane

s an

d Po

ints

© 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

A

ctio

nsCh

ecki

ng U

nder

stan

ding

No

w w

ith

yo

ur

pen

cil a

nd

»

rule

r, st

arti

ng

at

C, d

raw

in

a lin

e p

assi

ng

th

rou

gh

D

and

go

ing

on

as

far

as y

ou

lik

e.

This

is c

alle

d t

he

HA

LF-L

INE

»C

D o

r si

mp

ly t

he

RA

Y [

CD

.

No

tice

ho

w t

he

squ

are

»b

rack

et in

dic

ates

a s

tart

ing

p

oin

t an

d t

her

e is

no

b

rack

et a

t th

e o

ther

sid

e,

ind

icat

ing

th

at t

her

e is

no

en

d-

it k

eep

s g

oin

g o

n a

nd

o

n (

to in

fin

ity)

.

Wri

te in

th

e n

ame

on

th

e »

‘ray

’ on

yo

ur

pag

e.

Stu

den

ts d

raw

th

e ra

y [C

D.

» St

ud

ents

wri

te in

“ra

y [C

D”

»o

n t

he

ray.

Mo

ve a

bo

ut

the

roo

m a

nd

»

ob

serv

e th

e st

ud

ents

at

wo

rk, a

ll th

e ti

me

chec

kin

g

for

un

der

stan

din

g.

Do

th

e st

ud

ents

’ dra

win

gs

»an

d la

bel

ling

of

po

ints

sh

ow

an

y m

isco

nce

pti

on

s?

Is t

he

ray

[DC

th

e sa

me

set

»o

f p

oin

ts?

So w

e m

ust

be

care

ful

»o

f th

e o

rder

in w

hic

h w

e w

rite

th

e n

ame

of

a ra

y.

No

, bec

ause

th

is s

tart

s at

D

•an

d g

oes

th

rou

gh

C in

th

e o

pp

osi

te d

irec

tio

n.

Page 10: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teac

hing

& L

earn

ing

Plan

6: P

lane

s an

d Po

ints

© 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: T

each

er

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

U

nder

stan

ding

No

w d

raw

so

me

mo

re r

ays

star

ing

»

at C

go

ing

in d

iffe

ren

t d

irec

tio

ns.

(S

ay 5

mo

re).

Rem

emb

er y

ou

r ra

ys

do

no

t n

eed

to

pas

s th

rou

gh

an

y o

f yo

ur

po

ints

.

Can

yo

u t

hin

k w

hy

thes

e m

igh

t b

e »

calle

d r

ays?

Stu

den

ts d

raw

in 5

ray

s •

eman

atin

g f

rom

C.

They

loo

k a

bit

like

ray

s •

of

the

sun

.

Ad

d t

he

wo

rds

“RA

Y [

CD

” to

th

e »

new

wo

rds

list

on

th

e b

oar

d.

Dra

w t

he

ray

[CD

on

th

e b

oar

d.

»

Wri

te in

“ra

y [C

D”

on

th

e ra

y o

n

»th

e b

oar

d.

Hav

ing

ob

serv

ed p

rog

ress

, dra

w

»in

5 r

ays

eman

atin

g f

rom

C o

n

the

bla

ckb

oar

d.

Are

stu

den

ts

»ab

le t

o d

raw

an

d

lab

el a

ll lin

es,

rays

an

d p

oin

ts

succ

essf

ully

?

No

w w

ith

yo

ur

pen

cil a

nd

ru

ler

»jo

in u

p t

he

po

ints

E a

nd

F, t

his

ti

me

star

tin

g a

t E

and

sto

pp

ing

at

F.

Stu

den

ts d

raw

th

e lin

e »

seg

men

t [E

F].

This

is p

art

of

the

line

EF a

nd

is

»ca

lled

th

e lin

e se

gm

ent

[EF]

, sin

ce

it is

rea

lly p

art

of

the

full

line

EF.

A s

egm

ent

is a

“p

art

of”

, lik

e a

seg

men

t o

f an

ora

ng

e is

par

t o

f it

.

We

nam

e th

is [

EF].

No

tice

ho

w

»th

e sq

uar

e b

rack

ets

sho

w a

“b

egin

nin

g”

and

an

“en

d”.

Wri

te “

line

seg

men

t [E

F]”

on

it.

»

Stu

den

ts w

rite

“lin

e »

seg

men

t [E

F]”

on

th

e lin

e se

gm

ent.

Page 11: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teac

hing

& L

earn

ing

Plan

6: P

lane

s an

d Po

ints

© 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:

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

Dra

w [

EF]

on

th

e b

oar

d a

nd

»

wri

te “

line

seg

men

t [E

F]”

on

th

e lin

e se

gm

ent

on

th

e b

oar

d.

Ad

d t

he

wo

rds

“LIN

E »

SEG

MEN

T [E

F]”

to t

he

new

w

ord

s lis

t o

n t

he

bo

ard

.

No

w, f

or

extr

a p

ract

ice,

dra

w

»th

e lin

es G

H a

nd

JI.

Rem

emb

er

to e

xten

d y

ou

r lin

es b

eyo

nd

th

e n

amin

g p

oin

ts.

Stu

den

ts d

raw

th

e lin

es

»G

H a

nd

JI.

Wh

en y

ou

hav

e th

at d

on

e,

»d

raw

in t

he

line

seg

men

t [B

J]

and

th

e ra

y [D

E.

Stu

den

ts d

raw

th

e lin

e »

seg

men

t [B

J] a

nd

th

e ra

y [D

E.

Ob

serv

e th

e st

ud

ents

’ »

pro

gre

ss o

n t

his

tas

k, a

dd

th

ese

extr

a el

emen

ts t

o t

he

dia

gra

m o

n t

he

bo

ard

.

Can

all

stu

den

ts s

ee t

he

»d

iffe

ren

ce b

etw

een

Lin

e A

B, R

ay [

AB

an

d li

ne

seg

men

t [A

B]

and

|AB

|, th

e le

ng

th o

f [A

B]

and

th

e w

ay b

rack

ets

are

use

d t

o

nam

e th

em?

No

w o

ne

last

tas

k. U

se y

ou

r »

rule

r to

mea

sure

th

e le

ng

th o

f lin

e se

gm

ent

[AB

].

This

is w

ritt

en a

s »

|AB|.

Wri

te in

»

|AB| =

“va

lue“

on

th

e [A

B].

Stu

den

ts m

easu

re

»th

e le

ng

th o

f th

e lin

e se

gm

ent

[AB

] an

d w

rite

|A

B| =

“va

lue“

on

it.

Mea

sure

th

e lin

e se

gm

ent

»[A

B]

on

th

e b

oar

d a

nd

w

rite

|AB| =

“va

lue“

on

it.

Fill

into

yo

ur

cop

ies

the

list

of

»n

ew w

ord

s fr

om

th

e b

oar

d.

Fill

in

»St

ud

ent

Act

ivit

y 1.

Stu

den

ts w

rite

th

e lis

t »

of

new

wo

rds

into

th

eir

cop

ies.

Dis

trib

ute

»

Stu

den

t A

ctiv

ity

1.

Page 12: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teac

hing

& L

earn

ing

Plan

6: P

lane

s an

d Po

ints

© 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

A

ctio

nsCh

ecki

ng U

nder

stan

ding

Refl

ecti

on

Wri

te d

ow

n 3

th

ing

s yo

u

»le

arn

ed a

bo

ut

pla

nes

an

d

po

ints

to

day

. W

rite

do

wn

an

yth

ing

yo

u

»fo

un

d d

iffi

cult

.

Wri

te d

ow

n a

ny

qu

esti

on

s »

you

may

hav

e.

Un

der

stan

d t

he

wo

rds

1.

pla

ne

and

po

ints

.

Ho

w t

o la

bel

po

ints

wit

h

2.

cap

ital

lett

ers.

Ho

w t

o d

raw

a R

ay [

AB

an

d

3.

a lin

e se

gm

ent

[AB

].

Ho

w t

o u

se b

rack

ets

for

4.

a R

ay [

AB

, a li

ne

seg

men

t [A

B]

and

|AB

|, th

e le

ng

th o

f [A

B].

Cir

cula

te a

nd

tak

e »

no

te p

arti

cula

rly

of

any

qu

esti

on

s st

ud

ents

hav

e an

d h

elp

th

em t

o a

nsw

er

them

. Hav

e al

l stu

den

ts

lear

ned

an

d u

nd

erst

oo

d

thes

e it

ems?

Page 13: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teaching & Learning Plan 6: Planes and Points

© Project Maths Development Team 2009 www.projectmaths.ie 11

Student Activity 1

1. Join A to C. This is [AC]. Measure the length of [AC]. Write your answer in cm. and

mm. _________________. How do we name the length of [AC]? ___________________

2. Join D to E. This is [DE]. Measure the length of [DE]. Write your answer in cm. and

mm. _________________. How do we name the length of [DE]? ___________________

3. Draw line AB.

4. Draw ray [DE.

5. How big is a point? ___________________________________________________________

6. Write down the symbol for infinity. ____________________________________________

7. How many points are on a line? _______________________________________________

8. How many points do you need to know to define a line? ________________________

Answer true/false to the following questions.

9. Line AB contains H. ___________________________________________________________

10. Line CD contains B ____________________________________________________________

11. Line AB and F lie in the same plane ____________________________________________

12. A, B and H are collinear _______________________________________________________

13. C,D and B are collinear. _______________________________________________________

14. More than one line can be drawn through E and H? _____________________________

15. More than one line can be drawn through B and D? _____________________________

16. CG intersects EG at G _________________________________________________________

17. Points A,B,C,D,E,F,G,H all lie in the same plane which I will call X _________________

18. Points A,B,C,D,E,F,G,H are the only points in plane X. ____________________________

19. [CH is the same as [HC. ________________________________________________________

20. Line AB is the same as line BA. ________________________________________________

Page 14: Plan 6: Planes and Points · Student Learning Tasks: Teacher Input Student Activities: Possible and Expected Responses Teacher’s Support and Actions Checking Understanding This

Teaching & Learning Plan 6: Planes and Points

© Project Maths Development Team 2009 www.projectmaths.ie 12

Appendix

An example of the Teacher’s Board at the end of class

Plane

infinity

Points

Line AB

Collinear points

Ray [CD

Line segment [EF]

NEW WORDS