mathematics: senior phase · exemplar lesson plans to assist teachers in developing, managing and...

1MULTIGRADE TOOLKIT MATHEMATICS SENIOR PHASE

Mathematics: Senior 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. .

2 MULTIGRADE TOOLKIT MATHEMATICS SENIOR PHASE

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.


M

ulti-

Gra

de A

nnua

l Tea

chin

g Pl

ans


TER

M 1

TI

ME

(HO

UR

S)

GR

ADE

7

GR

ADE

8

GR

ADE

9

9

Who

le n

umbe

rs (

9)

Pr

oper

ties

C

alcu

latio

ns

C

alcu

latio

n te

chni

ques

Mul

tiple

s an

d fa

ctor

s

Solv

ing

prob

lem

s

Rat

io a

nd ra

te

Fi

nanc

ial m

athe

mat

ics

Who

le n

umbe

rs(6

)

Prop

ertie

s

Cal

cula

tions

Cal

cula

tion

tech

niqu

es

M

ultip

les

and

fact

ors

So

lvin

g pr

oble

ms

R

atio

and

rate

Fina

ncia

l mat

hem

atic

s

Who

le n

umbe

rs (4

.5)

Pr

oper

ties

C

alcu

latio

ns

C

alcu

latio

n te

chni

ques

Mul

tiple

s an

d fa

ctor

s

Solv

ing

prob

lem

s

Rat

io, r

ate

& pr

opor

tion

Fi

nanc

ial m

athe

mat

ics

9

* Int

eger

s (9

)

Cou

ntin

g, o

rder

ing

and

com

parin

g

Cal

cula

tions

Prop

ertie

s

Solv

ing

prob

lem

s

Inte

gers

( 9)

C

ount

ing,

ord

erin

g an

d co

mpa

ring

C

alcu

latio

ns

Pr

oper

ties

So

lvin

g pr

oble

ms

Inte

gers

(4.5

)

Cou

ntin

g, o

rder

ing

and

com

parin

g (R

evis

ion)

Cal

cula

tions

(Rev

isio

n)

Pr

oper

ties

(Rev

isio

n)

So

lvin

g pr

oble

ms

9

Expo

nent

s (9

)

Com

parin

g an

d re

pres

entin

g

Cal

cula

tions

Solv

ing

prob

lem

s

Expo

nent

s (9

)

Com

parin

g an

d re

pres

entin

g

Cal

cula

tions

(inc

lude

law

s of

exp

onen

ts)

So

lvin

g pr

oble

ms

Expo

nent

s (5

)

Com

parin

g an

d re

pres

entin

g

Cal

cula

tions

(inc

lude

law

s of

exp

onen

ts)

So

lvin

g pr

oble

ms

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 N

umer

ic a

nd g

eom

etric

pat

tern

s (6

)

Inve

stig

ate

and

exte

nd

Num

eric

and

geo

met

ric p

atte

rns

(6)

In

vest

igat

e an

d ex

tend

N

umer

ic a

nd g

eom

etric

pat

tern

s (6

)

Inve

stig

ate

and

exte

nd

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

.

4 Fu

nctio

ns a

nd re

latio

nshi

ps (3

)

Inpu

t and

out

put v

alue

s

Equi

vale

nt fo

rms

Func

tions

and

rela

tions

hips

(3)

In

put a

nd o

utpu

t val

ues

Eq

uiva

lent

form

s

Func

tions

and

rela

tions

hips

(4)

In

put a

nd o

utpu

t val

ues

Equi

vale

nt fo

rms

4 G

raph

s (4

)

Inte

rpre

ting

G

raph

s( 4

)

Inte

rpre

ting

G

raph

s ( 4

)

Inte

rpre

ting


D

raw

ing

Dra

win

g

Dra

win

g

2 Fo

rmal

SB

A Ta

sk: T

est

Form

al S

BA

Task

: Tes

t Fo

rmal

SB

A Ta

sk: T

est

6 R

evis

ion

Rev

isio

n R

evis

ion

50

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

mat

hs to

pics

, co

ncep

ts a

nd s

kills

.


TER

M 2

TI

ME

(HO

UR

S)

GR

ADE

7

GR

ADE

8

GR

ADE

9

5 C

onst

ruct

ion

of g

eom

etric

figu

res

(5)

M

easu

ring

angl

es

C

onst

ruct

ion

Con

stru

ctio

n of

geo

met

ric fi

gure

s (4

)

Con

stru

ctio

n

Prop

ertie

s

Con

stru

ctio

n of

geo

met

ric fi

gure

s (4

)

Con

stru

ctio

n

Prop

ertie

s

10

Geo

met

ry o

f 2D

sha

pes

(10)

Cla

ssify

Sim

ilarit

y an

d co

ngru

ency

Solv

e pr

oble

ms

Geo

met

ry o

f 2D

sha

pes(

8)

C

lass

ify

Si

mila

rity

and

cong

ruen

cy

So

lve

prob

lem

s

Geo

met

ry o

f 2D

sha

pes(

9)

C

lass

ify

Si

mila

rity

and

cong

ruen

cy

So

lve

prob

lem

s

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

9 G

eom

etry

of s

trai

ght l

ines

(2)

D

efin

ition

of l

ines

and

line

rela

tions

hips

G

eom

etry

of s

trai

ght l

ines

(9)

An

gle

rela

tions

hips

Solv

ing

prob

lem

s

Geo

met

ry o

f str

aigh

t lin

es (9

)

Angl

e re

latio

nshi

ps

So

lvin

g pr

oble

ms

9

Alge

brai

c ex

pres

sion

s (3

)

Alge

brai

c la

ngua

ge

Alge

brai

c ex

pres

sion

s (9

)

Alge

brai

c la

ngua

ge

Ex

pand

and

sim

plify

Alge

brai

c ex

pres

sion

s( 9

)

Alge

brai

c la

ngua

ge

Ex

pand

and

sim

plify

Fact

oriz

atio

n 1

Form

al S

BA

Task

: Tes

t Fo

rmal

SB

A Ta

sk: T

est

Form

al S

BA

Task

: Tes

t

8 Al

gebr

aic

equa

tions

(3)

N

umbe

r sen

tenc

es

Alge

brai

c eq

uatio

ns (3

)

Equa

tions

Al

gebr

aic

equa

tions

(8)

Eq

uatio

ns

2 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

5 R

evis

ion

Rev

isio

n R

evis

ion

50

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 m

aths

topi

cs,

conc

epts

and

ski

lls.


TER

M 3

TI

ME

(HO

UR

S)

GR

ADE

7

GR

ADE

8

GR

ADE

9

8

Com

mon

frac

tions

Ord

erin

g, c

ompa

ring

and

sim

plify

ing

C

alcu

latio

ns w

ith fr

actio

ns

C

alcu

latio

n te

chni

ques

Solv

ing

prob

lem

s

Pe

rcen

tage

s

Equi

vale

nt fo

rm

Com

mon

frac

tions

Cal

cula

tions

with

frac

tions

Cal

cula

tion

tech

niqu

es

So

lvin

g pr

oble

ms

Perc

enta

ges

Eq

uiva

lent

form

s

Com

mon

frac

tions

Cal

cula

tions

with

frac

tions

Cal

cula

tion

tech

niqu

es

So

lvin

g pr

oble

ms

Eq

uiva

lent

form

s

8

Dec

imal

frac

tions

Ord

erin

g an

d co

mpa

ring

C

alcu

latio

ns w

ith d

ecim

al fr

actio

ns

C

alcu

latio

ns te

chni

ques

Solv

ing

Prob

lem

s

Eq

uiva

lent

form

s

Dec

imal

frac

tions

Ord

erin

g an

d co

mpa

ring

C

alcu

latio

ns w

ith d

ecim

al fr

actio

ns

C

alcu

latio

ns te

chni

ques

Solv

ing

Prob

lem

s

Eq

uiva

lent

form

s

Dec

imal

frac

tions

Ord

erin

g an

d co

mpa

ring

C

alcu

latio

ns te

chni

ques

Solv

ing

Prob

lem

s

Eq

uiva

lent

form

s

7

Dat

a ha

ndlin

g

Col

lect

dat

a

Org

anis

e an

d su

mm

aris

e da

ta

R

epre

sent

dat

a

Inte

rpre

t dat

a

Anal

yse

data

Rep

ort d

ata

Dat

a ha

ndlin

g

Col

lect

dat

a

Org

anis

e an

d su

mm

aris

e da

ta

R

epre

sent

dat

a

Inte

rpre

t dat

a

Anal

yse

data

Rep

ort d

ata

Dat

a ha

ndlin

g

Col

lect

dat

a

Org

anis

e an

d su

mm

aris

e da

ta

R

epre

sent

dat

a

Inte

rpre

t dat

a

Anal

yse

data

Rep

ort d

ata

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

5

2D G

eom

etry

Cla

ssify

ing

2D s

hape

s

Area

of s

quar

e, re

ctan

gle

and

trian

gle

Theo

rem

of P

ytha

gora

s

D

evel

op a

nd u

se T

heor

em o

f Pyt

hago

ras

Theo

rem

of P

ytha

gora

s

So

lve

prob

lem

s us

ing

the

theo

rem

of

Pyth

agor

as


7 Ar

ea a

nd p

erim

eter

of 2

D s

hape

s

Area

and

per

imet

er

C

alcu

latio

ns a

nd s

olvi

ng p

robl

ems

Area

and

per

imet

er o

f 2D

sha

pes

Ar

ea a

nd p

erim

eter

Cal

cula

tions

and

sol

ving

pro

blem

s

Area

and

per

imet

er o

f 2D

sha

pes

Ar

ea a

nd p

erim

eter

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

8 Su

rfac

e ar

ea a

nd v

olum

e of

3D

obj

ects

Surfa

ce a

rea

and

volu

me

C

alcu

latio

ns a

nd s

olvi

ng p

robl

ems

Surf

ace

area

and

vol

ume

of 3

D o

bjec

ts

Su

rface

are

a an

d vo

lum

e

Cal

cula

tions

and

sol

ving

pro

blem

s

Surf

ace

area

and

vol

ume

of 3

D o

bjec

ts

Su

rface

are

a an

d vo

lum

e

2 Fo

rmal

SB

A Ta

sk: T

est

Form

al S

BA

Task

: Tes

t Fo

rmal

SB

A Ta

sk: T

est

3 R

evis

ion

Rev

isio

n R

evis

ion

50

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

mat

hs to

pics

, con

cept

s an

d sk

ills.


TER

M 4

TI

ME

(HO

UR

S)

GR

ADE

7

GR

ADE

8

GR

ADE

9

6 Fu

nctio

ns a

nd re

latio

nshi

ps

In

put a

nd o

utpu

t val

ues

Eq

uiva

lent

form

s

Func

tions

and

rela

tions

hips

Inpu

t and

out

put v

alue

s

Equi

vale

nt fo

rms

Func

tions

and

rela

tions

hips

Inpu

t and

out

put v

alue

s

Equi

vale

nt fo

rms

2 G

raph

s

Inte

rpre

t gr

aphs

Dra

wl g

raph

s

Gra

phs

In

terp

ret

grap

hs

D

raw

gra

phs

Gra

phs

In

terp

ret l

gra

phs

D

raw

gra

phs

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

5

Con

stru

ctio

n of

geo

met

ric s

hape

s

Mea

surin

g of

ang

les

Con

stru

ctio

ns

Con

stru

ctio

n of

geo

met

ric s

hape

s

Con

stru

ctio

ns

In

vest

igat

ing

prop

ertie

s of

geo

met

ric

figur

es

Con

stru

ctio

n of

geo

met

ric s

hape

s

Con

stru

ctio

ns

In

vest

igat

ing

prop

ertie

s of

geo

met

ric

figur

es

9

Tran

sfor

mat

ion

geo

met

ry

Tr

ansf

orm

atio

ns

En

larg

emen

t and

Red

uctio

n

Tran

sfor

mat

ion

geo

met

ry

Tr

ansf

orm

atio

ns

En

larg

emen

t and

Red

uctio

n of

geo

met

ric

figur

es.

Tran

sfor

mat

ion

geo

met

ry

Tr

ansf

orm

atio

ns

En

larg

emen

t and

Red

uctio

n

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

9 G

eom

etry

of 3

D o

bjec

ts

C

lass

ifyin

g 3-

D o

bjec

ts

Bu

ildin

g 3-

D m

odel

s

Geo

met

ry o

f 3D

obj

ects

Cla

ssify

ing

3-D

obj

ects

Build

ing

3-D

mod

els

Geo

met

ry o

f 3D

obj

ects

Cla

ssify

ing

3-D

obj

ects

Build

ing

3-D

mod

els

4.

5

Prob

abili

ty

Pro

babi

lity

P

roba

bilit

y 4

Rev

isio

n R

evis

ion

Rev

isio

n 3

Form

al T

ask:

End

of y

ear E

xam

inat

ion

Form

al T

ask:

End

of y

ear E

xam

inat

ion

Form

al T

ask:

End

of y

ear E

xam

inat

ion

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

mat

hs to

pics

, con

cept

s an

d sk

ills.


LESS

ON

PLA

NS:

TER

M 1


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

1

TER

M 1

Dat

e : f

rom

....

to ..

....

T

ime:

9 ho

urs

G

rade

7

8 9

Topi

c W

HO

LE N

UM

BER

S C

APS

page

s 40

- 42

75

- 77

11

9 - 1

21

Skills

and

Kn

owle

dge

Ord

erin

g an

d co

mpa

ring

who

le n

umbe

rs

Rev

ise

the

follo

win

g do

ne in

Gra

de 6

:

Ord

er, c

ompa

re a

nd re

pres

ent n

umbe

rs

to a

t lea

st

9-di

git n

umbe

rs

R

ecog

nise

and

repr

esen

t prim

e nu

mbe

rs

to a

t lea

st 1

00

R

ound

ing

off n

umbe

rs to

the

near

est 5

, 10

, 100

or

1

000

Pr

oper

ties

of w

hole

num

bers

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

R

ecog

nise

and

use

the

com

mut

ativ

e;

asso

ciat

ive;

dis

tribu

tive

prop

ertie

s w

ith

who

le n

umbe

rs

R

ecog

nise

and

use

0 in

term

s of

its

addi

tive

prop

erty

(ide

ntity

ele

men

t for

ad

ditio

n)

R

ecog

nise

and

use

1 in

term

s of

its

mul

tiplic

ativ

e pr

oper

ty (i

dent

ity e

lem

ent

for m

ultip

licat

ion)

C

alcu

latio

ns w

ith w

hole

num

bers

R

evis

e th

e fo

llow

ing

done

in G

rade

6,

with

out u

se o

f cal

cula

tors

:

Addi

tion

and

subt

ract

ion

of w

hole

nu

mbe

rs to

at l

east

6 –

digi

t num

bers

Ord

erin

g an

d co

mpa

ring

who

le

num

bers

R

evis

e Pr

ime

num

bers

to a

t lea

st 1

00

Prop

ertie

s of

who

le n

umbe

rs

Rev

ise:

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

(id

entit

y el

emen

t for

add

ition

)

1 in

term

s of

its

mul

tiplic

ativ

e pr

oper

ty

(iden

tify

elem

ent f

or m

ultip

licat

ion)

Rec

ogni

se th

e di

visi

on p

rope

rty o

f 0,

whe

reby

any

num

ber d

ivid

ed b

y 0

is

unde

fined

C

alcu

latio

ns u

sing

who

le n

umbe

rs

Rev

ise:

C

alcu

latio

ns u

sing

all

four

ope

ratio

ns o

n w

hole

num

bers

, est

imat

ing

and

usin

g ca

lcul

ator

s w

here

app

ropr

iate

Prop

ertie

s of

num

bers

D

escr

ibe

the

real

num

ber s

yste

m b

y re

cogn

isin

g, d

efin

ing

and

dist

ingu

ishi

ng

prop

ertie

s of

:

natu

ral n

umbe

rs

w

hole

num

bers

inte

gers

ratio

nal n

umbe

rs

ir

ratio

nal n

umbe

rs

Cal

cula

tions

usi

ng w

hole

num

bers

R

evis

e:

Cal

cula

tions

usi

ng a

ll fo

ur o

pera

tions

on

who

le n

umbe

rs, e

stim

atin

g an

d us

ing

calc

ulat

ors

whe

re a

ppro

pria

te


M

ultip

licat

ion

of a

t lea

st w

hole

4-d

igit

by

2-di

git n

umbe

rs

D

ivis

ion

of a

t lea

st w

hole

4-d

igit

by 2

-di

git n

umbe

rs

Perfo

rm c

alcu

latio

ns u

sing

all

four

op

erat

ions

on

who

le n

umbe

rs, e

stim

atin

g an

d us

ing

calc

ulat

ors

whe

re a

ppro

pria

te

Cal

cula

tion

tech

niqu

es

Use

a ra

nge

of te

chni

ques

to p

erfo

rm a

nd

chec

k w

ritte

n an

d m

enta

l cal

cula

tions

of

who

le n

umbe

rs in

clud

ing:

Estim

atio

n

addi

ng, s

ubtra

ctin

g an

d m

ultip

lyin

g in

co

lum

ns

lo

ng d

ivis

ion

ro

undi

ng o

ff an

d co

mpe

nsat

ing

u

sing

a c

alcu

lato

r M

ultip

les

and

fact

ors

Rev

ise

the

follo

win

g do

ne in

Gra

de 6

:

Mul

tiple

s of

2-d

igit

and

3-di

git w

hole

nu

mbe

rs

F

acto

rs o

f 2-d

igit

and

3-di

git w

hole

nu

mbe

rs

P

rime

fact

ors

of n

umbe

rs to

at l

east

100

Li

st p

rime

fact

ors

of n

umbe

rs to

at l

east

3-

digi

t who

le n

umbe

rs

Find

the

LCM

and

HC

F of

num

bers

to a

t le

ast 3

-dig

it w

hole

num

bers

, by

insp

ectio

n or

fa

ctor

isat

ion

Cal

cula

tion

tech

niqu

es

Use

a ra

nge

of s

trate

gies

to p

erfo

rm a

nd

chec

k w

ritte

n an

d m

enta

l cal

cula

tions

w

ith w

hole

num

bers

in

clud

ing:

Estim

atio

n

add

ing,

sub

tract

ing

and

mul

tiply

ing

in

colu

mns

long

div

isio

n

ro

undi

ng o

ff an

d co

mpe

nsat

ing

us

ing

a ca

lcul

ator

M

ultip

les

and

fact

ors

Rev

ise:

Prim

e fa

ctor

s of

num

bers

to a

t lea

st 3

-di

git w

hole

num

bers

LCM

and

HC

F of

num

bers

to a

t lea

st

3-di

git w

hole

num

bers

, by

insp

ectio

n or

fact

oris

atio

n

Cal

cula

tion

tech

niqu

es

Use

a ra

nge

of s

trate

gies

to p

erfo

rm a

nd

chec

k w

ritte

n an

d m

enta

l cal

cula

tions

of

who

le n

umbe

rs

incl

udin

g:

Es

timat

ion

a

ddin

g, s

ubtra

ctin

g an

d m

ultip

lyin

g in

co

lum

ns

lo

ng d

ivis

ion

ro

undi

ng o

ff an

d co

mpe

nsat

ing

u

sing

a c

alcu

lato

r M

ultip

les

and

fact

ors

Use

prim

e fa

ctor

isat

ion

of n

umbe

rs to

find

LC

M a

nd H

CF


Solv

ing

prob

lem

s So

lve

prob

lem

s in

volv

ing

who

le n

umbe

rs,

incl

udin

g:

C

ompa

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)

Sh

arin

g in

a g

iven

ratio

whe

re th

e w

hole

is

giv

en

Solv

e pr

oble

ms

that

invo

lve

who

le n

umbe

rs,

perc

enta

ges

and

deci

mal

frac

tions

in

finan

cial

con

text

s su

ch a

s:

Pr

ofit,

loss

and

dis

coun

t

Budg

ets

Ac

coun

ts

Lo

ans

Si

mpl

e in

tere

st

Solv

ing

prob

lem

s So

lve

prob

lem

s in

volv

ing

who

le n

umbe

rs,

incl

udin

g:

C

ompa

ring

two

or m

ore

quan

titie

s of

th

e sa

me

kind

(rat

io)

C

ompa

ring

two

quan

titie

s of

diff

eren

t ki

nds

(rate

)

Shar

ing

in a

giv

en ra

tio w

here

the

who

le is

giv

en

In

crea

sing

or d

ecre

asin

g of

a n

umbe

r in

a g

iven

ratio

So

lve

prob

lem

s th

at in

volv

e w

hole

nu

mbe

rs, p

erce

ntag

es a

nd d

ecim

al

fract

ions

in fi

nanc

ial c

onte

xts

such

as:

Prof

it, lo

ss, d

isco

unt a

nd V

AT

Bu

dget

s

Acco

unts

Loan

s

Sim

ple

inte

rest

Hire

Pur

chas

e

Exch

ange

rate

s

Solv

ing

prob

lem

s So

lve

prob

lem

s in

con

text

s in

volv

ing

ratio

and

rate

dire

ct a

nd in

dire

ct p

ropo

rtion

So

lve

prob

lem

s th

at in

volv

e w

hole

nu

mbe

rs, p

erce

ntag

es a

nd d

ecim

al

fract

ions

in fi

nanc

ial c

onte

xts

such

as:

prof

it, lo

ss, d

isco

unt a

nd V

AT

bu

dget

s

acco

unts

and

loan

s

sim

ple

inte

rest

and

hire

pur

chas

e

exch

ange

rate

s an

d co

mm

issi

on

R

enta

ls

co

mpo

und

inte

rest

Sugg

este

d m

etho

dolo

gy

Ord

erin

g an

d co

mpa

ring

num

bers

Le

arne

rs s

houl

d be

giv

en a

rang

e of

exe

rcis

es s

uch

as:

Ar

rang

e gi

ven

num

bers

from

the

smal

lest

to th

e bi

gges

t or

big

gest

to s

mal

lest

Fill

in m

issi

ng n

umbe

rs in

a s

eque

nce;

on

a nu

mbe

r grid

; on

a nu

mbe

r lin

e e.

g. w

hich

who

le n

umbe

r is

halfw

ay b

etw

een

471

340

and

471

350.

Fi

ll in

<, =

or >

Ex

ampl

es:

a)

247

889

* 247

898

b)

78

4 10

9 * 7

85 1

90

Prop

ertie

s of

who

le n

umbe

rs

R

evis

ing

the

prop

ertie

s of

who

le n

umbe

rs s

houl

d be

the

star

ting

poin

t for

wor

k w

ith w

hole

num

bers

. The

pro

perti

es o

f num

bers

sh

ould

pro

vide

the

mot

ivat

ion

for w

hy a

nd h

ow o

pera

tions

with

num

bers

wor

k.


W

hen

lear

ners

are

intro

duce

d to

new

num

bers

, suc

h as

inte

gers

for e

xam

ple,

they

can

aga

in e

xplo

re h

ow th

e pr

oper

ties

of

num

bers

wor

k fo

r the

new

set

of n

umbe

rs.

Le

arne

rs a

lso

have

to a

pply

the

prop

ertie

s of

num

bers

in a

lgeb

ra, w

hen

they

wor

k w

ith v

aria

bles

in p

lace

of n

umbe

rs.

Le

arne

rs s

houl

d kn

ow a

nd b

e ab

le to

use

the

follo

win

g pr

oper

ties:

o

The

com

mut

ativ

e pr

oper

ty o

f add

ition

and

mul

tiplic

atio

n:

♦♦

a +

b =

b +

a

♦♦

a x

b =

b x

a

o Th

e as

soci

ativ

e (g

roup

ing)

pro

perty

of a

dditi

on a

nd m

ultip

licat

ion:

♦♦

(a +

b) +

c =

a +

(b +

a)

♦♦

(a x

b) x

c =

a x

(b x

c)

o Th

e di

strib

utiv

e pr

oper

ty o

f mul

tiplic

atio

n ov

er a

dditi

on a

nd s

ubtra

ctio

n:

♦♦

a(b

+ c)

= (a

x b

) + (a

x c

)

♦

♦ a(

b –

c) =

(a x

b) –

(a x

c)

o Ad

ditio

n an

d su

btra

ctio

n as

inve

rse

oper

atio

ns

o M

ultip

licat

ion

and

divi

sion

as

inve

rse

oper

atio

ns

o 0

is th

e id

entit

y el

emen

t for

add

ition

: t +

0 =

t o

1 is

the

iden

tity

elem

ent f

or m

ultip

licat

ion:

t x

1 =

t Ill

ustr

atin

g th

e pr

oper

ties

with

who

le n

umbe

rs

Exam

ples

a)

33

+ 9

9 =

99 +

33

= 13

2 b)

51

+ (1

9 +

46) =

(51

+ 19

) + 4

6 =

116

c)

4(12

+ 9

) = (4

x 1

2) +

(4 x

9) =

48

+ 36

= 8

4 d)

(9

x 6

4) +

(9 x

36)

= 9

x (6

4 +

36) =

9 x

100

= 9

00

e)

If 33

+ 9

9 =

132,

then

132

– 9

9 =

33 a

nd 1

32 –

33

= 99

f)

If 20

x 5

= 1

10, t

hen

110

÷ 20

= 5

and

110

÷ 5

= 2

0 C

alcu

latio

ns w

ith w

hole

num

bers

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

beco

me

mor

e co

nfid

ent i

n an

d m

ore

inde

pend

ent a

t m

athe

mat

ics,

if th

ey h

ave

tech

niqu

es

o to

che

ck th

eir s

olut

ions

them

selv

es, e

.g. u

sing

inve

rse

oper

atio

ns; u

sing

cal

cula

tors

o

to ju

dge

the

reas

onab

lene

ss o

f the

ir so

lutio

ns e

.g. e

stim

ate

by ro

undi

ng o

ff; e

stim

ate

by d

oubl

ing

or h

alvi

ng;

Ad

ding

, sub

tract

ing

and

mul

tiply

ing

in c

olum

ns, a

nd lo

ng d

ivis

ion,

sho

uld

only

be

used

to p

ract

ice

num

ber f

acts

and

cal

cula

tion


tech

niqu

es, a

nd h

ence

sho

uld

be d

one

with

fam

iliar a

nd s

mal

ler n

umbe

r ran

ges.

For

big

and

unw

ield

y ca

lcul

atio

ns, l

earn

ers

shou

ld

be e

ncou

rage

d to

use

a c

alcu

lato

r. M

ultip

les

and

fact

ors

Pr

actic

e w

ith fi

ndin

g m

ultip

les

and

fact

ors

of w

hole

num

bers

are

esp

ecia

lly im

porta

nt w

hen

lear

ners

do

calc

ulat

ions

with

frac

tions

. Th

ey u

se th

is k

now

ledg

e to

find

the

LCM

whe

n on

e de

nom

inat

or is

a m

ultip

le o

f ano

ther

, and

als

o w

hen

they

sim

plify

frac

tions

or

have

to fi

nd e

quiv

alen

t fra

ctio

ns.

Fa

ctor

isin

g w

hole

num

bers

lays

the

foun

datio

n fo

r fac

toris

atio

n of

alg

ebra

ic e

xpre

ssio

ns.

U

sing

the

defin

ition

of p

rime

num

bers

and

em

phas

ize

that

1 is

not

cla

ssifi

ed a

s a

prim

e nu

mbe

r

Exam

ples

a)

Th

e m

ultip

les

of 6

are

6 ,

12 ,

18 ,

24,..

. or M

6 =

{6; 1

2; 1

8; 2

4;...

} b)

LC

M o

f 6 a

nd 1

8 is

18

and

LCM

of 6

and

7 is

42

c)

The

fact

ors

of 2

4 ar

e 1,

2, 3

, 4, 6

, 12

and

24 b

y in

spec

tion

and,

the

prim

e fa

ctor

s of

24

are

2 an

d 3

d)

The

fact

ors

of 1

40 a

re 1

, 2, 5

, 7, 1

0, 1

4, 2

8, 3

5, 7

0 an

d 14

0 e)

D

eter

min

e th

e H

CF

of 1

20; 3

00 a

nd 9

00

Lear

ners

do

this

by

findi

ng th

e pr

ime

fact

ors

of th

e nu

mbe

rs fi

rst.

120

= 5

x 3

x 23 .

Initi

ally

lear

ners

may

writ

e th

is a

s: 5

x 3

x 2

x 2

x 2

30

0 =

52 x 3

x 2

2

900

= 52

x 3

2 x 2

2

HC

F =

5 x

3 x

22 =

60

(Mul

tiply

the

com

mon

prim

e fa

ctor

s of

the

thre

e nu

mbe

rs)

Solv

ing

prob

lem

s So

lvin

g pr

oble

ms

in c

onte

xts

shou

ld ta

ke a

ccou

nt o

f the

num

ber r

ange

s le

arne

rs a

re fa

milia

r with

. o

Con

text

s in

volv

ing

ratio

and

rate

sho

uld

incl

ude

spee

d, d

ista

nce

and

time

prob

lem

s.

o In

fina

ncia

l con

text

s, le

arne

rs a

re n

ot e

xpec

ted

to u

se fo

rmul

ae fo

r cal

cula

ting

sim

ple

inte

rest

. In

Gra

de 8

, rev

isin

g th

e pr

oper

ties

of w

hole

num

bers

sho

uld

be th

e st

artin

g po

int f

or w

ork

with

who

le n

umbe

rs. T

he p

rope

rties

of

num

bers

sho

uld

prov

ide

the

mot

ivat

ion

for w

hy a

nd h

ow o

pera

tions

with

num

bers

wor

k. W

hen

lear

ners

are

intro

duce

d to

new

nu

mbe

rs, s

uch

as in

tege

rs fo

r exa

mpl

e, th

ey c

an a

gain

exp

lore

how

the

prop

ertie

s of

num

bers

wor

k fo

r the

new

set

of n

umbe

rs.

Lear

ners

als

o ha

ve to

app

ly th

e pr

oper

ties

of n

umbe

rs in

alg

ebra

, whe

n th

ey w

ork

with

var

iabl

es in

pla

ce o

f num

bers

. In

Gra

de 9

lear

ners

con

solid

ate

num

ber k

now

ledg

e an

d ca

lcul

atio

n te

chni

ques

for w

hole

num

bers

, dev

elop

ed in

Gra

de 8

. The

focu

s in

G

rade

9 s

houl

d be

on

deve

lopi

ng a

n un

ders

tand

ing

of d

iffer

ent n

umbe

r sys

tem

s an

d th

e pr

oper

ties

of o

pera

tions

that

app

ly fo

r di

ffere

nt n

umbe

r sys

tem

s. T

he c

onte

xts

for s

olvi

ng p

robl

ems

shou

ld b

e m

ore

com

plex

and

var

ied,

invo

lvin

g w

hole

num

bers

, int

eger

s an

d ra

tiona

l num

bers

. Fin

anci

al c

onte

xts

are

espe

cial

ly ri

ch in

this

rega

rd. L

earn

ers

shou

ld b

e gi

ven

a cl

ear i

ndic

atio

n of

whe

n th

e us

e of

cal

cula

tors

is p

erm

issi

ble

or n

ot. C

alcu

lato

rs s

houl

d be

use

d ro

utin

ely

for c

alcu

latio

ns w

ith b

ig n

umbe

rs a

nd w

here

kno

wle

dge

of


num

ber f

acts

or c

once

pts

is n

ot e

xplic

itly

asse

ssed

. How

ever

, gua

rd a

gain

st le

arne

rs b

ecom

ing

depe

nden

t on

calc

ulat

ors

for a

ll ca

lcul

atio

ns. C

alcu

lato

rs re

mai

n a

usef

ul to

ol fo

r che

ckin

g so

lutio

ns. C

ompe

tenc

y in

find

ing

mul

tiple

s an

d fa

ctor

s, a

nd p

rime

fact

oris

atio

n of

who

le n

umbe

rs, r

emai

ns im

porta

nt fo

r dev

elop

ing

com

pete

ncy

in fa

ctor

isin

g al

gebr

aic

expr

essi

ons

and

solv

ing

alge

brai

c eq

uatio

ns.

By d

istin

guis

hing

the

prop

ertie

s of

diff

eren

t num

ber s

yste

ms,

lear

ners

sho

uld

reco

gniz

e th

at n

atur

al n

umbe

rs is

a s

ubse

t of w

hole

nu

mbe

rs, w

hich

in tu

rn is

a s

ubse

t of i

nteg

ers,

whi

ch in

turn

is a

sub

set o

f rat

iona

l num

bers

. All

of th

ese

num

bers

form

par

t of t

he re

al

num

ber s

yste

m.

Not

e th

at 0

may

som

etim

es b

e in

clud

ed in

the

set o

f nat

ural

num

bers

. Le

arne

rs s

houl

d re

cogn

ize

the

follo

win

g di

stin

guis

hing

feat

ures

of t

he n

umbe

r sys

tem

s

in

tege

rs e

xten

d th

e na

tura

l and

who

le n

umbe

r sys

tem

s by

incl

udin

g th

e op

erat

ion

a –

b, w

here

a <

b.

ra

tiona

l num

bers

ext

end

the

set o

f int

eger

s by

incl

udin

g th

e op

erat

ion

𝑎𝑎 𝑏𝑏 whe

re a

< b

ratio

nal n

umbe

rs a

re d

efin

ed a

s nu

mbe

rs th

at c

an b

e w

ritte

n in

the

form

𝑎𝑎 𝑏𝑏 whe

re a

and

b a

re in

tege

rs a

nd b

≠ 0

sinc

e in

tege

rs a

re a

sub

set o

f rat

iona

l num

bers

, eve

ry in

tege

r, ca

n be

exp

ress

ed a

s a

ratio

nal n

umbe

r a

irr

atio

nal n

umbe

rs a

re n

umbe

rs th

at c

anno

t be

expr

esse

d as

ratio

nal n

umbe

rs

Pi

(π) i

s an

irra

tiona

l num

ber,

even

thou

gh w

e us

e 22 7

or 3

,14

as ra

tiona

l num

ber a

ppro

xim

atio

ns fo

r π in

cal

cula

tions

R

atio

and

rate

pro

blem

s in

clud

e pr

oble

ms

invo

lvin

g sp

eed,

dis

tanc

e an

d tim

e. L

earn

ers

shou

ld b

e fa

milia

r with

the

follo

win

g fo

rmul

ae

for t

hese

cal

cula

tions

:

a)

spee

d =

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑎𝑎𝑑𝑑

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑡𝑡𝑑𝑑

b)

di

stan

ce =

spe

ed x

tim

e c)

tim

e =

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑎𝑎𝑑𝑑

𝑑𝑑𝑑𝑑𝑑𝑑𝑠𝑠𝑑𝑑𝑑𝑑𝑑𝑑

Sp

eed

is u

sual

ly g

iven

as

cons

tant

spe

ed o

r ave

rage

spe

ed. M

ake

sure

lear

ners

reco

gniz

e an

d ar

e ab

le to

con

vert

corre

ctly

bet

wee

n un

its fo

r tim

e an

d di

stan

ce.

Exam

ples

a)

A ca

r tra

vellin

g at

a c

onst

ant s

peed

trav

els

60 k

m in

18

min

utes

. How

far,

trave

lling

at th

e sa

me

cons

tant

spe

ed, w

ill th

e ca

r tra

vel i

n 1

hour

12

min

utes

? b)

A

car t

rave

lling

at a

n av

erag

e sp

eed

of 1

00 k

m/h

cov

ers

a ce

rtain

dis

tanc

e in

3 h

ours

20

min

utes

. At w

hat c

onst

ant s

peed

m

ust t

he c

ar tr

avel

to c

over

the

sam

e di

stan

ce in

2 h

ours

40

min

utes

?


Dire

ct a

nd In

dire

ct p

ropo

rtio

n G

rade

9 le

arne

rs s

houl

d be

fam

iliar w

ith th

e fo

llow

ing

rela

tions

hips

:

x is

dire

ctly

pro

porti

onal

to y

if 𝑥𝑥 𝑦𝑦 =

con

stan

t

x an

d y

are

dire

ctly

pro

porti

onal

if, a

s th

e va

lue

of x

incr

ease

s th

e va

lue

of y

incr

ease

s in

the

sam

e pr

opor

tion,

and

as

the

valu

e of

x d

ecre

ases

the

valu

e of

y d

ecre

ases

in th

e sa

me

prop

ortio

n

The

dire

ct p

ropo

rtion

al re

latio

nshi

p is

repr

esen

ted

by a

stra

ight

line

gra

ph

x

is in

dire

ctly

or i

nver

sely

pro

porti

onal

to y

if x

x y

= a

con

stan

t. In

oth

er w

ords

y =

𝑐𝑐 𝑥𝑥

x an

d y

are

indi

rect

ly p

ropo

rtion

al if

, as

the

valu

e of

x in

crea

ses

the

valu

e of

y d

ecre

ases

and

as

the

valu

e of

x d

ecre

ases

the

valu

e of

y in

crea

ses

an

indi

rect

pro

porti

onal

rela

tions

hip

is re

pres

ente

d by

a n

on-li

near

cur

ve

Fina

ncia

l con

text

s O

nce

Gra

de 9

lear

ners

hav

e do

ne s

uffic

ient

cal

cula

tions

for s

impl

e an

d co

mpo

und

inte

rest

thro

ugh

repe

ated

cal

cula

tions

, the

y co

uld

use

give

n fo

rmul

ae fo

r the

se c

alcu

latio

ns.

Exam

ples

a)

Cal

cula

te th

e si

mpl

e in

tere

st o

n R

600

at 7

% p

.a fo

r 3 y

ears

usi

ng th

e fo

rmul

a S

I = 𝑃𝑃𝑃𝑃

𝑃𝑃10

0 or s

i = P

.n.i

for i

= 𝑖𝑖 100 .

b)

R80

0 in

vest

ed a

t r%

per

ann

um s

impl

e in

tere

st fo

r a p

erio

d of

3 y

ears

yie

lds

R16

8. C

alcu

late

the

valu

e of

r c)

H

ow lo

ng w

ill it

take

for R

3 00

0 in

vest

ed a

t 6%

per

ann

um s

impl

e in

tere

st to

gro

w to

R4

260?

d)

Te

mos

o bo

rrow

ed R

500

from

the

bank

for 3

yea

rs a

t 8%

p.a

. com

poun

d in

tere

st. W

ithou

t usi

ng a

form

ula,

cal

cula

te h

ow m

uch

Tem

oso

owes

the

bank

at t

he e

nd o

f thr

ee y

ears

. e)

U

se th

e fo

rmul

a A

= P(

1 +

𝑃𝑃 100 )n

to c

alcu

late

the

com

poun

d in

tere

st o

n a

loan

of R

3 45

0 at

6,5

% p

er a

nnum

for 5

yea

rs.

LT

SM

Res

ourc

es

Cal

cula

tors

, num

ber l

ine.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

G

rade

7 W

B 1

Activ

ities

(R

2a&b

; R3;

R4;

R5a

&b; R

6; 1

7-23

R13

G

rade

8 W

B 1

Activ

ities

(1

; 2a&

b; 3

-5; 6

-10)

G

rade

9 W

B 1

Activ

ities

(1

a&b;

3a&

b - 9

)


Te

xtbo

ok

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

2

TER

M 1

Dat

e : f

rom

....

to ..

....

Tim

e:

9 h

ours

G

rade

7

8 9

Topi

c IN

TEG

ERS

CAP

S pa

ges

67 –

68

78 -

80

121

Skills

and

Kno

wle

dge

Cou

ntin

g, o

rder

ing

and

com

parin

g in

tege

rs

C

ount

forw

ards

and

bac

kwar

ds in

in

tege

rs fo

r any

inte

rval

Rec

ogni

ze, o

rder

and

com

pare

in

tege

rs

Cal

cula

tions

with

inte

gers

• A

dd a

nd s

ubtra

ct w

ith in

tege

rs

Prop

ertie

s of

inte

gers

• R

ecog

nize

and

use

com

mut

ativ

e an

d as

soci

ativ

e pr

oper

ties

of a

dditi

on a

nd

mul

tiplic

atio

n fo

r int

eger

s

Cou

ntin

g, o

rder

ing

and

com

parin

g in

tege

rs

Rev

ise:

coun

ting

forw

ards

and

bac

kwar

ds in

in

tege

rs fo

r any

inte

rval

reco

gniz

ing,

ord

erin

g an

d co

mpa

ring

inte

gers

C

alcu

latio

ns w

ith in

tege

rs

R

evis

e ad

ditio

n an

d su

btra

ctio

n w

ith

inte

gers

Mul

tiply

and

div

ide

with

inte

gers

Perfo

rm c

alcu

latio

ns in

volv

ing

all f

our

oper

atio

ns w

ith in

tege

rs

Pe

rform

cal

cula

tions

invo

lvin

g al

l fou

r op

erat

ions

with

num

bers

that

invo

lve

the

squa

res,

cub

es, s

quar

e ro

ots

and

cube

root

s of

inte

gers

Prop

ertie

s of

inte

gers

Rec

ogni

ze a

nd u

se c

omm

utat

ive,

as

soci

ativ

e an

d di

strib

utiv

e pr

oper

ties

of a

dditi

on a

nd m

ultip

licat

ion

for

inte

gers

Rec

ogni

ze a

nd u

se a

dditi

ve a

nd

mul

tiplic

ativ

e in

vers

es fo

r int

eger

s

Cou

ntin

g, o

rder

ing

and

com

parin

g in

tege

rs -

Rev

isio

n R

evis

e:

co

untin

g fo

rwar

ds a

nd b

ackw

ards

in

inte

gers

for a

ny in

terv

al

re

cogn

izin

g, o

rder

ing

and

com

parin

g in

tege

rs

Cal

cula

tions

with

inte

gers

R

evis

e:

pe

rform

cal

cula

tions

invo

lvin

g al

l fou

r op

erat

ions

with

inte

gers

perfo

rm c

alcu

latio

ns in

volv

ing

all f

our

oper

atio

ns w

ith n

umbe

rs th

at in

volv

e th

e sq

uare

s, c

ubes

, squ

are

root

s an

d cu

be

root

s of

inte

gers

Pr

oper

ties

of in

tege

rs

Rev

ise:

com

mut

ativ

e, a

ssoc

iativ

e an

d di

strib

utiv

e pr

oper

ties

of a

dditi

on a

nd

mul

tiplic

atio

n fo

r int

eger

s

ad

ditiv

e an

d m

ultip

licat

ive

inve

rses

for

inte

gers


Solv

ing

prob

lem

s • S

olve

pro

blem

s in

con

text

s in

volv

ing

ad

ditio

n an

d su

btra

ctio

n of

inte

gers

Solv

ing

prob

lem

s So

lve

prob

lem

s in

con

text

s in

volv

ing

mul

tiple

ope

ratio

ns w

ith in

tege

rs

Solv

ing

prob

lem

s So

lve

prob

lem

s in

con

text

s in

volv

ing

mul

tiple

ope

ratio

ns w

ith in

tege

rs

Su

gges

ted

met

hodo

logy

In

tege

rs a

re n

ew n

umbe

rs in

trodu

ced

in G

rade

7.

Cou

ntin

g, o

rder

ing

and

com

parin

g in

tege

rs

Cou

ntin

g sh

ould

not

onl

y be

thou

ght o

f as

verb

al c

ount

ing.

Lea

rner

s ca

n co

unt u

sing

:

stru

ctur

ed, s

emi-s

truct

ured

or e

mpt

y nu

mbe

r lin

es

ch

ain

diag

ram

s fo

r cou

ntin

g Le

arne

rs s

houl

d be

giv

en a

rang

e of

exe

rcis

es s

uch

as:

ar

rang

e gi

ven

num

bers

from

the

smal

lest

to th

e bi

gges

t: or

big

gest

to s

mal

lest

fill i

n m

issi

ng n

umbe

rs in

a s

eque

nce;

on

a nu

mbe

r grid

; or o

n a

num

ber l

ine

fil

l in

<, =

or >

Ex

ampl

e:

– 4

25 *

– 45

0 C

alcu

latio

ns u

sing

inte

gers

• St

art c

alcu

latio

ns u

sing

inte

gers

in s

mal

l num

ber r

ange

s.

• D

evel

op a

n un

ders

tand

ing

that

sub

tract

ing

an in

tege

r is

the

sam

e as

add

ing

its a

dditi

ve in

vers

e.

Exam

ple:

7

– 4

= 7

+ (–

4) =

3 O

R –

7 –

4 =

–7 +

(– 4

) = –

11

So to

o, 7

– (–

4) =

7 +

(+4)

= 1

1 O

R –

7 –

(– 4

) = –

7 +

(+4)

= –

3 H

ere

the

use

of b

rack

ets

arou

nd th

e in

tege

rs is

use

ful.

Prop

ertie

s of

inte

gers

•

Lear

ners

sho

uld

inve

stig

ate

the

prop

ertie

s fo

r ope

ratio

ns u

sing

who

le n

umbe

rs o

n th

e se

t of i

nteg

ers.

•

Thes

e pr

oper

ties

shou

ld s

erve

as

mot

ivat

ion

for t

he o

pera

tions

they

can

per

form

usi

ng in

tege

rs.

• Le

arne

rs s

houl

d se

e th

at th

e co

mm

utat

ive

prop

erty

for a

dditi

on h

olds

for i

nteg

ers

e.g.

8 +

(–3)

= (–

3) +

8 =

5

• Le

arne

rs s

houl

d se

e th

at th

ey c

an s

till u

se s

ubtra

ctio

n to

che

ck a

dditi

on o

r vic

e ve

rsa.

Exa

mpl

e: If

8 +

(–3)

= 5

, the

n 5

– 8

= –

3 an

d 5

–(–3

) = 8

•

Lear

ners

sho

uld

see

that

the

asso

ciat

ive

prop

erty

for a

dditi

on h

olds

for i

nteg

ers.

Exa

mpl

e: [(

–6) +

4] +

(–1)

= (–

6) +

[4 +

(–1)

] = –

3 •

Lear

ners

sho

uld

only

exp

lore

the

dist

ribut

ive

prop

erty

onc

e th

ey c

an m

ultip

ly w

ith in

tege

rs


In G

rade

8 le

arne

rs:

• C

onso

lidat

e nu

mbe

r kno

wle

dge

and

calc

ulat

ion

tech

niqu

es fo

r int

eger

s, d

evel

oped

in G

rade

7.

• M

ultip

ly a

nd d

ivid

e w

ith in

tege

rs

• Pe

rform

all

four

ope

ratio

ns w

ith in

tege

rs

• Pe

rform

all

four

ope

ratio

ns w

ith s

quar

es, c

ubes

, squ

are

and

cube

root

s of

inte

gers

C

ount

ing,

ord

erin

g an

d co

mpa

ring

inte

gers

Lear

ners

sho

uld

cont

inue

pra

ctis

ing

coun

ting,

ord

erin

g an

d co

mpa

ring

inte

gers

. Cou

ntin

g sh

ould

not

onl

y be

thou

ght o

f as

verb

al

coun

ting.

Lea

rner

s ca

n co

unt u

sing

: o

stru

ctur

ed, s

emi-s

truct

ured

or e

mpt

y nu

mbe

r lin

es

o ch

ain

diag

ram

s fo

r cou

ntin

g

Lear

ners

sho

uld

be g

iven

a ra

nge

of e

xerc

ises

Th

ey s

houl

d

o Ar

rang

e gi

ven

num

bers

from

the

smal

lest

to th

e bi

gges

t: or

big

gest

to s

mal

lest

o

Fill

in m

issi

ng n

umbe

rs in

a s

eque

nce;

on

a nu

mbe

r grid

; or o

n a

num

ber l

ine

o Fi

ll in

<, =

or >

e.g

. – 4

25 *

– 45

0;

Cal

cula

tions

usi

ng in

tege

rs

See

note

s fo

r Gra

de 7

abo

ve.

A us

eful

stra

tegy

is to

use

repe

ated

add

ition

and

num

ber p

atte

rns

to s

how

lear

ners

the

reas

onab

lene

ss o

f rul

es fo

r the

resu

ltant

sig

n fo

r mul

tiplic

atio

n w

ith in

tege

rs.

Exam

ple:

a)

R

epea

ted

addi

tion

of (–

3): (

–3) +

(–3)

+ (–

3) =

–9

= 3

x (–

3)

b)

Rep

eate

d ad

ditio

n of

(–2)

: (–2

) + (–

2) +

(–2)

+ (–

2) =

–8

= 4

x (–

2)

c)

Cou

ntin

g do

wn

in in

terv

als

of 3

from

9:

3 x

3 =

9 3

x 2

= 6

3 x

1 =

3 3

x 0

= 0

3 x

–1 =

–3

3 x

–2 =

?

3 x

–3 =

?

Hen

ce th

e ru

le: a

pos

itive

inte

ger x

a n

egat

ive

inte

ger =

a n

egat

ive

inte

ger


d)

U

sing

the

rule

that

a p

ositi

ve in

tege

r x a

neg

ativ

e in

tege

r = a

neg

ativ

e in

tege

r, es

tabl

ishe

d fro

m e

xam

ples

abo

ve, t

he

follo

win

g pa

ttern

can

be

used

: –1

x 3

= –

3 –1

x 2

= –

2 –1

x 1

= –

1 –1

x 0

= 0

–1

x –

1 =

1 –1

x –

2 =

? –1

x –

3 =

? H

ence

the

rule

: a n

egat

ive

inte

ger x

a n

egat

ive

inte

ger =

a p

ositi

ve in

tege

r U

se th

e in

vers

e op

erat

ion

for m

ultip

licat

ion

and

divi

sion

to d

evel

op a

rule

for t

he re

sulta

nt s

ign

for d

ivis

ion

with

inte

gers

. Ex

ampl

e:

a)

If 4

x (–

2) =

–8,

then

–8

÷ 4

= –2

and

–8

÷ (–

2) =

4

b)

If (–

1) x

(–3)

= 3

, the

n 3

÷ (–

1) =

–3

and

3 ÷

(–3)

= –

1 H

ence

the

rule

s: d

ivis

ion

of a

pos

itive

and

neg

ativ

e in

tege

r equ

als

a ne

gativ

e in

tege

r and

div

isio

n of

two

nega

tive

inte

gers

equ

al a

po

sitiv

e in

tege

r. Fi

ndin

g th

e sq

uare

s, c

ubes

, squ

are

root

s an

d cu

be ro

ots

of in

tege

rs a

re a

lso

oppo

rtuni

ties

to c

heck

that

lear

ners

kno

w th

e ru

les

for

resu

ltant

sig

ns w

hen

mul

tiply

ing

inte

gers

. The

refo

re, m

ake

sure

that

lear

ners

und

erst

and

why

you

can

not f

ind

the

squa

re ro

ot o

f a

nega

tive

inte

ger,

and

that

the

squa

re o

f a n

egat

ive

inte

ger i

s al

way

s po

sitiv

e.

Exam

ple:

a)

(−

5)2

= (–

5) x

(–5)

= 2

5 b)

)

(− 4)

3 = (–

4) x

(–4)

x (–

4) =

– 6

4 c)

√−

273

= –

3 be

caus

e –3

x –

3 x–

3 =

–27

Prop

ertie

s of

inte

gers

Le

arne

rs s

houl

d in

vest

igat

e th

e pr

oper

ties

for o

pera

tions

with

who

le n

umbe

rs o

n th

e se

t of i

nteg

ers.

The

se p

rope

rties

sho

uld

serv

e as

mot

ivat

ion

for t

he o

pera

tions

they

can

per

form

with

inte

gers

. Lea

rner

s sh

ould

: •

see

that

the

com

mut

ativ

e pr

oper

ty fo

r add

ition

and

mul

tiplic

atio

n ho

lds

for i

nteg

ers,

e.g

. 8 +

(–3)

= (–

3) +

8 =

5; 8

x (–

3) =

(–3)

x 8

= –

24

• se

e th

at th

ey c

an s

till u

se s

ubtra

ctio

n to

che

ck a

dditi

on o

r vic

e ve

rsa,

e.g

. if 8

+ (–

3) =

5, t

hen

5 –

8 =

–3 a

nd 5

–(–

3) =

8

• se

e th

at th

e as

soci

ativ

e pr

oper

ty fo

r add

ition

hol

ds fo

r int

eger

s, e

.g. [

(–6)

+ 4

] + (–

1) =

(–6)

+ [4

+ (–

1)] =

–3


• se

e th

at th

e in

vers

e op

erat

ion

for m

ultip

licat

ion

and

divi

sion

hol

ds fo

r int

eger

s, e

.g. i

f 5 x

(–6)

= –

30, t

hen

–30

÷ 5

= –6

and

–30

÷ (–

6) =

5

• de

velo

p th

e ru

les,

thro

ugh

patte

rnin

g, fo

r res

ulta

nt s

igns

whe

n m

ultip

lyin

g an

d di

vidi

ng in

tege

rs:

Exam

ples

(+

5) x

(+5)

= (+

25);

(–5)

x (–

5) =

(+25

); (–

5) x

(+5)

= (–

25);

(+25

) ÷ (+

5) =

(+5)

; (–

25) ÷

(–5)

= (+

5);

(–25

) ÷ (+

5) =

(–5)

; In

Gra

de 9

lear

ners

: •

cons

olid

ate

num

ber k

now

ledg

e an

d ca

lcul

atio

n te

chni

ques

for i

nteg

ers,

dev

elop

ed in

Gra

de 8

. •

wor

k w

ith in

tege

rs m

ostly

as

coef

ficie

nts

in a

lgeb

raic

exp

ress

ions

and

equ

atio

ns.

The

y ar

e ex

pect

ed to

be

com

pete

nt in

per

form

ing

all f

our o

pera

tions

with

inte

gers

and

usi

ng th

e pr

oper

ties

of in

tege

rs a

ppro

pria

tely

w

here

nec

essa

ry.

LTSM

Res

ourc

es

Num

ber l

ine

with

neg

ativ

e an

d po

sitiv

e nu

mbe

rs, t

herm

omet

er, m

easu

ring

jugs

, ice

, cha

rts.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

G

rade

7 W

B 2

Activ

ities

(1

05 -

113)

Gra

de 8

WB

1 Ac

tiviti

es

(1; 1

1; 1

2; 1

3)

Gra

de 9

WB

1 Ac

tiviti

es

(R4)

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – te

st 1

5 m

arks

max


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTIG

RAD

E LE

SSO

N P

LAN

3

TER

M 1

Dat

e: fr

om...

. to.

.....

Tim

e:

9 ho

urs

Gra

de

7 8

9 To

pic

EXPO

NEN

TS

CAP

S pa

ges

43 –

44

81 -

84

124

- 126

Sk

ills a

nd

Know

ledg

e C

ompa

ring

and

repr

esen

ting

num

bers

in

exp

onen

tial f

orm

C

ompa

re a

nd re

pres

ent w

hole

num

bers

in

exp

onen

tial f

orm

:

b a=

a x

a x

a x.

.. fo

r b n

umbe

r of

fact

ors

Cal

cula

tions

usi

ng n

umbe

rs in

ex

pone

ntia

l for

m

R

ecog

nize

and

use

the

appr

opria

te

law

s of

ope

ratio

ns w

ith n

umbe

rs

invo

lvin

g ex

pone

nts

and

squa

re a

nd

cube

root

s

Com

parin

g an

d re

pres

entin

g nu

mbe

rs in

exp

onen

tial f

orm

Rev

ise

com

pare

and

repr

esen

t who

le

num

bers

in e

xpon

entia

l for

m

C

ompa

re a

nd re

pres

ent i

nteg

ers

in

expo

nent

ial f

orm

Com

pare

and

repr

esen

t num

bers

in

scie

ntifi

c no

tatio

n, li

mite

d to

pos

itive

ex

pone

nts

Cal

cula

tions

usi

ng n

umbe

rs in

ex

pone

ntia

l for

m

Es

tabl

ish

gene

ral l

aws

of e

xpon

ents

, lim

ited

to n

atur

al n

umbe

r exp

onen

ts:

o n

mn

ma

aa

o n

mn

ma

aa

o

nm

nm

aa

)(

o n

nn

ta

ta

)

(

o 1

)(

0

a

R

ecog

nize

and

use

the

appr

opria

te

law

s of

ope

ratio

ns u

sing

num

bers

Com

parin

g an

d re

pres

entin

g nu

mbe

rs in

ex

pone

ntia

l for

m

R

evis

e:

o co

mpa

re a

nd re

pres

ent i

nteg

ers

in

expo

nent

ial f

orm

o

com

pare

and

repr

esen

t num

bers

in

scie

ntifi

c no

tatio

n

Exte

nd s

cien

tific

not

atio

n to

incl

ude

nega

tive

expo

nent

s C

alcu

latio

ns u

sing

num

bers

in

expo

nent

ial f

orm

Rev

ise

the

follo

win

g ge

nera

l law

s of

ex

pone

nts:

o

am x

an =

am

+n

o am

÷ a

n = a

m-n

, if m

>n

o (a

m)n =

am

x n

o

(a x

t)n =

an x

t n

o a0 =

1

Ex

tend

the

gene

ral l

aws

of e

xpon

ents

to

incl

ude

inte

ger e

xpon

ents

𝑎𝑎−𝑛𝑛

= 1 𝑎𝑎𝑛𝑛


Perfo

rm c

alcu

latio

ns in

volv

ing

all f

our

oper

atio

ns u

sing

num

bers

in

expo

nent

ial f

orm

, lim

ited

to

expo

nent

s up

to 5

, and

squ

are

and

cube

root

s

So

lvin

g pr

oble

ms

Solv

e pr

oble

ms

in c

onte

xts

invo

lvin

g nu

mbe

rs in

exp

onen

tial f

orm

invo

lvin

g ex

pone

nts

and

squa

re a

nd

cube

root

s

Pe

rform

cal

cula

tions

invo

lvin

g al

l fou

r op

erat

ions

with

num

bers

that

invo

lve

squa

res,

cub

es, s

quar

e ro

ots

and

cube

ro

ots

of in

tege

rs

C

alcu

late

the

squa

res,

cub

es, s

quar

e ro

ots

and

cube

root

s of

ratio

nal

num

bers

So

lvin

g pr

oble

ms

Solv

e pr

oble

ms

in c

onte

xts

invo

lvin

g nu

mbe

rs in

exp

onen

tial f

orm

.

Pe

rform

cal

cula

tions

invo

lvin

g al

l fou

r op

erat

ions

usi

ng n

umbe

rs in

exp

onen

tial

form

So

lvin

g pr

oble

ms

Solv

e pr

oble

ms

in c

onte

xts

invo

lvin

g nu

mbe

rs in

exp

onen

tial f

orm

, inc

ludi

ng

scie

ntifi

c no

tatio

n

Sugg

este

d m

etho

dolo

gy

Alth

ough

Gra

de 7

lear

ners

may

hav

e en

coun

tere

d sq

uare

num

bers

in G

rade

6, t

hey

wer

e no

t exp

ecte

d to

writ

e th

ese

num

bers

in

expo

nent

ial f

orm

. C

ompa

ring

and

repr

esen

ting

num

bers

in e

xpon

entia

l for

m

Lear

ners

nee

d to

und

erst

and

that

in th

e ex

pone

ntia

l for

m a

b , th

e nu

mbe

r is

read

as

‘a to

the

pow

er b

’, w

here

a is

cal

led

the

base

an

d b

is c

alle

d th

e ex

pone

nt o

r ind

ex.(b

) ind

icat

es th

e nu

mbe

r of f

acto

rs th

at a

re m

ultip

lied.

Ex

ampl

e:

a) a

3 = a

x a

x a

; b)

a5 =

a x

a x

a x

a x

a

Lear

ners

can

repr

esen

t any

num

ber i

n ex

pone

ntia

l for

m, w

ithou

t nee

ding

to c

ompu

te th

e va

lue.


Exam

ple:

50

x 5

0 x

50 x

50

x 50

x 5

0 x

50 =

(50)

7

Mak

e su

re le

arne

rs u

nder

stan

d th

at s

quar

e ro

ots

and

cube

root

s ar

e th

e in

vers

e op

erat

ions

of s

quar

ing

and

cubi

ng n

umbe

rs.

Exam

ples

: 32 =

9 th

eref

ore √92

= 3

M

ake

sure

lear

ners

und

erst

and

that

any

num

ber r

aise

d to

the

pow

er 1

is e

qual

to th

e nu

mbe

r. Ex

ampl

e:

m1 =

m

At th

is p

oint

, lea

rner

s do

not

nee

d to

kno

w th

e ru

le fo

r rai

sing

a n

umbe

r to

the

pow

er 0

. Thi

s w

ill on

ly b

e in

trodu

ced

in G

rade

8 w

hen

they

use

oth

er la

ws

of e

xpon

ents

in c

alcu

latio

ns. T

o av

oid

com

mon

mis

conc

eptio

ns, e

mph

asiz

e th

e fo

llow

ing

with

exa

mpl

es:

(1

2)2 =

12

x 12

and

not

12

x 2

13 m

eans

1 x

1 x

1 a

nd n

ot 1

x 3

1001 =

100

√81

2 =

9 b

ecau

se 9

2 = 8

1

√27

3 =

3 b

ecau

se 3

3 = 2

7

The

squa

re o

f 9

= 81

, whe

reas

the

squa

re ro

ot o

f 9 =

3

Le

arne

rs s

houl

d us

e th

eir k

now

ledg

e of

repr

esen

ting

num

bers

in e

xpon

entia

l l fo

rm w

hen

sim

plify

ing

and

expa

ndin

g al

gebr

aic

expr

essi

ons

and

solv

ing

alge

brai

c e

quat

ions

C

alcu

latio

ns u

sing

num

bers

in e

xpon

entia

l for

m

Know

ing

the

rule

s of

ope

ratio

ns fo

r cal

cula

tions

invo

lvin

g ex

pone

nts

is im

porta

nt.

Exam

ples

: a)

(7 –

4)3 =

33 a

nd N

OT

73 – 4

3

b) √

16+

9 =

√25

, and

NO

T √1

6 + √9

In

Gra

de 8

:

• In

tege

rs a

nd ra

tiona

l num

bers

in e

xpon

entia

l for

m


• Sc

ient

ific

nota

tion

of n

umbe

rs

Law

s of

exp

onen

ts

The

law

s of

exp

onen

ts s

houl

d be

intro

duce

d th

roug

h a

rang

e of

num

eric

exa

mpl

es fi

rst,

then

var

iabl

es c

an b

e us

ed. I

n ot

her w

ords

, th

e nu

mbe

rs a

re re

plac

ed w

ith le

tters

, but

the

rule

s w

ork

the

sam

e. T

he fo

llow

ing

law

s of

exp

onen

ts s

houl

d be

intro

duce

d, w

here

m

and

n ar

e na

tura

l num

bers

and

a a

nd t

are

not e

qual

to 0

:

nm

nm

aa

a

if

m >

n Ex

ampl

es

a)

74

34

32

22

2

b)

74

34

3x

xx

x

n

mn

ma

aa

if

m >

n

Exam

ples

a)

273

33

32

5

b)

23

53

5x

xx

x

nm

nm

aa

)(

Exam

ples

: a)

62

32

32

2)

2(

b)

62

32

3)

(x

xx


nn

nt

at

a

)(

Ex

ampl

es:

a)

63

23

32

27)

(3

)3(

xx

x

b)

4000

625

6425

8)

5()

2()

52(

22

22

23

22

3

1

)(

0

a

Exam

ples

: a)

1)

37(0

b)

1)

4(0

2

x

Mak

e su

re th

at le

arne

rs u

nder

stan

d th

e la

ws

of e

xpon

ents

read

ing

from

bot

h si

des

of th

e eq

ual s

ign

i.e. i

f the

LH

S =

RH

S, th

en th

e R

HS

= LH

S.

The

law

1

)(

0

aca

n be

der

ived

by

usin

g th

e la

w o

f exp

onen

ts fo

r div

isio

n in

a fe

w e

xam

ples

.

1

44

a

aa

aa

aa

aa

a

ther

efor

e 1

04

4

aa

Lear

ners

sho

uld

be a

ble

to u

se th

e la

ws

of e

xpon

ents

in c

alcu

latio

ns a

nd fo

r sol

ving

sim

ple

expo

nent

ial e

quat

ions

as

wel

l as

expa

ndin

g or

sim

plify

ing

alge

brai

c ex

pres

sion

s.

Look

out

for t

he fo

llow

ing

com

mon

mis

conc

eptio

ns w

here

: •

Lear

ners

mul

tiply

unl

ike

base

s an

d ad

d th

e ex

pone

nt.

Ex

ampl

e:

a)

nm

nm

xyy

x

)(

•

Lear

ners

mul

tiply

like

bas

es a

nd a

dd th

e ex

pone

nts


Exam

ple:

127

57

54

22

2

In

stea

d of

the

corre

ct a

nsw

er 2

12.

• Le

arne

rs fo

rget

, for

exa

mpl

e, th

at w

hen

squa

ring

a bi

nom

ial t

here

is a

mid

dle

term

. Ex

ampl

e:

mm

my

xy

x

)(

Lear

ners

con

fuse

add

ing

the

expo

nent

s an

d ad

ding

the

term

s

Exam

ple:

n

mn

mx

xx

o

r m

nx

C

alcu

latio

ns u

sing

num

bers

in e

xpon

entia

l for

m

Know

ing

the

rule

s of

ope

ratio

ns fo

r cal

cula

tions

invo

lvin

g ex

pone

nts

are

impo

rtant

, e.g

. a)

(7

– 4

)3 = 3

3 and

NO

T 73 –

43

b) √1

6+

9 =

√25

, and

NO

T √1

6 + √9

Le

arne

rs c

an a

lso

do s

impl

e ca

lcul

atio

ns w

here

the

num

erat

or a

nd d

enom

inat

or o

f a fr

actio

n ar

e w

ritte

n in

exp

onen

tial f

orm

, e.g

., 23 22

= 2

× 2

× 2

2 ×2

= 8 4

=

2

Lear

ners

can

als

o fin

d sq

uare

s, c

ubes

, squ

are

root

s an

d cu

be ro

ots

of d

ecim

al a

nd c

omm

on fr

actio

ns b

y in

spec

tion.


Exam

ples

a)

(0,7

)2 = 0

,49

b)

(0,1

)3 = 0

,001

c)

09,0

=0,3

d)

16943

2222

23

e)

259=

259=

53

Scie

ntifi

c no

tatio

n W

hen

writ

ing

num

bers

in s

cien

tific

not

atio

n, le

arne

rs h

ave

to u

nder

stan

d th

e re

latio

nshi

p be

twee

n th

e nu

mbe

r of d

ecim

al p

lace

s an

d th

e in

dex

of 1

0 Ex

ampl

es:

a)

25

= 2

,5 x

101

b)

250

= 2,

5 x

102

c)

2 50

0 =

2,5

x 10

3

Scie

ntifi

c no

tatio

n lim

ited

to p

ositi

ve e

xpon

ents

, inc

lude

s w

ritin

g ve

ry la

rge

num

bers

in s

cien

tific

not

atio

n.

Exam

ple:

25

milli

on =

2,5

x 1

07

Lear

ners

pra

ctic

e w

ritin

g la

rge

num

bers

in s

cien

tific

not

atio

n, th

ey w

ill re

aliz

e th

ey h

ave

enco

unte

red

thes

e in

Nat

ural

Sci

ence

. It i

s us

eful

to re

fer t

o th

ese

cont

exts

whe

n ta

lkin

g ab

out s

cien

tific

not

atio

n.

In G

rade

9 le

arne

rs

C

onso

lidat

e nu

mbe

r kno

wle

dge

and

calc

ulat

ion

tech

niqu

es fo

r exp

onen

ts, d

evel

oped

in G

rade

8.

D

o ad

ditio

nal l

aws

of e

xpon

ents

invo

lvin

g in

tege

r exp

onen

ts


D

o sc

ient

ific

nota

tion

for n

umbe

rs, i

nclu

ding

neg

ativ

e ex

pone

nts

Law

s of

exp

onen

ts in

volv

ing

inte

ger e

xpon

ents

mm

aa

1

Exam

ples

:

a)

1251

515

33

b)

49171

77

77

22

53

53

Lo

ok o

ut fo

r the

follo

win

g co

mm

on m

isco

ncep

tions

whe

re:

Lear

ners

con

fuse

the

expo

nent

of t

he v

aria

ble

and

the

coef

ficie

nt, e

.g.,

33

212

xx

inst

ead

of

312

x

C

alcu

latio

ns a

nd s

impl

e eq

uatio

ns u

sing

num

bers

in e

xpon

entia

l for

m

The

calc

ulat

ions

and

equ

atio

ns s

houl

d pr

ovid

e op

portu

nitie

s to

app

ly th

e la

ws

of e

xpon

ents

and

sho

uld

not b

e un

duly

com

plex

. Ex

ampl

es

a)

Cal

cula

te:

23

13

62

b)

Si

mpl

ify:

22

)2

)(2

(

xx

c)

So

lve

x:

93

x

d)

Solv

e x:

(i)

412

x


(ii)

1

51

x

Sc

ient

ific

nota

tion

W

hen

writ

ing

num

bers

in s

cien

tific

not

atio

n, le

arne

rs h

ave

to u

nder

stan

d th

e re

latio

nshi

p be

twee

n th

e nu

mbe

r of d

ecim

al p

lace

s an

d th

e in

dex

of 1

0.

Exam

ple:

1

105.2

25

a

nd

210

5.225

0

Sc

ient

ific

nota

tion

that

ext

ends

to n

egat

ive

expo

nent

s in

clud

es w

ritin

g ve

ry s

mal

l num

bers

in s

cien

tific

not

atio

n Ex

ampl

e:

510

5.225

m

illio

nth

Le

arne

rs p

ract

ice

writ

ing

smal

l and

larg

e nu

mbe

rs in

sci

entif

ic n

otat

ion,

whi

ch th

ey m

ight

alre

ady

have

enc

ount

ered

in N

atur

al

Scie

nce.

It is

use

ful t

o re

fer t

o th

ese

cont

exts

whe

n di

scus

sing

sci

entif

ic n

otat

ion.

C

alcu

latio

ns c

an b

e do

ne w

ith o

r with

out a

cal

cula

tor.

Exam

ples

a)

C

alcu

late

: 7

510

910

6.2

with

out u

sing

a c

alcu

lato

r and

giv

e an

swer

in s

cien

tific

not

atio

n.

b)

Writ

e in

sci

entif

ic n

otat

ion:

0,0

0053

c)

C

alcu

late

: 5

410

3.210

8.5

with

out u

sing

a c

alcu

lato

r.

LTSM

Res

ourc

es

Cha

rts.

G

rade

7

Gra

de 8

G

rade

8

Wor

kboo

k re

fere

nce

Gra

de 7

WB

1 Ac

tiviti

es

(14;

15;

16;

17;

18;

19

Gra

de 8

WB

1 Ac

tiviti

es

(R3a

&b; 1

4 –

24; 2

6)

Gra

de 9

WB

1 Ac

tiviti

es

(R3a

&b; 2

2-26

a&b)


Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – te

st

15 m

arks

max


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

4

TER

M 1

Dat

e : f

rom

....

to ..

....

T

ime:

6 ho

urs

G

rade

7

8 9

Topi

c N

UM

ERIC

AN

D G

EOM

ETR

IC P

ATTE

RN

S C

APS

page

s 58

– 6

1; 6

8 85

– 8

8 12

6 - 1

29

Skills

and

Kn

owle

dge

Inve

stig

ate

and

exte

nd p

atte

rns

In

vest

igat

e an

d ex

tend

num

eric

and

ge

omet

ric p

atte

rns

look

ing

for

rela

tions

hips

bet

wee

n nu

mbe

rs, i

nclu

ding

pa

ttern

s:

o re

pres

ente

d in

phy

sica

l or d

iagr

am

form

o

not l

imite

d to

seq

uenc

es in

volv

ing

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

and

just

ify th

e ge

nera

l rul

es fo

r ob

serv

ed re

latio

nshi

ps b

etw

een

num

bers

in

ow

n w

ords

Inve

stig

ate

and

exte

nd p

atte

rns

In

vest

igat

e an

d ex

tend

num

eric

and

ge

omet

ric p

atte

rns

look

ing

for

rela

tions

hips

bet

wee

n nu

mbe

rs,

incl

udin

g pa

ttern

s:

o re

pres

ente

d in

phy

sica

l or d

iagr

am

form

o

not l

imite

d to

seq

uenc

es in

volv

ing

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

o re

pres

ente

d al

gebr

aica

lly

Des

crib

e an

d ju

stify

the

gene

ral r

ules

fo

r obs

erve

d re

latio

nshi

ps b

etw

een

num

bers

in o

wn

wor

ds o

r in

alge

brai

c la

ngua

ge

Inve

stig

ate

and

exte

nd p

atte

rns

In

vest

igat

e an

d ex

tend

num

eric

and

ge

omet

ric p

atte

rns

look

ing

for

rela

tions

hips

bet

wee

n nu

mbe

rs

incl

udin

g pa

ttern

s:

o re

pres

ente

d in

phy

sica

l or d

iagr

am

form

o

not l

imite

d to

seq

uenc

es in

volv

ing

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

o re

pres

ente

d al

gebr

aica

lly

Des

crib

e an

d ju

stify

the

gene

ral r

ules

for

obse

rved

rela

tions

hips

bet

wee

n nu

mbe

rs in

ow

n w

ords

or i

n al

gebr

aic

lang

uage

Sugg

este

d m

etho

dolo

gy

In th

e Se

nior

Pha

se th

e em

phas

is is

less

on

mer

ely

exte

ndin

g a

patte

rn, a

nd m

ore

on d

escr

ibin

g a

gene

ral r

ule

for t

he p

atte

rn o

r seq

uenc

e an

d be

ing

able

to p

redi

ct u

nkno

wn

term

s in

a s

eque

nce

usin

g a

gene

ral r

ule.

Inve

stig

atin

g nu

mbe

r pat

tern

s is

an

oppo

rtuni

ty to

gen

eral

ize

– to

giv

e ge

nera

l alg

ebra

ic d

escr

iptio

ns o

f the

rela

tions

hip

betw

een

term

s an

d its

pos

ition

in a

seq

uenc

e an

d to

just

ify s

olut

ions

. The

rang

e of

num

ber p

atte

rns

are

exte

nded

to in

clud

e pa

ttern

s in

tege

rs, s

quar

e nu

mbe

rs a

nd c

ubic

num

bers

As

lear

ners

bec

ome

used

to d

escr

ibin

g pa

ttern

s in

thei

r ow

n w

ords

, the

ir de

scrip

tions

sho

uld

beco

me

mor

e pr

ecis

e an

d ef

ficie

nt w

ith th

e us

e of

alg

ebra

ic la

ngua

ge to

des

crib

e ge

nera

l rul

es o

f pat

tern

s. It

is u

sefu

l als

o to

intro

duce

the

lang

uage

of ‘

term

in a

seq

uenc

e’ in

ord

er

to d

istin

guis

h th

e te

rm fr

om th

e po

sitio

n of

a te

rm in

a s

eque

nce


Kin

ds o

f num

eric

pat

tern

s Pr

ovid

e a

sequ

ence

of n

umbe

rs; l

earn

ers

have

to id

entif

y a

patte

rn o

r rel

atio

nshi

p be

twee

n co

nsec

utiv

e te

rms

in o

rder

to e

xten

d th

e pa

ttern

. Ex

ampl

es

Giv

e a

rule

to d

escr

ibe

the

rela

tions

hip

betw

een

the

num

bers

in th

e se

quen

ces

belo

w. U

se th

is ru

le to

giv

e th

e ne

xt th

ree

num

bers

in th

e se

quen

ce:

a)

3

; 7 ;

11 ;

15 ;

... ;

...

b)

120

; 115

; 11

0 ; 1

05 ;

... ;

...

c)

2 ; 4

; 8

; 16

; ...

; ...

d)

1 ; 2

; 4

; 7 ;

11 ;

16 ;

... ;

...

Her

e le

arne

rs c

ould

iden

tify

the

cons

tant

diff

eren

ce b

etw

een

cons

ecut

ive

term

s in

ord

er to

ext

end

the

patte

rn. T

hese

pat

tern

s ca

n be

de

scrib

ed in

lear

ners

’ ow

n w

ords

as

a)

‘add

ing

4’ o

r ‘co

untin

g in

4s’

or ‘

add

4 to

the

prev

ious

num

ber i

n th

e pa

ttern

’ b)

‘s

ubtra

ctin

g 5’

or ‘

coun

ting

dow

n in

5s’

, or ‘

subt

ract

5 fr

om th

e pr

evio

us n

umbe

r in

the

patte

rn’.

c)

Her

e le

arne

rs c

ould

iden

tify

the

cons

tant

ratio

bet

wee

n co

nsec

utiv

e te

rms.

Thi

s pa

ttern

can

be

desc

ribed

in le

arne

rs’ o

wn

wor

ds

as ‘m

ultip

ly th

e pr

evio

us n

umbe

r by

2’.

d)

This

pat

tern

has

nei

ther

a c

onst

ant d

iffer

ence

nor

con

stan

t rat

io. T

his

patte

rn c

an b

e de

scrib

ed in

lear

ners

’ ow

n w

ords

as

‘incr

ease

the

diffe

renc

e be

twee

n co

nsec

utiv

e te

rms

by 1

eac

h tim

e’ o

r ‘ad

d 1

mor

e th

an w

as a

dded

to g

et th

e pr

evio

us te

rm’.

Usi

ng th

is ru

le, t

he n

ext 3

term

s w

ill be

22

, 29

, 37.

Pr

ovid

e a

sequ

ence

of n

umbe

rs; l

earn

ers

have

to id

entif

y a

patte

rn o

r rel

atio

nshi

p be

twee

n th

e te

rm a

nd it

s po

sitio

n in

the

sequ

ence

. Th

is e

nabl

es le

arne

rs to

pre

dict

a te

rm in

a s

eque

nce

base

d on

the

posi

tion

of th

at te

rm in

the

sequ

ence

. It i

s us

eful

for l

earn

ers

to

repr

esen

t the

se s

eque

nces

in ta

bles

so

that

they

can

con

side

r the

pos

ition

of t

he te

rm.

Exam

ples

:

a)

Prov

ide

a ru

le to

des

crib

e th

e re

latio

nshi

p be

twee

n th

e nu

mbe

rs in

this

seq

uenc

e:1;

4; 9

; 16;

... ..

. Use

the

rule

to fi

nd th

e 10

th te

rm

in th

is s

eque

nce.

F

irstly

, lea

rner

s ha

ve to

und

erst

and

that

the

‘10t

h te

rm’ r

efer

s to

pos

ition

10

in th

e nu

mbe

r seq

uenc

e. T

hey

have

to fi

nd a

rule

in o

rder

to

dete

rmin

e th

e 10

th te

rm,

rath

er th

an c

ontin

uing

the

sequ

ence

to th

e te

nth

term

. Thi

s se

quen

ce c

an b

e re

pres

ente

d in

the

follo

win

g ta

ble:


Lear

ners

sho

uld

reco

gniz

e th

at e

ach

term

in th

e bo

ttom

row

is o

btai

ned

by s

quar

ing

the

posi

tion

num

ber i

n th

e to

p ro

w. T

hus

the

10th

term

w

ill be

'10

squa

red'

or 1

02 w

hich

is 1

00. U

sing

the

sam

e ru

le, l

earn

ers

can

also

be

aske

d w

hat t

erm

num

ber o

r pos

ition

will

625

be?

If th

e te

rm is

obt

aine

d by

squ

arin

g th

e po

sitio

n nu

mbe

r of t

he te

rm, t

hen

the

posi

tion

num

ber c

an b

e ob

tain

ed b

y fin

ding

the

squa

re ro

ot o

f the

te

rm. H

ence

, 625

will

be th

e 25

th te

rm in

the

sequ

ence

sin

ce √

625

= 2

5.

b)

Pr

ovid

e a

rule

to d

escr

ibe

the

rela

tions

hip

betw

een

the

num

bers

in th

is s

eque

nce:

4 ;

7 ; 1

0 ; 1

3 ; …

... U

se th

e ru

le to

find

the

20th

te

rm in

the

sequ

ence

. If

lear

ners

con

side

r onl

y th

e re

latio

nshi

p be

twee

n co

nsec

utiv

e te

rms,

then

they

can

con

tinue

the

patte

rn (‘

add

3 to

pre

viou

s nu

mbe

r’)

to th

e 20

th te

rm to

find

the

answ

er. H

owev

er, i

f the

y lo

ok fo

r a re

latio

nshi

p or

rule

bet

wee

n th

e te

rm a

nd th

e po

sitio

n of

the

term

, the

y ca

n pr

edic

t the

ans

wer

with

out c

ontin

uing

the

patte

rn. U

sing

num

ber s

ente

nces

can

be

usef

ul to

find

the

rule

: 1s

t ter

m: 4

= 3

(1) +

1

2nd

term

: 7 =

3 (2

) + 1

3r

d te

rm: 1

0 =

3 (3

) + 1

4t

h te

rm: 1

3 =

3 (4

) + 1

Th

e nu

mbe

r in

the

brac

kets

cor

resp

onds

to th

e po

sitio

n of

the

term

. Hen

ce, t

he 2

0th

term

will

be: 3

(20)

+ 1

= 6

1 Th

e ru

le in

lear

ners

’ ow

n w

ords

can

be

writ

ten

as ‘3

x th

e po

sitio

n of

the

term

+ 1

. Th

ese

type

s of

num

eric

pat

tern

s de

velo

p an

und

erst

andi

ng o

f fun

ctio

nal

rela

tions

hips

, in

whi

ch y

ou h

ave

a de

pend

ent v

aria

ble

(pos

ition

of t

he te

rm) a

nd in

depe

nden

t var

iabl

e (th

e te

rm it

self)

, and

whe

re y

ou

have

a u

niqu

e ou

tput

for a

ny g

iven

inpu

t val

ue.

K

inds

of g

eom

etric

pat

tern

s

Geo

met

ric p

atte

rns

are

num

ber p

atte

rns

repr

esen

ted

diag

ram

mat

ical

ly. T

he d

iagr

amm

atic

repr

esen

tatio

n re

veal

s th

e st

ruct

ure

of th

e nu

mbe

r pat

tern

.

H

ence

, rep

rese

ntin

g th

e nu

mbe

r pat

tern

s in

tabl

es, m

akes

it e

asie

r for

lear

ners

to d

escr

ibe

the

gene

ral r

ule

for t

he p

atte

rn.

Exam

ple

Con

side

r thi

s pa

ttern

for b

uild

ing

hexa

gons

with

mat

chst

icks

. How

man

y m

atch

stic

ks w

ill be

use

d to

bui

ld th

e 10

th h

exag

on?


Th

e ru

le fo

r the

pat

tern

is c

onta

ined

in th

e st

ruct

ure

(con

stru

ctio

n) o

f the

suc

cess

ive

hexa

gona

l sha

pes:

(1

) ad

d 1

on m

atch

stic

k pe

r sid

e (2

) th

ere

are

6 si

des,

so

(3)

add

on 6

mat

chst

icks

per

hex

agon

as

you

proc

eed

from

a g

iven

hex

agon

to th

e ne

xt o

ne.

For t

he 2

nd h

exag

on, y

ou h

ave

2 x

6 m

atch

es; f

or th

e 3r

d he

xago

n yo

u ha

ve 3

x 6

mat

ches

. Usi

ng th

is p

atte

rn fo

r bui

ldin

g he

xago

ns, t

he

10th

hex

agon

will

have

10

x 6

mat

ches

. Lea

rner

s ca

n al

so u

se a

tabl

e to

reco

rd th

e nu

mbe

r of m

atch

es u

sed

for e

ach

hexa

gon.

Thi

s w

ay th

ey c

an lo

ok a

t the

nu

mbe

r pat

tern

rela

ted

to th

e nu

mbe

r of m

atch

es u

sed

for e

ach

new

hex

agon

.

D

escr

ibin

g pa

ttern

s It

does

not

mat

ter i

f lea

rner

s ar

e al

read

y fa

milia

r with

a p

artic

ular

pat

tern

. The

ir de

scrip

tions

of t

he s

ame

patte

rn c

an b

e di

ffere

nt w

hen

they

en

coun

ter i

t at d

iffer

ent s

tage

s of

thei

r mat

hem

atic

al d

evel

opm

ent.

Exam

ple

The

rule

for t

he s

eque

nce:

4 ;

7 ; 1

0 ; 1

3 ca

n be

des

crib

ed in

the

follo

win

g w

ays:

a)

ad

d th

ree

to th

e pr

evio

us te

rm

b)

3 tim

es th

e po

sitio

n of

the

term

+ 1

or 3

x th

e po

sitio

n of

the

term

+ 1

c)

3(

n) +

1, w

here

n is

the

posi

tion

of th

e te

rm

d)

3(n)

+ 1

, whe

re n

is a

Nat

ural

num

ber.

In G

rade

8:

Th

e ra

nge

of n

umbe

r pat

tern

s ar

e ex

tend

ed to

incl

ude

patte

rns

with

mul

tiplic

atio

n an

d di

visi

on w

ith in

tege

rs, n

umbe

rs in

ex

pone

ntia

l for

m

A

s le

arne

rs b

ecom

e us

ed to

des

crib

ing

patte

rns

in th

eir o

wn

wor

ds, t

heir

desc

riptio

ns s

houl

d be

com

e m

ore

prec

ise

and

effic

ient

w

ith th

e us

e of

alg

ebra

ic la

ngua

ge to

des

crib

e ge

nera

l rul

es o

f pat

tern

s


It

is u

sefu

l als

o to

intro

duce

the

lang

uage

of ‘

term

in a

seq

uenc

e’ in

ord

er to

dis

tingu

ish

the

term

from

the

posi

tion

of a

term

in a

se

quen

ce

In

vest

igat

ing

num

ber p

atte

rns

is a

n op

portu

nity

to g

ener

aliz

e –

to g

ive

gene

ral a

lgeb

raic

des

crip

tions

of t

he re

latio

nshi

p be

twee

n te

rms

and

thei

r pos

ition

in a

seq

uenc

e an

d to

just

ify s

olut

ions

. K

inds

of n

umer

ic p

atte

rns

Giv

en a

seq

uenc

e of

num

bers

, lea

rner

s ha

ve to

iden

tify

a pa

ttern

or r

elat

ions

hip

betw

een

cons

ecut

ive

term

s in

ord

er to

ext

end

the

patte

rn.

Exam

ples

Pr

ovid

e a

rule

to d

escr

ibe

the

rela

tions

hip

betw

een

the

num

bers

in th

e se

quen

ces

belo

w. U

se th

is ru

le to

pro

vide

the

next

thre

e nu

mbe

rs

in th

e se

quen

ce:

a)

–3

; –7

; –1

1 ; –

15 ;

... ;

...

Her

e le

arne

rs s

houl

d id

entif

y th

e co

nsta

nt d

iffer

ence

bet

wee

n co

nsec

utiv

e te

rms

in o

rder

to e

xten

d th

e pa

ttern

. Thi

s pa

ttern

can

be

desc

ribed

in le

arne

rs’ o

wn

wor

ds a

s ‘a

ddin

g –4

’ or ‘

coun

ting

in –

4s’ o

r ‘ad

d –4

to th

e pr

evio

us n

umbe

r in

the

patte

rn’.

b)

2

; –4

; 8 ;

–16

; 32

; ...

; ...

Her

e le

arne

rs s

houl

d id

entif

y th

e co

nsta

nt ra

tio b

etw

een

cons

ecut

ive

term

s. T

his

patte

rn c

an b

e de

scrib

ed in

lear

ners

’ ow

n w

ords

as

‘mul

tiply

the

prev

ious

num

ber b

y

–2’.

c)

1

; 2 ;

4 ; 7

; 11

; 16

; ...

; ...

Th

is p

atte

rn h

as n

eith

er a

con

stan

t diff

eren

ce n

or c

onst

ant r

atio

. Thi

s pa

ttern

can

be

desc

ribed

in le

arne

rs’ o

wn

wor

ds a

s ‘in

crea

se th

e di

ffere

nce

betw

een

cons

ecut

ive

term

s by

1 e

ach

time’

or ‘

add

1 m

ore

than

was

add

ed to

get

the

prev

ious

term

’. U

sing

this

rule

, the

ne

xt 3

term

s w

ill be

22

; 29

; 37.

G

iven

a s

eque

nce

of n

umbe

rs, l

earn

ers

have

to id

entif

y a

patte

rn o

r rel

atio

nshi

p be

twee

n th

e te

rm a

nd it

s po

sitio

n in

the

sequ

ence

. Th

is e

nabl

es le

arne

rs to

pre

dict

a te

rm in

a s

eque

nce

base

d on

the

posi

tion

of th

at te

rm in

the

sequ

ence

. It i

s us

eful

for l

earn

ers

to

repr

esen

t the

se s

eque

nces

in ta

bles

so

that

they

can

con

side

r the

pos

ition

of t

he te

rm.

In G

rade

9:

Le

arne

rs c

onso

lidat

e w

ork

invo

lvin

g nu

mer

ic a

nd g

eom

etric

pat

tern

s do

ne in

Gra

de 8

.

Inve

stig

atin

g nu

mbe

r pat

tern

s is

an

oppo

rtuni

ty to

gen

eral

ize

– to

giv

e ge

nera

l alg

ebra

ic d

escr

iptio

ns o

f the

rela

tions

hip

betw

een

term

s an

d th

eir p

ositi

on in

a s

eque

nce

and

to ju

stify

sol

utio

ns.


Kin

ds o

f num

eric

pat

tern

s G

iven

a s

eque

nce

of n

umbe

rs, l

earn

ers

have

to id

entif

y a

patte

rn o

r rel

atio

nshi

p be

twee

n co

nsec

utiv

e te

rms

in o

rder

to e

xten

d th

e pa

ttern

. Ex

ampl

es

Prov

ide

a ru

le to

des

crib

e th

e re

latio

nshi

p be

twee

n th

e nu

mbe

rs in

the

sequ

ence

s be

low

. Use

this

rule

to g

ive

the

next

thre

e nu

mbe

rs in

th

e se

quen

ce:

a) –

1; –

1,5;

–2;

–2,

5 ...

...

Her

e le

arne

rs s

houl

d id

entif

y th

e co

nsta

nt d

iffer

ence

bet

wee

n co

nsec

utiv

e te

rms

in o

rder

to e

xten

d th

e pa

ttern

. Thi

s pa

ttern

can

be

desc

ribed

in le

arne

rs’ o

wn

wor

ds a

s ‘a

ddin

g –0

,5’ o

r ‘co

untin

g in

–0,

5s ’

or ‘a

dd –

0,5

to th

e pr

evio

us n

umbe

r in

the

patte

rn’.

b). 2

; –1;

0,5

; –0,

25 ;

0,12

5 ...

...

Her

e le

arne

rs s

houl

d id

entif

y th

e co

nsta

nt ra

tio b

etw

een

cons

ecut

ive

term

s. T

his

patte

rn c

an b

e de

scrib

ed in

lear

ners

’ ow

n w

ords

as

‘mul

tiply

the

prev

ious

num

ber b

y –

0,5

’. c)

. 1; 0

; –2;

–5;

–9;

–14

... .

Th

is p

atte

rn h

as n

eith

er a

con

stan

t diff

eren

ce n

or c

onst

ant r

atio

. Thi

s pa

ttern

can

be

desc

ribed

in le

arne

rs’ o

wn

wor

ds a

s ‘s

ubtra

ct 1

mor

e th

an w

as s

ubtra

cted

to g

et th

e pr

evio

us te

rm’.

Usi

ng th

is ru

le, t

he n

ext 3

term

s w

ill be

–20

, –27

, –35

G

iven

a s

eque

nce

of n

umbe

rs, l

earn

ers

have

to id

entif

y a

patte

rn o

r rel

atio

nshi

p be

twee

n th

e te

rm a

nd it

s po

sitio

n in

the

sequ

ence

. Th

is e

nabl

es le

arne

rs to

pre

dict

a te

rm in

a s

eque

nce

base

d on

the

posi

tion

of th

at te

rm in

the

sequ

ence

. It i

s us

eful

for l

earn

ers

to

repr

esen

t the

se s

eque

nces

in ta

bles

so

that

they

can

con

side

r the

pos

ition

of t

he te

rm.

Exam

ples

a)

Ref

er to

exa

mpl

es g

iven

abo

ve.

b)

Prov

ide

a ru

le to

des

crib

e th

e re

latio

nshi

p be

twee

n th

e nu

mbe

rs in

this

seq

uenc

e: –

2 ; –

5 ; –

8 ;

–11

; ...

. Use

this

rule

to fi

nd th

e 20

th te

rm in

this

seq

uenc

e.

If le

arne

rs c

onsi

der o

nly

the

rela

tions

hip

betw

een

cons

ecut

ive

term

s, th

en th

ey c

an c

ontin

ue th

e pa

ttern

(‘ad

d -3

to p

revi

ous

num

ber’)

up

to th

e 20

th te

rm to

find

the

answ

er. H

owev

er, i

f the

y lo

ok fo

r a re

latio

nshi

p or

rule

bet

wee

n th

e te

rm a

nd th

e po

sitio

n of

the

term

, th

ey c

an p

redi

ct th

e an

swer

with

out c

ontin

uing

the

patte

rn. U

sing

num

ber s

ente

nces

can

be

usef

ul to

find

the

rule

: 1s

t ter

m: –

2 =

–3(1

) + 1

2n

d te

rm: –

5 =

–3(2

) + 1

3r

d te

rm: –

8 =

–3(3

) + 1

4t

h te

rm: –

11 =

–3(

4) +

1

Th

e nu

mbe

r in

the

brac

kets

cor

resp

onds

to th

e po

sitio

n of

the

term

. Hen

ce, t

he 2

0th

term

will

be: –

3(2

0) +

1 =

– 5

9. T

he ru

le in

lear

ners

’


own

wor

ds c

an b

e w

ritte

n as

–

3 x

the

posi

tion

of th

e te

rm +

1’ o

r –3n

+ 1

, whe

re n

is th

e po

sitio

n of

the

term

. The

se ty

pes

of n

umer

ic p

atte

rns

deve

lop

an

unde

rsta

ndin

g of

func

tiona

l re

latio

nshi

ps, i

n w

hich

ther

e is

a d

epen

dent

var

iabl

e (p

ositi

on o

f the

term

) and

an

inde

pend

ent v

aria

ble

(the

term

itse

lf), a

nd w

here

you

ha

ve a

uni

que

outp

ut fo

r any

giv

en in

put v

alue

. K

inds

of g

eom

etric

pat

tern

s G

eom

etric

pat

tern

s ar

e nu

mbe

r pat

tern

s re

pres

ente

d di

agra

mm

atic

ally

. The

dia

gram

mat

ic re

pres

enta

tion

reve

als

the

stru

ctur

e of

the

num

ber p

atte

rn. •

Hen

ce, r

epre

sent

ing

the

num

ber p

atte

rns

in ta

bles

mak

es it

eas

ier f

or le

arne

rs to

des

crib

e th

e ge

nera

l rul

e fo

r the

pa

ttern

. Ex

ampl

e C

onsi

der t

his

patte

rn fo

r bui

ldin

g he

xago

ns u

sing

mat

chst

icks

. How

man

y m

atch

stic

ks w

ill be

use

d to

bui

ld th

e 10

th h

exag

on?

Pr

ovid

e an

exp

ress

ion

to d

escr

ibe

the

gene

ral t

erm

for t

his

num

ber s

eque

nce.

The

rule

for t

he p

atte

rn is

con

tain

ed in

the

stru

ctur

e (c

onst

ruct

ion)

of t

he

succ

essi

ve h

exag

onal

sha

pes:

(1

) ad

d on

1 m

atch

stic

k pe

r sid

e (2

) th

ere

are

6 si

des,

so

(3)

add

on 6

mat

chst

icks

per

hex

agon

as

you

proc

eed

from

a g

iven

hex

agon

to th

e ne

xt o

ne.

So, f

or th

e 2n

d he

xago

n, y

ou h

ave

2 x

6 m

atch

es; f

or th

e 3r

d he

xago

n yo

u ha

ve 3

x 6

mat

ches

. Usi

ng th

is p

atte

rn fo

r bui

ldin

g he

xago

ns,

the

10th

hex

agon

will

have

10

x 6

mat

ches

. Lea

rner

s ca

n al

so u

se a

tabl

e to

reco

rd th

e nu

mbe

r of m

atch

es u

sed

for e

ach

hexa

gon.

Thi

s w

ay th

e nu

mbe

r pat

tern

is

rela

ted

to th

e nu

mbe

r of m

atch

es u

sed

for e

ach

new

hex

agon

.

Th

e nt

h te

rm fo

r thi

s se

quen

ce c

an b

e w

ritte

n as

6n

or 6

+ (n

– 1

)6


LTSM

Res

ourc

es

Cha

rts w

ith p

ictu

res

or p

atte

rns

and

num

bers

, too

thpi

cks,

mat

ch s

ticks

, pat

tern

blo

cks.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce)

W

B 1

Activ

ities

(R9a

&b)

WB

2 Ac

tiviti

es (6

5 -7

1; 1

14 –

117

; 141

)

WB

1 Ac

tiviti

es (2

7)

W

B 1

Activ

ities

(2

7; 2

8)

TEXT

BO

OK

R

EFER

ENC

E

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – te

st 1

5 m

arks

max


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

5

TER

M 1

Dat

e : f

rom

....

to ..

....

T

ime:

4 ho

urs

G

rade

7

8 9

Topi

c FU

NC

TIO

NS

AND

REL

ATIO

NSH

IPS

CAP

S pa

ges

62

88 -

89

129

Skills

and

Kn

owle

dge

Inpu

t and

out

put v

alue

s D

eter

min

e in

put v

alue

s, o

utpu

t val

ues

or

rule

s fo

r pa

ttern

s an

d re

latio

nshi

ps u

sing

:

flow

dia

gram

s

tabl

es

fo

rmul

ae

Equi

vale

nt fo

rms

Det

erm

ine,

inte

rpre

t and

just

ify e

quiv

alen

ce

of d

iffer

ent d

escr

iptio

ns o

f the

sam

e re

latio

nshi

p or

rule

pre

sent

ed:

ve

rbal

ly

in

flow

dia

gram

s

in ta

bles

by fo

rmul

ae

by

num

ber s

ente

nces

Inpu

t and

out

put v

alue

s D

eter

min

e in

put v

alue

s, o

utpu

t val

ues

or

rule

s fo

r pat

tern

s an

d re

latio

nshi

ps u

sing

:

flow

dia

gram

s

tabl

es

fo

rmul

ae

eq

uatio

ns

Equi

vale

nt fo

rms

Det

erm

ine,

inte

rpre

t and

just

ify

equi

vale

nce

of d

iffer

ent d

escr

iptio

ns

of th

e sa

me

rela

tions

hip

or ru

le

pres

ente

d:

ve

rbal

ly

in

flow

dia

gram

s

in ta

bles

by fo

rmul

ae

--

by e

quat

ions

Inpu

t and

out

put v

alue

s D

eter

min

e in

put v

alue

s, o

utpu

t val

ues

or

rule

s fo

r pat

tern

s an

d re

latio

nshi

ps u

sing

:

flow

dia

gram

s

tabl

es

fo

rmul

ae

eq

uatio

ns

Equi

vale

nt fo

rms

Det

erm

ine,

inte

rpre

t and

just

ify e

quiv

alen

ce

of d

iffer

ent d

escr

iptio

ns o

f the

sam

e re

latio

nshi

p or

rule

pr

esen

ted:

verb

ally

in fl

ow d

iagr

ams

in

tabl

es

by

form

ulae

by e

quat

ions

by g

raph

s on

a C

arte

sian

pla

ne

Su

gges

ted

met

hodo

logy

In

this

pha

se, i

t is

usef

ul to

beg

in to

spe

cify

whe

ther

the

inpu

t val

ues

are

natu

ral n

umbe

rs, o

r int

eger

s or

ratio

nal n

umbe

rs. T

his

build

s le

arne

rs’ a

war

enes

s of

the

dom

ain

of in

put v

alue

s. H

ence

, to

find

outp

ut v

alue

s, le

arne

rs s

houl

d be

giv

en th

e ru

le/fo

rmul

a as

wel

l as

the

dom

ain

of th

e in

put v

alue

s.

In G

rade

7, t

he fo

cus

is o

n fin

ding

out

put v

alue

s fo

r giv

en fo

rmul

ae a

nd in

put v

alue

s. N

ote,

whe

n le

arne

rs fi

nd in

put o

r out

put v

alue

s fo

r gi

ven

rule

s or

form

ulae

, the

y ar

e ac

tual

ly fi

ndin

g th

e nu

mer

ical

val

ue o

f alg

ebra

ic e

xpre

ssio

ns u

sing

sub

stitu

tion.


Exam

ples

U

se th

e fo

rmul

a fo

r the

are

a of

a re

ctan

gle:

A =

l x

b to

cal

cula

te th

e fo

llow

ing:

a)

Th

e ar

ea, i

f the

leng

th is

4 c

m a

nd th

e w

idth

is 2

cm

b)

Th

e le

ngth

, if t

he a

rea

is 2

0 cm

2 an

d th

e w

idth

is 4

cm

c)

Th

e w

idth

, if t

he a

rea

is 2

4 cm

2 an

d th

e le

ngth

is 8

cm

Le

arne

rs c

an w

rite

thes

e as

num

ber s

ente

nces

, and

sol

ve b

y in

spec

tion.

In

Gra

de 8

:

The

focu

s is

on

findi

ng in

put o

r out

put v

alue

s us

ing

give

n eq

uatio

ns

Th

e ru

les

and

num

ber p

atte

rns

for w

hich

lear

ners

hav

e to

find

inpu

t and

out

put v

alue

s ar

e ex

tend

ed to

incl

ude

patte

rns

with

m

ultip

licat

ion

and

divi

sion

of i

nteg

ers

and

num

bers

in e

xpon

entia

l for

m.

Flow

dia

gram

s ar

e re

pres

enta

tions

of f

unct

iona

l rel

atio

nshi

ps. H

ence

, whe

n us

ing

flow

dia

gram

s, th

e co

rresp

onde

nce

betw

een

inpu

t and

ou

tput

val

ues

shou

ld b

e cl

ear i

n its

repr

esen

tatio

nal f

orm

i.e.

the

first

inpu

t pro

duce

s th

e fir

st o

utpu

t; th

e se

cond

inpu

t pro

duce

s th

e se

cond

ou

tput

, etc

. Ex

ampl

es

a)

Use

the

give

n ru

le to

cal

cula

te th

e va

lues

of t

for e

ach

valu

e of

p, w

here

p is

a n

atur

al n

umbe

r. In

this

kin

d of

flow

dia

gram

, lea

rner

s ca

n al

so b

e as

ked

to d

eter

min

e th

e va

lue

of p

for a

giv

en t

valu

e.

b)

Det

erm

ine

the

rule

for c

alcu

latin

g th

e ou

tput

val

ue fo

r eve

ry g

iven

inpu

t val

ue in

the

flow

dia

gram

bel

ow.


In

flow

dia

gram

s su

ch a

s th

ese,

mor

e th

an o

ne ru

le m

ight

be

poss

ible

to d

escr

ibe

the

rela

tions

hip

betw

een

inpu

t and

out

put v

alue

s. T

he

rule

s ar

e ac

cept

able

if th

ey m

atch

the

give

n in

put v

alue

s to

the

corre

spon

ding

out

put v

alue

s.

c)

If

the

rule

for f

indi

ng y

in th

e ta

ble

belo

w is

y =

–3x

– 1

, cal

cula

te y

for t

he g

iven

x v

alue

s:

d)

Des

crib

e th

e re

latio

nshi

p be

twee

n th

e nu

mbe

rs in

the

top

row

and

bot

tom

row

in th

e ta

ble.

The

n w

rite

dow

n th

e va

lue

of m

and

n

In

tabl

es s

uch

as th

ese,

mor

e th

an o

ne ru

le m

ight

be

poss

ible

to d

escr

ibe

the

rela

tions

hip

betw

een

x an

d y

valu

es. T

he ru

les

are

acce

ptab

le if

they

mat

ch th

e gi

ven

inpu

t val

ues

to th

e co

rresp

ondi

ng o

utpu

t val

ues.

For

exa

mpl

e, th

e ru

le y

= x

–3

desc

ribes

the

rela

tions

hip

betw

een

the

x va

lues

and

giv

en y

val

ues.

To

find

m a

nd n

, lea

rner

s ha

ve to

sub

stitu

te th

e co

rresp

ondi

ng v

alue

s fo

r x o

r y in

th

e ru

le a

nd s

olve

the

equa

tion

by in

spec

tion.

In

Gra

de 9

, lea

rner

s co

nsol

idat

e w

ork

with

inpu

t and

out

put v

alue

s do

ne in

Gra

de 8

. The

y sh

ould

con

tinue

to fi

nd in

put o

r out

put v

alue

s in

flo

w d

iagr

ams,

tabl

es, f

orm

ulae

and

equ

atio

ns. L

earn

ers

shou

ld b

egin

to re

cogn

ize

equi

vale

nt re

pres

enta

tions

of t

he s

ame

rela

tions

hips

sh

own

as a

n eq

uatio

n, a

set

of o

rder

ed p

airs

in a

tabl

e or

on

a gr

aph.


Exam

ples

a)

. If t

he ru

le fo

r fin

ding

in th

e ta

ble

belo

w is

y =

1 2 x +

1, d

eter

min

e th

e va

lues

of y

for t

he g

iven

x v

alue

s:

b)

. Des

crib

e th

e re

latio

nshi

p be

twee

n th

e nu

mbe

rs in

the

top

row

and

thos

e in

the

botto

m ro

w in

the

tabl

e. T

hen

writ

e do

wn

the

valu

e of

m

and

n

In

tabl

es s

uch

as th

ese,

mor

e th

an o

ne ru

le m

ight

be

poss

ible

to d

escr

ibe

the

rela

tions

hip

betw

een

x an

d y

valu

es. T

he ru

les

are

acce

ptab

le if

they

mat

ch th

e gi

ven

inpu

t val

ues

to th

e co

rresp

ondi

ng o

utpu

t val

ues.

For

exa

mpl

e, th

e ru

le y

= 2

x –

3 de

scrib

es th

e re

latio

nshi

p be

twee

n th

e gi

ven

valu

es fo

r x a

nd y

. To

find

m a

nd n

, lea

rner

s ha

ve to

sub

stitu

te th

e co

rresp

ondi

ng v

alue

s fo

r x o

r y in

to th

e ru

le a

nd s

olve

the

equa

tion

by in

spec

tion.

LTSM

Res

ourc

es

Cha

rts, s

quar

e pa

pers

.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

WB

2 Ac

tiviti

es (6

5 - 7

0)

WB

1 Ac

tivity

(R7;

28)

WB

1 Ac

tiviti

es (R

7)

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT


E.g.

Info

rmal

as

sess

men

t – te

st 1

5 m

arks

max


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

6

TER

M 1

Dat

e : f

rom

....

to ..

....

T

ime:

4 ho

urs

G

rade

7

8 9

Topi

c G

RAP

HS

CAP

S pa

ges

65

114

145

Skills

and

Kno

wle

dge

Inte

rpre

ting

grap

hs

Anal

yse

and

inte

rpre

t glo

bal g

raph

s of

pr

oble

m s

ituat

ions

, with

spe

cial

focu

s on

the

follo

win

g tre

nds

and

feat

ures

:

linea

r or n

on-li

near

cons

tant

, inc

reas

ing

or

decr

easi

ng

Dra

win

g gr

aphs

D

raw

glo

bal g

raph

s fro

m g

iven

de

scrip

tions

of a

pro

blem

situ

atio

n,

iden

tifyi

ng fe

atur

es li

sted

abo

ve

Inte

rpre

ting

grap

hs

Rev

ise

the

follo

win

g do

ne in

Gra

de 7

:

Anal

yse

and

inte

rpre

t glo

bal g

raph

s of

pr

oble

m s

ituat

ions

, with

a s

peci

al fo

cus

on th

e fo

llow

ing

trend

s an

d fe

atur

es:

♦♦

linea

r or n

on-li

near

♦♦

cons

tant

, inc

reas

ing

or d

ecre

asin

g

Exte

nd th

e fo

cus

on fe

atur

es o

f gra

phs

to in

clud

e:

♦♦

max

imum

or m

inim

um

♦♦

dis

cret

e or

con

tinuo

us

Dra

win

g gr

aphs

Dra

w g

loba

l gra

phs

from

giv

en

desc

riptio

ns o

f a p

robl

em s

ituat

ion,

id

entif

ying

feat

ures

list

ed a

bove

Use

tabl

es o

f ord

ered

pai

rs to

plo

t po

ints

and

dra

w g

raph

s on

the

Car

tesi

an p

lane

Inte

rpre

ting

grap

hs

Rev

ise

the

follo

win

g do

ne in

Gra

de 8

:

Anal

yse

and

inte

rpre

t glo

bal g

raph

s of

pr

oble

m s

ituat

ions

, with

a s

peci

al fo

cus

on th

e fo

llow

ing

trend

s an

d fe

atur

es:

♦♦

line

ar o

r non

-line

ar

♦♦

con

stan

t, in

crea

sing

or d

ecre

asin

g

♦♦

max

imum

or m

inim

um

♦♦

dis

cret

e or

con

tinuo

us

Ex

tend

the

abov

e w

ith s

peci

al fo

cus

on

the

follo

win

g fe

atur

es o

f lin

ear g

raph

s:

♦♦

x-in

terc

ept a

nd y

-inte

rcep

t

♦♦

grad

ient

D

raw

ing

grap

hs

Rev

ise

the

follo

win

g do

ne in

Gra

de 8

:

draw

glo

bal g

raph

s fro

m g

iven

de

scrip

tions

of a

pro

blem

situ

atio

n,

iden

tifyi

ng fe

atur

es li

sted

abo

ve.

u

se ta

bles

of o

rder

ed p

airs

to p

lot p

oint

s an

d dr

aw g

raph

s on

the

Car

tesi

an p

lane

Exte

nd th

e ab

ove

with

a s

peci

al fo

cus

on:

♦♦

dra

win

g lin

ear g

raph

s fro

m g

iven

eq

uatio

ns

♦♦

det

erm

ine

equa

tions

from

giv

en

linea

r gra

phs


Sugg

este

d m

etho

dolo

gy

In th

e In

term

edia

te P

hase

lear

ners

enc

ount

ered

gra

phs

in th

e fo

rm o

f dat

a ba

r gra

phs

and

pie

char

ts. T

his

mea

ns th

ey d

o ha

ve

som

e ex

perie

nce

read

ing

and

inte

rpre

ting

grap

hs. H

owev

er, i

n th

e Se

nior

Pha

se, t

hey

are

intro

duce

d to

line

gra

phs

that

sho

w

func

tiona

l rel

atio

nshi

ps d

escr

ibed

in te

rms

of d

epen

dent

and

inde

pend

ent v

aria

bles

. In

Gra

de 7

, the

focu

s is

on

draw

ing,

ana

lysi

ng a

nd in

terp

retin

g gl

obal

gra

phs

only

. Tha

t is,

lear

ners

do

not h

ave

to p

lot p

oint

s to

dr

aw g

raph

s an

d th

ey fo

cus

on th

e fe

atur

es o

f the

glo

bal r

elat

ions

hip

show

n in

the

grap

h.

Exam

ples

of c

onte

xts

for g

loba

l gra

phs

incl

ude:

the

rela

tions

hip

betw

een

time

and

dist

ance

trav

elle

d

the

rela

tions

hip

betw

een

tem

pera

ture

and

tim

e ov

er w

hich

it is

mea

sure

d

the

rela

tions

hip

betw

een

rain

fall

and

time

over

whi

ch it

is m

easu

red,

etc

. In

Gra

de 8

:

New

feat

ures

of g

loba

l gra

phs,

nam

ely,

max

imum

and

min

imum

; dis

cret

e an

d co

ntin

uous

, are

intro

duce

d

Lear

ners

plo

t poi

nts

to d

raw

gra

phs

See

Gra

de 7

abo

ve fo

r exa

mpl

es o

f con

text

s fo

r glo

bal g

raph

s.

Exam

ples

of d

raw

ing

grap

hs b

y pl

ottin

g po

ints

a)

C

ompl

ete

the

tabl

e of

ord

ered

pai

rs b

elow

for t

he e

quat

ion

y =

x +

3

N

ow, p

lot t

he a

bove

co-

ordi

nate

poi

nts

on th

e C

arte

sian

pla

ne. J

oin

poin

ts to

form

a g

raph

.

b)

Com

plet

e th

e ta

ble

of o

rder

ed p

airs

bel

ow fo

r the

equ

atio

n y

= x

2 + 3

N

ow, p

lot t

he a

bove

co-

ordi

nate

poi

nts

on th

e C

arte

sian

pla

ne. J

oin

poin

ts to

form

a g

raph

. In

Gra

de 9

,

x-in

terc

ept,

y-in

terc

ept a

nd g

radi

ent o

f lin

ear g

raph

s ar

e in

trodu

ced

Le

arne

rs d

raw

line

ar g

raph

s fro

m g

iven

equ

atio

ns

Th

ey d

eter

min

e eq

uatio

ns o

f lin

ear g

raph

s Le

arne

rs s

houl

d co

ntin

ue to

ana

lyse

and

inte

rpre

t gra

phs

of p

robl

em s

ituat

ions

.


Inve

stig

atin

g lin

ear g

raph

s

To

ske

tch

linea

r gra

phs

from

giv

en e

quat

ions

, lea

rner

s sh

ould

firs

t dra

w u

p a

tabl

e of

ord

ered

pai

rs, t

hat i

nclu

des

the

inte

rcep

t poi

nts

(x; 0

) and

(0; y

), an

d th

en p

lotti

ng th

e po

ints

.

Lear

ners

sho

uld

inve

stig

ate

grad

ient

s by

com

parin

g 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣

𝑣𝑣ℎ𝑣𝑣𝑎𝑎

𝑎𝑎𝑣𝑣ℎ𝑜𝑜

𝑣𝑣𝑣𝑣𝑜𝑜𝑜𝑜𝑎𝑎𝑣𝑣𝑣𝑣𝑣𝑣


𝑎𝑎𝑣𝑣 b

etw

een

any

two

poin

ts o

n a

stra

ight

line

gra

ph.

Le

arne

rs s

houl

d al

so in

vest

igat

e th

e re

latio

nshi

p be

twee

n th

e va

lue

of th

e gr

adie

nt a

nd th

e co

effic

ient

of x

in th

e eq

uatio

n of

a

stra

ight

line

gra

ph.

Le

arne

rs s

houl

d co

mpa

re y

-inte

rcep

ts o

f lin

ear g

raph

s to

the

valu

e of

the

cons

tant

in th

e eq

uatio

n of

the

stra

ight

line

gra

ph.

Ex

ampl

es o

f lin

ear g

raph

s

a)

Sket

ch a

nd c

ompa

re th

e gr

aphs

of:

y =

4 an

d x

= 4

b)

Sket

ch a

nd c

ompa

re th

e gr

aphs

of:

y =

x an

d y

= –x

c)

Sk

etch

and

com

pare

the

grap

hs o

f: y

= 2x

; y =

2x

+ 1;

y =

2x

– 1

d)

Sket

ch a

nd c

ompa

re th

e gr

aphs

of:

y =

3x; y

= 4

x; y

= 5

x

e)

Sket

ch th

e gr

aphs

of:

y =

–3x

+ 2;

usi

ng th

e ta

ble

met

hod

f) D

eter

min

e th

e eq

uatio

n of

the

stra

ight

line

pas

sing

thro

ugh

the

follo

win

g po

ints

:

LTSM

Res

ourc

es

Gra

ph p

aper

, cha

rts, r

uler

s, c

olou

r pen

s.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

WB

2 Ac

tiviti

es (8

0 - 8

5)

WB

1 Ac

tiviti

es (R

9)

Gra

de 9

WB

Activ

ities

(R9)

W

B 1

Activ

ities

(R9)

G

rade

9 W

B Ac

tiviti

es (R

9)


Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – te

st 1

5 m

arks

max


LESS

ON

PLA

NS:

TER

M 2


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

1

TER

M 2

Dat

e: fr

om ..

......

to ..

......

Tim

e:

5

hour

s

Gra

de

7 8

9 To

pic

CO

NST

RU

CTI

ON

OF

GEO

MET

RIC

FIG

UR

ES

CAP

S pa

ges

45

95

134

Skills

and

Kn

owle

dge

Mea

surin

g an

gles

Ac

cura

tely

use

a p

rotra

ctor

to m

easu

re

and

clas

sify

ang

les:

< 90

° (a

cute

ang

les)

Rig

ht-a

ngle

s

> 90

° (o

btus

e an

gles

)

Stra

ight

ang

les

>

180°

(ref

lex

angl

es)

Con

stru

ctio

ns

Accu

rate

ly c

onst

ruct

geo

met

ric

figur

es a

ppro

pria

tely

usi

ng c

ompa

ss,

rule

r and

pro

tract

or, i

nclu

ding

:

angl

es, t

o on

e de

gree

of

accu

racy

circ

les

pa

ralle

l lin

es

pe

rpen

dicu

lar l

ines

Con

stru

ctio

ns

Accu

rate

ly c

onst

ruct

geo

met

ric fi

gure

s ap

prop

riate

ly u

sing

a c

ompa

ss, r

uler

and

pr

otra

ctor

, inc

ludi

ng:

Bi

sect

ing

lines

and

ang

les

Pe

rpen

dicu

lar l

ines

at a

giv

en p

oint

or

from

a g

iven

poi

nt

Tr

iang

les

Q

uadr

ilate

rals

Angl

es o

f 30°

, 45°

and

60°

and

thei

r m

ultip

les

with

out u

sing

a p

rotra

ctor

In

vest

igat

ing

prop

ertie

s of

geo

met

ric

figur

es

By c

onst

ruct

ion,

inve

stig

ate

the

angl

es in

a

trian

gle,

focu

sing

on:

the

sum

of t

he in

terio

r ang

les

of tr

iang

les

th

e si

ze o

f ang

les

in a

n eq

uila

tera

l tri

angl

e

the

side

s an

d ba

se a

ngle

s of

an

Con

stru

ctio

ns

Ac

cura

tely

con

stru

ct g

eom

etric

figu

res

appr

opria

tely

usi

ng a

com

pass

, rul

er a

nd

prot

ract

or, i

nclu

ding

bis

ectin

g an

gles

of

a tri

angl

e

C

onst

ruct

ang

les

of 4

5°, 3

0°, 6

0°an

d th

eir m

ultip

les

with

out u

sing

a p

rotra

ctor

In

vest

igat

ing

prop

ertie

s of

geo

met

ric

figur

es

By

con

stru

ctio

n, in

vest

igat

e th

e an

gles

in

a tri

angl

e, fo

cusi

ng o

n th

e re

latio

nshi

p be

twee

n th

e ex

terio

r ang

le o

f a tr

iang

le

and

its in

terio

r ang

les

By

con

stru

ctio

n, e

xplo

re th

e m

inim

um


isos

cele

s tri

angl

e By

con

stru

ctio

n, in

vest

igat

e si

des

and

angl

es in

qua

drila

tera

ls, f

ocus

ing

on:

th

e su

m o

f the

inte

rior a

ngle

s of

qu

adril

ater

als

th

e si

des

and

oppo

site

ang

les

of

para

llelo

gram

s

cond

ition

s fo

r tw

o tri

angl

es to

be

cong

ruen

t

By c

onst

ruct

ion,

inve

stig

ate

side

s,

angl

es a

nd d

iago

nals

in q

uadr

ilate

rals

, fo

cusi

ng o

n th

e di

agon

als

of re

ctan

gles

, sq

uare

s, p

aral

lelo

gram

s, rh

ombi

and

ki

tes

By

con

stru

ctio

n ex

plor

e th

e su

m o

f the

in

terio

r ang

les

of p

olyg

ons

Sugg

este

d m

etho

dolo

gy

In G

rade

7, l

earn

ers

M

easu

re a

ngle

s w

ith a

pro

tract

or

D

o ge

omet

ric c

onst

ruct

ions

usi

ng a

com

pass

, rul

er a

nd p

rotra

ctor

M

easu

ring

angl

es

Le

arne

rs h

ave

to b

e sh

own

how

to p

lace

the

prot

ract

or o

n th

e ar

m o

f the

ang

le to

be

mea

sure

d.

Le

arne

rs a

lso

have

to le

arn

how

to re

ad th

e si

ze o

f ang

les

on a

pro

tract

or.

Con

stru

ctio

ns

C

onst

ruct

ions

pro

vide

a u

sefu

l con

text

to e

xplo

re o

r con

solid

ate

know

ledg

e of

ang

les

and

shap

es.

Le

arne

rs h

ave

to b

e sh

own

how

to u

se a

com

pass

to d

raw

circ

les,

alth

ough

they

mig

ht h

ave

done

this

in G

rade

6.

Le

arne

rs s

houl

d be

aw

are

that

the

cent

re o

f the

circ

le is

at t

he fi

xed

poin

t of t

he c

ompa

ss a

nd th

e ra

dius

of t

he c

ircle

is

depe

nden

t on

how

wid

e th

e co

mpa

ss is

ope

ned

up.

M

ake

sure

lear

ners

und

erst

and

that

arc

s ar

e pa

rts o

f the

circ

les

of a

par

ticul

ar ra

dius

.

Initi

ally

, lea

rner

s ha

ve to

be

give

n ca

refu

l ins

truct

ions

abo

ut h

ow to

do

the

cons

truct

ions

of t

he v

ario

us s

hape

s

O

nce

they

are

com

forta

ble

with

the

appa

ratu

s an

d ca

n do

the

cons

truct

ions

, the

y ca

n pr

actis

e by

dra

win

g pa

ttern

s, fo

r ex

ampl

e of

circ

les

or p

aral

lel l

ines

. In

Gra

de 8

, all

the

cons

truct

ions

are

new

. In

Gra

de 7

, lea

rner

s on

ly c

onst

ruct

ed a

ngle

s, p

erpe

ndic

ular

and

par

alle

l lin

es. G

rade

8

lear

ners

als

o us

e co

nstru

ctio

ns to

exp

lore

pro

perti

es o

f tria

ngle

s an

d qu

adril

ater

als

Con

stru

ctio

ns

C

onst

ruct

ions

pro

vide

a u

sefu

l con

text

to e

xplo

re o

r con

solid

ate

know

ledg

e of

ang

les

and

shap

es

M

ake

sure

lear

ners

are

com

pete

nt a

nd c

omfo

rtabl

e w

ith th

e us

e of

a c

ompa

ss a

nd k

now

how

to m

easu

re a

nd re

ad a

ngle


size

s on

a p

rotra

ctor

Rev

ise

the

cons

truct

ions

of a

ngle

s if

nece

ssar

y be

fore

pro

ceed

ing

with

the

new

con

stru

ctio

ns

St

art w

ith th

e co

nstru

ctio

ns o

f lin

es, s

o th

at le

arne

rs c

an fi

rst e

xplo

re a

ngle

rela

tions

hips

on

stra

ight

line

s.

W

hen

cons

truct

ing

trian

gles

lear

ners

sho

uld

draw

on

know

n pr

oper

ties

and

cons

truct

ion

of c

ircle

s.

C

onst

ruct

ion

of s

peci

al a

ngle

s w

ithou

t pro

tract

ors

are

done

by:

o

bise

ctin

g a

right

ang

le to

get

45°

o

draw

ing

an e

quila

tera

l tria

ngle

to g

et 6

0°

o bi

sect

ing

the

angl

es o

f an

equi

late

ral t

riang

le to

get

30°

In

Gra

de 9

, lea

rner

s:

Bi

sect

ang

les

in a

tria

ngle

Con

stru

ct 3

0° w

ithou

t a p

rotra

ctor

Inve

stig

atio

n of

new

pro

perti

es o

f tria

ngle

s, q

uadr

ilate

rals

and

pol

ygon

s C

onst

ruct

ions

Sa

me

as fo

r Gra

de 8

. LT

SM

Res

ourc

es

Mat

hem

atic

al In

stru

men

ts s

et.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

WB

1 Ac

tiviti

es

( 20

- 25

) W

B 1

Activ

ities

(45

- 51)

WB

1 Ac

tiviti

es (

39 -

47)

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

2

TER

M 2

Dat

e : f

rom

....

to ..

....

T

ime:

10 h

ours

G

rade

7

8 9

Topi

c G

EOM

ETR

Y O

F 2D

SH

APES

C

APS

page

s 46

- 47

96

- 98

13

5 - 1

36

Skills

and

Kn

owle

dge

Cla

ssify

ing

2D s

hape

s D

escr

ibe,

sor

t, na

me

and

com

pare

tria

ngle

s ac

cord

ing

to th

eir s

ides

and

ang

les,

fo

cusi

ng o

n:

eq

uila

tera

l tria

ngle

s

isos

cele

s tri

angl

es

rig

ht-a

ngle

d tri

angl

es

Des

crib

e, s

ort,

nam

e an

d co

mpa

re

quad

rilat

eral

s in

term

s of

:

leng

th o

f sid

es

pa

ralle

l and

per

pend

icul

ar s

ides

size

of a

ngle

s (ri

ght-a

ngle

s or

not

) D

escr

ibe

and

nam

e pa

rts o

f a c

ircle

Si

mila

r and

con

grue

nt 2

D s

hape

s R

ecog

nize

and

des

crib

e si

mila

r and

co

ngru

ent f

igur

es b

y co

mpa

ring:

shap

e

size

So

lvin

g pr

oble

ms

Solv

e si

mpl

e ge

omet

ric p

robl

ems

invo

lvin

g un

know

n si

des

and

angl

es in

tria

ngle

s an

d

Cla

ssify

ing

2D s

hape

s Id

entif

y an

d w

rite

clea

r def

initi

ons

of

trian

gles

in te

rms

of th

eir s

ides

and

ang

les,

di

stin

guis

hing

bet

wee

n:

eq

uila

tera

l tria

ngle

s

isos

cele

s tri

angl

es

rig

ht-a

ngle

d tri

angl

es

Iden

tify

and

writ

e cl

ear d

efin

ition

s of

qu

adril

ater

als

in te

rms

of th

eir s

ides

and

an

gles

, dis

tingu

ishi

ng b

etw

een:

Para

llelo

gram

Rec

tang

le

S

quar

e

Rho

mbu

s

Tra

pezi

um

K

ite

Sim

ilar a

nd c

ongr

uent

2-D

sha

pes

Id

entif

y an

d de

scrib

e th

e pr

oper

ties

of

cong

ruen

t sha

pes

Id

entif

y an

d de

scrib

e th

e pr

oper

ties

of

sim

ilar s

hape

s So

lvin

g pr

oble

ms

Solv

e ge

omet

ric p

robl

ems

invo

lvin

g

Cla

ssify

ing

2D s

hape

s R

evis

e pr

oper

ties

and

defin

ition

s of

tria

ngle

s in

term

s of

thei

r sid

es a

nd a

ngle

s,

dist

ingu

ishi

ng b

etw

een:

equi

late

ral t

riang

les

is

osce

les

trian

gles

right

-ang

led

trian

gles

R

evis

e an

d w

rite

clea

r def

initi

ons

of

quad

rilat

eral

s in

term

s of

thei

r sid

es, a

ngle

s an

d di

agon

als,

dis

tingu

ishi

ng b

etw

een:

Para

llelo

gram

Rec

tang

le

S

quar

e

Rho

mbu

s

Tra

pezi

um

K

ite

Sim

ilar a

nd c

ongr

uent

tria

ngle

s

Thro

ugh

inve

stig

atio

n, e

stab

lish

the

min

imum

con

ditio

ns fo

r con

grue

nt

trian

gles

Thro

ugh

inve

stig

atio

n, e

stab

lish

the

min

imum

con

ditio

ns fo

r sim

ilar t

riang

les

Solv

ing

prob

lem

s So

lve

geom

etric

pro

blem

s in

volv

ing


quad

rilat

eral

s, u

sing

kno

wn

prop

ertie

s.

unkn

own

side

s an

d an

gles

in tr

iang

les

and

quad

rilat

eral

s, u

sing

kno

wn

prop

ertie

s an

d de

finiti

ons.

unkn

own

side

s an

d an

gles

in tr

iang

les

and

quad

rilat

eral

s, u

sing

kno

wn

prop

ertie

s of

tri

angl

es a

nd q

uadr

ilate

rals

, as

wel

l as

prop

ertie

s of

con

grue

nt a

nd s

imila

r tria

ngle

s

Sugg

este

d m

etho

dolo

gy

In G

rade

7, l

earn

ers

are:

•

Dis

tingu

ishi

ng a

nd n

amin

g tri

angl

es in

term

s of

thei

r sid

es a

nd a

ngle

s •

Dis

tingu

ishi

ng q

uadr

ilate

rals

in te

rms

of p

aral

lel a

nd p

erpe

ndic

ular

sid

es

• D

istin

guis

hing

sim

ilar a

nd c

ongr

uent

figu

res

• U

sing

kno

wn

prop

ertie

s of

sha

pes

to s

olve

geo

met

ric p

robl

ems

Tria

ngle

s Le

arne

rs s

houl

d be

abl

e to

dis

tingu

ish

betw

een

an e

quila

tera

l tria

ngle

(all

the

side

s ar

e eq

ual),

an

isos

cele

s tri

angl

e (a

t lea

st tw

o eq

ual

side

s) a

nd a

righ

t-ang

led

trian

gle

(one

righ

t-ang

le).

Qua

drila

tera

ls

Lear

ners

sho

uld

be a

ble

to s

ort a

nd g

roup

qua

drila

tera

ls in

the

follo

win

g w

ays:

•

all s

ides

equ

al (s

quar

e an

d rh

ombu

s)

• op

posi

te s

ides

equ

al (r

ecta

ngle

, par

alle

logr

am, s

quar

e, rh

ombu

s)

• at

leas

t one

pai

r of a

djac

ent s

ides

equ

al (s

quar

e, rh

ombu

s, k

ite)

• al

l fou

r ang

les

right

ang

les

(squ

are,

rect

angl

e)

• pe

rpen

dicu

lar s

ides

(squ

are,

rect

angl

e)

• tw

o pa

irs o

f opp

osite

sid

es p

aral

lel (

rect

angl

e, s

quar

e, p

aral

lelo

gram

) •

only

one

pai

r of o

ppos

ite s

ides

par

alle

l (tra

pezi

um)

Circ

les

Parts

of a

circ

le le

arne

rs s

houl

d kn

ow:

• ra

dius

•

circ

umfe

renc

e •

diam

eter

•

chor

d •

segm

ents


• se

ctor

s Si

mila

rity

and

cong

ruen

cy

Sim

ilarit

y an

d co

ngru

ency

can

be

expl

ored

with

any

2D

figu

res.

•

Lear

ners

sho

uld

reco

gniz

e th

at tw

o or

mor

e fig

ures

are

con

grue

nt if

they

are

equ

al in

all

resp

ects

i.e.

ang

les

and

side

s ar

e eq

ual.

• Le

arne

rs s

houl

d re

cogn

ize

that

two

or m

ore

figur

es a

re s

imila

r if t

hey

have

the

sam

e sh

ape,

but

diff

er in

siz

e i.e

. ang

les

are

the

sam

e, b

ut s

ides

are

pro

porti

onal

ly lo

nger

or s

horte

r. Si

mila

r fig

ures

are

furth

er e

xplo

red

whe

n do

ing

enla

rgem

ents

and

redu

ctio

ns.

Ref

er to

“Cla

rific

atio

n N

otes

” und

er 3

.4 T

rans

form

atio

n G

eom

etry

. So

lvin

g pr

oble

ms

At th

is s

tage

lear

ners

can

sol

ve s

impl

e ge

omet

ric p

robl

ems

to fi

nd u

nkno

wn

side

s in

equ

ilate

ral a

nd is

osce

les

trian

gles

, and

unk

now

n si

des

and

angl

es in

qua

drila

tera

ls. L

earn

ers

shou

ld g

ive

reas

ons

for t

heir

solu

tions

. Ex

ampl

es

a)

If ΔA

BC is

an

equi

late

ral t

riang

le, a

nd s

ide

AB is

3 c

m, w

hat i

s th

e le

ngth

of B

C?

Her

e le

arne

rs s

houl

d an

swer

: BC

= 3

cm

, be

caus

e th

e si

des

of a

n eq

uila

tera

l tria

ngle

are

equ

al.

b)

If AB

CD

is a

kite

, and

AB

= 2,

5 cm

and

BC

= 4

,5 c

m, w

hat i

s th

e le

ngth

of A

D a

nd D

C?

Lear

ners

sho

uld

use

the

prop

erty

for k

ites,

th

at a

djac

ent p

airs

of s

ides

are

equ

al, t

o fin

d th

e un

know

n si

des.

In G

rade

8:

• N

ew p

rope

rties

in te

rms

of a

ngle

s of

tria

ngle

s •

Lear

ners

writ

e cl

ear d

efin

ition

s of

the

prop

ertie

s of

tria

ngle

s an

d qu

adril

ater

als

• Th

ey u

se d

efin

ition

s to

sol

ve g

eom

etric

pro

blem

s •

They

inve

stig

ate

cond

ition

s fo

r 2D

sha

pes

to b

e co

ngru

ent o

r sim

ilar

Tria

ngle

s C

onst

ruct

ions

ser

ve a

s a

usef

ul c

onte

xt fo

r exp

lorin

g pr

oper

ties

of tr

iang

les

(See

not

es o

n C

onst

ruct

ions

). Pr

oper

ties

of tr

iang

les

lear

ners

sh

ould

kno

w in

clud

e:

• th

e su

m o

f the

inte

rior a

ngle

s of

tria

ngle

s =

180°

•

an e

quila

tera

l tria

ngle

has

all

side

s eq

ual a

nd a

ll in

terio

r ang

les

= 60

° •

an is

osce

les

trian

gle

has

at le

ast t

wo

equa

l sid

es a

nd it

s ba

se a

ngle

s ar

e eq

ual

• a

right

-ang

led

trian

gle

has

one

angl

e th

at is

a ri

ght-a

ngle

•

the

side

opp

osite

the

right

-ang

le in

a ri

ght-a

ngle

d tri

angl

e, is

cal

led

the

hypo

tenu

se

• in

a ri

ght-a

ngle

d tri

angl

e, th

e sq

uare

of t

he h

ypot

enus

e is

equ

al to

the

sum

of t

he s

quar

es o

f the

oth

er tw

o si

des

(The

orem

of

Pyth

agor

as).


Qua

drila

tera

ls

Con

stru

ctio

ns s

erve

as

a us

eful

con

text

for e

xplo

ring

prop

ertie

s of

tria

ngle

s (S

ee n

otes

on

Con

stru

ctio

ns).

The

clas

sific

atio

n of

qu

adril

ater

als

shou

ld in

clud

e th

e re

cogn

ition

that

: •

rect

angl

es a

nd rh

ombi

are

spe

cial

kin

ds o

f par

alle

logr

ams

• a

squa

re is

a s

peci

al k

ind

of re

ctan

gle

and

rhom

bus.

Pr

oper

ties

of q

uadr

ilate

rals

lear

ners

sho

uld

know

incl

ude:

•

the

sum

of t

he in

terio

r ang

les

of q

uadr

ilate

rals

= 3

60°

• th

e op

posi

te s

ides

of p

aral

lelo

gram

s ar

e pa

ralle

l and

equ

al

• th

e op

posi

te a

ngle

s of

par

alle

logr

ams

are

equa

l •

the

oppo

site

ang

les

of a

rhom

bus

are

equa

l •

the

oppo

site

sid

es o

f a rh

ombu

s ar

e pa

ralle

l and

equ

al

• th

e si

ze o

f eac

h an

gle

of re

ctan

gles

and

squ

ares

is 9

0°

• a

trape

zium

has

one

pai

r of o

ppos

ite s

ides

par

alle

l •

a k

ite h

as tw

o pa

irs o

f adj

acen

t sid

es e

qual

Si

mila

rity

and

cong

ruen

cy

Ref

er to

“Cla

rific

atio

n N

otes

” und

er 3

.3 T

rans

form

atio

n G

eom

etry

and

not

es fo

r Gra

de 7

abo

ve..

Exam

ples

: •

Com

parin

g sq

uare

s to

oth

er re

ctan

gles

, lea

rner

s ca

n as

certa

in th

at h

avin

g co

rresp

ondi

ng a

ngle

s eq

ual d

oes

not n

eces

saril

y im

ply

that

the

side

s w

ill be

of p

ropo

rtion

al le

ngth

. Hen

ce h

avin

g eq

ual a

ngle

s al

one,

is n

ot a

suf

ficie

nt c

ondi

tion

for f

igur

es to

be

sim

ilar.

• C

ompa

ring

rhom

bii w

ith s

ides

pro

porti

onal

, lea

rner

s ca

n as

certa

in th

at h

avin

g si

des

prop

ortio

nal d

oes

not n

eces

saril

y im

ply

that

th

e co

rresp

ondi

ng a

ngle

s w

ill be

equ

al. S

o on

ly h

avin

g si

des

of p

ropo

rtion

al le

ngth

is n

ot a

suf

ficie

nt c

ondi

tion

for s

imila

rity

Solv

ing

prob

lem

s •

Lear

ners

can

sol

ve g

eom

etric

pro

blem

s to

find

unk

now

n si

des

and

angl

es in

tria

ngle

s an

d qu

adril

ater

als,

usi

ng k

now

n de

finiti

ons

as w

ell a

s an

gle

rela

tions

hips

on

stra

ight

line

s (s

ee n

otes

on

Geo

met

ry o

f Stra

ight

line

s.)

• Fo

r rig

ht-a

ngle

d tri

angl

es, l

earn

ers

can

also

use

the

Theo

rem

of P

ytha

gora

s to

find

unk

now

n le

ngth

s.

• Le

arne

rs s

houl

d gi

ve re

ason

s an

d ju

stify

thei

r sol

utio

ns fo

r eve

ry w

ritte

n st

atem

ent.

Not

e th

at s

olvi

ng g

eom

etric

pro

blem

s is

an

oppo

rtuni

ty to

pra

ctis

e so

lvin

g eq

uatio

ns.

Exam

ple:


Â

1, Â

2, Â

3 an

d ar

e th

ree

angl

es o

n a

stra

ight

line

. Â2

= 75

°, Â

3 =

55°.

Wha

t is

the

size

of Â

1?

Lear

ners

can

find

Â1

by s

olvi

ng th

e fo

llow

ing

equa

tion:

Â

1 +

75°

+ 55

° =

180°

(bec

ause

the

sum

of a

ngle

s on

a s

traig

ht li

ne =

180

°)

Â1

= 18

0° –

130

°(ad

d –5

5° a

nd –

75° t

o bo

th s

ides

of t

he e

quat

ion)

Â

1 =

50°

In G

rade

9, l

earn

ers

revi

se a

nd w

rite

clea

r des

crip

tions

of a

ngle

rela

tions

hips

on

stra

ight

line

s. A

ngle

rela

tions

hips

lear

ners

sho

uld

know

incl

ude:

•

the

sum

of t

he a

ngle

s on

a s

traig

ht li

ne is

180

° •

If lin

es a

re p

erpe

ndic

ular

line

s, th

en a

djac

ent s

uppl

emen

tary

ang

les

are

each

equ

al to

90°

•

If lin

es in

ters

ect,

then

ver

tical

ly o

ppos

ite a

ngle

s ar

e eq

ual.

• if

para

llel l

ines

are

cut

by

a tra

nsve

rsal

, the

n co

rresp

ondi

ng a

ngle

s ar

e eq

ual

• if

para

llel l

ines

cut

by

a tra

nsve

rsal

, the

n al

tern

ate

angl

es a

re e

qual

•

if pa

ralle

l lin

es c

ut b

y a

trans

vers

al, t

hen

co-in

terio

r ang

les

are

supp

lem

enta

ry

The

abov

e an

gles

hav

e to

be

iden

tifie

d an

d na

med

by

lear

ners

. So

lvin

g pr

oble

ms

See

note

s in

the

abov

e se

ctio

ns

Con

grue

nt tr

iang

les

Con

stru

ctio

ns a

re a

use

ful c

onte

xt fo

r est

ablis

hing

the

min

imum

con

ditio

ns fo

r tw

o tri

angl

es to

be

cong

ruen

t. Se

e no

tes

on C

onst

ruct

ions

ab

ove.

Con

ditio

ns fo

r tw

o tri

angl

es to

be

cong

ruen

t: •

thre

e co

rresp

ondi

ng s

ides

are

equ

al (S

,S,S

) •

two

corre

spon

ding

sid

es a

nd th

e in

clud

ed a

ngle

are

equ

al (S

,A,S

) •

two

corre

spon

ding

ang

les

and

a co

rresp

ondi

ng s

ide

are

equa

l (A,

A,S)

•

right

-ang

le, h

ypot

enus

e an

d on

e ot

her c

orre

spon

ding

sid

e ar

e eq

ual (

R,H

,S)


Sim

ilar t

riang

les

Con

stru

ctio

ns a

re a

use

ful c

onte

xt fo

r est

ablis

hing

the

min

imum

con

ditio

ns fo

r tw

o tri

angl

es to

be

sim

ilar.

See

note

s on

Con

stru

ctio

ns

abov

e.

Solv

ing

prob

lem

s Se

e no

tes

and

exam

ples

abo

ve.

LTSM

Res

ourc

es

2D s

hape

s an

d ch

arts

.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

WB

1 Ac

tiviti

es (2

6 - 2

9)

WB

1 Ac

tiviti

es (R

11a&

b; R

13)

WB

2 Ac

tiviti

es (5

2 - 6

0)

WB

1 A

ctiv

ities

(48

- 52

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

3

TER

M 2

Dat

e: fr

om ..

.. to

.....

.

Tim

e:

9

hour

s

Gra

de

7 8

9 To

pic

GEO

MET

RY

OF

STR

AIG

HT

LIN

ES

CAP

S pa

ges

46

98

137

Skills

and

Kn

owle

dge

Def

ine:

•

Line

seg

men

t •

Ray

•

Stra

ight

line

•

Para

llel l

ines

•

Perp

endi

cula

r lin

es

Angl

e re

latio

nshi

ps

Rec

ogni

se a

nd d

escr

ibe

pairs

of a

ngle

s fo

rmed

by:

•

perp

endi

cula

r lin

es

• in

ters

ectin

g lin

es

• pa

ralle

l lin

es c

ut b

y a

trans

vers

al

Solv

ing

prob

lem

s So

lve

geom

etric

pro

blem

s us

ing

the

rela

tions

hips

bet

wee

n pa

irs o

f ang

les

desc

ribed

abo

ve

Angl

e re

latio

nshi

ps

Rev

ise

and

writ

e cl

ear d

escr

iptio

ns o

f the

re

latio

nshi

p be

twee

n an

gles

form

ed b

y:

• pe

rpen

dicu

lar l

ines

•

inte

rsec

ting

lines

•

para

llel l

ines

cut

by

a tra

nsve

rsal

So

lvin

g pr

oble

ms

Solv

e ge

omet

ric p

robl

ems

usin

g th

e re

latio

nshi

ps b

etw

een

pairs

of a

ngle

s de

scrib

ed a

bove

.


Sugg

este

d m

etho

dolo

gy

Gra

de 7

lear

ners

sho

uld

know

that

: •

Line

seg

men

t is

a se

t of p

oint

s w

ith a

def

inite

sta

rting

-poi

nt a

nd a

n en

d-po

int.

• R

ay is

a s

et o

f poi

nts

with

a d

efin

ite s

tarti

ng-p

oint

and

no

defin

ite e

nd-p

oint

. •

Line

is a

set

of p

oint

s w

ith n

o de

finite

sta

rting

-poi

nt a

nd e

nd-p

oint

. •

If tw

o lin

es o

n th

e sa

me

plan

e ar

e a

cons

tant

dis

tanc

e ap

art,

then

the

lines

are

par

alle

l. E

xam

ple:

Thi

s is

writ

ten

as E

F ║

GH

•

If ve

rtica

l lin

e AO

mee

ts o

r int

erse

cts

with

hor

izon

tal l

ine

BC a

t rig

ht a

ngle

, the

n AO

is p

erpe

ndic

ular

to B

C.

Exam

ple:

T

his

is w

ritte

n as

AO

┴ B

C

In G

rade

7 le

arne

rs o

nly

defin

ed li

ne s

egm

ent,

ray,

stra

ight

line

, par

alle

l lin

es a

nd p

erpe

ndic

ular

line

s. In

Gra

de 8

, ang

le re

latio

nshi

ps

lear

ners

sho

uld

know

incl

ude:

•

the

sum

of t

he a

ngle

s on

a s

traig

ht li

ne is

180

° •

If lin

es a

re p

erpe

ndic

ular

, the

n ad

jace

nt s

uppl

emen

tary

ang

les

are

each

equ

al to

90°

. •

If lin

es in

ters

ect,

then

ver

tical

ly o

ppos

ite a

ngle

s ar

e eq

ual.

• if

para

llel l

ines

are

cut

by

a tra

nsve

rsal

, the

n co

rresp

ondi

ng a

ngle

s ar

e eq

ual

• if

para

llel l

ines

cut

by

a tra

nsve

rsal

, the

n al

tern

ate

angl

es a

re e

qual

•

if pa

ralle

l lin

es c

ut b

y a

trans

vers

al, t

hen

co-in

terio

r ang

les

are

supp

lem

enta

ry

The

abov

e an

gles

hav

e to

be

iden

tifie

d an

d na

med

by

lear

ner

Solv

ing

prob

lem

s Le

arne

rs s

houl

d so

lve

geom

etric

pro

blem

s to

find

unk

now

n an

gles

usi

ng th

e an

gle

rela

tions

hips

abo

ve, a

s w

ell a

s ot

her k

now

n pr

oper

ties

of tr

iang

les

and

quad

rilat

eral

s. L

earn

ers

shou

ld g

ive

reas

ons

and

just

ify th

eir s

olut

ions

for e

very

writ

ten

stat

emen

t.


Not

e th

at s

olvi

ng g

eom

etric

pro

blem

s is

an

oppo

rtuni

ty to

pra

ctis

e so

lvin

g eq

uatio

ns.

Exa

mpl

e:

Â, B

and

Ĉ a

re th

ree

angl

es o

n a

stra

ight

line

. Â =

55°

, B =

75°

. Wha

t is

the

size

of

Ĉ ?

Le

arne

rs c

an fi

nd Ĉ

by

solv

ing

the

follo

win

g eq

uatio

n:

55°

+ 75

° +

Ĉ =

180

° (be

caus

e th

e su

m o

f ang

les

on a

stra

ight

line

= 1

80°)

Ĉ

= 1

80° –

130

° (ad

d –5

5° a

nd –

75° t

o bo

th s

ides

of t

he e

quat

ion)

Ĉ

= 5

0°

Gra

de 9

lear

ners

revi

se a

nd w

rite

clea

r des

crip

tions

of a

ngle

rela

tions

hips

on

stra

ight

line

s. A

ngle

rela

tions

hips

lear

ners

sho

uld

know

ar

e th

e sa

me

as fo

r Gra

de 8

. So

lvin

g pr

oble

ms

See

Gra

de 7

and

8 n

otes

. Ex

ampl

e:

B1

and

B2

are

two

angl

es o

n a

stra

ight

line

. B1

= 35

°. W

hat i

s th

e si

ze o

f B2

?

Le

arne

rs c

an fi

nd B

2 by

sol

ving

the

follo

win

g eq

uatio

n:

35°

+ B

2 =

180°

(bec

ause

the

sum

of a

ngle

s on

a s

traig

ht li

ne 1

80°)

B

2 =

180°

– 3

5° (a

dd –

35°

to b

oth

side

s of

the

equa

tion)

B

2 =

145°

LTSM

Res

ourc

es

Prot

ract

or, c

harts

, rul

ers,

col

our p

ens.

G

rade

7

Gra

de 8

G

rade

9


Wor

kboo

k re

fere

nce

WB

1 Ac

tiviti

es (2

4)

W

B 1

Activ

ities

(6

1 - 6

3)

WB

1 Ac

tiviti

es

(53

- 57

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTIG

RAD

E LE

SSO

N P

LAN

4

TER

M 2

Dat

e : f

rom

....

to ..

....

Tim

e:

9 ho

urs

Gra

de

7 8

9 To

pic

ALG

EBR

AIC

EXP

RES

SIO

NS

CAP

S pa

ges

63 &

69

90 &

(92

– 93

) (1

30 –

131

) & (1

42 –

144

) Sk

ills a

nd

Know

ledg

e Al

gebr

aic

lang

uage

•

Rec

ogni

ze a

nd in

terp

ret r

ules

or

rela

tions

hips

rep

rese

nted

in s

ymbo

lic

form

•

Iden

tify

varia

bles

and

con

stan

ts in

giv

en

form

ulae

and

equ

atio

ns

Alge

brai

c la

ngua

ge

• R

evis

e th

e fo

llow

ing

done

in G

rade

7:

o re

cogn

ize

and

inte

rpre

t rul

es o

r re

latio

nshi

ps re

pres

ente

d in

sym

bolic

fo

rm

o id

entif

y va

riabl

es a

nd c

onst

ants

in

give

n fo

rmul

ae a

nd e

quat

ions

•

Rec

ogni

ze a

nd id

entif

y co

nven

tions

for

writ

ing

alge

brai

c ex

pres

sion

s •

Iden

tify

and

clas

sify

like

and

unl

ike

term

s in

alg

ebra

ic e

xpre

ssio

ns

• R

ecog

nize

and

iden

tify

coef

ficie

nts

and

expo

nent

s in

alg

ebra

ic e

xpre

ssio

ns

Expa

nd a

nd s

impl

ify a

lgeb

raic

ex

pres

sion

s U

se c

omm

utat

ive,

ass

ocia

tive

and

dist

ribut

ive

law

s fo

r rat

iona

l num

bers

and

la

ws

of e

xpon

ents

to:

Ad

d an

d su

btra

ct li

ke te

rms

in a

lgeb

raic

ex

pres

sion

s.

M

ultip

ly in

tege

rs a

nd m

onom

ials

by:

♦♦

mon

omia

ls

♦♦

bino

mia

ls

♦♦

trin

omia

ls

D

eter

min

e th

e sq

uare

s, c

ubes

, squ

are

root

s an

d cu

be ro

ots

of s

ingl

e al

gebr

aic

Alge

brai

c la

ngua

ge

• R

evis

e th

e fo

llow

ing

done

in G

rade

8:

o R

ecog

nize

and

iden

tify

conv

entio

ns

for w

ritin

g al

gebr

aic

expr

essi

ons

o Id

entif

y an

d cl

assi

fy li

ke a

nd u

nlik

e te

rms

in a

lgeb

raic

exp

ress

ions

o

Rec

ogni

ze a

nd id

entif

y co

effic

ient

s an

d ex

pone

nts

in a

lgeb

raic

ex

pres

sion

s

Rec

ogni

ze a

nd d

iffer

entia

te b

etw

een

mon

omia

ls, b

inom

ials

and

trin

omia

ls

Expa

nd a

nd s

impl

ify a

lgeb

raic

ex

pres

sion

s R

evis

e th

e fo

llow

ing

done

in G

rade

8, u

sing

th

e co

mm

utat

ive,

ass

ocia

tive

and

dist

ribut

ive

law

s fo

r rat

iona

l num

bers

and

la

ws

of e

xpon

ents

to:

• ad

d an

d su

btra

ct li

ke te

rms

in a

lgeb

raic

ex

pres

sion

s •

mul

tiply

inte

gers

and

mon

omia

ls b

y:

♦♦

mon

omia

ls

♦♦

bin

omia

ls

♦♦

trin

omia

ls


term

s or

like

alg

ebra

ic te

rms

D

eter

min

e th

e nu

mer

ical

val

ue o

f al

gebr

aic

expr

essi

ons

by s

ubst

itutio

n

• di

vide

the

follo

win

g by

inte

gers

or

mon

omia

ls:

♦♦

mon

omia

ls

♦♦

bi

nom

ials

♦♦

trin

omia

ls

Si

mpl

ify a

lgeb

raic

exp

ress

ions

invo

lvin

g th

e ab

ove

oper

atio

ns

D

eter

min

e th

e sq

uare

s, c

ubes

, squ

are

root

s an

d cu

be ro

ots

of s

ingl

e al

gebr

aic

term

s or

like

a

lgeb

raic

term

s

Det

erm

ine

the

num

eric

al v

alue

of

alge

brai

c ex

pres

sion

s by

sub

stitu

tion

Ex

tend

the

abov

e al

gebr

aic

m

anip

ulat

ions

to in

clud

e:

o m

ultip

ly in

tege

rs a

nd m

onom

ials

by

poly

nom

ials

o

divi

de p

olyn

omia

ls b

y in

tege

rs o

r m

onom

ials

o

the

prod

uct o

f tw

o bi

nom

ials

o

the

squa

re o

f a b

inom

ial

Fact

oriz

e al

gebr

aic

expr

essi

ons

• Fa

ctor

ize

alge

brai

c ex

pres

sion

s th

at

invo

lve:

o

com

mon

fact

ors

o di

ffere

nce

of tw

o sq

uare

s o

trino

mia

ls o

f the

form

:

♦♦

cbx

x

2

♦♦

cbx

ax

2

, whe

re a

is a

com

mon

fa

ctor

•

Sim

plify

alg

ebra

ic e

xpre

ssio

ns th

at

invo

lve

the

abov

e fa

ctor

izat

ion

proc

esse

s •

Sim

plify

alg

ebra

ic fr

actio

ns u

sing

fa

ctor

izat

ion


Sugg

este

d m

etho

dolo

gy

GR

ADE

7 Th

is is

an

intro

duct

ion

to fo

rmal

alg

ebra

ic la

ngua

ge a

nd is

new

in th

e Se

nior

Pha

se. T

he u

se o

f sym

bolic

lang

uage

hel

ps to

dev

elop

an

unde

rsta

ndin

g of

var

iabl

es.

Lear

ners

hav

e op

portu

nitie

s to

writ

e an

d in

terp

ret a

lgeb

raic

exp

ress

ions

whe

n th

ey w

rite

gene

ral r

ules

to d

escr

ibe

rela

tions

hips

bet

wee

n nu

mbe

rs in

num

ber p

atte

rns,

an

d w

hen

they

find

inpu

t and

out

put v

alue

s fo

r giv

en ru

les

in fl

ow d

iagr

ams,

tabl

es a

nd fo

rmul

ae.

Exam

ples

a)

W

hat d

oes

the

rule

2 x

n –

1 m

ean

for t

he fo

llow

ing

num

ber s

eque

nce:

1; 3

; 5; 7

; 9;..

.. H

ere

lear

ners

sho

uld

reco

gniz

e th

at 2

x n

–1

repr

esen

ts th

e ge

nera

l ter

m in

this

seq

uenc

e, w

here

n re

pres

ents

the

posi

tion

of th

e te

rm

in th

e se

quen

ce. T

hus

it is

the

rule

that

can

be

used

to fi

nd a

ny te

rm in

the

give

n se

quen

ce

b)

The

rela

tions

hip

betw

een

a bo

y’s

age

(x y

rs o

ld) a

nd h

is m

othe

r’s a

ge is

giv

en a

s 25

+ x

. How

can

this

rela

tions

hip

be u

sed

to fi

nd th

e m

othe

r’s a

ge w

hen

the

boy

is 1

1 ye

ars

old?

H

ere

lear

ners

sho

uld

reco

gniz

e th

at to

find

the

mot

her’s

age

, the

y sh

ould

sub

stitu

te th

e bo

y’s

give

n ag

e in

to th

e ru

le 2

5 +

x. T

hey

shou

ld a

lso

reco

gniz

e th

at th

e gi

ven

rule

mea

ns th

e m

othe

r is

25 y

ears

old

er th

an th

e bo

y. S

ee fu

rther

exa

mpl

es g

iven

for f

unct

ions

an

d re

latio

nshi

ps.

Alge

brai

c ex

pres

sion

s sh

ould

incl

ude

inte

gers

in th

e ru

les

or re

latio

nshi

ps re

pres

ente

d in

sym

bolic

form

. G

RAD

E 8

In g

rade

8 le

arne

rs w

ill be

doi

ng th

e fo

llow

ing:

Intro

duct

ion

to c

onve

ntio

ns o

f alg

ebra

ic la

ngua

ge.

M

anip

ulat

ing

alge

brai

c ex

pres

sion

s.

Lear

ners

hav

e op

portu

nitie

s to

writ

e an

d in

terp

ret a

lgeb

raic

exp

ress

ions

whe

n th

ey w

rite

gene

ral r

ules

to d

escr

ibe

rela

tions

hips

bet

wee

n nu

mbe

rs in

num

ber p

atte

rns,

and

whe

n th

ey fi

nd in

put o

r out

put v

alue

s fo

r giv

en ru

les

in fl

ow d

iagr

ams,

tabl

es, f

orm

ulae

and

equ

atio

ns.

Exam

ples

of i

nter

pret

ing

alge

brai

c ex

pres

sion

s a)

W

hat d

oes

the

rule

2n m

ean

for t

he fo

llow

ing

num

ber s

eque

nce:

2; 4

; 8; 1

6; 3

2...

Her

e le

arne

rs s

houl

d re

cogn

ize

that

2n r

epre

sent

s th

e ge

nera

l ter

m in

this

seq

uenc

e, w

here

n re

pres

ents

the

posi

tion

of th

e te

rm in

the

sequ

ence

. Thu

s, it

is th

e ru

le th

at c

an b

e us

ed to

find

any

term

in th

e gi

ven

sequ

ence

. b)

Th

e re

latio

nshi

p be

twee

n a

boy’

s ag

e (x

yrs

old

) and

his

mot

her’s

age

is g

iven

as

25 +

x. H

ow c

an th

is re

latio

nshi

p be

use

d to

find

th

e m

othe

r’s a

ge w

hen

the

boy

is 1

1 ye

ars

old?

Her

e le

arne

rs s

houl

d re

cogn

ize

that

to fi

nd th

e m

othe

r’s a

ge, t

hey

mus

t sub

stitu

te

the

boy’

s gi

ven

age

into

the

rule

25

+ x.

The

y sh

ould

als

o re

cogn

ize

that

the

give

n ru

le m

eans

the

mot

her i

s 25

yea

rs o

lder

than


the

boy

GR

ADE

9 G

rade

lear

ners

will

do th

e fo

llow

ing

alge

brai

c m

anip

ulat

ions

whi

ch in

clud

e:

• m

ultip

ly in

tege

rs a

nd m

onom

ials

by

poly

nom

ials

•

divi

de p

olyn

omia

ls b

y in

tege

rs o

r mon

omia

ls

• th

e pr

oduc

t of t

wo

bino

mia

ls

• th

e sq

uare

of a

bin

omia

l M

anip

ulat

ing

alge

brai

c ex

pres

sion

s M

ake

sure

lear

ners

und

erst

and

that

the

rule

s fo

r ope

ratin

g w

ith in

tege

rs a

nd ra

tiona

l num

bers

, inc

ludi

ng la

ws

of e

xpon

ents

, app

ly e

qual

ly

whe

n nu

mbe

rs a

re re

plac

ed w

ith v

aria

bles

. The

var

iabl

es a

re n

umbe

rs o

f a g

iven

type

(e.g

. int

eger

s or

ratio

nal n

umbe

rs) i

n ge

nera

lized

fo

rm. W

hen

mul

tiply

ing

or d

ivid

ing

expr

essi

ons,

mak

e su

re le

arne

rs u

nder

stan

d ho

w th

e di

strib

utiv

e ru

le w

orks

. The

ass

ocia

tive

rule

allo

ws

for g

roup

ing

of li

ke te

rms

whe

n ad

ding

. Loo

k ou

t for

the

follo

win

g co

mm

on m

isco

ncep

tions

: •

x +

x =

2x a

nd N

OT

x2 . N

ote

the

conv

entio

n is

to w

rite

2x ra

ther

than

x2

• x2 +

x2 =

2x2 a

nd N

OT

2x4

• a

+b =

a +

b a

nd N

OT

ab

• (–

2x2 )

3 = –

8x6 a

nd N

OT

–6x5

• -x

(3x

+ 1)

= –

3x2 –

x a

nd N

OT

–3x2 +

1

• 6𝑥𝑥

2 +1

𝑥𝑥2 =

6 +

1 𝑥𝑥2 a

nd N

OT

6 +

1

• If

x =

2 th

en –

3x2

= –3

(2)2

= 3

x 4

= 1

2 an

d N

OT

(–6)

2 •

If x

= –2

then

–x2 –

x =

–(–

2)2 –

(–2)

= –4

+ 2

= –

2 an

d N

OT

4 +

2 =

6 •

√25𝑥𝑥

2−

9𝑥𝑥2

= √16𝑥𝑥2

= 4

x an

d N

OT

5x –

3x

= 2x

•

(x +

2)2 =

x2 +

4x

+ 4

and

NO

T x2 +

4

See

CAP

S p.

131

for e

xam

ples

of e

xpre

ssio

ns a

Gra

de 9

lear

ner s

houl

d be

abl

e to

sim

plify

. LT

SM


Res

ourc

es

Cha

rts.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

W

B 2

Activ

ities

(74

– 76

; 120

- 12

2)

W

B 1

Activ

ities

(R

8; 2

9 –

31; 4

0 - 4

1)

WB

Activ

ities

(R

8; 3

5 - 3

6)

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTIG

RAD

E LE

SSO

N P

LAN

5

TER

M 2

Dat

e : f

rom

....

to ..

....

Tim

e:

8 ho

urs

Gra

de

7 8

9 To

pic

ALG

EBR

AIC

EQ

UAT

ION

S C

APS

page

s 64

& 6

9 91

& 9

4 13

2 - 1

33 &

144

Sk

ills a

nd

Know

ledg

e N

umbe

r sen

tenc

es

W

rite

num

ber s

ente

nces

to d

escr

ibe

prob

lem

situ

atio

ns

An

alys

e an

d in

terp

ret n

umbe

r sen

tenc

es

that

des

crib

e a

give

n si

tuat

ion

Solv

e an

d co

mpl

ete

num

ber s

ente

nces

by

: o

insp

ectio

n o

trial

and

impr

ovem

ent

Id

entif

y va

riabl

es a

nd c

onst

ants

in g

iven

fo

rmul

ae o

r equ

atio

ns

D

eter

min

e th

e nu

mer

ical

val

ue o

f an

expr

essi

on b

y su

bstit

utio

n.

Equa

tions

Rev

ise

the

follo

win

g do

ne in

Gra

de 7

: o

set u

p eq

uatio

ns to

des

crib

e pr

oble

m

situ

atio

ns

o an

alys

e an

d in

terp

ret e

quat

ions

that

de

scrib

e a

give

n si

tuat

ion

o so

lve

equa

tions

by

insp

ectio

n o

dete

rmin

e th

e nu

mer

ical

val

ue o

f an

expr

essi

on b

y su

bstit

utio

n.

o id

entif

y va

riabl

es a

nd c

onst

ants

in

give

n fo

rmul

ae o

r equ

atio

ns

Ex

tend

sol

ving

equ

atio

ns to

incl

ude:

o

Usi

ng a

dditi

ve a

nd m

ultip

licat

ive

inve

rses

o

Usi

ng la

ws

of e

xpon

ents

Use

sub

stitu

tion

in e

quat

ions

to g

ener

ate

tabl

es o

f ord

ered

pai

rs

Equa

tions

Rev

ise

the

follo

win

g do

ne in

Gra

de 8

: o

Set u

p eq

uatio

ns to

des

crib

e pr

oble

m

situ

atio

ns

o An

alys

e an

d in

terp

ret e

quat

ions

that

de

scrib

e a

give

n si

tuat

ion

o So

lve

equa

tions

by:

♦♦

insp

ectio

n

♦♦

usi

ng a

dditi

ve a

nd m

ultip

licat

ive

inv

erse

s

♦♦

usi

ng la

ws

of e

xpon

ents

o

Det

erm

ine

the

num

eric

al v

alue

of a

n ex

pres

sion

by

subs

titut

ion.

o

Use

sub

stitu

tion

in e

quat

ions

to

gene

rate

tabl

es o

f ord

ered

pai

rs

Ex

tend

sol

ving

equ

atio

ns to

incl

ude:

o

usin

g fa

ctor

isat

ion

o eq

uatio

ns o

f the

form

: a p

rodu

ct o

f fa

ctor

s =

0

Sugg

este

d m

etho

dolo

gy

GR

ADE

7 In

Gra

de 7

, the

num

ber s

ente

nces

that

lear

ners

can

sol

ve a

re e

xten

ded

to in

clud

e nu

mbe

r sen

tenc

es w

ith in

tege

rs, s

quar

e nu

mbe

rs a

nd

cubi

c nu

mbe

rs.

Num

ber s

ente

nces

are

use

d he

re a

s a

mor

e fa

milia

r ter

m fo

r Gra

de 7

lear

ners

than

equ

atio

ns. H

owev

er, t

he te

rm e

quat

ion

will

be u

sed

inst

ead

of n

umbe

r sen

tenc

es in

late

r gra

des.


Lear

ners

hav

e op

portu

nitie

s to

writ

e, s

olve

and

com

plet

e nu

mbe

r sen

tenc

es w

hen

they

writ

e ge

nera

l rul

es to

des

crib

e re

latio

nshi

ps

betw

een

num

bers

in n

umbe

r pa

ttern

s, a

nd w

hen

they

find

inpu

t and

out

put v

alue

s fo

r giv

en ru

les

in fl

ow d

iagr

ams,

tabl

es a

nd fo

rmul

ae. R

athe

r tha

n us

e fo

rmal

al

gebr

aic

proc

esse

s, le

arne

rs s

olve

num

ber s

ente

nces

by

insp

ectio

n or

det

erm

ine

the

num

eric

al v

alue

of e

xpre

ssio

ns b

y su

bstit

utio

n. In

th

is p

hase

, it i

s us

eful

whe

n so

lvin

g eq

uatio

ns to

beg

in to

spe

cify

whe

ther

x is

a n

atur

al n

umbe

r, in

tege

r or r

atio

nal n

umbe

r. Th

is b

uild

s le

arne

rs’ a

war

enes

s of

the

dom

ain

of x

. Ex

ampl

es

a)

Solv

e 𝑥𝑥

if 𝑥𝑥

+4

=7,

whe

re x

is

a na

tura

l num

ber.

(Wha

t mus

t be

adde

d to

4 to

giv

e 7?

) b)

So

lve

x if

𝑥𝑥+

4=

−7,

whe

re x

is a

n in

tege

r. (W

hat m

ust b

e ad

ded

to 4

to g

ive 7

?)

c)

Solv

e x

if 2𝑥𝑥

=30

, whe

re x

is a

nat

ural

num

ber.

(Wha

t mus

t be

mul

tiplie

d by

2 to

giv

e 30

?)

d)

Writ

e a

num

ber s

ente

nces

to fi

nd th

e ar

ea o

f a re

ctan

gle

with

leng

th 4

,5 c

m a

nd b

reat

h 2

cm.

e)

If 𝑦𝑦

=𝑥𝑥2

+1,

cal

cula

te y

whe

n x

= 3.

G

RAD

E 8

Up

to a

nd in

clud

ing

Gra

de 7

lear

ners

use

the

term

'num

bers

sen

tenc

es'.

From

Gra

de 8

the

term

'equ

atio

ns' i

s us

ed. S

olvi

ng e

quat

ions

us

ing

addi

tive

and

mul

tiplic

ativ

e in

vers

es a

s w

ell a

s la

ws

of e

xpon

ents

Ag

ain,

lear

ners

hav

e op

portu

nitie

s to

writ

e an

d so

lve

equa

tions

whe

n th

ey w

rite

gene

ral r

ules

to d

escr

ibe

rela

tions

hips

bet

wee

n nu

mbe

rs

in n

umbe

r pat

tern

s, a

nd w

hen

they

find

inpu

t or o

utpu

t val

ues

for g

iven

rule

s in

flow

dia

gram

s, ta

bles

and

form

ulae

. In

this

Gra

de, l

earn

ers

are

intro

duce

d to

:

Solv

ing

equa

tions

usi

ng a

dditi

ve a

nd m

ultip

licat

ive

inve

rses

as

wel

l as

law

s of

exp

onen

ts

Lear

ners

hav

e op

portu

nitie

s to

writ

e an

d so

lve

equa

tions

whe

n th

ey w

rite

gene

ral r

ules

to d

escr

ibe

rela

tions

hips

bet

wee

n nu

mbe

rs in

nu

mbe

r pat

tern

s, a

nd w

hen

they

find

inpu

t or o

utpu

t val

ues

for g

iven

rule

s in

flow

dia

gram

s, ta

bles

and

form

ulae

.


Exam

ples

of e

quat

ions

EQU

ATIO

N

HIN

T a)

So

lve 𝑥𝑥

if 𝑥𝑥

+6

= −

9 Ad

d −6

to b

oth

side

s of

the

equa

tion.

b)

So

lve 𝑥𝑥

if −2

𝑥𝑥=

8 D

ivid

e bo

th s

ides

of t

he e

quat

ion

by −

2.

c)

Solv

e x

if −𝑥𝑥

= −

5 D

ivid

e bo

th s

ides

of t

he e

quat

ion

by −

1 d)

So

lve

x if

3𝑥𝑥+

1=

7 Ad

d −1

to b

oth

side

s of

the

equa

tion

and

then

div

ide

both

sid

es o

f the

equ

atio

n by

3.

e)

Pr

ovid

e an

equ

atio

n to

find

the

area

of a

rect

angl

e w

ith le

ngth

2x

cm a

nd w

idth

( 2𝑥𝑥

+1)

cm

f) If

the

area

of a

rect

angl

e is

( 4𝑥𝑥2

−6𝑥𝑥

) 𝑐𝑐𝑐𝑐

2 , a

nd it

s w

idth

is 2𝑥𝑥 𝑐𝑐𝑐𝑐

, wha

t will

be it

s le

ngth

in te

rms

of 𝑥𝑥

? g)

If 𝑦𝑦

= 𝑥𝑥

2 +

1, C

alcu

late

y w

hen

x =

4.

h)

Than

di is

6 y

ears

old

er th

an S

ophi

e. In

3 y

ears

’ tim

e Th

andi

will

be tw

ice

as o

ld a

s So

phie

. How

old

is T

hand

i now

? G

RAD

E 9

Gra

de 9

lear

ners

are

taug

ht:

• So

lvin

g eq

uatio

ns u

sing

fact

oriz

atio

n •

Solv

ing

equa

tions

of t

he fo

rm: a

pro

duct

of f

acto

rs =

0

Agai

n le

arne

rs h

ave

oppo

rtuni

ties

to w

rite

and

solv

e eq

uatio

ns w

hen

they

writ

e ge

nera

l rul

es to

des

crib

e re

latio

nshi

ps b

etw

een

num

bers

in

num

ber p

atte

rns,

and

whe

n th

ey fi

nd in

put o

r out

put v

alue

s fo

r giv

en ru

les

in fl

ow d

iagr

ams,

tabl

es a

nd fo

rmul

ae.

In G

rade

9, l

earn

ers

can

be g

iven

equ

atio

ns w

here

they

hav

e to

exp

and,

sim

plify

or f

acto

rize

expr

essi

ons

first

, bef

ore

solv

ing

the

equa

tion.

Fo

r equ

atio

ns o

f the

form

: a p

rodu

ct o

f tw

o fa

ctor

s =

0, le

arne

rs h

ave

to u

nder

stan

d th

at if

the

prod

uct o

f tw

o fa

ctor

s eq

uals

0, t

hen

at

leas

t one

of t

he fa

ctor

s m

ust b

e eq

ual t

o 0.

Hen

ce to

sol

ve th

e eq

uatio

n, e

ach

fact

or m

ust b

e w

ritte

n as

an

equa

tion

equa

l to

0, a

nd

ther

efor

e m

ore

than

one

sol

utio

n fo

r x is

pos

sibl

e. W

hen

wor

king

with

alg

ebra

ic fr

actio

ns, l

earn

ers

mus

t be

rem

inde

d th

at th

e de

nom

inat

or

cann

ot e

qual

0, s

o an

y va

lue

of x

that

mak

es th

e de

nom

inat

or 0

can

not b

e a

solu

tion

to th

e eq

uatio

n.

Exam

ples

of e

quat

ions

Se

e C

APS

page

132

and

144

LTSM


Res

ourc

es

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

W

B 2

Activ

ities

(77

– 79

; 123

- 12

5)

WB

1 Ac

tiviti

es (3

2 - 3

8)

W

B 2

Activ

ities

(111

-113

)

WB

Act

iviti

es (8

1 - 8

6)

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


LE

SSO

N P

LAN

S: T

ERM

3


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

1

TER

M 3

Dat

e : f

rom

....

to ..

....

Tim

e:

8

hou

rs

Gra

de

7 8

9 To

pic

CO

MM

ON

FR

ACTI

ON

S C

APS

page

s 49

- 51

10

0 - 1

02

122

Skills

and

Kn

owle

dge

Orde

ring,

com

parin

g an

d si

mpl

ifyin

g fra

ctio

ns

C

ompa

re a

nd o

rder

com

mon

fra

ctio

ns, i

nclu

ding

spe

cific

ally

te

nths

and

hun

dred

ths

Ex

tend

to th

ousa

ndth

s Ca

lculat

ions w

ith fr

actio

ns

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

o ad

ditio

n an

d su

btra

ctio

n of

co

mm

on fr

actio

ns, i

nclu

ding

m

ixed

num

bers

, lim

ited

to

fract

ions

with

the

sam

e de

nom

inat

or o

r whe

re o

ne

deno

min

ator

is a

mul

tiple

of

anot

her

o fin

ding

frac

tions

of w

hole

nu

mbe

rs

Ex

tend

o

addi

tion

and

subt

ract

ion

to

fract

ions

whe

re o

ne

deno

min

ator

is n

ot a

mul

tiple

of

the

othe

r

Calcu

lation

s with

frac

tions

Rev

ise:

-

addi

tion

and

subt

ract

ion

of

com

mon

frac

tions

, in

clud

ing

mix

ed n

umbe

rs

- fin

ding

frac

tions

of w

hole

nu

mbe

rs

- m

ultip

licat

ion

of c

omm

on

fract

ions

, inc

ludi

ng

mix

ed n

umbe

rs

D

ivid

e w

hole

num

bers

and

co

mm

on fr

actio

ns b

y co

mm

on

fract

ions

Cal

cula

te th

e sq

uare

s, c

ubes

, sq

uare

root

s an

d cu

be ro

ots

of

com

mon

frac

tions

Calcu

lation

s with

frac

tions

All f

our o

pera

tions

with

com

mon

frac

tions

an

d m

ixed

num

bers

All f

our o

pera

tions

, with

num

bers

that

in

volv

e th

e sq

uare

s, c

ubes

, squ

are

root

s an

d cu

be ro

ots

of c

omm

on fr

actio

ns


o m

ultip

licat

ion

of c

omm

on

fract

ions

, inc

ludi

ng m

ixed

nu

mbe

rs, n

ot li

mite

d to

fra

ctio

ns w

here

one

de

nom

inat

or is

a m

ultip

le o

f an

othe

r Ca

lculat

ion te

chniq

ues

C

onve

rt m

ixed

num

bers

to c

omm

on

fract

ions

in

orde

r to

perfo

rm c

alcu

latio

ns w

ith th

em

U

se k

now

ledg

e of

mul

tiple

s an

d fa

ctor

s to

writ

e fra

ctio

ns in

the

sim

ples

t for

m

befo

re o

r afte

r cal

cula

tions

Use

kno

wle

dge

of e

quiv

alen

t fra

ctio

ns to

ad

d an

d su

btra

ct c

omm

on fr

actio

ns

Solvi

ng p

robl

ems

So

lve

prob

lem

s in

con

text

s in

volv

ing

com

mon

frac

tions

and

mix

ed n

umbe

rs,

incl

udin

g gr

oupi

ng, s

harin

g an

d fin

ding

fra

ctio

ns o

f who

le n

umbe

rs

Calcu

lation

tech

nique

s

Rev

ise:

-

conv

ert m

ixed

num

bers

to

com

mon

frac

tions

in

orde

r to

perfo

rm c

alcu

latio

ns w

ith

them

-

use

know

ledg

e of

mul

tiple

s an

d fa

ctor

s to

writ

e fra

ctio

ns in

the

sim

ples

t for

m b

efor

e or

afte

r ca

lcul

atio

ns

- us

e kn

owle

dge

of e

quiv

alen

t fra

ctio

ns to

add

and

sub

tract

co

mm

on fr

actio

ns

U

se k

now

ledg

e of

reci

proc

al

rela

tions

hips

to d

ivid

e co

mm

on

fract

ions

So

lving

pro

blem

s

Solv

e pr

oble

ms

in c

onte

xts

invo

lvin

g co

mm

on fr

actio

ns a

nd

mix

ed n

umbe

rs, i

nclu

ding

gr

oupi

ng, s

harin

g an

d fin

ding

fra

ctio

ns o

f who

le n

umbe

rs

Calcu

lation

tech

nique

s

Rev

ise:

-

conv

ert m

ixed

num

bers

to c

omm

on

fract

ions

in

orde

r to

perfo

rm c

alcu

latio

ns w

ith th

em

- us

e kn

owle

dge

of m

ultip

les

and

fact

ors

to w

rite

fract

ions

in th

e si

mpl

est f

orm

be

fore

or a

fter c

alcu

latio

ns

- us

e kn

owle

dge

of e

quiv

alen

t fra

ctio

ns

to a

dd a

nd s

ubtra

ct c

omm

on fr

actio

ns

- us

e kn

owle

dge

of re

cipr

ocal

re

latio

nshi

ps to

div

ide

com

mon

fra

ctio

ns

Solvi

ng p

robl

ems

So

lve

prob

lem

s in

con

text

s in

volv

ing

com

mon

frac

tions

, mix

ed n

umbe

rs

and

perc

enta

ges

Perc

entag

es

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

- Fi

ndin

g pe

rcen

tage

s of

who

le n

umbe

rs

C

alcu

late

the

perc

enta

ge o

f par

t of a

who

le

C

alcu

late

per

cent

age

incr

ease

or

decr

ease

of w

hole

num

bers

Solv

e pr

oble

ms

in c

onte

xts

invo

lvin

g pe

rcen

tage

s

Perc

entag

es

R

evis

e:

- fin

ding

per

cent

ages

of w

hole

nu

mbe

rs

- ca

lcul

atin

g th

e pe

rcen

tage

of p

art

of a

who

le

- ca

lcul

atin

g pe

rcen

tage

incr

ease

or

dec

reas

e

Cal

cula

te a

mou

nts

if gi

ven


Equiv

alent

form

s R

evis

e th

e fo

llow

ing

done

in G

rade

6:

re

cogn

ize

and

use

equi

vale

nt fo

rms

of

com

mon

frac

tions

with

1-d

igit

or 2

-dig

it de

nom

inat

ors

(frac

tions

whe

re o

ne

deno

min

ator

is a

mul

tiple

of t

he o

ther

)

reco

gniz

e eq

uiva

lenc

e be

twee

n co

mm

on

fract

ion

and

deci

mal

frac

tion

form

s of

the

sam

e nu

mbe

r

reco

gniz

e eq

uiva

lenc

e be

twee

n co

mm

on

fract

ion,

dec

imal

frac

tion

and

perc

enta

ge

form

s of

the

sam

e nu

mbe

r

perc

enta

ge in

crea

se o

r de

crea

se

So

lve

prob

lem

s in

con

text

s in

volv

ing

perc

enta

ges

Equiv

alent

form

s R

evis

e eq

uiva

lent

form

s be

twee

n:

co

mm

on fr

actio

ns

(frac

tions

whe

re o

ne

deno

min

ator

is a

mul

tiple

of

the

othe

r)

com

mon

frac

tion

and

deci

mal

fra

ctio

n fo

rms

of th

e sa

me

num

ber

co

mm

on fr

actio

n,

deci

mal

frac

tion

and

perc

enta

ge fo

rms

of th

e sa

me

num

ber

Equiv

alent

form

s R

evis

e eq

uiva

lent

form

s be

twee

n:

co

mm

on fr

actio

ns w

here

one

de

nom

inat

or is

a m

ultip

le o

f ano

ther

com

mon

frac

tion

and

deci

mal

frac

tion

form

s of

the

sam

e nu

mbe

r

com

mon

frac

tion,

dec

imal

fra

ctio

n an

d pe

rcen

tage

form

s of

th

e sa

me

num

ber

Sugg

este

d m

etho

dolo

gy

Calcu

lation

s with

frac

tions

Le

arne

rs s

houl

d do

con

text

free

cal

cula

tions

and

sol

ve p

robl

ems

in c

onte

xts.

It

is n

ot e

xpec

ted

that

lear

ners

kno

w ru

les

for s

impl

ifyin

g fra

ctio

ns o

r for

con

verti

ng b

etw

een

mix

ed n

umbe

rs a

nd fr

actio

n fo

rms.

Lear

ners

sho

uld

know

from

wor

king

with

equ

ival

ence

, whe

n a

fract

ion

is e

qual

to o

r gre

ater

than

1.

LC

M’s

hav

e to

be

foun

d w

hen

addi

ng a

nd s

ubtra

ctin

g fra

ctio

ns o

f diff

eren

t den

omin

ator

s. H

ere

lear

ners

use

kno

wle

dge

of c

omm

on

mul

tiple

s to

find

the

LCM

i.e.

wha

t num

ber c

an b

oth

deno

min

ator

s be

div

ided

into

.

To

sim

plify

frac

tions

, lea

rner

s us

e kn

owle

dge

of c

omm

on fa

ctor

s i.e

. wha

t can

div

ide

equa

lly in

to th

e nu

mer

ator

and

den

omin

ator

of a

fract

ion.

Em

phas

ize

that

whe

n si

mpl

ifyin

g, th

e fra

ctio

ns m

ust r

emai

n eq

uiva

lent

.

Le

arne

rs s

houl

d re

cogn

ize

that

find

ing

a ‘fr

actio

n of

a w

hole

num

ber’

or ‘f

indi

ng a

frac

tion

of a

frac

tion’

mea

ns m

ultip

lyin

g th

e fra

ctio

n

and

the

who

le n

umbe

r or t

he fr

actio

n w

ith th

e fra

ctio

n.

W

hen

lear

ners

find

frac

tions

of w

hole

num

bers

, the

exa

mpl

es c

an b

e ch

osen

to re

sult

eith

er in

who

le n

umbe

rs o

r fra

ctio

ns o

r bot

h.

Le

arne

rs s

houl

d al

so u

se th

e co

nven

tion

of w

ritin

g th

e w

hole

num

ber a

s a

fract

ion

over

whe

n m

ultip

lyin

g.


Calcu

lation

usin

g pe

rcen

tages

Le

arne

rs s

houl

d do

con

text

free

cal

cula

tions

and

sol

ve p

robl

ems

in c

onte

xts.

W

hen

doin

g ca

lcul

atio

ns u

sing

per

cent

ages

, lea

rner

s ha

ve to

use

the

equi

vale

nt c

omm

on fr

actio

n fo

rm, w

hich

is a

frac

tion

with

deno

min

ator

100

.

Lear

ners

sho

uld

beco

me

fam

iliar w

ith th

e eq

uiva

lent

frac

tion

and

deci

mal

form

s of

com

mon

per

cent

ages

like

To

cal

cula

te p

erce

ntag

e of

par

t of a

who

le, o

r per

cent

age

incr

ease

or d

ecre

ase,

lear

ners

hav

e to

lear

n th

e st

rate

gy o

f

mul

tiply

ing

by 1

00. I

t is

usef

ul fo

r lea

rner

s to

lear

n to

use

cal

cula

tors

for s

ome

of th

ese

calc

ulat

ions

whe

re th

e fra

ctio

ns

are

not e

asily

sim

plifi

ed.

W

hen

usin

g ca

lcul

ator

s, le

arne

rs c

an a

lso

use

the

equi

vale

nt d

ecim

al fr

actio

n fo

rm fo

r per

cent

ages

to d

o th

e

calc

ulat

ions

.

Grad

e 8

Wha

t is di

ffere

nt to

Gra

de 7?

D

ivid

e by

com

mon

fra

ctio

ns

Sq

uare

s, c

ubes

, squ

are

root

s an

d cu

be ro

ots

of c

omm

on fr

actio

ns

Multip

licati

on

Fo

r mul

tiplic

atio

n of

frac

tions

, lea

rner

s sh

ould

be

enco

urag

ed to

sim

plify

frac

tions

by

divi

ding

num

erat

ors

and

deno

min

ator

s by

com

mon

fact

ors.

Le

arne

rs s

houl

d no

te th

e di

ffere

nce

betw

een

addi

ng o

r sub

tract

ing

fract

ions

, and

mul

tiply

ing

fract

ions

W

hen

lear

ners

find

frac

tions

of w

hole

num

bers

, the

exa

mpl

es c

an b

e ch

osen

to re

sult

eith

er in

who

le n

umbe

rs o

r fra

ctio

ns o

r bot

h.

Le

arne

rs s

houl

d al

so u

se th

e co

nven

tion

of w

ritin

g th

e w

hole

num

ber a

s a

fract

ion

over

whe

n m

ultip

lyin

g.


Divi

sion

Th

e te

chni

que

of ‘i

nver

t and

mul

tiply

’ app

lies

to d

ivis

ion

in g

ener

al a

nd n

ot ju

st to

div

isio

n by

frac

tions

. Hen

ce, a

use

ful w

ay o

f mak

ing

lear

ners

com

forta

ble

with

div

isio

n by

frac

tions

is to

sta

rt w

ith e

xam

ples

of d

ivis

ion

by w

hole

num

bers

.

Le

arne

rs h

ave

to u

nder

stan

d th

at d

ivid

ing

by a

num

ber i

s th

e sa

me

as m

ultip

lyin

g by

the

reci

proc

al o

f the

num

ber i

.e. t

he re

cipr

ocal

of n

is 1

Kn

owin

g th

e ru

les

of o

pera

tions

for c

alcu

latin

g sq

uare

s, c

ubes

, squ

are

root

s an

d cu

be ro

ots

of c

omm

on fr

actio

ns is

impo

rtant

, onc

e

lear

ners

are

com

forta

ble

doin

g al

l the

ope

ratio

ns w

ith fr

actio

ns, c

alcu

latio

ns d

o no

t hav

e to

be

rest

ricte

d to

pos

itive

frac

tions

.

Grad

e 9

Wha

t is di

ffere

nt to

Gra

de 8?

In G

rade

9, l

earn

ers

wor

k w

ith d

ecim

al fr

actio

ns m

ostly

as

coef

ficie

nts

in a

lgeb

raic

exp

ress

ions

and

equ

atio

ns. T

hey

are

expe

cted

to b

e

com

pete

nt in

per

form

ing

mul

tiple

ope

ratio

ns u

sing

dec

imal

frac

tions

and

mix

ed n

umbe

rs, a

pply

ing

prop

er- t

ies

of ra

tiona

l num

bers

appr

opria

tely.

The

y ar

e al

so e

xpec

ted

to re

cogn

ize

and

use

equi

vale

nt fo

rms

for d

ecim

al fr

actio

ns a

ppro

pria

tely

in c

alcu

latio

ns.

LTSM

Res

ourc

es

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 c

ards

, Bas

e 10

bloc

ks, 1

00 c

harts

, mul

tiplic

atio

n ta

ble

G

rade

7

Gra

de 8

Gra

de 9

Wor

kboo

k re

fere

nce

1

Activ

ities

(30

- 43)

WB

1 Ac

tiviti

es (R

5; R

6)

WB

2 Ac

tiviti

es (6

5 - 6

8)

WB

1 Ac

tiviti

es (R

5; 1

6

Text

book

refe

renc

e


HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

ass

essm

ent

– Te

st: m

arks

max


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

2

TER

M 3

Dat

e : f

rom

....

to ..

....

Tim

e: 8

hou

rs

Gra

de

7 8

9 To

pic

DEC

IMAL

FR

ACTI

ON

S C

APS

page

s 51

- 53

10

3 - 1

05

123

Skills

and

Kn

owle

dge

Ord

erin

g an

d co

mpa

ring

deci

mal

fr

actio

ns

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

-

coun

t for

war

ds a

nd b

ackw

ards

in

deci

mal

frac

tions

to a

t lea

st tw

o de

cim

al p

lace

s

- co

mpa

re a

nd o

rder

dec

imal

frac

tions

to

at le

ast t

wo

deci

mal

pla

ces

-

plac

e va

lue

of d

igits

to a

t lea

st tw

o de

cim

al p

lace

s

- ro

undi

ng o

ff de

cim

al fr

actio

ns to

at l

east

1

deci

mal

pla

ce

Ex

tend

al

l of

th

e ab

ove

to

deci

mal

fra

ctio

ns to

at l

east

thre

e de

cim

al p

lace

s an

d ro

undi

ng o

ff to

at

leas

t 2

deci

mal

pl

aces

Ord

erin

g an

d co

mpa

ring

deci

mal

fr

actio

ns

R

evis

e:

-

orde

ring,

com

parin

g an

d pl

ace

valu

e of

dec

imal

fra

ctio

ns to

at l

east

3

deci

mal

pla

ces

-

roun

ding

off

deci

mal

fra

ctio

ns to

at l

east

2

deci

mal

pla

ce

Ord

erin

g an

d co

mpa

ring

deci

mal

fr

actio

ns

R

evis

e:

-

orde

ring,

com

parin

g an

d pl

ace

valu

e of

dec

imal

fra

ctio

ns to

at l

east

3

deci

mal

pla

ces

-

roun

ding

off

deci

mal

fra

ctio

ns to

at l

east

2

deci

mal

pla

ce


Calcu

lation

s with

dec

imal

fracti

ons

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

-

addi

tion

and

subt

ract

ion

of d

ecim

al

fract

ions

of a

t lea

st tw

o de

cim

al p

lace

s

- m

ultip

licat

ion

of d

ecim

al fr

actio

ns b

y 10

and

100

Exte

nd a

dditi

on a

nd s

ubtra

ctio

n to

dec

imal

fra

ctio

ns o

f at l

east

thre

e de

cim

al p

lace

s

mul

tiply

dec

imal

frac

tions

to in

clud

e:

-

deci

mal

frac

tions

to a

t lea

st 3

dec

imal

pl

aces

by

who

le n

umbe

rs

-

deci

mal

frac

tions

to a

t lea

st 2

dec

imal

pl

aces

by

deci

mal

frac

tions

to a

t lea

st 1

de

cim

al p

lace

Div

ide

deci

mal

frac

tions

to in

clud

e de

cim

al fr

actio

ns to

at l

east

3 d

ecim

al

plac

es b

y w

hole

num

bers

Ca

lculat

ion te

chniq

ues

U

se

know

ledg

e of

pl

ace

valu

e to

es

timat

e th

e nu

mbe

r of

de

cim

al

plac

es in

the

resu

lt be

fore

per

form

ing

calc

ulat

ions

Use

roun

ding

off

and

a ca

lcul

ator

to c

heck

re

sults

whe

re a

ppro

pria

te

Calcu

lation

s with

dec

imal

fracti

ons

R

evis

e:

-

addi

tion,

sub

tract

ion,

mul

tiplic

atio

n an

d of

de

cim

al fr

actio

ns to

at l

east

3 d

ecim

al

plac

es

-

divi

sion

of d

ecim

al fr

actio

ns b

y w

hole

nu

mbe

rs

Ex

tend

mul

tiplic

atio

n to

'mul

tiplic

atio

n by

dec

imal

frac

tions

' not

lim

ited

to

one

deci

mal

pla

ce

Ex

tend

div

isio

n to

'div

isio

n of

dec

imal

fra

ctio

ns b

y de

cim

al fr

actio

ns'

C

alcu

late

the

squa

res,

cub

es,

squa

re ro

ots

and

cube

root

s of

de

cim

al fr

actio

ns

Calcu

lation

tech

nique

s

Use

kno

wle

dge

of p

lace

val

ue t

o es

timat

e th

e nu

mbe

r of

dec

imal

pl

aces

in

th

e re

sult

befo

re

perfo

rmin

g ca

lcul

atio

ns

U

se ro

undi

ng o

ff an

d a

calc

ulat

or to

ch

eck

resu

lts w

here

app

ropr

iate

Calcu

lation

s with

dec

imal

fracti

ons

m

ultip

le

oper

atio

ns

with

de

cim

al

fract

ions

, us

ing

a ca

lcul

ator

whe

re

appr

opria

te

m

ultip

le o

pera

tions

with

or

with

out

brac

kets

, with

num

bers

that

invo

lve

the

squa

res,

cub

es,

squa

re r

oots

an

d cu

be ro

ots

of d

ecim

al fr

actio

ns

Calcu

lation

tech

nique

s

Use

kno

wle

dge

of p

lace

val

ue t

o es

timat

e th

e nu

mbe

r of

dec

imal

pl

aces

in

th

e re

sult

befo

re

perfo

rmin

g ca

lcul

atio

ns

U

se ro

undi

ng o

ff an

d a

calc

ulat

or to

ch

eck

resu

lts w

here

app

ropr

iate

So

lving

pro

blem

s

Solv

e pr

oble

ms

in c

onte

xt in

volv

ing

deci

mal

Fr

actio

ns

Solvi

ng p

robl

ems

So

lve

prob

lem

s in

con

text

invo

lvin

g de

cim

al

fract

ions

Solvi

ng p

robl

ems

So

lve

prob

lem

s in

con

text

invo

lvin

g de

cim

al

fract

ions


Equiv

alent

form

s

Rev

ise

the

follo

win

g do

ne in

Gra

de 6

:

- re

cogn

ize

equi

vale

nce

betw

een

com

mon

frac

tion

and

deci

mal

frac

tion

form

s of

the

sam

e nu

mbe

r

- re

cogn

ize

equi

vale

nce

betw

een

com

mon

fra

ctio

n, d

ecim

al fr

actio

n an

d pe

rcen

tage

form

s of

the

sam

e nu

mbe

r

Equiv

alent

form

s

Rev

ise

equi

vale

nt fo

rms

betw

een:

- co

mm

on fr

actio

n an

d de

cim

al

fract

ion

form

s of

the

sam

e nu

mbe

r

- co

mm

on fr

actio

n, d

ecim

al

fract

ion

and

perc

enta

ge

form

s of

the

sam

e nu

mbe

r

Equiv

alent

form

s

Rev

ise

equi

vale

nt fo

rms

betw

een:

- co

mm

on fr

actio

n an

d de

cim

al

fract

ion

form

s of

the

sam

e nu

mbe

r

- co

mm

on fr

actio

n, d

ecim

al

fract

ion

and

perc

enta

ge

form

s of

the

sam

e nu

mbe

r

Sugg

este

d m

etho

dolo

gy

Orde

ring,

coun

ting a

nd co

mpa

ring d

ecim

al fra

ctio

ns

C

ount

ing

shou

ld n

ot o

nly

be th

ough

t of a

s ve

rbal

cou

ntin

g. L

earn

ers

can

coun

t in

deci

mal

inte

rval

s us

ing:

- st

ruct

ured

, sem

i-stru

ctur

ed o

r em

pty

num

ber l

ines

- ch

ain

diag

ram

s fo

r cou

ntin

g

Lear

ners

sho

uld

be g

iven

a ra

nge

of e

xerc

ises

suc

h as

:

- ar

rang

e gi

ven

num

bers

from

the

smal

lest

to th

e bi

gges

t: or

big

gest

to s

mal

lest

- fil

l in

mis

sing

num

bers

in

◆

a s

eque

nce

◆

on

a nu

mbe

r grid

◆ o

n a

num

ber l

ine

◆

fill i

n <,

= o

r > e

xam

ple:

0,4

* 0.

04∗0

,004

( no

te g

rade

8 d

o up

tp 3

dec

imal

pla

ces)

C

ount

ing

exer

cise

s in

cha

in d

iagr

ams

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.


Calcu

lating

with

dec

imal

fracti

ons

Le

arne

rs s

houl

d do

con

text

free

cal

cula

tions

and

sol

ve p

robl

ems

in c

onte

xts.

Lear

ners

sho

uld

estim

ate

thei

r ans

wer

s be

fore

cal

cula

ting,

esp

ecia

lly w

ith m

ultip

licat

ion

by d

ecim

al fr

actio

ns. T

hey

shou

ld b

e ab

le to

ju

dge

the

reas

onab

lene

ss o

f ans

wer

s re

latin

g to

how

man

y de

cim

al p

lace

s an

d al

so c

heck

thei

r ow

n an

swer

s.

m

ultip

licat

ion

by d

ecim

al fr

actio

ns s

houl

d st

art w

ith fa

milia

r num

bers

that

lear

ners

can

cal

cula

te b

y in

spec

tion,

so

that

lear

ners

ge

t a s

ense

of h

ow d

ecim

al p

lace

s ar

e af

fect

ed b

y m

ultip

licat

ion.

Eq

uiva

lence

betw

een c

omm

on fr

actio

ns an

d dec

imal

frac

tions

Lear

ners

are

not

exp

ecte

d to

be

able

to c

onve

rt an

y co

mm

on fr

actio

n in

to it

s de

cim

al fo

rm, m

erel

y to

see

the

rela

tions

hip

betw

een

tent

hs, h

undr

edth

s an

d th

ousa

ndth

s in

thei

r dec

imal

form

s.

Le

arne

rs s

houl

d st

art b

y re

writ

ing

and

conv

ertin

g te

nths

, hun

dred

ths

and

thou

sand

ths

in c

omm

on fr

actio

n fo

rm to

dec

imal

frac

tions

. W

here

den

omin

ator

s of

oth

er fr

actio

ns a

re fa

ctor

s of

10

e.g.

2,5

or f

acto

rs o

f 100

e.g

. 2, 4

, 20,

25

lear

ners

can

con

vert

thes

e to

hu

ndre

dths

usi

ng w

hat t

hey

know

abo

ut e

quiv

alen

ce.

It is

use

ful t

o us

e ca

lcul

ator

s to

hel

p le

arne

rs c

onve

rt be

twee

n co

mm

on fr

actio

ns a

nd d

ecim

al fr

actio

ns (h

ere

lear

ners

will

use

wha

t the

y kn

ow a

bout

the

rela

tions

hip

betw

een

fract

ions

and

div

isio

n).

- D

ivid

ing

who

le n

umbe

rs b

y 10

, 100

, 1 0

00, e

tc. c

an h

elp

to b

uild

lear

ners

’ und

erst

andi

ng o

f pla

ce v

alue

with

dec

imal

s. T

his

is a

lso

usef

ul to

do

on th

e ca

lcul

ator

– le

arne

rs c

an d

iscu

ss th

e pa

ttern

s th

ey s

ee w

hen

divi

ding

.

- Si

mila

rly c

alcu

lato

rs c

an b

e us

eful

tool

s fo

r lea

rner

s to

lear

n ab

out p

atte

rns

whe

n m

ultip

lyin

g de

cim

als

by 1

0, 1

00 o

r,1 0

00 e

tc.

n

Gra

de 8

W

hat is

diffe

rent

to G

rade

7?

M

ultip

licat

ion

by d

ecim

al fr

actio

ns n

ot li

mite

d to

one

dec

imal

pla

ce

D

ivis

ion

of d

ecim

al fr

actio

ns b

y de

cim

al fr

actio

ns

Sq

uare

s, c

ubes

, squ

are

root

s an

d cu

be ro

ots

of d

ecim

al fr

actio

ns


Calcu

lating

usin

g de

cimal

fracti

ons

Fo

r div

isio

n by

dec

imal

frac

tions

with

out c

alcu

lato

rs, l

earn

ers

have

to u

se th

eir k

now

ledg

e of

mul

tiplic

atio

n by

10

or m

ultip

les

of 1

0 to

m

ake

the

divi

sor a

who

le n

umbe

r. H

ence

sta

rt w

ith fa

milia

r num

bers

that

lear

ners

can

cal

cula

te b

y in

spec

tion,

so

that

lear

ners

get

a

sens

e of

how

dec

imal

pla

ces

are

affe

cted

by

divi

sion

.

For b

igge

r and

unf

amilia

r dec

imal

frac

tions

, lea

rner

s sh

ould

use

cal

cula

tors

for m

ultip

licat

ion

and

divi

sion

, but

stil

l jud

ge th

e re

ason

able

ness

of t

heir

solu

tions

.

Sim

ilarly

, fin

ding

squ

ares

, cu

bes,

squ

are

root

s an

d cu

be r

oots

for

dec

imal

fra

ctio

ns s

houl

d st

art

with

fam

iliar

num

bers

tha

t le

arne

rs c

an c

alcu

late

by

insp

ectio

n.

O

nce

lear

ners

are

com

forta

ble

with

all

the

oper

atio

ns u

sing

dec

imal

frac

tions

, cal

cula

tions

sho

uld

not b

e re

stric

ted

to p

ositi

ve

deci

mal

frac

tions

. G

rade

9

Wha

t is di

ffere

nt to

Gra

de 8?

In

Gra

de 9

, lea

rner

s w

ork

with

dec

imal

frac

tions

mos

tly a

s co

effic

ient

s in

alg

ebra

ic e

xpre

ssio

ns a

nd e

quat

ions

. The

y ar

e ex

pect

ed to

be

com

pete

nt in

per

form

ing

mul

tiple

ope

ratio

ns u

sing

dec

imal

frac

tions

and

mix

ed n

umbe

rs, a

pply

ing

prop

er- t

ies

of ra

tiona

l num

bers

appr

opria

tely.

The

y ar

e al

so e

xpec

ted

to re

cogn

ize

and

use

equi

vale

nt fo

rms

for d

ecim

al fr

actio

ns a

ppro

pria

tely

in c

alcu

latio

ns.

LTSM

Res

ourc

es

Num

ber l

ines

, fla

sh c

ards

, cha

rts.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

WB

1 Ac

tiviti

es (4

4 - 4

6)

W

B 1

Activ

ities

(R6a

&b )

WB

2 Ac

tiviti

es (7

1 - 7

4)

WB

1 Ac

tiviti

es

(R6;

16

- 17)

Text

book

refe

renc

e


HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

ass

essm

ent

– Te

st: m

arks

max

MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

3

TER

M 3

Dat

e : f

rom

....

to ..

....

Tim

e:

7 ho

urs

Gra

de

7 8

9 To

pic

DAT

A H

AND

LIN

G

CAP

S pa

ges

70 –

72

109

- 111

14

9 - 1

51

Or

gani

ze an

d su

mm

arize

data

Org

aniz

e (in

clud

ing

grou

ping

whe

re

appr

opria

te)

and

reco

rd d

ata

usin

g -

tally

mar

ks

- ta

bles

-

stem

-and

-leaf

dis

play

s

Gro

up d

ata

into

inte

rval

s

Sum

mar

ize

and

dist

ingu

ishi

ng b

etw

een

ungr

oupe

d nu

mer

ical

dat

a by

det

erm

inin

g:

- m

ean

Orga

nize

and

sum

mar

ize da

ta

O

rgan

ize

(incl

udin

g gr

oupi

ng w

here

ap

prop

riate

) and

reco

rd d

ata

usin

g -

tally

mar

ks

- ta

bles

-

stem

-and

-leaf

dis

play

s

Gro

up d

ata

into

inte

rval

s

Sum

mar

ize

data

usi

ng m

easu

res

of

cent

ral

tend

ency

, incl

udin

g:

- m

ean

- m

edia

n

Orga

nize

and

sum

mar

ize da

ta

O

rgan

ize

num

eric

al d

ata

in d

iffer

ent

way

s in

ord

er to

sum

mar

ize

by

dete

rmin

ing:

-

mea

sure

s of

cen

tral t

ende

ncy

- m

easu

res

of d

ispe

rsio

n, in

clud

ing

extre

mes

and

ou

tlier

s

Org

aniz

e da

ta a

ccor

ding

to m

ore

than

on

e cr

iteria


-

med

ian

- m

ode

Id

entif

y th

e la

rges

t and

sm

alle

st s

core

s in

a d

ata

set a

nd d

eter

min

e th

e di

ffere

nce

betw

een

them

in o

rder

to

dete

rmin

e th

e sp

read

of t

he d

ata

(rang

e)

Repr

esen

t da

ta •

Dra

w a

var

iety

of g

raph

s by

ha

nd/te

chno

logy

to d

ispl

ay a

nd

inte

rpre

t dat

a (g

roup

ed a

nd

ungr

oupe

d) i

nclu

ding

:

- ba

r gra

phs

and

doub

le b

ar g

raph

s

- hi

stog

ram

s w

ith g

iven

inte

rval

s

- pi

e ch

arts

Int

erpret

data

•

Crit

ical

ly re

ad a

nd in

terp

ret d

ata

repr

esen

ted

in:

-

wor

ds

-

bar g

raph

s

- do

uble

bar

gra

phs

-

pie

char

ts

-

hist

ogra

ms

- m

ode

Su

mm

ariz

e da

ta u

sing

mea

sure

s of

di

sper

sion

, inc

ludi

ng:

- ra

nge

- ex

trem

es

Repr

esen

t da

ta •

Dra

w a

var

iety

of g

raph

s by

ha

nd/te

chno

logy

to d

ispl

ay a

nd

inte

rpre

t dat

a in

clud

ing:

- ba

r gra

phs

and

doub

le b

ar g

raph

s

- hi

stog

ram

s w

ith g

iven

and

ow

n in

terv

als

-

pie

char

ts

-

brok

en-li

ne g

raph

s Int

erpret

data

•

Crit

ical

ly re

ad a

nd in

terp

ret d

ata

repr

esen

ted

in:

-

wor

ds

-

bar g

raph

s

- do

uble

bar

gra

phs

-

pie

char

ts

-

hist

ogra

ms

-

brok

en-li

ne g

raph

s

Repr

esen

t da

ta •

Dra

w a

var

iety

of g

raph

s by

ha

nd/te

chno

logy

to d

ispl

ay a

nd

inte

rpre

t dat

a in

clud

ing:

- ba

r gra

phs

and

doub

le b

ar g

raph

s

- hi

stog

ram

s w

ith g

iven

and

ow

n in

terv

als

-

pie

char

ts

-

brok

en-li

ne g

raph

s -

scat

ter p

lots

Int

erpret

data

•

Crit

ical

ly re

ad a

nd in

terp

ret d

ata

repr

esen

ted

in a

var

iety

of w

ays

• C

ritic

ally

com

pare

two

sets

of d

ata

rela

ted

to th

e sa

me

issu

e


Analy

se d

ata

• C

ritic

ally

ana

lyse

dat

a by

ans

wer

ing

ques

tions

rela

ted

to:

-

data

cat

egor

ies,

incl

udin

g da

ta

inte

rval

s

- da

ta s

ourc

es a

nd c

onte

xts

-

cent

ral t

ende

ncie

s (m

ean,

mod

e,

med

ian)

- sc

ales

use

d on

gra

phs

Repo

rt da

ta •

Sum

mar

ize

data

in s

hort

para

grap

hs th

at

incl

ude

-

draw

ing

conc

lusi

ons

abou

t the

dat

a

- m

akin

g pr

edic

tions

bas

ed o

n th

e da

ta

-

iden

tifyi

ng s

ourc

es o

f erro

r and

bia

s in

th

e da

ta

-

choo

sing

app

ropr

iate

sum

mar

y st

atis

tics

for t

he

data

(mea

n, m

edia

n, m

ode)

Analy

se d

ata

• C

ritic

ally

ana

lyse

dat

a by

ans

wer

ing

ques

tions

rela

ted

to:

-

data

cat

egor

ies,

incl

udin

g da

ta

inte

rval

s

- da

ta s

ourc

es a

nd c

onte

xts

-

cent

ral t

ende

ncie

s (m

ean,

mod

e,

med

ian)

- sc

ales

use

d on

gra

phs

-

sam

ples

and

pop

ulat

ions

- di

sper

sion

of d

ata

-

erro

r and

bia

s in

the

data

Re

port

data

• Su

mm

ariz

e da

ta in

sho

rt pa

ragr

aphs

that

in

clud

e

- dr

awin

g co

nclu

sion

s ab

out t

he d

ata

-

mak

ing

pred

ictio

ns b

ased

on

the

data

- id

entif

ying

sou

rces

of e

rror a

nd b

ias

in

the

data

- ch

oosi

ng a

ppro

pria

te s

umm

ary

stat

istic

s fo

r the

dat

a (m

ean,

med

ian,

m

ode,

rang

e)

-

the

role

of e

xtre

mes

in th

e da

ta

Analy

se d

ata

• C

ritic

ally

ana

lyse

dat

a by

ans

wer

ing

ques

tions

rela

ted

to:

-

data

col

lect

ion

met

hods

- su

mm

ary o

f dat

a

- so

urce

s of

erro

r and

bia

s in

the

data

Re

port

data

• Su

mm

ariz

e da

ta in

sho

rt pa

ragr

aphs

that

in

clud

e

- dr

awin

g co

nclu

sion

s ab

out t

he d

ata

-

mak

ing

pred

ictio

ns b

ased

on

the

data

- m

akin

g co

mpa

rison

s be

twee

n tw

o se

ts

of d

ata

-

iden

tifyi

ng s

ourc

es o

f erro

r and

bia

s in

th

e da

ta

-

choo

sing

app

ropr

iate

sum

mar

y st

atis

tics

for t

he

data

(mea

n, m

edia

n, m

ode,

ra

nge)

- th

e ro

le o

f ext

rem

es a

nd o

utlie

rs in

the

data


Sugg

este

d m

etho

dolo

gy

The

follo

win

g ar

e ne

w in

Gra

de 7

•

sam

ples

and

pop

ulat

ions

•

mul

tiple

cho

ice

ques

tionn

aire

s •

stem

-and

-leaf

dis

play

s •

grou

ping

dat

a in

inte

rval

s •

mea

n •

rang

e •

hist

ogra

ms

• sc

ales

on

grap

hs

Data

sets

and c

ontex

ts Le

arne

rs s

houl

d be

exp

osed

to a

var

iety

of c

onte

xts

that

dea

l with

soc

ial a

nd e

nviro

nmen

tal i

ssue

s, a

nd s

houl

d w

ork

with

giv

en d

ata

sets

, rep

rese

nted

in a

var

iety

of w

ays,

that

incl

ude

big

num

ber r

ange

s, p

erce

ntag

es a

nd d

ecim

al fr

actio

ns. L

earn

ers

shou

ld th

en

prac

tice

orga

nizi

ng a

nd s

umm

ariz

ing

this

dat

a, a

naly

sing

and

inte

rpre

ting

the

data

, and

writ

ing

a re

port

abou

t the

dat

a Co

mplet

e a d

ata cy

cle

Lear

ners

sho

uld

com

plet

e at

leas

t one

dat

a cy

cle

for t

he y

ear,

star

ting

with

pos

ing

thei

r ow

n qu

estio

ns, s

elec

ting

the

sour

ces

and

met

hod

for c

olle

ctin

g da

ta, r

ecor

ding

the

data

, org

aniz

ing

the

data

, rep

rese

ntin

g th

e da

ta, t

hen

anal

ysin

g,

sum

mar

izin

g, in

terp

retin

g an

d re

porti

ng th

e da

ta. C

halle

nge

lear

ners

to th

ink

abou

t wha

t kin

ds o

f que

stio

ns a

nd d

ata

need

to b

e co

llect

ed

to b

e re

pres

ente

d in

a h

isto

gram

, pie

cha

rt, b

ar g

raph

or a

line

grap

h.

Repr

esen

ting

data

• D

raw

ing

pie

char

ts to

repr

esen

t dat

a do

not

hav

e to

be

accu

rate

ly d

raw

n w

ith a

com

pass

and

pro

tract

or, e

tc. L

earn

ers

can

use

any

roun

d ob

ject

to d

raw

a c

ircle

, the

n di

vide

the

circ

le in

to h

alve

s an

d qu

arte

rs a

nd e

ight

hs if

nee

ded,

as

a gu

ide

to e

stim

ate

the

prop

ortio

ns o

f the

circ

le th

at n

eed

to b

e sh

own

to re

pres

ent t

he d

ata.

Wha

t is

impo

rtant

is th

at th

e va

lues

or p

erce

ntag

es a

ssoc

iate

d w

ith th

e da

ta, a

re s

how

n pr

opor

tiona

lly o

n th

e pi

e ch

art.

D

raw

ing,

read

ing

and

inte

rpre

ting

pie

char

ts is

a u

sefu

l con

text

to re

-vis

it eq

uiva

lenc

e be

twee

n fra

ctio

ns a

nd p

erce

ntag

es, e

.g. 2

5% o

f th

e da

ta is

repr

esen

ted

by a

1 4 se

ctor

of t

he c

ircle

.


• It

is a

lso

a co

ntex

t in

whi

ch le

arne

rs c

an fi

nd p

erce

ntag

es o

f who

le n

umbe

rs e

.g. i

f 25%

of 3

00 le

arne

rs li

ke ru

gby,

how

man

y (a

ctua

l nu

mbe

r) le

arne

rs li

ke ru

gby?

•

His

togr

ams

are

used

to re

pres

ent g

roup

ed d

ata

show

n in

inte

rval

s on

the

horiz

onta

l axi

s of

the

grap

h. P

oint

out

the

diffe

renc

es

betw

een

hist

ogra

ms

and

bar g

raph

s, in

par

ticul

ar b

ar g

raph

s th

at re

pres

ent d

iscr

ete

data

(e.g

. fav

ourit

e sp

orts

) com

pare

d to

hi

stog

ram

s th

at s

how

cat

egor

ies

in c

onse

cutiv

e, n

on- o

verla

ppin

g in

terv

als,

(e.g

. tes

t sco

res

out o

f 100

sho

wn

in in

terv

als

of 1

0). T

he

bars

on

bar g

raph

s do

not

hav

e to

touc

h ea

ch o

ther

, whi

le in

a h

isto

gram

they

hav

e to

touc

h si

nce

they

sho

w c

onse

cutiv

e in

terv

als.

De

velop

ing c

ritica

l ana

lysis

skills

•

Lear

ners

sho

uld

com

pare

the

sam

e da

ta re

pres

ente

d in

diff

eren

t way

s e.

g. in

a p

ie c

hart

or a

bar

gra

ph o

r a ta

ble,

and

dis

cuss

wha

t in

form

atio

n is

sho

wn

and

wha

t is

hidd

en; t

hey

shou

ld e

valu

ate

wha

t for

m o

f rep

rese

ntat

ion

wor

ks b

est f

or th

e gi

ven

data

. •

Lear

ners

sho

uld

com

pare

gra

phs

on th

e sa

me

topi

c bu

t whe

re d

ata

has

been

col

lect

ed fr

om d

iffer

ent g

roup

s of

peo

ple,

at d

iffer

ent

times

, in

diffe

rent

pla

ces

or in

diff

eren

t way

s. H

ere

lear

ners

sho

uld

disc

uss

diffe

renc

es b

etw

een

the

data

with

an

awar

enes

s of

bia

s re

late

d to

the

impa

ct o

f dat

a so

urce

s an

d m

etho

ds o

f dat

a co

llect

ion

on th

e in

terp

reta

tion

of th

e da

ta.

• Le

arne

rs s

houl

d co

mpa

re d

iffer

ent w

ays

of s

umm

aris

ing

the

sam

e da

ta s

ets,

dev

elop

ing

an a

war

enes

s of

how

dat

a re

porti

ng c

an b

e m

anip

ulat

ed; e

valu

atin

g w

hich

sum

mar

y st

atis

tics

best

repr

esen

t the

dat

a.

• Le

arne

rs s

houl

d co

mpa

re g

raph

s of

the

sam

e da

ta, w

here

the

scal

es o

f the

gra

phs

are

diffe

rent

. Her

e le

arne

rs s

houl

d di

scus

s di

ffere

nces

with

an

awar

enes

s of

how

repr

esen

tatio

n of

dat

a ca

n be

man

ipul

ated

; the

y sh

ould

eva

luat

e w

hich

form

of

repr

esen

tatio

n w

orks

bes

t for

the

give

n da

ta.

Lear

ners

sho

uld

writ

e re

ports

on

the

data

in s

hort

para

grap

hs.

Gra

de 8

W

hat is

diffe

rent

to G

rade

7?

The

follo

win

g ar

e ne

w in

Gra

de 8

•

extre

mes

•

brok

en li

ne g

raph

s •

disp

ersi

on o

f dat

a •

erro

r and

bia

s in

dat

a

.


Repr

esen

ting

data

• Br

oken

-line

gra

phs

refe

r to

dat

a gr

aphs

that

rep

rese

nt d

ata

poin

ts jo

ined

by

a lin

e an

d ar

e no

t the

sam

e as

stra

ight

line

gra

phs

that

are

dra

wn

usin

g th

e eq

uatio

n of

the

line.

•

Brok

en-li

ne g

raph

s ar

e us

ed to

repr

esen

t dat

a th

at c

hang

es c

ontin

uous

ly o

ver t

ime,

e.g

. ave

rage

dai

ly te

mpe

ratu

re fo

r a m

onth

. Ea

ch d

ay’s

tem

pera

ture

is re

pres

ente

d w

ith a

poi

nt o

n th

e gr

aph,

and

onc

e th

e w

hole

mon

th h

as b

een

plot

ted,

the

poin

ts a

re jo

ined

to

sho

w a

bro

ken-

line

grap

h.

• Br

oken

-line

gra

phs

are

usef

ul to

read

‘tre

nds’

and

pat

tern

s in

the

data

, for

pre

dict

ive

purp

oses

e.g

. will

the

tem

pera

ture

s go

up

or

dow

n in

the

next

mon

th.

Deve

loping

crit

ical a

nalys

is sk

ills

. • Le

arne

rs s

houl

d co

mpa

re d

ata

on th

e sa

me

topi

c, w

here

one

set

of d

ata

has

extre

mes

, and

dis

cuss

diff

eren

ces

with

an

awar

enes

s of

the

effe

ct o

f the

ext

rem

es o

n th

e in

terp

reta

tion

of th

e da

ta, i

n pa

rticu

lar,

extre

mes

affe

ct th

e ra

nge.

•

Lear

ners

sho

uld

writ

e re

ports

on

the

data

in s

hort

para

grap

hs.

Gra

de 9

W

hat is

diffe

rent

to G

rade

8?

• O

rgan

izin

g da

ta a

ccor

ding

to m

ore

than

one

crit

eria

•

Out

liers

•

Scat

ter p

lots

Co

mplet

e a d

ata cy

cle

Al

l wha

t is

done

gra

de 8

plu

s sc

atte

r plo

t. Re

pres

entin

g da

ta


All w

hat i

s do

ne in

gra

de 7

and

8 in

clud

ing

wha

t is

men

tione

d be

low

•

A sc

atte

r plo

t is

used

to re

pres

ent d

ata

that

invo

lves

two

diffe

rent

crit

eria

and

the

grap

h is

use

d to

look

at t

he re

latio

nshi

p be

twee

n th

e tw

o cr

iteria

. e.g

. How

doe

s th

e pe

rform

ance

of l

earn

ers

in m

athe

mat

ics

com

pare

to th

eir p

erfo

rman

ce in

Eng

lish?

Eac

h po

int o

n th

e gr

aph

repr

esen

ts th

e re

sults

of o

ne le

arne

r in

Mat

hem

atic

s an

d En

glis

h. A

fter a

ll th

e re

sults

hav

e be

en p

lotte

d, y

ou c

an c

ompa

re th

e re

latio

nshi

p be

twee

n pe

rform

ance

in E

nglis

h an

d m

athe

mat

ics

for a

ll th

e le

arne

rs i.

e. if

they

sco

re h

igh

in M

athe

mat

ics,

do

they

als

o sc

ore

high

in E

nglis

h? o

r, if

they

sco

re h

igh

in m

athe

mat

ics

do th

ey s

core

low

in E

nglis

h, o

r is

ther

e no

rela

tions

hip

betw

een

wha

t the

y sc

ore

on m

athe

mat

ics

to w

hat t

hey

scor

e in

Eng

lish?

•

The

scat

ter p

lot a

llow

s on

e to

see

tren

ds a

nd m

ake

pred

ictio

ns, a

s w

ell a

s id

entif

y ou

tlier

s in

the

data

.

LT

SM

Res

ourc

es

Cha

rts, s

quar

e pa

pers

, col

our p

ens.

G

rade

7

G

rade

8

Gra

de 9

Wor

kboo

k re

fere

nce

WB

1 Ac

tiviti

es (R

15,1

6)

WB

2 A

ctiv

ities

(126

- 14

0)

WB

1 Ac

tiviti

es (R

16a&

b)

WB

2 Ac

tiviti

es (9

2 - 1

04)

WB

1 Ac

tiviti

es (R

16a&

b)

WB

2 Ac

tiviti

es

(123

– 1

43)

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

4

TER

M 3

Dat

e : f

rom

....

to ..

....

T

ime:

5 h

ours

G

rade

7

8 9

Topi

c 2D

GEO

MET

RY

& P

RO

PER

TIES

OF

TRIA

NG

LES

AND

TH

EOR

EM O

F PY

THAG

OR

AS

CAP

S pa

ges

46 a

nd 5

5 10

5 13

8 Sk

ills a

nd K

now

ledg

e Cl

assif

ying

2D s

hape

s

Des

crib

e, s

ort,

nam

e an

d co

mpa

re

trian

gles

acc

ordi

ng to

thei

r sid

es

and

angl

es, f

ocus

ing

on:

- eq

uila

tera

l tria

ngle

s -

isos

cele

s tri

angl

es

- rig

ht-a

ngle

d tri

angl

es

U

se a

ppro

pria

te fo

rmul

ae to

cal

cula

te

the

area

of:

- sq

uare

s -

rect

angl

es

- tri

angl

es

Deve

lop

and

use

the

theo

rem

of P

ythag

oras

Inve

stig

ate

the

rela

tions

hip

betw

een

the

leng

ths

of th

e si

des

of a

rig

ht-

angl

ed

trian

gle

to

deve

lop

the

Theo

rem

of P

ytha

gora

s

Det

erm

ine

whe

ther

a tr

iang

le is

a

right

-ang

led

trian

gle

or n

ot if

the

leng

th o

f the

thre

e si

des

of th

e tri

angl

e ar

e kn

own

U

se th

e Th

eore

m o

f Pyt

hago

ras

to

calc

ulat

e a

mis

sing

leng

th in

a ri

ght-

angl

ed tr

iang

le, l

eavi

ng ir

ratio

nal

answ

ers

in s

urd

form

Solve

pro

blem

s us

ing

the

theo

rem

of

Pyth

agor

as

U

se th

e Th

eore

m o

f Pyt

hago

ras

to

solv

e pr

oble

ms

invo

lvin

g un

know

n le

ngth

s in

geo

met

ric fi

gure

s th

at

cont

ain

right

-ang

led

trian

gles

Sugg

este

d m

etho

dolo

gy

Trian

gles

Le

arne

rs s

houl

d be

abl

e to

dis

tingu

ish

betw

een

an e

quila

tera

l tria

ngle

(all

the

side

s ar

e eq

ual),

an

isos

cele

s tri

angl

e (a

t lea

st

two

equa

l sid

es) a

nd a

righ

t- an

gled

tria

ngle

(one

righ

t-ang

le).

Form

ulae

lear

ners

sho

uld

know

and

use

are

:

- ar

ea o

f a s

quar

e =

l2

- ar

ea o

f a re

ctan

gle

= l x

b

- Ar

ea of

a tri

angle

= 1 2

(b×

h)


Gra

de 8

and

9

Th

e th

eore

m o

f Pyt

hago

ras

is n

ew in

Gra

de 8

.

It

is im

porta

nt th

at le

arne

rs u

nder

stan

d th

at th

e Th

eore

m o

f Pyt

hago

ras

appl

ies

only

to ri

ght-a

ngle

d tri

angl

es.

Th

e Th

eore

m o

f Pyt

hago

ras

is b

asic

ally

a fo

rmul

a to

cal

cula

te u

nkno

wn

leng

th o

f sid

es in

righ

t-ang

led

trian

gles

.

In

the

FET

phas

e, th

e Th

eore

m o

f Pyt

hago

ras

is c

ruci

al to

the

furth

er s

tudy

of G

eom

etry

and

Trig

onom

etry

In

par

ticul

ar, t

he T

heor

em o

f Pyt

hago

ras

can

be th

e fir

st s

tep

in c

alcu

latio

ns o

f per

imet

ers

or a

reas

of c

ompo

site

figu

res,

whe

n

one

of th

e fig

ures

is a

righ

t-ang

led

trian

gle

with

an

unkn

own

leng

th.

G

rade

9 w

ill so

lve

prob

lem

s in

volv

ing

geom

etric

figu

res

LT

SM

Res

ourc

es

Cha

rts w

ith p

ictu

res

and

shap

es.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

WB

1 Ac

tiviti

es (R

10)

WB

2 (1

42)

WB

2 Ac

tiviti

es (7

7- 8

1)

W

B 1

Activ

ities

(58;

59)

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

GR

ADE

LESS

ON

PLA

N 5

TER

M 3

Dat

e : f

rom

....

to ..

....

Ti

me:

7 h

ours

G

rade

7

8 9

Topi

c AR

EA A

ND

PER

IMET

ER O

F 2D

SH

APES

C

APS

page

s 56

10

6 - 1

07

139

- 140

Sk

ills a

nd K

now

ledg

e Ar

ea an

d per

imete

r

Cal

cula

te th

e pe

rimet

er o

f re

gula

r and

irre

gula

r pol

ygon

s

U

se a

ppro

pria

te fo

rmul

ae to

ca

lcul

ate

perim

eter

and

are

a of

: -

squa

res

- re

ctan

gles

-

trian

gles

Ca

lculat

ions a

nd so

lving

prob

lems

• So

lve

prob

lem

s in

volv

ing

perim

eter

an

d ar

ea o

f pol

ygon

s

Area

and p

erim

eter

U

se a

ppro

pria

te fo

rmul

ae to

cal

cula

te

perim

eter

an

d ar

ea o

f: -

squa

res

- re

ctan

gles

-

trian

gles

-

circ

les

• C

alcu

late

the

area

s of

pol

ygon

s,

to a

t lea

st 2

dec

imal

pla

ces,

by

deco

mpo

sing

them

into

re

ctan

gles

and

/or t

riang

les

• U

se a

nd d

escr

ibe

the

rela

tions

hip

betw

een

the

radi

us,

diam

eter

and

circ

umfe

renc

e of

a

circ

le in

cal

cula

tions

• U

se a

nd d

escr

ibe

the

rela

tions

hip

betw

een

the

radi

us a

nd a

rea

of a

circ

le in

ca

lcul

atio

ns

Calcu

latio

ns an

d solv

ing pr

oblem

s •

Solv

e pr

oble

ms,

with

or w

ithou

t a

calc

ulat

or, i

nvol

ving

per

imet

er

and

area

of p

olyg

ons

and

circ

les

Area

and p

erim

eter

U

se a

ppro

pria

te fo

rmul

ae a

nd

conv

ersi

ons

betw

een

SI u

nits

, to

solv

e pr

oble

ms

and

calc

ulat

e pe

rimet

er a

nd a

rea

of:

- po

lygo

ns

- ci

rcle

s

Inve

stig

ate

how

dou

blin

g an

y or

all

of th

e di

men

sion

s of

a 2

D fi

gure

af

fect

s its

per

imet

er a

nd it

s ar

ea


• C

alcu

late

to a

t lea

st 1

dec

imal

pla

ce

• U

se a

nd c

onve

rt be

twee

n ap

prop

riate

SI

uni

ts,

incl

udin

g:

-

mm

2 ↔

cm

2

- cm

2 ↔

m2

• C

alcu

late

to a

t lea

st 2

dec

imal

pla

ces

• U

se a

nd d

escr

ibe

the

mea

ning

of t

he

irrat

iona

l num

ber P

i (π

) in

calc

ulat

ions

in

volv

ing

circ

les

• U

se a

nd c

onve

rt be

twee

n ap

prop

riate

SI

uni

ts,

in

clud

ing:

mm

2 ↔

cm

2 ↔

m2 ↔

km

2 Su

gges

ted

met

hodo

logy

Fo

rmul

ae le

arne

rs s

houl

d kn

ow a

nd u

se a

re:

-

perim

eter

of a

squ

are

= 4s

-

perim

eter

of a

rect

angl

e =

2(l +

b) o

r 2l +

2b

- ar

ea o

f a s

quar

e =

l2

- ar

ea o

f a re

ctan

gle

= l x

b

- ar

ea o

f a tr

iang

le =

2

(b x

h)

Solvi

ng e

quati

ons

usin

g fo

rmula

e •

The

use

of fo

rmul

ae p

rovi

des

a co

ntex

t to

prac

tice

solv

ing

equa

tions

by

insp

ectio

n.

Exam

ple

1.

If

the

perim

eter

of a

squ

are

is 3

2 cm

wha

t is

the

leng

th o

f eac

h si

de?

Lear

ners

sho

uld

writ

e th

is a

s:

4s =

32

and

solv

e by

insp

ectio

n by

ask

ing:

4 ti

mes

wha

t will

be 3

2?

2.

If

the

area

of a

rect

angl

e is

200

cm

2 , a

nd it

s le

ngth

is 5

0 cm

wha

t is

its w

idth

? Le

arne

rs s

houl

d w

rite

this

as:

50

x b

= 20

and

sol

ve b

y in

spec

tion

by a

skin

g: 5

0 tim

es w

hat w

ill be

200

? Fo

r area

s of t

riang

les:

• M

ake

sure

lear

ners

kno

w th

at th

e he

ight

of a

tria

ngle

is a

line

seg

men

t dra

wn

from

any

ver

tex

perp

endi

cula

r to

the

oppo

site

sid

e.

• Po

int o

ut th

at e

very

tria

ngle

has

3 b

ases

, eac

h w

ith a

rela

ted

heig

ht o

r alti

tude

.


• Fo

r con

vers

ions,

note:

-

if 1

cm =

10

mm

then

1 c

m2

= 10

0 m

m2

- if

1 m

= 1

00 c

m th

en 1

m2

= 10

000

cm

2 G

rade

8

Wha

t is di

ffere

nt to

Gra

de 7?

•

Area

s of

pol

ygon

s by

dec

ompo

sitio

n •

Circ

umfe

renc

e an

d ar

ea o

f a c

ircle

•

Form

ulae

lear

ners

sho

uld

know

and

use

: -

diam

eter

of a

circ

le: d

= 2

r -

circ

umfe

renc

e of

circ

le: c

= π

d or

2π

r -

area

of a

circ

le: A

= π

r2

Solvi

ng e

quati

ons

usin

g fo

rmula

e Th

e us

e of

form

ulae

pro

vide

s a

cont

ext t

o pr

actis

e so

lvin

g eq

uatio

ns b

y in

spec

tion

or u

sing

add

itive

or m

ultip

licat

ive

inve

rses

Ci

rcles

•

mak

e su

re le

arne

rs c

an id

entif

y th

e ce

ntre

, rad

ius,

dia

met

er a

nd c

ircum

fere

nce

of th

e ci

rcle

. •

Spen

d tim

e in

vest

igat

ing

the

rela

tions

hip

betw

een

radi

us, c

ircum

fere

nce

and

diam

eter

, so

that

lear

ners

dev

elop

a s

ense

of

whe

re th

e irr

atio

nal n

umbe

r Pi (π

) is

deriv

ed fr

om.

• D

evel

op a

n un

ders

tand

ing

of π

, mak

ing

sure

lear

ners

und

erst

and

that

:

- π

repr

esen

ts th

e va

lue

of th

e ci

rcum

fere

nce

divi

ded

by th

e di

amet

er, f

or a

ny c

ircle

- π

is a

n irr

atio

nal n

umbe

r and

is g

iven

as

3,14

1 59

2 65

4 co

rrect

to 9

dec

imal

pl

aces

on

the

calc

ulat

or

722

or 3

,14

are

appr

oxim

ate

ratio

nal v

alue

s of

π in

eve

ryda

y us

e.


Gra

de 9

W

hat is

diffe

rent

to G

rade

8?

• Th

e ca

lcul

atio

ns a

re th

e sa

me

as in

Gra

de 8

, but

lear

ners

can

find

per

imet

ers

and

area

s of

mor

e co

mpo

site

and

com

plex

fig

ures

•

Poly

gons

can

incl

ude

trape

zium

s, p

aral

lelo

gram

s, rh

ombi

and

kite

s Fo

rmul

a fo

r lea

rner

s to

kno

w a

nd u

se.

𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴

𝑜𝑜𝑜𝑜 𝐴𝐴

𝐴𝐴ℎ𝑜𝑜𝑜𝑜

𝑜𝑜𝑜𝑜𝑜𝑜

=𝑙𝑙𝐴𝐴𝑙𝑙𝑙𝑙

𝑙𝑙ℎ ×

ℎ𝐴𝐴𝑒𝑒𝑙𝑙ℎ𝑙𝑙



𝑘𝑘𝑒𝑒𝑙𝑙𝐴𝐴

=1 2

(𝑑𝑑𝑒𝑒𝐴𝐴𝑙𝑙𝑜𝑜𝑙𝑙𝐴𝐴𝑙𝑙 1

×𝑑𝑑𝑒𝑒𝐴𝐴𝑙𝑙

𝑜𝑜𝑙𝑙𝐴𝐴𝑙𝑙

2)



𝑝𝑝𝐴𝐴𝐴𝐴𝐴𝐴𝑙𝑙𝑙𝑙𝐴𝐴𝑙𝑙𝑜𝑜𝑙𝑙𝐴𝐴𝐴𝐴𝑜𝑜

=𝑜𝑜𝐴𝐴𝑜𝑜𝐴𝐴

×ℎ𝐴𝐴𝑒𝑒𝑙𝑙ℎ𝑙𝑙



𝑙𝑙𝐴𝐴𝐴𝐴𝑝𝑝𝐴𝐴𝑡𝑡𝑒𝑒𝑜𝑜𝑜𝑜

=1 2

(𝑜𝑜𝑜𝑜𝑜𝑜

𝑜𝑜𝑜𝑜 𝑝𝑝𝐴𝐴

𝐴𝐴𝐴𝐴𝑙𝑙𝑙𝑙𝐴𝐴𝑙𝑙 𝑜𝑜𝑒𝑒𝑑𝑑𝐴𝐴)

×ℎ𝐴𝐴𝑒𝑒𝑙𝑙ℎ𝑙𝑙

Th

e us

e of

form

ulae

pro

vide

s a

cont

ext t

o pr

actis

e so

lvin

g eq

uatio

ns b

y in

spec

tion

or u

sing

add

itive

or m

ultip

licat

ive

inve

rses

. E

xpla

natio

n of

the

effe

ct o

f dou

blin

g of

any

dim

ensi

ons

of 2

D.

LT

SM

Res

ourc

es

Met

er s

tick,

trun

dle

whe

el, m

eter

stic

k, c

harts

, squ

are

pape

rs.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

WB

1 Ac

tiviti

es

(52

- 55)

WB

1 Ac

tiviti

es (R

14)

WB

2 Ac

tiviti

es

( 82

- 86)

WB

1 Ac

tiviti

es

(R14

; 60-

64)

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

6

TER

M 3

Dat

e : f

rom

....

to ..

....

Tim

e:

8 ho

urs

Gra

de

7 8

9 To

pic

SUR

FAC

E AR

EA A

ND

VO

LUM

E O

F 3D

C

APS

page

s 57

10

8 14

6 Sk

ills a

nd

Know

ledg

e Su

rface

area

and

volu

me

U

se a

ppro

pria

te fo

rmul

ae to

ca

lcul

ate

the

surfa

ce

area

, vol

ume

and

capa

city

of:

- cu

bes

- re

ctan

gula

r pris

ms

D

escr

ibe

the

inte

rrela

tions

hip

betw

een

surfa

ce a

rea

and

volu

me

of th

e ob

ject

s m

entio

ned

abov

e Ca

lculat

ions a

nd so

lving

prob

lems

So

lve

prob

lem

s in

volv

ing

surfa

ce a

rea,

vol

ume

and

capa

city

Surfa

ce ar

ea a

nd v

olume

Use

app

ropr

iate

form

ulae

to c

alcu

late

the

surfa

ce

area

, vol

ume

and

capa

city

of:

- cu

bes

- re

ctan

gula

r pris

ms

- tri

angu

lar p

rism

s

D

escr

ibe

the

inte

rrela

tions

hip

betw

een

surfa

ce a

rea

and

volu

me

of th

e ob

ject

s m

entio

ned

abov

e Ca

lculat

ions a

nd so

lving

prob

lems

So

lve

prob

lem

s, w

ith o

r with

out a

ca

lcul

ator

, inv

olvi

ng s

urfa

ce a

rea,

vo

lum

e an

d ca

paci

ty

Surfa

ce ar

ea a

nd v

olume

Use

app

ropr

iate

form

ulae

and

co

nver

sion

s be

twee

n SI

uni

ts to

sol

ve

prob

lem

s an

d ca

lcul

ate

the

surfa

ce

area

, vol

ume

and

capa

city

of:

- cu

bes

- re

ctan

gula

r pris

ms

- tri

angu

lar p

rism

s -

cylin

ders

Inve

stig

ate

how

dou

blin

g an

y or

all

the

dim

ensi

ons

of ri

ght p

rism

s an

d cy

linde

rs a

ffect

s th

eir v

olum

e


U

se a

nd c

onve

rt be

twee

n ap

prop

riate

SI u

nits

, in

clud

ing:

-

mm

2 ↔

cm

2 -

cm2

↔ m

2 -

mm

3 ↔

cm

3 -

cm3

↔ m

3

Use

equ

ival

ence

bet

wee

n un

its w

hen

solv

ing

prob

lem

s:

- 1

cm3

↔ 1

ml

- 1

m3

↔ 1

kl

U

se a

nd c

onve

rt be

twee

n ap

prop

riate

SI

units

, in

clud

ing:

-

mm

2 ↔

cm

2 ↔

m2

↔ k

m2

- m

m3

↔ c

m3

↔ m

3 -

ml (

cm3 )

↔ l

↔ k

l

Sugg

este

d m

etho

dolo

gy

Wha

t is di

ffere

nt to

Gra

de 6?

Fo

rmul

ae le

arne

rs s

houl

d kn

ow a

nd u

se:

- th

e vo

lum

e of

a p

rism

= th

e ar

ea o

f the

bas

e x

the

heig

ht

- th

e su

rface

are

a of

a p

rism

= th

e su

m o

f the

are

a of

all

its fa

ces

- th

e vo

lum

e of

a c

ube

= l3

- th

e vo

lum

e of

a re

ctan

gula

r pris

m =

l x

b x

h

Fo

r con

vers

ions

, not

e:

- if

1 cm

= 1

0 cm

then

1 c

m3

= 1

000

mm

3 an

d

- if

1 m

= 1

0 cm

then

1 m

3 =

1 00

0 00

0 m

m3

or 1

000

000

or 1

06 c

m3 .

- an

obj

ect w

ith a

vol

ume

of 1

cm

3 w

ill di

spla

ce e

xact

ly 1

ml o

f wat

er; a

nd

- an

obj

ect w

ith a

vol

ume

of 1

m3

will

disp

lace

exa

ctly

1 k

l of w

ater


Em

phas

ize

that

the

amou

nt o

f spa

ce in

side

a p

rism

is c

alle

d its

cap

acity

; and

the

amou

nt o

f spa

ce o

ccup

ied

by a

pris

m is

cal

led

its v

olum

e.

In

vest

igat

e th

e ne

ts o

f cub

es a

nd re

ctan

gula

r pris

ms

in o

rder

to d

educ

e fo

rmul

ae fo

r cal

cula

ting

thei

r sur

face

are

as.

Gra

de 8

Wha

t is di

ffere

nt to

Gra

de 7?

Surfa

ce a

rea

and

volu

me

of tr

iang

ular

pris

ms

Fo

rmul

ae le

arne

rs s

houl

d kn

ow a

nd u

se:

- th

e vo

lum

e of

a tr

iang

ular

pris

m =

(1b

x h)

x h

eigh

t of p

rism

Fo

r con

vers

ions

, not

e:

- if

1 cm

= 1

0 m

m th

en 1

cm

3 =

1 00

0 m

m3

and

- if

1 m

= 1

00 c

m th

en 1

m3

= 1

000

000

cm3

or 1

06 c

m3

- an

obj

ect w

ith a

vol

ume

of 1

cm

3 w

ill di

spla

ce e

xact

ly 1

ml o

f wat

er

- an

obj

ect w

ith a

vol

ume

of 1

m3

will

disp

lace

exa

ctly

1 k

l of w

ater

.

Em

phas

ize

that

the

amou

nt o

f spa

ce in

side

a p

rism

is c

alle

d its

cap

acity

; and

the

amou

nt o

f spa

ce o

ccup

ied

by a

pris

m is

cal

led

its v

olum

e.

In

vest

igat

e th

e ne

ts o

f cub

es a

nd re

ctan

gula

r pris

ms

in o

rder

to d

educ

e fo

rmul

ae fo

r cal

cula

ting

thei

r sur

face

are

as.


Gra

de 9

Wha

t is di

ffere

nt to

Gra

de 8?

Surfa

ce a

rea

and

volu

me

of c

ylin

ders

Fo

rmul

ae le

arne

rs s

houl

d kn

ow a

nd u

se:

- th

e vo

lum

e of

a c

ylin

der =

(πr2

) x th

e he

ight

of t

he c

ylin

der

Fo

r con

vers

ions

, not

e:

- if

1 cm

= 1

0 m

m th

en 1

cm

3 =

1 00

0 m

m3 ;

and

- if

1 m

= 1

00 c

m th

en 1

m3

= 1

000

000

or 1

06 c

m3

7

LTSM

Res

ourc

es

Empt

y bo

xes,

geo

solid

s, m

easu

ring

jugs

,cub

es.

G

rade

7

Gra

de 8

G

rade

9

Wor

kboo

k re

fere

nce

WB

1 Ac

tiviti

es

(56

- 64)

W

B 2

Activ

ity (1

43)

WB

1 Ac

tiviti

es (R

15a&

b)

WB

2 Ac

tiviti

es

(87

- 91)

WB

1 Ac

tiviti

es (R

15a&

b)

WB

2

Activ

ities

(1

00 –

104

)

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:


mar

ks m

ax

MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

7

TER

M 3

Dat

e : f

rom

....

to ..

....

T

ime:

4 ho

urs

G

rade

7

8 9

Topi

c G

RAP

HS

CAP

S pa

ges

65

114

145

Skills

and

Kn

owle

dge

Inte

rpre

ting

grap

hs

Anal

yse

and

inte

rpre

t glo

bal g

raph

s of

pr

oble

m s

ituat

ions

, with

spe

cial

focu

s on

the

follo

win

g tre

nds

and

feat

ures

:

linea

r or n

on-li

near

cons

tant

, inc

reas

ing

or d

ecre

asin

g D

raw

ing

grap

hs

Dra

w g

loba

l gra

phs

from

giv

en d

escr

iptio

ns o

f a

pro

blem

situ

atio

n, id

entif

ying

feat

ures

list

ed

abov

e

Inte

rpre

ting

grap

hs

Rev

ise

the

follo

win

g do

ne in

Gra

de 7

:

Anal

yse

and

inte

rpre

t glo

bal g

raph

s of

pr

oble

m s

ituat

ions

, with

a s

peci

al fo

cus

on th

e fo

llow

ing

trend

s an

d fe

atur

es:

♦♦

linea

r or n

on-li

near

♦

♦ co

nsta

nt, i

ncre

asin

g or

dec

reas

ing

Ex

tend

the

focu

s on

feat

ures

of g

raph

s to

incl

ude:

♦♦

max

imum

or m

inim

um

♦♦ d

iscr

ete

or c

ontin

uous

D

raw

ing

grap

hs

D

raw

glo

bal g

raph

s fro

m g

iven

de

scrip

tions

of a

pro

blem

situ

atio

n,

iden

tifyi

ng fe

atur

es li

sted

abo

ve

Inte

rpre

ting

grap

hs

Rev

ise

the

follo

win

g do

ne in

Gra

de 8

:

Anal

yse

and

inte

rpre

t glo

bal g

raph

s of

pr

oble

m s

ituat

ions

, with

a s

peci

al fo

cus

on th

e fo

llow

ing

trend

s an

d fe

atur

es:

♦♦ li

near

or n

on-li

near

♦♦

con

stan

t, in

crea

sing

or d

ecre

asin

g

♦♦

max

imum

or m

inim

um

♦♦ d

iscr

ete

or c

ontin

uous

Exte

nd th

e ab

ove

with

spe

cial

focu

s on

th

e fo

llow

ing

feat

ures

of l

inea

r gra

phs:

♦♦

x-in

terc

ept a

nd y

-inte

rcep

t

♦

♦ gr

adie

nt

Dra

win

g gr

aphs

R

evis

e th

e fo

llow

ing

done

in G

rade

8:

dr

aw g

loba

l gra

phs

from

giv

en

desc

riptio

ns o

f a p

robl

em s

ituat

ion,


U

se ta

bles

of o

rder

ed p

airs

to p

lot

poin

ts a

nd d

raw

gra

phs

on th

e C

arte

sian

pla

ne

iden

tifyi

ng fe

atur

es li

sted

abo

ve.

u

se ta

bles

of o

rder

ed p

airs

to p

lot p

oint

s an

d dr

aw g

raph

s on

the

Car

tesi

an p

lane

Exte

nd th

e ab

ove

with

a s

peci

al fo

cus

on:

♦♦

dra

win

g lin

ear g

raph

s fro

m g

iven

eq

uatio

ns

♦♦

det

erm

ine

equa

tions

from

giv

en

linea

r gra

phs

Sugg

este

d m

etho

dolo

gy

In th

e In

term

edia

te P

hase

lear

ners

enc

ount

ered

gra

phs

in th

e fo

rm o

f dat

a ba

r gra

phs

and

pie

char

ts. T

his

mea

ns th

ey d

o ha

ve s

ome

expe

rienc

e re

adin

g an

d in

terp

retin

g gr

aphs

. How

ever

, in

the

Seni

or P

hase

, the

y ar

e in

trodu

ced

to li

ne g

raph

s th

at s

how

func

tiona

l re

latio

nshi

ps d

escr

ibed

in te

rms

of d

epen

dent

and

inde

pend

ent v

aria

bles

. In

Gra

de 7

, the

focu

s is

on

draw

ing,

ana

lysi

ng a

nd in

terp

retin

g gl

obal

gra

phs

only

. Tha

t is,

lear

ners

do

not h

ave

to p

lot p

oint

s to

dra

w

grap

hs a

nd th

ey fo

cus

on th

e fe

atur

es o

f the

glo

bal r

elat

ions

hip

show

n in

the

grap

h.

Exam

ples

of c

onte

xts

for g

loba

l gra

phs

incl

ude:

the

rela

tions

hip

betw

een

time

and

dist

ance

trav

elle

d

the

rela

tions

hip

betw

een

tem

pera

ture

and

tim

e ov

er w

hich

it is

mea

sure

d

the

rela

tions

hip

betw

een

rain

fall

and

time

over

whi

ch it

is m

easu

red,

etc

. In

Gra

de 8

:

New

feat

ures

of g

loba

l gra

phs,

nam

ely,

max

imum

and

min

imum

; dis

cret

e an

d co

ntin

uous

, are

intro

duce

d

Lear

ners

plo

t poi

nts

to d

raw

gra

phs

See

Gra

de 7

abo

ve fo

r exa

mpl

es o

f con

text

s fo

r glo

bal g

raph

s.

Exam

ples

of d

raw

ing

grap

hs b

y pl

ottin

g po

ints

a)

C

ompl

ete

the

tabl

e of

ord

ered

pai

rs b

elow

for t

he e

quat

ion

y =

x +

3


Now

, plo

t the

abo

ve c

o-or

dina

te p

oint

s on

the

Car

tesi

an p

lane

. Joi

n po

ints

to fo

rm a

gra

ph.

b)

Com

plet

e th

e ta

ble

of o

rder

ed p

airs

bel

ow fo

r the

equ

atio

n y

= x

2 + 3

N

ow, p

lot t

he a

bove

co-

ordi

nate

poi

nts

on th

e C

arte

sian

pla

ne. J

oin

poin

ts to

form

a g

raph

. In

Gra

de 9

, •

x-in

terc

ept,

y-in

terc

ept a

nd g

radi

ent o

f lin

ear g

raph

s ar

e in

trodu

ced

• Le

arne

rs d

raw

line

ar g

raph

s fro

m g

iven

equ

atio

ns

• Th

ey d

eter

min

e eq

uatio

ns o

f lin

ear g

raph

s Le

arne

rs s

houl

d co

ntin

ue to

ana

lyse

and

inte

rpre

t gra

phs

of p

robl

em s

ituat

ions

. In

vest

igat

ing

linea

r gra

phs

To

ske

tch

linea

r gra

phs

from

giv

en e

quat

ions

, lea

rner

s sh

ould

firs

t dra

w u

p a

tabl

e of

ord

ered

pai

rs, t

hat i

nclu

des

the

inte

rcep

t poi

nts

(x; 0

) and

(0; y

), an

d th

en p

lotti

ng th

e po

ints

.

Lear

ners

sho

uld

inve

stig

ate

grad

ient

s by

com

parin






𝑎𝑎𝑣𝑣 b

etw

een

any

two

poin

ts o

n a

stra

ight

line

gra

ph.

Le

arne

rs s

houl

d al

so in

vest

igat

e th

e re

latio

nshi

p be

twee

n th

e va

lue

of th

e gr

adie

nt a

nd th

e co

effic

ient

of x

in th

e eq

uatio

n of

a s

traig

ht

line

grap

h.

Le

arne

rs s

houl

d co

mpa

re y

-inte

rcep

ts o

f lin

ear g

raph

s to

the

valu

e of

the

cons

tant

in th

e eq

uatio

n of

the

stra

ight

line

gra

ph.

Ex

ampl

es o

f lin

ear g

raph

s a)

Ske

tch

and

com

pare

the

grap

hs o

f: y

= 4

and

x =

4 b)

Ske

tch

and

com

pare

the

grap

hs o

f: y

= x

and

y =

–x

c) S

ketc

h an

d co

mpa

re th

e gr

aphs

of:

y =

2x; y

= 2

x +

1; y

= 2

x –

1 d)

Ske

tch

and

com

pare

the

grap

hs o

f: y

= 3x

; y =

4x;

y =

5x

e) S

ketc

h th

e gr

aphs

of:

y =

–3x

+ 2;

usi

ng th

e ta

ble

met

hod

f) D

eter

min

e th

e eq

uatio

n of

the

stra

ight

line

pas

sing

thro

ugh

the

follo

win

g po

ints

:


LTSM

Res

ourc

es

G

raph

pap

er, r

uler

s, c

olou

r pen

s.

G

rade

7

Gra

de 8

G

rade

9

W

orkb

ook

refe

renc

e

WB

2 Ac

tiviti

es (8

0 - 8

5)

W

B 2

Activ

ities

(114

- 12

0)

W

B 1

Activ

ities

(88

– 99

)

Text

book

re

fere

nce

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


LESS

ON P

LANS

: TER

M 4


LESS

ON

PLA

NS:

TER

M 4

MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

1

TER

M 4

Dat

e : f

rom

....

to ..

....

T

ime:

4 ho

urs

G

rade

7

8 9

Topi

c FU

NC

TIO

NS

AND

REL

ATIO

NSH

IPS

CAP

S pa

ges

62

88 -

89

129

Skills

and

Kn

owle

dge

Inpu

t and

out

put v

alue

s D

eter

min

e in

put v

alue

s, o

utpu

t val

ues

or ru

les

for

patte

rns

and

rela

tions

hips

usi

ng:

flo

w d

iagr

ams

ta

bles

form

ulae

Eq

uiva

lent

form

s D

eter

min

e, in

terp

ret a

nd ju

stify

equ

ival

ence

of

diffe

rent

des

crip

tions

of t

he s

ame

rela

tions

hip

or ru

le p

rese

nted

:

verb

ally

in fl

ow d

iagr

ams

in

tabl

es

by

form

ulae

by n

umbe

r sen

tenc

es

Inpu

t and

out

put v

alue

s D

eter

min

e in

put v

alue

s, o

utpu

t val

ues

or

rule

s fo

r pat

tern

s an

d re

latio

nshi

ps u

sing

:

flow

dia

gram

s

tabl

es

fo

rmul

ae

eq

uatio

ns

Equi

vale

nt fo

rms

• Det

erm

ine,

inte

rpre

t and

just

ify

equi

vale

nce

of d

iffer

ent d

escr

iptio

ns

of th

e sa

me

rela

tions

hip

or ru

le

pres

ente

d:

-- ve

rbal

ly

-- in

flow

dia

gram

s --

in ta

bles

--

by fo

rmul

ae

-- by

equ

atio

ns

Inpu

t and

out

put v

alue

s D

eter

min

e in

put v

alue

s, o

utpu

t val

ues

or

rule

s fo

r pat

tern

s an

d re

latio

nshi

ps u

sing

:

flow

dia

gram

s

tabl

es

fo

rmul

ae

eq

uatio

ns

Equi

vale

nt fo

rms

• Det

erm

ine,

inte

rpre

t and

just

ify

equi

vale

nce

of d

iffer

ent d

escr

iptio

ns o

f the

sa

me

rela

tions

hip

or ru

le

pres

ente

d:

ve

rbal

ly

in

flow

dia

gram

s

in ta

bles

by fo

rmul

ae

by

equ

atio

ns

by

gra

phs

on a

Car

tesi

an p

lane

Sugg

este

d m

etho

dolo

gy

In th

is p

hase

, it i

s us

eful

to b

egin

to s

peci

fy w

heth

er th

e in

put v

alue

s ar

e na

tura

l num

bers

, or i

nteg

ers

or ra

tiona

l num

bers

. Thi

s bu

ilds

lear

ners

’ aw

aren

ess

of th

e do

mai

n of

inpu

t val

ues.

Hen

ce, t

o fin

d ou

tput

val

ues,

lear

ners

sho

uld

be g

iven

the

rule

/form

ula

as w

ell a

s th

e do

mai

n of

the

inpu

t val

ues.

In

Gra

de 7

, the

focu

s is

on

findi

ng o

utpu

t val

ues

for g

iven

form

ulae

and

inpu

t val

ues.

Not

e, w

hen

lear

ners

find

inpu

t or o

utpu

t val

ues

for


give

n ru

les

or fo

rmul

ae, t

hey

are

actu

ally

find

ing

the

num

eric

al v

alue

of a

lgeb

raic

exp

ress

ions

usi

ng s

ubst

itutio

n.

Exam

ples

U

se th

e fo

rmul

a fo

r the

are

a of

a re

ctan

gle:

A =

l x

b to

cal

cula

te th

e fo

llow

ing:

a)

The

are

a, if

the

leng

th is

4 c

m a

nd th

e w

idth

is 2

cm

b)

The

leng

th, i

f the

are

a is

20

cm2

and

the

wid

th is

4 c

m

c) T

he w

idth

, if t

he a

rea

is 2

4 cm

2 an

d th

e le

ngth

is 8

cm

Le

arne

rs c

an w

rite

thes

e as

num

ber s

ente

nces

, and

sol

ve b

y in

spec

tion.

In

Gra

de 8

:

The

focu

s is

on

findi

ng in

put o

r out

put v

alue

s us

ing

give

n eq

uatio

ns

Th

e ru

les

and

num

ber p

atte

rns

for w

hich

lear

ners

hav

e to

find

inpu

t and

out

put v

alue

s ar

e ex

tend

ed to

incl

ude

patte

rns

with

m

ultip

licat

ion

and

divi

sion

of i

nteg

ers

and

num

bers

in e

xpon

entia

l for

m.

Flow

dia

gram

s ar

e re

pres

enta

tions

of f

unct

iona

l rel

atio

nshi

ps. H

ence

, whe

n us

ing

flow

dia

gram

s, th

e co

rresp

onde

nce

betw

een

inpu

t and

ou

tput

val

ues

shou

ld b

e cl

ear i

n its

repr

esen

tatio

nal f

orm

i.e.

the

first

inpu

t pro

duce

s th

e fir

st o

utpu

t; th

e se

cond

inpu

t pro

duce

s th

e se

cond

ou

tput

, etc

. Ex

ampl

es

a) U

se th

e gi

ven

rule

to c

alcu

late

the

valu

es o

f t fo

r eac

h va

lue

of p

, whe

re p

is a

nat

ural

num

ber.

In th

is k

ind

of fl

ow d

iagr

am, l

earn

ers

can

also

be

aske

d to

det

erm

ine

the

valu

e of

p fo

r a g

iven

t va

lue.

b)

Det

erm

ine

the

rule

for c

alcu

latin

g th

e ou

tput

val

ue fo

r eve

ry g

iven

inpu

t val

ue in

the

flow

dia

gram

bel

ow.


In

flow

dia

gram

s su

ch a

s th

ese,

mor

e th

an o

ne ru

le m

ight

be

poss

ible

to d

escr

ibe

the

rela

tions

hip

betw

een

inpu

t and

out

put v

alue

s. T

he

rule

s ar

e ac

cept

able

if th

ey m

atch

the

give

n in

put v

alue

s to

the

corre

spon

ding

out

put v

alue

s.

c) If

the

rule

for f

indi

ng y

in th

e ta

ble

belo

w is

y =

–3x

– 1

, cal

cula

te y

for t

he g

iven

x v

alue

s:

b)

Des

crib

e th

e re

latio

nshi

p be

twee

n th

e nu

mbe

rs in

the

top

row

and

bot

tom

row

in th

e ta

ble.

The

n w

rite

dow

n th

e va

lue

of m

and

n

In

tabl

es s

uch

as th

ese,

mor

e th

an o

ne ru

le m

ight

be

poss

ible

to d

escr

ibe

the

rela

tions

hip

betw

een

x an

d y

valu

es. T

he ru

les

are

acce

ptab

le if

they

mat

ch th

e gi

ven

inpu

t val

ues

to th

e co

rresp

ondi

ng o

utpu

t val

ues.

For

exa

mpl

e, th

e ru

le y

= x

–3

desc

ribes

the

rela

tions

hip

betw

een

the

x va

lues

and

giv

en y

val

ues.

To

find

m a

nd n

, lea

rner

s ha

ve to

sub

stitu

te th

e co

rresp

ondi

ng v

alue

s fo

r x o

r y in

th

e ru

le a

nd s

olve

the

equa

tion

by in

spec

tion.

In

Gra

de 9

, lea

rner

s co

nsol

idat

e w

ork

with

inpu

t and

out

put v

alue

s do

ne in

Gra

de 8

. The

y sh

ould

con

tinue

to fi

nd in

put o

r out

put v

alue

s in

flo

w d

iagr

ams,

tabl

es, f

orm

ulae

and

equ

atio

ns. L

earn

ers

shou

ld b

egin

to re

cogn

ize

equi

vale

nt re

pres

enta

tions

of t

he s

ame

rela

tions

hips

sh

own

as a

n eq

uatio

n, a

set

of o

rder

ed p

airs

in a

tabl

e or

on

a gr

aph.


Exam

ples

a)

If th

e ru

le fo

r fin

ding

in th

e ta

ble

belo

w is

y =

1 2 x +

1, d

eter

min

e th

e va

lues

of y

for t

he g

iven

x v

alue

s:

b

) Des

crib

e th

e re

latio

nshi

p be

twee

n th

e nu

mbe

rs in

the

top

row

and

thos

e in

the

botto

m ro

w in

the

tabl

e. T

hen

writ

e do

wn

the

valu

e of

m

and

n

In

tabl

es s

uch

as th

ese,

mor

e th

an o

ne ru

le m

ight

be

poss

ible

to d

escr

ibe

the

rela

tions

hip

betw

een

x an

d y

valu

es. T

he ru

les

are

acce

ptab

le if

they

mat

ch th

e gi

ven

inpu

t val

ues

to th

e co

rresp

ondi

ng o

utpu

t val

ues.

For

exa

mpl

e, th

e ru

le y

= 2

x –

3 de

scrib

es th

e re

latio

nshi

p be

twee

n th

e gi

ven

valu

es fo

r x a

nd y

. To

find

m a

nd n

, lea

rner

s ha

ve to

sub

stitu

te th

e co

rresp

ondi

ng v

alue

s fo

r x o

r y in

to th

e ru

le a

nd s

olve

the

equa

tion

by in

spec

tion.

LT

SM

Res

ourc

es

C

harts

.

G

rade

7

Gra

de 8

Gra

de 9

Wor

kboo

k re

fere

nce

W

B 1

Activ

ities

(48

- 51)

W

B 2

Activ

ities

(72

– 73

)

WB

2 Ac

tiviti

es (7

2 - 7

3)

Text

book

re

fere

nce


HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

2

TER

M 4

Dat

e : f

rom

....

to ..

....

T

ime:

4 ho

urs

G

rade

7

8 9

Topi

c G

RAP

HS

CAP

S pa

ges

65

114

145

Skills

and

Kn

owle

dge

Inte

rpre

ting

grap

hs

Anal

yse

and

inte

rpre

t glo

bal g

raph

s of

pr

oble

m s

ituat

ions

, with

spe

cial

focu

s on

the

follo

win

g tre

nds

and

feat

ures

:

linea

r or n

on-li

near

cons

tant

, inc

reas

ing

or d

ecre

asin

g D

raw

ing

grap

hs

Dra

w g

loba

l gra

phs

from

giv

en d

escr

iptio

ns o

f a

pro

blem

situ

atio

n, id

entif

ying

feat

ures

list

ed

abov

e

Inte

rpre

ting

grap

hs

Rev

ise

the

follo

win

g do

ne in

Gra

de 7

:

Anal

yse

and

inte

rpre

t glo

bal g

raph

s of

pr

oble

m s

ituat

ions

, with

a s

peci

al fo

cus

on th

e fo

llow

ing

trend

s an

d fe

atur

es:

♦♦

linea

r or n

on-li

near

♦

♦ co

nsta

nt, i

ncre

asin

g or

dec

reas

ing

Ex

tend

the

focu

s on

feat

ures

of g

raph

s to

incl

ude:

♦♦

max

imum

or m

inim

um

♦♦ d

iscr

ete

or c

ontin

uous

D

raw

ing

grap

hs

D

raw

glo

bal g

raph

s fro

m g

iven

de

scrip

tions

of a

pro

blem

situ

atio

n,

iden

tifyi

ng fe

atur

es li

sted

abo

ve

U

se ta

bles

of o

rder

ed p

airs

to p

lot

poin

ts a

nd d

raw

gra

phs

on th

e C

arte

sian

pla

ne

Inte

rpre

ting

grap

hs

Rev

ise

the

follo

win

g do

ne in

Gra

de 8

:

Anal

yse

and

inte

rpre

t glo

bal g

raph

s of

pr

oble

m s

ituat

ions

, with

a s

peci

al fo

cus

on th

e fo

llow

ing

trend

s an

d fe

atur

es:

♦♦ li

near

or n

on-li

near

♦♦

con

stan

t, in

crea

sing

or d

ecre

asin

g

♦♦

max

imum

or m

inim

um

♦♦ d

iscr

ete

or c

ontin

uous

Exte

nd th

e ab

ove

with

spe

cial

focu

s on

th

e fo

llow

ing

feat

ures

of l

inea

r gra

phs:

♦♦

x-in

terc

ept a

nd y

-inte

rcep

t

♦

♦ gr

adie

nt

Dra

win

g gr

aphs

R

evis

e th

e fo

llow

ing

done

in G

rade

8:

dr

aw g

loba

l gra

phs

from

giv

en

desc

riptio

ns o

f a p

robl

em s

ituat

ion,

id

entif

ying

feat

ures

list

ed a

bove

.

use

tabl

es o

f ord

ered

pai

rs to

plo

t poi

nts

and

draw

gra

phs

on th

e C

arte

sian

pla

ne

Ex

tend

the

abov

e w

ith a

spe

cial

focu

s on

:

♦♦

dra

win

g lin

ear g

raph

s fro

m g

iven

eq

uatio

ns

♦♦ d

eter

min

e eq

uatio

ns fr

om g

iven

lin

ear g

raph

s


Sugg

este

d m

etho

dolo

gy

In th

e In

term

edia

te P

hase

lear

ners

enc

ount

ered

gra

phs

in th

e fo

rm o

f dat

a ba

r gra

phs

and

pie

char

ts. T

his

mea

ns th

ey d

o ha

ve s

ome

expe

rienc

e re

adin

g an

d in

terp

retin

g gr

aphs

. How

ever

, in

the

Seni

or P

hase

, the

y ar

e in

trodu

ced

to li

ne g

raph

s th

at s

how

func

tiona

l re

latio

nshi

ps d

escr

ibed

in te

rms

of d

epen

dent

and

inde

pend

ent v

aria

bles

. In

Gra

de 7

, the

focu

s is

on

draw

ing,

ana

lysi

ng a

nd in

terp

retin

g gl

obal

gra

phs

only

. Tha

t is,

lear

ners

do

not h

ave

to p

lot p

oint

s to

dra

w

grap

hs a

nd th

ey fo

cus

on th

e fe

atur

es o

f the

glo

bal r

elat

ions

hip

show

n in

the

grap

h.

Exam

ples

of c

onte

xts

for g

loba

l gra

phs

incl

ude:

the

rela

tions

hip

betw

een

time

and

dist

ance

trav

elle

d

the

rela

tions

hip

betw

een

tem

pera

ture

and

tim

e ov

er w

hich

it is

mea

sure

d

the

rela

tions

hip

betw

een

rain

fall

and

time

over

whi

ch it

is m

easu

red,

etc

. In

Gra

de 8

:

New

feat

ures

of g

loba

l gra

phs,

nam

ely,

max

imum

and

min

imum

; dis

cret

e an

d co

ntin

uous

, are

intro

duce

d

Lear

ners

plo

t poi

nts

to d

raw

gra

phs

See

Gra

de 7

abo

ve fo

r exa

mpl

es o

f con

text

s fo

r glo

bal g

raph

s.

Exam

ples

of d

raw

ing

grap

hs b

y pl

ottin

g po

ints

c)

C

ompl

ete

the

tabl

e of

ord

ered

pai

rs b

elow

for t

he e

quat

ion

y =

x +

3

N

ow, p

lot t

he a

bove

co-

ordi

nate

poi

nts

on th

e C

arte

sian

pla

ne. J

oin

poin

ts to

form

a g

raph

. d)

C

ompl

ete

the

tabl

e of

ord

ered

pai

rs b

elow

for t

he e

quat

ion

y =

x2 +

3


N

ow, p

lot t

he a

bove

co-

ordi

nate

poi

nts

on th

e C

arte

sian

pla

ne. J

oin

poin

ts to

form

a g

raph

. In

Gra

de 9

, •

x-in

terc

ept,

y-in

terc

ept a

nd g

radi

ent o

f lin

ear g

raph

s ar

e in

trodu

ced

• Le

arne

rs d

raw

line

ar g

raph

s fro

m g

iven

equ

atio

ns

• Th

ey d

eter

min

e eq

uatio

ns o

f lin

ear g

raph

s Le

arne

rs s

houl

d co

ntin

ue to

ana

lyse

and

inte

rpre

t gra

phs

of p

robl

em s

ituat

ions

. In

vest

igat

ing

linea

r gra

phs

To

ske

tch

linea

r gra

phs

from

giv

en e

quat

ions

, lea

rner

s sh

ould

firs

t dra

w u

p a

tabl

e of

ord

ered

pai

rs, t

hat i

nclu

des

the

inte

rcep

t poi

nts

(x; 0

) and

(0; y

), an

d th

en p

lotti

ng th

e po

ints

.

Lear

ners

sho

uld

inve

stig

ate

grad

ient

s by

com

parin






𝑎𝑎𝑣𝑣 b

etw

een

any

two

poin

ts o

n a

stra

ight

line

gra

ph.

Le

arne

rs s

houl

d al

so in

vest

igat

e th

e re

latio

nshi

p be

twee

n th

e va

lue

of th

e gr

adie

nt a

nd th

e co

effic

ient

of x

in th

e eq

uatio

n of

a s

traig

ht

line

grap

h.

Le

arne

rs s

houl

d co

mpa

re y

-inte

rcep

ts o

f lin

ear g

raph

s to

the

valu

e of

the

cons

tant

in th

e eq

uatio

n of

the

stra

ight

line

gra

ph.

Ex

ampl

es o

f lin

ear g

raph

s a)

Ske

tch

and

com

pare

the

grap

hs o

f: y

= 4

and

x =

4 b)

Ske

tch

and

com

pare

the

grap

hs o

f: y

= x

and

y =

–x

c) S

ketc

h an

d co

mpa

re th

e gr

aphs

of:

y =

2x; y

= 2

x +

1; y

= 2

x –

1 d)

Ske

tch

and

com

pare

the

grap

hs o

f: y

= 3x

; y =

4x;

y =

5x

e) S

ketc

h th

e gr

aphs

of:

y =

–3x

+ 2;

usi

ng th

e ta

ble

met

hod

f) D

eter

min

e th

e eq

uatio

n of

the

stra

ight

line

pas

sing

thro

ugh

the

follo

win

g po

ints

:


LTSM

Res

ourc

es

G

raph

pap

ers,

rule

rs, c

olou

r pen

s.

G

rade

7

Gra

de 8

G

rade

9

W

orkb

ook

refe

renc

e

WB

2 Ac

tiviti

es (8

0 - 8

5)

W

B 2

Activ

ities

(114

- 12

0)

W

B 1

Activ

ities

(88

– 99

)

Text

book

re

fere

nce

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

3

TER

M 4

Dat

e: fr

om ..

......

to ..

......

Tim

e:

5

hour

s

Gra

de

7 8

9 To

pic

CO

NST

RU

CTI

ON

OF

GEO

MET

RIC

FIG

UR

ES

CAP

S pa

ges

45

95

134

Skills

and

Kno

wle

dge

Mea

surin

g an

gles

Ac

cura

tely

use

a p

rotra

ctor

to

mea

sure

and

cla

ssify

ang

les:

< 90

° (a

cute

ang

les)

Rig

ht-a

ngle

s

> 90

° (o

btus

e an

gles

)

Stra

ight

ang

les

>

180°

(ref

lex

angl

es)

Con

stru

ctio

ns

Accu

rate

ly c

onst

ruct

geo

met

ric

figur

es a

ppro

pria

tely

usi

ng c

ompa

ss,

rule

r and

pro

tract

or, i

nclu

ding

:

angl

es, t

o on

e de

gree

of

accu

racy

circ

les

pa

ralle

l lin

es

pe

rpen

dicu

lar l

ines

Con

stru

ctio

ns

Accu

rate

ly c

onst

ruct

geo

met

ric fi

gure

s ap

prop

riate

ly u

sing

a c

ompa

ss, r

uler

and

pr

otra

ctor

, inc

ludi

ng:

Bi

sect

ing

lines

and

ang

les

Pe

rpen

dicu

lar l

ines

at a

giv

en p

oint

or

from

a g

iven

poi

nt

Tr

iang

les

Q

uadr

ilate

rals

Angl

es o

f 30°

, 45°

and

60°

and

thei

r m

ultip

les

with

out u

sing

a p

rotra

ctor

In

vest

igat

ing

prop

ertie

s of

geo

met

ric

figur

es

Con

stru

ctio

ns

Ac

cura

tely

con

stru

ct g

eom

etric

figu

res

appr

opria

tely

usi

ng a

com

pass

, rul

er a

nd

prot

ract

or, i

nclu

ding

bis

ectin

g an

gles

of

a tri

angl

e

C

onst

ruct

ang

les

of 4

5°, 3

0°, 6

0°an

d th

eir m

ultip

les

with

out u

sing

a p

rotra

ctor

In

vest

igat

ing

prop

ertie

s of

geo

met

ric

figur

es


By c

onst

ruct

ion,

inve

stig

ate

the

angl

es in

a

trian

gle,

focu

sing

on:

the

sum

of t

he in

terio

r ang

les

of tr

iang

les

th

e si

ze o

f ang

les

in a

n eq

uila

tera

l tri

angl

e

the

side

s an

d ba

se a

ngle

s of

an

isos

cele

s tri

angl

e By

con

stru

ctio

n, in

vest

igat

e si

des

and

angl

es in

qua

drila

tera

ls, f

ocus

ing

on:

th

e su

m o

f the

inte

rior a

ngle

s of

qu

adril

ater

als

th

e si

des

and

oppo

site

ang

les

of

para

llelo

gram

s

By

con

stru

ctio

n, in

vest

igat

e th

e an

gles

in

a tri

angl

e, fo

cusi

ng o

n th

e re

latio

nshi

p be

twee

n th

e ex

terio

r ang

le o

f a tr

iang

le

and

its in

terio

r ang

les

By

con

stru

ctio

n, e

xplo

re th

e m

inim

um

cond

ition

s fo

r tw

o tri

angl

es to

be

cong

ruen

t

By c

onst

ruct

ion,

inve

stig

ate

side

s,

angl

es a

nd d

iago

nals

in q

uadr

ilate

rals

, fo

cusi

ng o

n th

e di

agon

als

of re

ctan

gles

, sq

uare

s, p

aral

lelo

gram

s, rh

ombi

and

ki

tes

By

con

stru

ctio

n ex

plor

e th

e su

m o

f the

in

terio

r ang

les

of p

olyg

ons

Sugg

este

d m

etho

dolo

gy

In G

rade

7, l

earn

ers

M

easu

re a

ngle

s w

ith a

pro

tract

or

D

o ge

omet

ric c

onst

ruct

ions

usi

ng a

com

pass

, rul

er a

nd p

rotra

ctor

M

easu

ring

angl

es

Le

arne

rs h

ave

to b

e sh

own

how

to p

lace

the

prot

ract

or o

n th

e ar

m o

f the

ang

le to

be

mea

sure

d.

Le

arne

rs a

lso

have

to le

arn

how

to re

ad th

e si

ze o

f ang

les

on a

pro

tract

or.

Con

stru

ctio

ns

C

onst

ruct

ions

pro

vide

a u

sefu

l con

text

to e

xplo

re o

r con

solid

ate

know

ledg

e of

ang

les

and

shap

es.

Le

arne

rs h

ave

to b

e sh

own

how

to u

se a

com

pass

to d

raw

circ

les,

alth

ough

they

mig

ht h

ave

done

this

in G

rade

6.

Le

arne

rs s

houl

d be

aw

are

that

the

cent

re o

f the

circ

le is

at t

he fi

xed

poin

t of t

he c

ompa

ss a

nd th

e ra

dius

of t

he c

ircle

is

depe

nden

t on

how

wid

e th

e co

mpa

ss is

ope

ned

up.

M

ake

sure

lear

ners

und

erst

and

that

arc

s ar

e pa

rts o

f the

circ

les

of a

par

ticul

ar ra

dius

.

Initi

ally

, lea

rner

s ha

ve to

be

give

n ca

refu

l ins

truct

ions

abo

ut h

ow to

do

the

cons

truct

ions

of t

he v

ario

us s

hape

s

O

nce

they

are

com

forta

ble

with

the

appa

ratu

s an

d ca

n do

the

cons

truct

ions

, the

y ca

n pr

actis

e by

dra

win

g pa

ttern

s, fo

r ex

ampl

e of

circ

les

or p

aral

lel l

ines

. In

Gra

de 8

, all

the

cons

truct

ions

are

new

. In

Gra

de 7

, lea

rner

s on

ly c

onst

ruct

ed a

ngle

s, p

erpe

ndic

ular

and

par

alle

l lin

es. G

rade

8

lear

ners

als

o us

e co

nstru

ctio

ns to

exp

lore

pro

perti

es o

f tria

ngle

s an

d qu

adril

ater

als


Con

stru

ctio

ns

C

onst

ruct

ions

pro

vide

a u

sefu

l con

text

to e

xplo

re o

r con

solid

ate

know

ledg

e of

ang

les

and

shap

es

M

ake

sure

lear

ners

are

com

pete

nt a

nd c

omfo

rtabl

e w

ith th

e us

e of

a c

ompa

ss a

nd k

now

how

to m

easu

re a

nd re

ad a

ngle

si

zes

on a

pro

tract

or

R

evis

e th

e co

nstru

ctio

ns o

f ang

les

if ne

cess

ary

befo

re p

roce

edin

g w

ith th

e ne

w c

onst

ruct

ions

Star

t with

the

cons

truct

ions

of l

ines

, so

that

lear

ners

can

firs

t exp

lore

ang

le re

latio

nshi

ps o

n st

raig

ht li

nes.

Whe

n co

nstru

ctin

g tri

angl

es le

arne

rs s

houl

d dr

aw o

n kn

own

prop

ertie

s an

d co

nstru

ctio

n of

circ

les.

Con

stru

ctio

n of

spe

cial

ang

les

with

out p

rotra

ctor

s ar

e do

ne b

y:

o bi

sect

ing

a rig

ht a

ngle

to g

et 4

5°

o dr

awin

g an

equ

ilate

ral t

riang

le to

get

60°

o

bise

ctin

g th

e an

gles

of a

n eq

uila

tera

l tria

ngle

to g

et 3

0°

In G

rade

9, l

earn

ers:

Bise

ct a

ngle

s in

a tr

iang

le

C

onst

ruct

30°

with

out a

pro

tract

or

In

vest

igat

ion

of n

ew p

rope

rties

of t

riang

les,

qua

drila

tera

ls a

nd p

olyg

ons

Con

stru

ctio

ns

Sam

e as

for G

rade

8.

LTSM

Res

ourc

es

Mat

hem

atic

al in

stru

men

ts, g

eom

etric

set

s, c

olou

r pen

s, c

harts

.

G

rade

7

Gra

de 8

Gra

de 9

Wor

kboo

k re

fere

nce

W

B-1

Act

iviti

es (2

5)

W

B 2

Activ

ities

(132

- 13

3)

WB

1 Ac

tiviti

es (3

9 –

46)

WB

2 Ac

tiviti

es (

121

– 12

2)

Text

book

refe

renc

e

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

4

TER

M 4

Dat

e : f

rom

....

to ..

....

T

ime:

6 ho

urs

G

rade

7

8 (6

hou

rs)

9 To

pic

TRAN

SFO

RM

ATIO

N G

EOM

ETR

Y C

APS

page

s 65

11

5 12

9 Sk

ills a

nd

Know

ledg

e Tr

ansf

orm

atio

ns

R

ecog

nise

, des

crib

e an

d pe

rform

tra

nsla

tions

, ref

lect

ions

and

rota

tions

with

ge

omet

ric fi

gure

s an

d sh

apes

on

squa

red

pape

r.

Id

entif

y an

d dr

aw li

nes

of s

ymm

etry

in

geom

etric

figu

res

Enla

rgem

ents

and

redu

ctio

ns

D

raw

enl

arge

men

ts a

nd re

duct

ions

of

geom

etric

figu

res

on s

quar

ed p

aper

and

co

mpa

re th

em in

term

s of

sha

pe a

nd s

ize

Tran

sfor

mat

ions

Rec

ogni

se, d

escr

ibe

and

perfo

rm

trans

form

atio

ns w

ith p

oint

s on

a c

o-or

dina

te p

lane

, foc

usin

g on

: -

Ref

lect

ing

a po

int i

n th

e X

-axi

s or

Y-

axis

-

Tran

slat

ing

a po

int w

ithin

and

ac

ross

qua

dran

ts

R

ecog

nise

, des

crib

e an

d pe

rform

tra

nsfo

rmat

ions

with

tria

ngle

s on

a c

o-or

dina

te p

lane

, foc

usin

g on

the

co-

ordi

nate

s of

the

verti

ces

whe

n:

- R

efle

ctin

g a

trian

gle

in th

e X

-axi

s or

Y-a

xis

- Tr

ansl

atin

g a

poin

t with

in a

nd

acro

ss q

uadr

ants

-

Rot

atin

g a

trian

gle

arou

nd th

e or

igin

En

larg

emen

ts a

nd re

duct

ions

Use

pro

porti

on to

des

crib

e th

e ef

fect

of

enla

rgem

ent o

r red

uctio

n on

are

a an

d

Tran

sfor

mat

ions

Rec

ogni

se, d

escr

ibe

and

perfo

rm

trans

form

atio

ns w

ith p

oint

s, li

ne

segm

ents

and

sim

ple

geom

etric

figu

res

on

a c

o-or

dina

te p

lane

, foc

usin

g on

: -

Ref

lect

ing

a po

int i

n th

e X

-axi

s or

Y-

axis

-

Tran

slat

ing

a po

int w

ithin

and

ac

ross

qua

dran

ts

- R

efle

ctin

g in

the

line

y =

x

Iden

tify

wha

t the

tran

sfor

mat

ion

of a

po

int i

s, if

giv

en th

e co

-ord

inat

es o

f its

im

age.

En

larg

emen

ts a

nd re

duct

ions

Use

pro

porti

on to

des

crib

e th

e ef

fect

of

enla

rgem

ent o

r red

uctio

n on

are

a an

d pe

rimet

er o

f geo

met

ric fi

gure

s.


perim

eter

of g

eom

etric

figu

res.

Inve

stig

ate

the

co-o

rdin

ates

of t

he

verti

ces

of fi

gure

s th

at h

ave

been

en

larg

ed o

r red

uced

by

a gi

ven

scal

e fa

ctor

.

Sugg

este

d m

etho

dolo

gy

Wha

t is

diffe

rent

to G

rade

6

Unl

ike

in G

rade

6,

Le

arne

rs in

Gra

de 7

hav

e to

do

trans

form

atio

ns o

n sq

uare

d pa

per f

or a

ccur

acy

and

for e

nabl

ing

them

to c

ompa

re th

e sh

ape

and

size

of

figu

res.

Al

l Gra

des

Le

arne

rs s

houl

d re

cogn

ize

that

tran

slat

ions

, ref

lect

ions

and

rota

tions

onl

y ch

ange

the

posi

tion

of th

e fig

ure

and

not t

he s

hape

or s

ize.

They

sho

uld

reco

gniz

e th

at th

e ab

ove

trans

form

atio

ns p

rodu

ce c

ongr

uent

figu

res.

They

sho

uld

reco

gniz

e th

at e

nlar

gem

ents

and

redu

ctio

ns c

hang

e si

ze o

f fig

ures

by

incr

easi

ng o

r dec

reas

ing

the

leng

th o

f sid

es, b

ut

keep

ing

angl

es th

e sa

me,

pro

duci

ng s

imila

r rat

her t

han

cong

ruen

t fig

ures

.

They

sho

uld

also

be

able

to w

ork

out t

he fa

ctor

of e

nlar

gem

ent o

r red

uctio

n.

G

rade

8 a

nd 9

•

Doi

ng tr

ansf

orm

atio

ns o

n a

co-o

rdin

ate

plan

e fo

cuse

s at

tent

ion

on th

e co

ordi

nate

s of

poi

nts

and

verti

ces

of s

hape

s.

• Le

arne

rs d

o no

t hav

e to

lear

n ge

nera

l rul

es fo

r the

tran

sfor

mat

ions

at t

his

stag

e, b

ut s

houl

d ex

plor

e th

e w

ay th

e co

-ord

inat

es o

f poi

nts

chan

ge w

hen

perfo

rmin

g di

ffere

nt tr

ansf

orm

atio

ns w

ith li

nes

or s

hape

s.

Exam

ples

of t

rans

form

atio

n pr

oble

ms

• Pl

ot p

oint

A(4

;3) a

nd A

', its

imag

e, a

fter r

efle

ctio

n in

: a)

th

e x-

axis

b)

th

e y-

axis

. •

Writ

e do

wn

the

co-o

rdin

ates

of T

' if T

(–2;

3) is

tran

slat

ed 4

uni

ts d

ownw

ards

. •

The

perim

eter

of s

quar

e ab

cd =

48c

m

a)

Writ

e do

wn

the

perim

eter

of t

he s

quar

e if

the

leng

th o

f eac

h si

de is

dou

bled

. b)

W

ill th

e ar

ea o

f the

enl

arge

d sq

uare

be

twic

e or

four

tim

es th

at o

f the

orig

inal

squ

are?

G

rade

9

Wha

t is

diffe

rent

to G

rade

8?


• R

efle

ctio

n in

the

line

y =

x •

Iden

tify

trans

form

atio

ns fr

om c

o-or

dina

te p

oint

s of

the

imag

e •

Co-

ordi

nate

s of

ver

tices

C

o-or

dina

te p

lane

•

Doi

ng tr

ansf

orm

atio

ns o

n th

e co

-ord

inat

e pl

ane

is a

n op

portu

nity

to p

ract

ise

read

ing

and

plot

ting

poin

ts w

ith o

rder

ed p

airs

, and

link

s to

dr

awin

g al

gebr

aic

grap

hs.

• M

ake

sure

lear

ners

kno

w h

ow to

plo

t poi

nts

on th

e co

-ord

inat

e pl

ane

and

can

read

the

co-o

rdin

ates

of p

oint

s of

f the

x-a

xis

and

y-ax

is.

• M

ake

sure

lear

ners

kno

w th

e co

nven

tion

for w

ritin

g or

dere

d pa

irs (x

; y)

• Po

int o

ut th

e di

ffere

nces

bet

wee

n th

e ax

es in

the

four

qua

dran

ts.

Focu

s of

tran

sfor

mat

ions

•

Doi

ng tr

ansf

orm

atio

ns o

n a

co-o

rdin

ate

plan

e fo

cuse

s at

tent

ion

on th

e co

ordi

nate

s of

poi

nts

and

verti

ces

of s

hape

s.

• Le

arne

rs s

houl

d be

gin

to s

ee p

atte

rns

in te

rms

of th

e co

-ord

inat

e po

ints

, for

the

diffe

rent

tran

sfor

mat

ions

, suc

h as

: --

for t

rans

latio

ns to

the

right

or l

eft,

the

x–va

lue

chan

ges

and

y–va

lue

stay

s th

e sa

me

-- fo

r tra

nsla

tions

up

or d

own,

the

y–va

lue

chan

ges

and

the

x–va

lue

stay

s th

e sa

me

-- fo

r ref

lect

ions

in th

e y–

axis

, the

x–v

alue

cha

nges

sig

n an

d th

e y–

valu

e st

ays

the

sam

e --

for r

efle

ctio

ns in

the

x–ax

is, t

he y

–val

ue c

hang

es s

ign

and

the

x–va

lue

stay

s th

e sa

me

-- fo

r ref

lect

ions

in th

e lin

e y

= x,

the

x–va

lue

and

y–va

lue

are

inte

rcha

nged

. •

Lear

ners

sho

uld

also

be

able

-- re

flect

ion

in th

e lin

e y

= x

• Id

entif

y w

hat t

he tr

ansf

orm

atio

n of

a p

oint

is, i

f giv

en th

e co

-ord

inat

es o

f its

imag

e En

larg

emen

ts a

nd re

duct

ions

•

Use

pro

porti

on to

des

crib

e th

e ef

fect

of e

nlar

gem

ent o

r red

uctio

n on

are

a an

d pe

rimet

er o

f geo

met

ric fi

gure

s •

Inve

stig

ate

the

co-o

rdin

ates

of t

he fi

gure

s th

at h

ave

been

enl

arge

d or

redu

ced

by a

giv

en s

cale

fact

or L

earn

ers

shou

ld a

lso

be a

ble

to

wor

k ou

t the

fact

or o

f enl

arge

men

t or r

educ

tion

of a

figu

re.

LT

SM

Res

ourc

es

R

uler

s, s

quar

e pa

per,

dotte

d pa

per.


G

rade

7

Gra

de 8

Gra

de 9

Wor

kboo

k re

fere

nce

W

B 2

Act

iviti

es (8

6 - 9

4)

W

B 1

Activ

ities

(R12

) W

B 2

Activ

ities

(121

- 12

6)

WB

1 Ac

tiviti

es (R

12)

WB

2 Ac

tiviti

es (1

05 –

113

)

Text

book

re

fere

nce

HO

MEW

OR

K

ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t –

Test

: mar

ks

max


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

5

TER

M 4

Dat

e: fr

om ..

.. to

.....

.

Tim

e:

9

hour

s

Gra

de

7 8

9 To

pic

GEO

MET

RY

OF

3-D

OB

JEC

TS

CAP

S pa

ges

66

116

148

Skills

and

Kn

owle

dge

Cla

ssify

ing

3-D

obj

ects

Des

crib

e, s

ort a

nd c

ompa

re p

olyh

edra

in

term

s of

o

shap

e an

d nu

mbe

r of f

aces

o

num

ber o

f ver

tices

o

num

ber o

f edg

es

Bui

ldin

g 3-

D m

odel

Rev

ise

usin

g ne

ts to

cre

ate

mod

els

of

geom

etric

sol

ids,

incl

udin

g:

o cu

bes

o pr

ism

s

Cla

ssify

ing

3-D

obj

ects

Des

crib

e, n

ame

and

com

pare

the

5 Pl

aton

ic s

olid

s in

term

s of

the

shap

e an

d nu

mbe

r of f

aces

, the

num

ber o

f ve

rtice

s an

d th

e nu

mbe

r of e

dges

Bui

ldin

g 3-

D m

odel

s

Rev

ise

usin

g ne

ts to

mak

e m

odel

s of

ge

omet

ric s

olid

s, in

clud

ing:

o

cube

s o

pris

ms

o py

ram

ids

Cla

ssify

ing

3-D

obj

ects

Rev

ise

prop

ertie

s an

d de

finiti

ons

of th

e 5

Plat

onic

sol

ids

in te

rms

of th

e sh

ape

and

num

ber o

f fac

es, t

he n

umbe

r of

verti

ces

and

the

num

ber o

f edg

es

R

ecog

nize

and

des

crib

e th

e pr

oper

ties

of: o

sphe

res

o cy

linde

rs

B

uild

ing

3-D

mod

els

U

se n

ets

to c

reat

e m

odel

s of

geo

met

ric

solid

s, in

clud

ing:

o

cube

s o

pris

ms

o py

ram

ids

o cy

linde

rs


Sugg

este

d m

etho

dolo

gy

GR

ADE

7 W

hat i

s di

ffere

nt to

Gra

de 6

?

Mos

t of t

his

wor

k co

nsol

idat

es w

hat h

as b

een

done

in G

rade

6.

Poly

hedr

a Ex

ampl

es o

f sor

ting

or g

roup

ing

cate

gorie

s:

cu

bes

(onl

y sq

uare

face

s)

re

ctan

gula

r pris

ms

(onl

y re

ctan

gula

r fac

es)

tri

angu

lar p

rism

s (o

nly

trian

gula

r and

rect

angu

lar f

aces

)

pyra

mid

s (s

quar

e an

d tri

angu

lar f

aces

)

cylin

ders

(circ

ular

and

rect

angu

lar f

aces

). U

sing

and

con

stru

ctin

g ne

ts

U

sing

and

con

stru

ctin

g ne

ts a

re u

sefu

l con

text

s fo

r exp

lorin

g or

con

solid

atin

g pr

oper

ties

of p

olyh

edra

.

Lear

ners

sho

uld

reco

gniz

e th

e ne

ts o

f diff

eren

t sol

ids.

Lear

ners

sho

uld

draw

ske

tche

s of

the

nets

usi

ng th

eir k

now

ledg

e of

sha

pe a

nd n

umbe

r of f

aces

of t

he s

olid

s, b

efor

e dr

awin

g an

d cu

tting

out

the

nets

to b

uild

mod

els.

The

cons

truct

ion

of n

ets

is b

ased

on

the

num

ber a

nd s

hape

of f

aces

of t

he s

olid

s, a

nd d

o no

t req

uire

mea

surin

g of

inte

rnal

ang

les

of

poly

gons

.

Lear

ners

hav

e to

wor

k ou

t the

rela

tive

posi

tion

of th

e fa

ces

of th

e ne

ts, a

nd u

se tr

ial a

nd e

rror t

o m

atch

up

the

edge

s an

d ve

rtice

s, in

or

der t

o bu

ild th

e 3D

obj

ect.

GR

ADE

8 W

hat i

s di

ffere

nt to

Gra

de 7

? •

Nam

ing

and

com

parin

g Pl

aton

ic s

olid

s •

Net

s of

pyr

amid

s

Plat

onic

sol

ids

• Pl

aton

ic s

olid

s ar

e a

spec

ial g

roup

of p

olyh

edra

that

hav

e fa

ces

that

are

con

grue

nt re

gula

r pol

ygon

s.

• Th

ere

are

only

5 P

lato

nic

solid

s:

o Te

trahe

dron

o

Hex

ahed

ron

(cub

e)

o O

ctah

edro

n o

Dod

ecah

edro

n o

Icos

ahed

rons

•

The

nam

e of

eac

h Pl

aton

ic s

olid

is d

eriv

ed fr

om it

s nu

mbe

r of f

aces

. •

Plat

onic

sol

ids

prov

ide

an in

tere

stin

g co

ntex

t in

whi

ch to

inve

stig

ate

the

rela

tions

hip

betw

een

the

num

ber o

f fac

es, v

ertic

es a

nd e

dges

.


By li

stin

g th

ese

prop

ertie

s fo

r all

the

Plat

onic

sol

ids,

lear

ners

can

inve

stig

ate

the

patte

rn th

at e

mer

ges,

to c

ome

up w

ith th

e ge

nera

l ru

le: V

– e

+ f

= 2,

whe

re V

= n

umbe

r of v

ertic

es; e

= n

umbe

r of e

dges

; f =

num

ber o

f fac

es.

U

sing

and

con

stru

ctin

g ne

ts

• U

sing

and

con

stru

ctin

g ne

ts a

re u

sefu

l con

text

s fo

r exp

lorin

g or

con

solid

atin

g pr

oper

ties

of p

olyh

edra

. •

Lear

ners

sho

uld

reco

gniz

e th

e ne

ts o

f diff

eren

t sol

ids.

•

Lear

ners

sho

uld

mak

e sk

etch

es o

f the

net

s us

ing

thei

r kno

wle

dge

of th

e sh

ape

and

num

ber o

f fac

es o

f the

sol

ids,

bef

ore

draw

ing

and

cutti

ng o

ut th

e ne

ts to

bui

ld m

odel

s.

• Si

nce

lear

ners

hav

e m

ore

know

ledg

e ab

out t

he s

ize

of a

ngle

s in

equ

ilate

ral t

riang

les,

and

can

mea

sure

ang

les,

thei

r con

stru

ctio

ns o

f ne

ts s

houl

d be

mor

e ac

cura

te.

• Le

arne

rs h

ave

to w

ork

out t

he re

lativ

e po

sitio

n of

face

s of

the

nets

in o

rder

to b

uild

the

3D m

odel

. G

RAD

E 9

Wha

t is

diffe

rent

to G

rade

8?

• Pr

oper

ties

of s

pher

es a

nd c

ylin

ders

•

Net

s of

cyl

inde

rs

Pl

aton

ic s

olid

s (S

ame

as G

rade

8)

U

sing

and

con

stru

ctin

g ne

ts (S

ame

as G

rade

9)

LT

SM

Res

ourc

es

So

lids,

3D

obj

ects

.

G

rade

7

Gra

de 8

Gra

de 9

Wor

kboo

k re

fere

nce

W

B 2

Act

iviti

es (9

6 - 1

04)

W

B 2

Activ

ities

(127

- 13

2)

WB

2 Ac

tiviti

es (1

14; 1

22

Text

book

re

fere

nce

HO

MEW

OR

K


ASSE

SSM

ENT

E.g.

Info

rmal

as

sess

men

t – T

est:

mar

ks m

ax


MAT

HEM

ATIC

S SE

NIO

R P

HAS

E

MU

LTI G

RAD

E LE

SSO

N P

LAN

6

TER

M 4

Dat

e: fr

om ..

......

to ..

......

Tim

e:

4.

5 ho

urs

G

rade

7

8 9

Topi

c PR

OB

ABIL

ITY

CAP

S pa

ges

73

117

152

Skills

and

Kn

owle

dge

Prob

abili

ty

P

erfo

rm s

impl

e ex

perim

ents

whe

re th

e po

ssib

le o

utco

mes

are

equ

ally

like

ly

and:

o

list t

he p

ossi

ble

outc

omes

bas

ed

on th

e co

nditi

ons

of th

e ac

tivity

o

dete

rmin

e th

e pr

obab

ility

of e

ach

poss

ible

out

com

e us

ing

the

defin

ition

of p

roba

bilit

y

Prob

abili

ty

C

onsi

der a

sim

ple

situ

atio

n (w

ith e

qual

ly

likel

y ou

tcom

es) t

hat c

an b

e de

scrib

ed

usin

g pr

obab

ility

and:

o

list a

ll th

e po

ssib

le o

utco

mes

o

dete

rmin

e th

e pr

obab

ility

of e

ach

poss

ible

o

outc

ome

usin

g th

e de

finiti

on o

f pr

obab

ility

o pr

edic

t with

reas

ons

the

rela

tive

frequ

ency

o

of th

e po

ssib

le o

utco

mes

for a

se

ries

of tr

ials

o

base

d on

pro

babi

lity

o co

mpa

re re

lativ

e fre

quen

cy w

ith

prob

abilit

y an

d ex

plai

ns p

ossi

ble

diffe

renc

es

Prob

abili

ty

C

onsi

der s

ituat

ions

with

equ

ally

pr

obab

le o

utco

mes

, and

: o

dete

rmin

e pr

obab

ilitie

s fo

r co

mpo

und

even

ts u

sing

two-

way

ta

bles

and

tree

dia

gram

s o

dete

rmin

e th

e pr

obab

ilitie

s fo

r ou

tcom

es o

f eve

nts

and

pred

ict t

heir

rela

tive

frequ

ency

in s

impl

e ex

perim

ents

o

com

pare

rela

tive

frequ

ency

with

pr

obab

ility

and

expl

ains

pos

sibl

e di

ffere

nces

Sugg

este

d m

etho

dolo

gy

GR

ADE

7 Pr

obab

ility

exp

erim

ents

In

the

Inte

rmed

iate

Pha

se le

arne

rs d

id e

xper

imen

ts w

ith c

oins

, dic

e an

d sp

inne

rs. I

n th

is g

rade

exp

erim

ents

can

be

done

with

oth

er

obje

cts,

like

, diff

eren

t col

oure

d bu

ttons

in a

bag

; cho

osin

g sp

ecifi

c ca

rds

from

a d

eck

of c

ards

, etc

. Ex

ampl

e If

you

toss

a c

oin

ther

e ar

e tw

o po

ssib

le o

utco

mes

(hea

d or

tail)

. The

pro

babi

lity

of a

hea

d is

1 2

whi

ch is

equ

ival

ent t

o 50

% (s

ince

it is

one

ou

t of t

wo

poss

ible

.


GR

ADE

8 Pr

obab

ility

exp

erim

ents

In

the

Inte

rmed

iate

Pha

se a

nd G

rade

7 le

arne

rs d

id p

roba

bilit

y ex

perim

ents

with

coi

ns, d

ice

and

spin

ners

. In

Gra

de 8

doi

ng a

ctua

l tria

ls o

f ex

perim

ents

bec

ome

less

impo

rtant

, and

lear

ners

sho

uld

cons

ider

pro

babi

lity

for h

ypot

hetic

al e

vent

s e.

g. th

e pr

obab

ility

of w

hite

as

a su

cces

sful

out

com

e on

a ro

ulet

te ta

ble,

or t

he p

roba

bilit

y of

get

ting

a C

oca

Col

a at

the

shop

if y

ou k

now

wha

t the

tota

l num

ber o

f drin

ks is

th

at th

ey s

tock

and

how

man

y ca

ns o

f Coc

a C

ola

they

hav

e.

Com

parin

g re

lativ

e fr

eque

ncy

and

prob

abili

ty

Th

e re

lativ

e fre

quen

cy is

the

obse

rved

num

ber o

f suc

cess

ful o

utco

mes

for a

fini

te s

ampl

e of

tria

ls.

Fo

r exa

mpl

e, if

you

toss

a c

oin

50 ti

mes

, the

resu

lts a

re 2

7 he

ads

and

23 ta

ils. D

efin

e a

head

as

a su

cces

sful

out

com

e. T

he

rela

tive

frequ

ency

of h

eads

is: 2

7 50

= 5

4%

Th

e pr

obab

ility

of a

hea

d is

50%

(one

of t

wo

likel

y ou

tcom

es).

The

diffe

renc

e be

twee

n th

e re

lativ

e fre

quen

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TASKS & MEMORANDA


INVESTIGATION EXEMPLAR: GRADE 7 TERM 2

ACTIVITY: INTERSECTING LINES Intersecting lines are any lines that cut each other at a point, and that point where they cut each other

is called the point of intersection.

Example

a) Describe the above diagram (diagram in the example) to a friend who does not see it.

_____________________________________________________________________________

___________________________________________________________________

(2)

b) Draw at least three diagrams with two intersecting lines and label the lines and the diagrams

(Diagram 1, Diagram 2, etc.). Label the points of intersection too. The lines in all the sets should

not be perpendicular to each other

(3)

c) Measure ALL angles that are formed at the points of intersection. Record your measurements in

the table like the one drawn below.

DIAGRAM ANGLE NAME SIZE

(3 x 4)

d) Explain what you notice about these angles

_____________________________________________________________________________

___________________________________________________________________

(1)

e) Which angles are equal in each diagram?

_____________________________________________________________________________

___________________________________________________________________

________________________________________________________________________

(1)


f) Describe the position of equal angles in relation to each other. [Hint: Are thy next to each other OR on opposite sides of the common vertex?] ________________________________________________________________________

(1)

g) How many sets of equal angles are there in each diagram?

________________________________________________________________________

(1)

h) The equal pairs of angles in the diagram are called VERTICALLY OPPOSITE ANGLES. In your

own words, define what vertically opposite angles are.

_____________________________________________________________________________

___________________________________________________________________

(2)

i) From the observations made during the activity, what conclusion can one make about vertically

opposite angles formed by intersecting lines?

_____________________________________________________________________________

___________________________________________________________________

(2)

TOTAL 25


INVESTIGATION EXEMPLAR: GRADE 8 TERM 2

Activity: Corresponding angles

A transversal is a line that is drawn such that it intersects other lines. Angles on the same side of the

transversal, and also on the same side of the lines cut by the transversal are called corresponding

angles.

Example

In the diagram, AD is a transversal. Angles FBC and GCD are corresponding angles.

Activity

Use the diagrams below for the activity. Parallel lines and corresponding angles are indicated.

Diagram 1 Diagram 2

CB

F

E

G

H

A

D

KHG

I

J

C

D

A B

E

F


Diagram 3 j) Measure ALL corresponding angles and then complete the table that follows.

DIAGRAM ANGLE NAME SIZE

1

2

3

(9)

k) Specify equal pairs of corresponding angles in each diagram.

_____________________________________________________________________________

___________________________________________________________________

________________________________________________________________________

(3)

l) Which lines form equal corresponding angles if cut by a transversal? ________________________________________________________________________

(1)

m) Construct and label your own parallel lines that are cut by a transversal. (2)

________________________________________________________________________

E

D

C

F

G

A

BH

I

J

K


n) Measure and compare corresponding angles

______________________________________________________________________

______________________________________________________________________

(3)

o) From the observations made during the activity, what conclusion can one make about

corresponding angles formed if parallel lines are cut by a transversal?

_____________________________________________________________________________

___________________________________________________________________

(2)

TOTAL 25


INVESTIGATION EXEMPLAR: GRADE 9

Relating angles in a triangle

In the diagram 1 below, the marked angle ACD is an exterior angle of triangle ABE. An exterior angle is formed by producing one of the sides. The marked angles BAC and ABC are interior, opposite angles to the exterior angle ACD.

Diagram 1 Diagram 2

Diagram 3

(a) Measure the marked angles and complete the table below. Diagram Interior angle 1 Interior angle 2 Exterior angle Sum of interior angles

1 2 3

(12)

S

Q

P

R

P

NO

M


(b) How does the exterior angle compare to the sum of the interior opposite angles? _________________________________________________________________ (1)

(c) Draw your own triangle with one side produced to form an exterior angle. (2)

(d) Measure and record the size of the exterior angle and the interior opposite angles. __________________________________________________________________ (3)

(e) Is the exterior angle equal to the sum of the interior angle? _________________________________________________________________ (1)

(f) What conclusion can be drawn from the activities? ____________________________________________________________________________________________________________________________________________________ (1)

TOTAL 25


MULTIGRADE FORMAL ASSESSMENT

MATHEMATICS GRADE 7, 8, 9: FORMAL ASSESSMENT TASK: TERM 1 TEST

Examiner: ________________________ Time: 1 Hour

Moderator: ________________________ Date: __________

Total Grade 7 40

Total Grade 8 50

Total Grade 9 75

INSTRUCTIONS:

Answer all the questions underneath each other. Leave a line open between every sum. Show all your calculations. Write legibly. Round off to 2 decimal digits. Answer the questions relevant to your grade

QUESTION 1

1.1Calculate:

GRADE No Marks

7,8,9 1.1.1 −10 + (18)

(1)

8,9 1.1.2 (-2)2(-3)3 (3)

8,9 1.1.3

−4 × 5 + (−5)2

(3)

8,9 1.1.4 √−643 +(−2)3

(3)

7,8,9 1.1.5 (37)2

(2)

8,9 1.1.6 √2 7

9

(3)

9 1.1.7

−42 + (−4)3

(3)

9 1.1.8

√169 − √−0,0643

(3)

9 1.1.9

√1 916 × 1 2

3 ÷ 9, 3̇

(4)


7 1.1.10 7 836 524 + 4 853 477 (2)

7 1.1.11 42 746 ÷ 274 (2)

7,8 1.2 Arrange the following numbers in ascending order (2)

20; −18; −22; 2; −8; 6

7,8,9 1.3 Write 54 as the product of its prime factors (3)

Grade 7 [7]

Grade 8 [15]

Grade 9 [25]

9 1.4 Use prime factors and determine the HCF of 112 and 210 (3)

7,8,9 1.5.1 Write the following ratios in their simplest form

20 : 24 : 44

(1) 7,8,9 1.5.2 Divide R2500 in the ratio of 2 : 3

(3) 7,8,9 1.6.1 You cover a distance of 18km in 2h30 min. What is your

average speed in km/h?

(3) 7,8,9 1.6.2 John buys and sells T-shirts. He buys the shirts at a cost of

R50. He sells them at a profit of 70%. Calculate his selling price.

(2) Grade 7 [9]

Grade 8 [9]

Grade 9 [12]

QUESTION 2

7,8,9 7,8,9 7,8,9

2.1 2.1.1 2.1.2 2.1.3

Use the number sequence below to answer the questions that follow:

1; 4 ; 9; 16; …. Write down the next term in the number sequence. Determine the 7th term in the number sequence. State the rule in words of the number sequence.

(1)

(2)

(1)

7,8,9 2.2 Calculate the value of the following expression if : a = -2 ; b = 3 and c = -1

Expression: a + b – (2c)2

(2)


7,8,9 2.3 Write the following relationship as a symbolic formula: To calculate the output number (y), 7 is subtracted from the input number(x) and the answer is multiplied by 5.

(2)

7,8,9

2.4

Write 620 000 000 000 in scientific notation.

(2)

Grade 7 [10]

Grade 8 [10]

Grade 9 [10]

QUESTION 3

3.1 Consider the following expression and answer the questions that follow.

2x4 + y − 3x + 5 + 2y

7,8,9 3.1.1 How many terms does the expression have? (1)

7,8,9 3.1.2 Write down two terms which are alike. (1)

7,8,9 3.1.3 What is the exponent of x in the first term? (1)

7,8,9 3.1.4 Which term is a constant? (1)

8,9 3.1.5 What is the coefficient of the third term? (1)

Grade 7 [4]

Grade 8 [5]

Grade 9 [5]

QUESTION 4

4.1 Consider the following pattern that is built with matches and answer the questions.

figure 1 figure 2 figure 3

7,8,9 4.1.1 Draw the next figure (Fig 4) in the pattern.

(1)

7,8,9 4.1.2 Consider the following table and write down the values of a and b. (2)

Figure (n) 1 2 3 4 10 Number of matches (Tn) 8 15 22 a b

8,9 4.1.3 Write down the formula for the nth term. (2)

7,8,9 4.1.4 Which figure will consist of 50 matches? (2)


7,8,9 4.1.5 How many matches will be needed to make the 25th figure? (1)

Grade 7 [6]

Grade 8 [8]

Grade 9 [8]

QUESTION 5

5.1 You receive R2500 from your father on your birthday. You decide to invest the money in the bank for you studies four years from now. The bank gives you the following two options. OPTION A: Invest with 8% compound interest per year for four years. OPTION B: Invest at 7,5% simple interest rate for four years.

9 5.1.1 Decide which one will generate more money in the given time period.

(7)

9 5.1.2 Calculate the percentage increase if the price of diesel increases from R11,21 per litre to R12,30 per litre. Round your answer off to 2 decimal places.

(4)

9 5.1.3 An aircraft travels at a speed of 0,9 x 103 km/h for 24 hours. How far has the aircraft travelled? Give the answer in scientific notation.

(3)

Grade 9 [14]

QUESTION 6

6.1 Study the weather temperature graph provided and answer the questions that follow

14

12

10

8

6

4

2

- 2

Temperature in °C

18:0017:0016:0015:0014:0013:0012:0011:0010:0009:0008:0007:00


7,8 6.1.1 What was the temperature at 7 am?

(1)

7,8 6.1.2 What was the maximum day temperature?

(1)

7,8 6.1.3 What is the difference in temperatures at 18:00 and at 8:00? (1)

7,9 6.1.4 During which period did the temperature increase? (1)

Grade 7 [4]

Grade 8 [3]

Grade 9 [1]

TOTAL Grade 7 [40]

TOTAL Grade 8 [50]

TOTAL Grade 9 [75]


TEST

TERM 1

Gr 7,8,9

M Method S Simplification KA / CA Constant accuracy A Answer

QUESTION 1 1.1.1 -10 + (18)

= 8 A A= 1 mark

1.1.2 (-2)2(-3)3 4A × -27A = -108 CA

A=2 marks CA = 1 mark

1.1.3 -4 × 5 + (-5)2

= -20 S+ 25S = 5CA/KA

S = -20 1 mark S = 25 1 mark CA/KA = 5 1 mark

1.1.4 -4 S + (-8) S

= -12CA/KA S = -4 1 mark S = -8 1 mark CA/KA = -12 1 mark

1.1.5

499AA

A = 9 1 mark A = 49 1 mark (Answer must be a fraction)

1.1.6 259

53

SA A

S = 25/9 1 mark A = 5 1 mark A = 3 1 mark

1.1.7 -42 + (-4)3 = -16-64 M = -80 KA/CA

-16: 1 mark -64: 1 mark answer: 1 mark

1.1.8 3 064,0169 = 13 - (-0,4) M = 13 + 0,4 = 13,4 KA/CA

13: 1 mark -0,4: 1 mark/answer: 1 mark

1.1.9

319

321

1691 M

= 328

35

1625

M

= 283

35

54

M

= 11225

KA/CA

319 : 1 mark

1625

: 1 mark

reciprocal: 1 mark answer: 1 mark


1.1.10 7 836 542 + 4 853 477 12 690 019

019 - 1 mark 12 690 – 1 mark

1.1.11 42 746 ÷ 274 = 156 r 2

156 – 1 mark Remainder 2 – 1 mark

1.2 -22 ; -18 ; -8 ; 2 ; 6 ; 20 A A

A = -22 ; -18 ; -8 1 mark A = 2 ; 6 ; 20 1 mark

1.3 2 54 3 27 3 9 3 3 1 M M 2 × 3× 3 × 3 = 54 CA

M = correctly divide l 2 (1 mark)

M = correctly divide l 3

(1 mark

CA/KA = Write as a product (1 mark)

1.4 2 112 2 210 2 56 3 105 2 48 5 35 2 24 7 7 7 14 1 7 7 1

S S 2 × 7 = 14 S

S = 112 correctly divide by

prime numbers (1 mark)

S = 210 correctly divide by

prime numbers (1 mark)

A = GGF / HCF = 14

1.5.1 5 : 6 : 11 A

A = 4 : 6 : 11 (1 A punt/mark)

1.5.2 2 2500 1000

53 2500 15005

M A

A

M = 2 25005 (1 mark)

A = R1000 (1 mark)

A = R1500 (1 mark)

1.6.1 Average speed = 18 km2,5 h

= 7,2 km/h M ; C ; CA/KA

M = formula (1 mark) C = convert to 2,5 h (1 mark)

CA/KA = 7,2 km(1 mark)

1.6.2

10070

R50 = R35 S

= R50 + R35 = R85 OF /OR 1,7 S × 50 = R85 CA/KA

S = R35/1,7 (1 mark) CA/KA = R85 (1 mark)

QUESTION 2 2.1.1 25 A A = 1 mark 2.1.2 T7 = 49 A A = 2 marks 2.1.3 Each term number is squared. A A = 1 mark 2.2 = -2 + 3 – (2. -1)2S

= -2 + 3 – 4 = -3CA / KA

S = 1 mark CA/KA = 1 mark

2.3 y = 5( x – 7) AA A = 2 marks 2.4 A 6,2 × 1011A A =2 marks


QUESTION 3 3.1 3.1.1 5 A A = 1 mark 3.1.2 y + 2y A A = 1 mark 3.1.3 4 A A = 1 mark 3.1.4 4th term A A = 1 mark 3.1.5 -3 A A = 1 mark

QUESTION 4 4.1.1

correct pattern (1)

4.1.2 a = 29 b = 71

value of a (1) value of b (1)

4.1.3 Tn = 7n + 1

7n (1) 1 (1)

4.1.4 Tn = 7n + 1 50 = 7n + 1 n = 7

substitution of 50 (1) (CA) answer (1)

4.1.5 T25 = 7(25) + 1 = 176

correct answer (1)

QUESTION 5 5.1.1 Option A:

A = P(1 + i)n M = 2 500(1 + 0,08)4 M = R3 401,22 KA/CA Option B: A = P(1 + in) M = 2 500(1 + 0,75 x 4) M = R3 250 KA/CA ∴ Option A is better KA/CA

formula: 1 mark substitution: 1 mark

answer: 1 mark formula: 1 mark

substitution: 1 mark answer: 1 mark

Option A: 1 mark

5.1.2

%72,9

100x21,11

21,1130,12

100xOP

OPNPincrease/verhoging%

12.30 – 11,21: 1 mark 11,21/divide by 11,21: 1 mark

X 100: 1 mark answer: 1 mark

If answer not rounded off to 2 dec places: only ¾

5.1.3 distance = speed x time M = 0,9 x 103 x 24 M = 2,16 x 104 km KA/CA

Formula/: 1 mark 0,9 x 103 x 24: 1 mark

answer: 1 mark


EXEMPLAR TEST GRADE 8 TERM 1 Marks : 60 Instructions to learners: 1. Read all the instructions carefully. 2. Answer Questions 1 – 8 in the spaces or frames provided. 3. Show all working on the question paper. 4. The test duration is 90 minutes.

QUESTION 1 Calculate each of the following: 1.1 235 292 + 782 354

_________________________________________________ _________________________________________________ _________________________________________________

(2)

1.2 9 634 567 – 6 546 321 _________________________________________________ _________________________________________________ _________________________________________________

(2)


QUESTION 2

Given the following numbers: 144 and 150 2.1 Write down the first 5 multiples of 144 and 150

_________________________________________________ _________________________________________________ _________________________________________________

(2)

1.3 12 421 × 25 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________

(3)

1.3 12 421 × 25 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________

(3)

1.4 10 625 ÷ 25 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________

(3)

1.5

90 + 18 ÷ 2 × 8 - 13 _________________________________________________ _________________________________________________ _________________________________________________

(3)

_________________________________________________ _________________________________________________ _________________________________________________


QUESTION 5

5.1 Arrange the following sets of numbers in an ascending order. 63 ; − 49 ; − 56 ; 0 ; − 28 _____________________________________________________

(1)

5.2 Fill in <; > , =

2.2 Write 144 and 150 as product of their prime factors. (2) 2.3 Write down the HCF of 120 and 144 (2) QUESTION 3 3.1 Lucy earned R4500 and gave 10% of it to her mother. How much did she give to her? (2) 3.2 Tshepo invested R1 500 into his savings account. The investment grew/increased by 10%

simple interest per year. How much was the investment worth at the end of the third year? (1)

3.3 Thobeka wants to order a book that costs $56,67. The rand-dollar exchange rate is R11 to a dollar. What is the price of the book in rands?

(3)

3.4 Calculate a discount of 6% on each of the following marked prices of article R3 600. (3) QUESTION 4 4.1 Write down the ratio 15 : 27 as a fraction and then simplify if possible.

_________________________________________________ _________________________________________________ _________________________________________________

(2)

4.2 Tom has R7 and Lucy has R9; what is the ratio of the money Tom has to Lucy?

____________________________________________

(1)

4.3 The ratio of boys to girls in a class is 7 : 5. If there are 36 learners in a class, how many are boys and how many are girls? _________________________________________________ _________________________________________________ _________________________________________________

(4)

4.4 Divide 24 in the ratio 1 : 2 : 5 ______________________________________________________ ______________________________________________________ ______________________________________________________

(3)

4.5 If 5kg of nuts cost R40 how much will 7kg cost? ______________________________________________________ ______________________________________________________ ______________________________________________________

(2)


5.2.1 0 ____ − 999

(1)

52.2 − 5,5 _____ 0,5

(1)

5.2.3 67 ____ 60 + 7

(1)

5.3 Fill in the missing numbers:

3; 12, 48; -------; -------

(2)

5.4 Calculate each of the following.

5.4.1 4 + (−1) – (−9) ________________________________________________

(1)

5.4.2 200 ÷(+4) × (−2) _________________________________________________

(1)

[8]

QUESTION 6

6.1 (− 6)2 ________________________________________________________________________

(1)

6.2 √1253 _____________________________________________________

(1)

[2]

QUESTION 7

7.1 Determine the rule and solve m and n.

x 1 2 3 m 15 y 1 4 9 64 n

__________________________________________________ _________________________________________________ __________________________________________________

(3)


QUESTION 8

Study the weather temperature graph provided and answer the questions that follow

8.1 What was the temperature at 7 am? _________________________________________________

(1)

8.2 What was the maximum day temperature? _________________________________________________

(1)

8.3 What is the difference in temperatures at 18:00 and at 8:00? __________________________________________________

(1)

8.4

During which period did the temperature increase? __________________________________________________

(1)

8.5 Do you think the graph represents a summer or winter day in South Africa? Give a reason for your answer.

(2)

14

12

10

8

6

4

2

- 2

Temperature in °C

18:0017:0016:0015:0014:0013:0012:0011:0010:0009:0008:0007:00


EXEMPLAR TEST MEMO GRADE 8 TERM 1 Marks : 60

QUESTION 1

1.1 235 292 + 782 354 1 017 646 √ √

For the correct answer: full marks.

(2) 1.2 9 634 567

– 6 546 321 3 088 246 √ √


(2) 1.3 12 421

× 25 62 105 + 248 420 √ 310 525 √ √


(3) 1.4 10 625 ÷ 25

425

000000012500125005000621001062525

√√√ QUESTION 2


(3)

1.5 90 + 18 ÷ 2 × 8 − 13 = 90 + 9 x 8 – 13 = 90+72-13√ = 149 √


(3) 2.1 Write down the first 5 multiples of 144 and 150

Multiples of 144 = {144 ; 288 ; 432 ; 576 ; 702} √ Multiples of 150 = {150 ; 300 ; 450 ; 600 ; 750} √

(2)

2.2 120 = 23 x 3 x 5

144 = 24x32

(2) 2.3 HCF of 120 and 144 = 24 √

(1) [5]


QUESTION 3

3.1 10% of R4 500 = 10% × 4 500 √ = 450 She gave her mother R450. √

(2)

3.2 SI = 𝑃𝑃𝑃𝑃𝑃𝑃100 = 1 500 ×3 ×10

100 √ = R450 √ At the end of the third year the investment was worth R1 950.√

(3)

3.3 11 x 56,67 = R623,37 √√√ (3) 3.4

216

3600100

6

R

[8]

QUESTION 4

4.1 Write down the ratio 15 : 27 as a fraction and then simplify if possible. 1527 = 59 √√

(2)

4.2 7 : 5 (1)

4.3 712 × 36 √ = 21 boys √ 512 × 36 √ = 15 girls. √

(4)

4.4 1 8 × 24 = 3 √ 28 × 24 = 6 √ 58 × 24 15 √

(3)

4.5 If 5kg of nuts cost R40 how much will 7kg cost? 5kg costs R40 1kg cost R8 ∴ 7kg will cost 7 × R8 = R56 √ √

(2)


QUESTION 5

5.1 − 56 ; − 49 ; ; − 28 ; 0 ; 63 (1) 5.2 5.2.1 0 > − 999

(1) 52.2 − 5,5 < 0,5

(1) 5.2.3 67 = 60 + 7

(1) 5.3 3; 12, 48; 192; 768 √ √

(2)

5.4 5.4.1 4 + (-1)-(-9) = 12

(1) 5.4.2 (+6) – (−2) = + 8

(1) 5.4.3 (+4) + (−1) – (−9)

= 4 – 1 + 9 = 12 √

(1) 5.4.4 200 ÷4 × (−2)

= − 100 √

(1)

[10]

QUESTION 6

6.1 (− 6)2 = 36 √

(1)

6.2 √1253 = 5 √

(1)

[2]

QUESTION 7

x 1 2 3 m 15 y 1 4 9 64 n

Rule y = x2 √ m = 8 √ n = 225 √

[3]

QUESTION 8

8.1 2C (1) 8.2 12C (1) 8.3 6C 0C = 6C (1) 8.4 From 7:00 to 12:00 (1) 8.5 The graph represents a winter day in South Africa.

The maximum temperature of 12C is very cold.

(2) [6]


GRADE 9 EXEMPLAR TEST - TERM 1 Marks : 60 Instructions to learners: 1. Read all the instructions carefully. 2. Answer Questions 1 – 8 in the spaces or frames provided. 3. Show all working on the question paper. 4. The test duration is 90 minutes

QUESTION 1

Calculate each of the following.

1.1 81 892 + 321 456 ________________________________________________ _________________________________________________ _________________________________________________

(2)

1.2 1 234 567 – 654 321 _________________________________________________ _________________________________________________ _________________________________________________

(2)

1.3 26 342 × 32 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________

(3)

1.4 7550 ÷ 25 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________

(3)

1.5

60 + 10 ÷ 2 × 5 - 1 _________________________________________________ _________________________________________________ _________________________________________________

(2)

[12]


QUESTION 2

Given the following numbers: 120 and 144

2.1 Write 120 and 144 as products of their prime factors. _________________________________________________ _________________________________________________ _________________________________________________

(2)

2.2 Write down the LCM and HCF in 120 and 144 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________

(2)

[4]

QUESTION 3 [calculators may be used]

3.1 Lucy earned R4500 and gave 15% of it to her mother, how much did she give to her?

_________________________________________________ _________________________________________________ _________________________________________________

(2) 3.2 Tshepo invested R1 500into his savings account. The investment grew /increased by

10 % compound interest per year. How much was the investment worth at the end of the third year? _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________

(3)

3.3 The marked prices of an article is R850. A discount of 15% is offered to customers who pay cash. Calculate how much a customer who pays cash will actually pay.

(3)

3.4 Sara buys a flat screen television on hire purchase. The cash price is R4 199. She

has to pay a deposit of R950 and 12 monthly instalments of R360. Calculate the total hire purchase price.

(4)

3.5 Tim bought £650 at the foreign exchange desk at Gatwick Airport in the UK at a rate (4)


of R15,66 per £1. The desk also charged 2,5% commission on the transaction. How much did Tim spend to buy the pounds?

(16)

QUESTION 4

4.1 Write down the ratio 45 : 60 as a fraction and then simplify if possible. _________________________________________________ _________________________________________________ _________________________________________________

(2)

4.2 To make biscuits of a certain kind, 5 parts of flour has to be mixed with 2 parts of

oatmeal, and 1 part of cocoa powder. How much oatmeal and how much cocoa powder must be used if 500 g of flour is used? _________________________________________________ _________________________________________________ _________________________________________________

(4)

4.4 Divide 60 in the ratio 3 : 2 : 1

______________________________________________________ ______________________________________________________ ______________________________________________________

(3)

4.5 If 7kg of nuts cost R50 how much will 16kg cost? ______________________________________________________ ______________________________________________________ ______________________________________________________

(2)

[11]

QUESTION 5

5.1 Calculate :−15 + (−14) − 9 ____________________________________________________

(2) 5.2 Calculate:

(–30) × (–10) – (–30) × (–8) (2)

5.3 Calculate each of the following:

4p - 6q + (-5p) - (4q)

(2)

[6]


QUESTION 6 Determine the values of each of the following.

6.1 (− 6)2

________________________________________________________________________

(1)

6.2

_________________________________________________

(1)

[2]

QUESTION 7

7.1 Study the table below.

x 1 2 3 m 15 y 2 5 10 65 n

7.1.1 Determine the value of m and n __________________________________________________ 7.1.2 Write down the rule you use to calculate m and n. ________________________________________________ __________________________________________________

(2)

(1)

[3]


QUESTION 8

Study the weather temperature graph provided and answer the questions that follow

8.1 What was the temperature at 7 am?

_________________________________________________

(1)

8.2 What was the maximum day temperature? _________________________________________________

(1)

8.3 What is the difference in temperatures at 18:00 and at 8:00? __________________________________________________

(1)

8.4 During which period did the temperature increase? __________________________________________________

(1)

8.5 Do you think the graph represents a summer or winter day in South Africa? Give a reason for your answer. ________________________________________________________ ________________________________________________________

(2)

[6]


Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8

%

Req %

12 6 11 12 8 2 3 6 60 100 R 12 6 5 3 26 43 45 CP 11 7 18 30 20 K 6 2 6 14 23 25 PS 2 2 3 10


GRADE 9 EXEMPLAR TEST MEMO - TERM 1 Marks : 60

QUESTION 1

1.1 81 892

+ 321 456 403 348 √ √


(2)

1.2 1 234 567 – 654 321 580 246 √ √


(2)

1.3 26 342 × 32 52 684 +790 260 √ 842 944 √ √


(3)

1.4 7550 ÷ 25 √√√


(3)

1.5 60 + 10 ÷ 2 × 5 − 1

= 60 + 25 – 1 √ = 84 √


(2)

[12]

QUESTION 2

2.1 120 = 2 × 2 × 2 × 3 × 5 √ 144 = 2 × 2 × 2 × 2 × 3 × 3 √

(2)

2.2 LCM of 120 and 144 = 720 √ HCF of 120 and 144 = 24 √

(2)

[4]

QUESTION 3


(2)


3.2 CI = P(1+i)n = 1500(1+0,1)3 √ = = R1996,50 √ At the end of the third year the investment was worth R1996,50.√

(3)

3.3 R850 x 15 ÷ 100 = R 127,50√

= R850 - R127,50√

= R722,50√

(3)

3.4 R950 + (R360 x 12) √√

= R950 + R4320√

= R5270√

(4)

3.5 R15,66 x £650 = R 10 179 x 2,5 ÷ 100

= R 254,48√√

= R254,48 + R 10 179 = R10 433, 48√√

(4)

[16]

QUESTION 4

4.1 Write down the ratio 15 : 27 as a fraction and then simplify if possible. = 15 √ 27 = 5 √ 9

(2)

4.2 200 g of oatmeal,√√ and 100g of cocoa powder. √√ (4)

4.4 60 x 3 ÷ 6 = 30 √

60 x 2 ÷ 6 = 20√ 60 × 1 ÷ 6 = 10 √

(3)

4.5 If 5kg of nuts cost R40 how much will 7kg cost? 5kg costs R40 1kg cost R8 7kg will cost 7 × R8 = R56 √ √

(2)

[11]


QUESTION 5

5.1 −15 + (−14) − 9 √ = -15 -14 - 9 = - 38 √

(2)

5.2 (–30) × (–10) – (–30) × (–8)

= 300 - 240 √ = 60√

(2)

5.3 5.3.1 4p - 6q + (-5p) - (4q)

= 4p - 5p - 6q - 4q = - p - 10q

(2)

[6]

QUESTION 6

6.1 (− 6)2 = 36 √

(1)

6.2 =

=

= 8

(1)

[2]

QUESTION 7

x 1 2 3 m 15 y 2 5 10 65 n

7.1.1 m = 8 √ and n = 226 √ 7.1.2 square the value of "x" and add 1 or y = x2 + 1 √

(2)

(1)

[3]

QUESTION 8

8.1 - 2oC (1) 8.2 12oC (1) 8.3 6oC - 0oC = 6C (1) 8.4 From 7:00 to 12:00 (1) 8.5 The graph represents a winter day in South Africa.

The minimum temperatue is - 2oC maximum temperature of 12oC is very cold. (2)

[6]


GRADE 9 EXEMPLAR TEST MEMO - TERM 1 Marks : 60

QUESTION 1

1.1 81 892

+ 321 456 403 348 √ √


(2)

1.2 1 234 567 – 654 321 580 246 √ √


(2)

1.3 26 342 × 32 52 684 +790 260 √ 842 944 √ √


(3)

1.4 7550 ÷ 25 √√√


(3)

1.5 60 + 10 ÷ 2 × 5 − 1 = 60 + 25 – 1 √ = 84 √


(2)

[12]

QUESTION 2

2.1 120 = 2 × 2 × 2 × 3 × 5 √ 144 = 2 × 2 × 2 × 2 × 3 × 3 √

(2)

2.2 LCM of 120 and 144 = 720 √ HCF of 120 and 144 = 24 √

(2)

[4]

QUESTION 3


(2)

3.2 CI = P(1+i)n


= 1500(1+0,1)3 √ = = R1996,50 √ At the end of the third year the investment was worth R1996,50.√

(3)

3.3 R850 x 15 ÷ 100 = R 127,50√

= R850 - R127,50√

= R722,50√

(3)

3.4 R950 + (R360 x 12) √√

= R950 + R4320√

= R5270√

(4)

3.5 R15,66 x £650 = R 10 179 x 2,5 ÷ 100

= R 254,48√√

= R254,48 + R 10 179 = R10 433, 48√√

(4)

[16]

QUESTION 4

4.1 Write down the ratio 15 : 27 as a fraction and then simplify if possible. = 15 √ 27 = 5 √ 9

(2)

4.2 200 g of oatmeal,√√ and 100g of cocoa powder. √√ (4)

4.4 60 x 3 ÷ 6 = 30 √

60 x 2 ÷ 6 = 20√ 60 × 1 ÷ 6 = 10 √

(3)

4.5 If 5kg of nuts cost R40 how much will 7kg cost? 5kg costs R40 1kg cost R8 7kg will cost 7 × R8 = R56 √ √

(2)

[11]

QUESTION 5

5.1 −15 + (−14) − 9 √ = -15 -14 - 9 = - 38 √

(2)


5.2 (–30) × (–10) – (–30) × (–8)

= 300 - 240 √ = 60√

(2)

(2) 5.3 5.3.1 4p - 6q + (-5p) - (4q)

= 4p - 5p - 6q - 4q = - p - 10q

(2) [6]

QUESTION 6

6.1 (− 6)2 = 36 √

(1)

6.2 =

=

= 8

(1)

[2]

QUESTION 7

x 1 2 3 m 15 y 2 5 10 65 n

7.1.1 m = 8 √ and n = 226 √ 7.1.2 square the value of "x" and add 1 or y = x2 + 1 √

(2)

(1)

[3]

QUESTION 8

8.1 - 2oC (1) 8.2 12oC (1) 8.3 6oC - 0oC = 6C (1) 8.4 From 7:00 to 12:00 (1) 8.5 The graph represents a winter day in South Africa.

The minimum temperatue is - 2oC maximum temperature of 12oC is very cold. (2)

[6]


SENIOR PHASE EXEMPLAR PROJECT QUESTION 1

Study the nets provided. [Grade 8 and 9 only]

1. 2. 3.

4. 5 Which net would you link to each of the polyhedra listed below? Write the number of the net next to the name of the correct polyhedron. Explain each answer

a) A tetrahedron - _____________________________________________________

b) A hexahedron/Cube - _____________________________________________________

c) An octahedron - _____________________________________________________

d) A dodecahedron - _____________________________________________________

e) An icosahedron - _____________________________________________________

(10)

f) What is the collective name for the group of polyhedra above?

_______________________________________________________________ (1)

g) What is common in the group of polyhedra provided above? Name any TWO things.

__________________________________________________________________

__________________________________________________________________ (4)

(15)


QUESTION 2 [All Grades]

Cut out each of the nets provided and build each polyhedron. You will need a pair of scissors and glue to complete this section. You may need to use cardboard to make your polyhedra rigid. Marks will be awarded for:

Cutting correctly leaving flaps for folding. Accuracy Neatness

QUESTION 3 [All Grades]

a) Complete the table below using the model of objects you made. Polyhedron Number of faces (F) Number of vertices (V) Number of Edges (E) Tetrahedron Cube Octahedron Dodecahedron Icosahedron

b) From your results in Question 3(a), write down an equation which relates the values F, V and E. ________________________________________________________________________________________________________________________________________________________________

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