curriculum and assessment policy...

MATHEMATIC

S

Curriculum and Assessment Policy Statement

Senior PhaseGrades 7-9

National Curriculum Statement (NCS)

CAPS

CurriCulum and assessment PoliCy statement Grades 7-9

matHematiCs

MATHEMATICS GRADES 7-9

CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)

disClaimer

In view of the stringent time requirements encountered by the Department of Basic Education to effect the necessary editorial changes and layout to the Curriculum and Assessment Policy Statements and the supplementary policy documents, possible errors may occur in the said documents placed on the official departmental websites.

There may also be vernacular inconsistencies in the language documents at Home-, First and Second Additional Language levels which have been translated in the various African Languages. Please note that the content of the documents translated and versioned in the African Languages are correct as they are based on the English generic language documents at all three language levels to be implemented in all four school phases.

If any editorial, layout or vernacular inconsistencies are detected, the user is kindly requested to bring this to the attention of the Department of Basic Education.

E-mail: [email protected] or fax (012) 328 9828

department of Basic education

222 Struben StreetPrivate Bag X895Pretoria 0001South AfricaTel: +27 12 357 3000Fax: +27 12 323 0601

120 Plein Street Private Bag X9023Cape Town 8000South Africa Tel: +27 21 465 1701Fax: +27 21 461 8110Website: http://www.education.gov.za

2011 department of Basic education

isBn: 978-1-4315-0525-8

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Printed by: Government Printing Works


CAPS

FOREWORD By THE mINISTER

Our national curriculum is the culmination of our efforts over a period of seventeen years to transform the curriculum bequeathed to us by apartheid. From the start of democracy we have built our curriculum on the values that inspired our Constitution (Act 108 of 1996). The Preamble to the Constitution states that the aims of the Constitution are to:

heal the divisions of the past and establish a society based on democratic values, social justice and fundamental human rights;

improve the quality of life of all citizens and free the potential of each person;

lay the foundations for a democratic and open society in which government is based on the will of the people and every citizen is equally protected by law; and

build a united and democratic South Africa able to take its rightful place as a sovereign state in the family of nations.

Education and the curriculum have an important role to play in realising these aims.

In 1997 we introduced outcomes-based education to overcome the curricular divisions of the past, but the experience of implementation prompted a review in 2000. This led to the first curriculum revision: the Revised National Curriculum Statement Grades R-9 and the National Curriculum Statement Grades 10-12 (2002).

Ongoing implementation challenges resulted in another review in 2009 and we revised the Revised National Curriculum Statement (2002) and the National Curriculum Statement Grades 10-12 to produce this document.

From 2012 the two National Curriculum Statements, for Grades R-9 and Grades 10-12 respectively, are combined in a single document and will simply be known as the National Curriculum Statement Grades R-12. The National Curriculum Statement for Grades R-12 builds on the previous curriculum but also updates it and aims to provide clearer specification of what is to be taught and learnt on a term-by-term basis.

The National Curriculum Statement Grades R-12 represents a policy statement for learning and teaching in South African schools and comprises of the following:

(a) Curriculum and Assessment Policy Statements (CAPS) for all approved subjects listed in this document;

(b) National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and

(c) National Protocol for Assessment Grades R-12.

mrs anGie motsHeKGa, mP minister oF BasiC eduCation


CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)


1CAPS

TABLE OF CONTENTS

seCtion 1: introduCtion and BaCKround ............................................................................... 3

1.1 Background ....................................................................................................................................................3

1.2 overview .....................................................................................................................................................3

1.3 General aims of the south african curriculum ............................................................................................4

1.4 time allocations .............................................................................................................................................6

1.4.1 Foundation Phase ..................................................................................................................................6

1.4.2 Intermediate Phase ................................................................................................................................6

1.4.3 Senior Phase..........................................................................................................................................7

1.4.4 Grades 10-12 .........................................................................................................................................7

seCtion 2: deFinition, aims, sKills and Content .................................................................... 8

2.1 introduction ....................................................................................................................................................8

2.2 What is mathematics?....................................................................................................................................8

2.3 Specificaims ..................................................................................................................................................8

2.4 Specificskills..................................................................................................................................................8

2.5 Focus of content areas ..................................................................................................................................9

mathematics content knowledge ....................................................................................................................10

2.6 Weighting of content areas .........................................................................................................................11

2.7 Specificationofcontent ..............................................................................................................................11

Numbers, Operations and Relationships ..................................................................................................12

Patterns, Functions and Algebra ...............................................................................................................21

Space and Shape (Geometry) ..................................................................................................................27

measurement ............................................................................................................................................31

Data Handling ...........................................................................................................................................33

seCtion 3: ClariFiCation oF Content ....................................................................................... 37

3.1 introduction ..................................................................................................................................................37

3.2 allocation of teaching time .........................................................................................................................37


2 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)

3.3 Clarificationnoteswithteachingguidelines .............................................................................................38

3.3.1 Clarification of content for Grade 7 ......................................................................................................39

Grade 7 term 1 ................................................................................................................................39

Grade 7 term 2 ................................................................................................................................49

Grade 7 term 3 ................................................................................................................................58

Grade 7 term 4 ................................................................................................................................67

3.3.2 Clarification of content for Grade 8 ......................................................................................................75

Grade 8 term 1 ................................................................................................................................75

Grade 8 term 2 ................................................................................................................................92

Grade 8 term 3 ..............................................................................................................................100

Grade 8 term 4 ..............................................................................................................................113

3.3.3 Clarification of content for Grade 9...............................................................................................................119

Grade 9 term 1 ..............................................................................................................................119

Grade 9 term 2 ..............................................................................................................................134

Grade 9 term 3 ..............................................................................................................................141

Grade 9 term 4 ..............................................................................................................................147

seCtion 4: assessment ................................................................................................................ 154 4.1 introduction ...............................................................................................................................................154

4.2 types of assessment .................................................................................................................................154

4.3 informal or daily assessment ....................................................................................................................155

4.4 Formal assessment ....................................................................................................................................155

4.5 recording and reporting ...........................................................................................................................157

4.6 moderation of assessment ........................................................................................................................158

4.7 General .................................................................................................................................................158


3CAPS

SECTION 1: INTRODUCTION AND BACKGROUND

1.1 BaCKGround

The National Curriculum Statement Grades R-12 (NCS) stipulates policy on curriculum and assessment in the schooling sector.

To improve implementation, the National Curriculum Statement was amended, with the amendments coming into effect in January 2012. A single comprehensive Curriculum and Assessment Policy document was developed for each subject to replace Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines in Grades R-12.

1.2 overvieW

(a) The National Curriculum Statement Grades R-12 (January 2012) represents a policy statement for learning and teaching in South African schools and comprises the following:

(i) Curriculum and Assessment Policy Statements for each approved school subject;

(ii) The policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and

(iii) The policy document, National Protocol for Assessment Grades R-12 (January 2012).

(b) The National Curriculum Statement Grades R-12 (January 2012) replaces the two current national curricula statements, namely the

(i) Revised National Curriculum Statement Grades R-9, Government Gazette No. 23406 of 31 May 2002, and

(ii) National Curriculum Statement Grades 10-12 Government Gazettes, No. 25545 of 6 October 2003 and No. 27594 of 17 May 2005.

(c) The national curriculum statements contemplated in subparagraphs b(i) and (ii) comprise the following policy documents which will be incrementally repealed by the National Curriculum Statement Grades R-12 (January 2012) during the period 2012-2014:

(i) The Learning Area/Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines for Grades R-9 and Grades 10-12;

(ii) The policy document, National Policy on assessment and qualifications for schools in the GeneralEducation and Training Band, promulgated in Government Notice No. 124 in Government Gazette No. 29626 of 12 February 2007;

(iii) The policy document, the National Senior Certificate: A qualification at Level 4 on the NationalQualificationsFramework(NQF),promulgatedinGovernmentGazetteNo.27819of20July2005;



(iv) The policy document, An addendum to the policy document, the National Senior Certificate: AqualificationatLevel4ontheNationalQualificationsFramework(NQF),regardinglearnerswithspecialneeds, published in Government Gazette, No.29466 of 11 December 2006, is incorporated in the policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and

(v) The policy document, An addendum to the policy document, the National Senior Certificate: AqualificationatLevel4ontheNationalQualificationsFramework(NQF),regardingtheNationalProtocolfor Assessment (Grades R-12), promulgated in Government Notice No.1267 in Government Gazette No. 29467 of 11 December 2006.

(d) The policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12, and the sections on the Curriculum and Assessment Policy as contemplated in Chapters 2, 3 and 4 of this document constitute the norms and standards of the National Curriculum Statement Grades R-12. It will therefore, in terms of section 6A of the South African Schools Act, 1996(ActNo.84of1996,) form the basis for the minister of Basic Education to determine minimum outcomes and standards, as well as the processes and procedures for the assessment of learner achievement to be applicable to public and independent schools.

1.3 General aims oF tHe soutH aFriCan CurriCulum

(a) The National Curriculum Statement Grades R-12 gives expression to the knowledge, skills and values worth learning in South African schools. This curriculum aims to ensure that children acquire and apply knowledge and skills in ways that are meaningful to their own lives. In this regard, the curriculum promotes knowledge in local contexts, while being sensitive to global imperatives.

(b) The National Curriculum Statement Grades R-12 serves the purposes of:

equipping learners, irrespective of their socio-economic background, race, gender, physical ability or intellectual ability, with the knowledge, skills and values necessary for self-fulfilment, and meaningful participation in society as citizens of a free country;

providing access to higher education;

facilitating the transition of learners from education institutions to the workplace; and

providing employers with a sufficient profile of a learners competences.

(c) The National Curriculum Statement Grades R-12 is based on the following principles:

Social transformation: ensuring that the educational imbalances of the past are redressed, and that equal educational opportunities are provided for all sections of the population;

Active and critical learning: encouraging an active and critical approach to learning, rather than rote and uncritical learning of given truths;

High knowledge and high skills: the minimum standards of knowledge and skills to be achieved at each grade are specified and set high, achievable standards in all subjects;

Progression: content and context of each grade shows progression from simple to complex;


5CAPS

Human rights, inclusivity, environmental and social justice: infusing the principles and practices of social and environmental justice and human rights as defined in the Constitution of the Republic of South Africa. The National Curriculum Statement Grades R-12 is sensitive to issues of diversity such as poverty, inequality, race, gender, language, age, disability and other factors;

Valuing indigenous knowledge systems: acknowledging the rich history and heritage of this country as important contributors to nurturing the values contained in the Constitution; and

Credibility, quality and efficiency: providing an education that is comparable in quality, breadth and depth to those of other countries.

(d) The National Curriculum Statement Grades R-12 aims to produce learners that are able to:

identify and solve problems and make decisions using critical and creative thinking;

work effectively as individuals and with others as members of a team;

organise and manage themselves and their activities responsibly and effectively;

collect, analyse, organise and critically evaluate information;

communicate effectively using visual, symbolic and/or language skills in various modes;

use science and technology effectively and critically showing responsibility towards the environment and the health of others; and

demonstrate an understanding of the world as a set of related systems by recognising that problem solving contexts do not exist in isolation.

(e) Inclusivity should become a central part of the organisation, planning and teaching at each school. This can only happen if all teachers have a sound understanding of how to recognise and address barriers to learning, and how to plan for diversity.

The key to managing inclusivity is ensuring that barriers are identified and addressed by all the relevant support structures within the school community, including teachers, District-Based Support Teams, Institutional-Level Support Teams, parents and Special Schools as Resource Centres. To address barriers in the classroom, teachers should use various curriculum differentiation strategies such as those included in the Department of Basic Educations Guidelines for Inclusive Teaching and Learning (2010).



1.4 time alloCation

1.4.1 Foundation Phase

(a) The instructional time in the Foundation Phase is as follows:

suBJeCtGrade r (Hours)

Grades 1-2 (Hours)

Grade 3 (Hours)

Home Language 10 8/7 8/7

First Additional Language 2/3 3/4

mathematics 7 7 7

Life Skills

Beginning Knowledge

Creative Arts

Physical Education

Personal and Social Well-being

6

(1)

(2)

(2)

(1)

6

(1)

(2)

(2)

(1)

7

(2)

(2)

(2)

(1)

total 23 23 25

(b) Instructional time for Grades R, 1 and 2 is 23 hours and for Grade 3 is 25 hours.

(c) Ten hours are allocated for languages in Grades R-2 and 11 hours in Grade 3. A maximum of 8 hours and a minimum of 7 hours are allocated for Home Language and a minimum of 2 hours and a maximum of 3 hours for Additional Language in Grades 1-2. In Grade 3 a maximum of 8 hours and a minimum of 7 hours are allocated for Home Language and a minimum of 3 hours and a maximum of 4 hours for First Additional Language.

(d) In Life Skills Beginning Knowledge is allocated 1 hour in Grades R 2 and 2 hours as indicated by the hours in brackets for Grade 3.

1.4.2 intermediate Phase

(a) The instructional time in the Intermediate Phase is as follows:

suBJeCt Hours

Home Language 6

First Additional Language 5

mathematics 6

Natural Sciences and Technology 3,5

Social Sciences 3

Life Skills

Creative Arts

Physical Education

Personal and Social Well-being

4

(1,5)

(1)

(1,5)

total 27,5


7CAPS

1.4.3 senior Phase

(a) The instructional time in the Senior Phase is as follows:

suBJeCt Hours

Home Language 5

First Additional Language 4

mathematics 4,5

Natural Sciences 3

Social Sciences 3

Technology 2

Economic management Sciences 2

Life Orientation 2

Creative Arts 2

total 27,5

1.4.4 Grades 10-12

(a) The instructional time in Grades 10-12 is as follows:

suBJeCt time alloCation Per WeeK (Hours)

Home Language 4.5

First Additional Language 4.5

mathematics 4.5

Life Orientation 2

A minimum of any three subjects selected from Group B Annexure B, Tables B1-B8 of the policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12, subject to the provisos stipulated in paragraph 28 of the said policy document.

12 (3x4h)

total 27,5

The allocated time per week may be utilised only for the minimum required NCS subjects as specified above, and may not be used for any additional subjects added to the list of minimum subjects. Should a learner wish to offer additional subjects, additional time must be allocated for the offering of these subjects.



SECTION 2: DEFINITION, AIMS, SKILLS AND CONTENT

2.1 introduCtion

In Section 2, the Senior Phase Mathematics Curriculum and Assessment Policy Statement (CAPS) provides teachers with a definition of mathematics, specific aims, specific skills, focus of content areas, weighting of content areas and content specification.

2.2 WHat is matHematiCs?

mathematics is a language that makes use of symbols and notations to describe numerical, geometric and graphical relationships. It is a human activity that involves observing, representing and investigating patterns and quantitative relationships in physical and social phenomena and between mathematical objects themselves. It helps to develop mental processes that enhance logical and critical thinking, accuracy and problem-solving that will contribute in decision-making.

2.3 sPeCiFiC aims

The teaching and learning of mathematics aims to develop

a critical awareness of how mathematical relationships are used in social, environmental, cultural and economic relations

confidence and competence to deal with any mathematical situation without being hindered by a fear of mathematics

an appreciation for the beauty and elegance of mathematics

a spirit of curiosity and a love for mathematics

recognition that mathematics is a creative part of human activity

deep conceptual understandings in order to make sense of mathematics

acquisition of specific knowledge and skills necessary for:

- the application of mathematics to physical, social and mathematical problems

- the study of related subject matter (e.g. other subjects)

- further study in Mathematics.

2.4 sPeCiFiC sKills

To develop essential mathematical skills the learner should

develop the correct use of the language of mathematics

develop number vocabulary, number concept and calculation and application skills


9CAPS

learn to listen, communicate, think, reason logically and apply the mathematical knowledge gained

learn to investigate, analyse, represent and interpret information

learn to pose and solve problems

build an awareness of the important role that mathematics plays in real life situations including the personal development of the learner.

2.5 FoCus oF Content areas

Mathematics in the Senior Phase covers five main Content Areas.

Numbers, Operations and Relationships;

Patterns, Functions and Algebra;

Space and Shape (Geometry);

measurement; and

Data Handling.

Each content area contributes towards the acquisition of specific skills. The table below shows the general focus of the content areas as well as the specific focus of the content areas for the Senior Phase.



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cy in

sim

ple

expe

rimen

ts


11CAPS

2.6 WeiGHtinG oF Content areas

The weighting of mathematics content areas serves two primary purposes:

guidance on the time needed to adequately address the content within each content area

guidance on the spread of content in the examination (especially end-of-year summative assessment).

WeiGHtinG oF Content areas

Content Area Grade 7 Grade 8 Grade 9

Number, Operations and Relations 30% 25% 15%

Patterns, Functions and Algebra 25% 30% 35%

Space and Shape (Geometry) 25% 25% 30%

measurement 10% 10% 10%

Data Handling 10% 10% 10%

100% 100% 100%

2.7 sPeCiFiCation oF Content

The Specification of Content in Section 2 shows progression in terms of concepts and skills from Grades 7 - 9 for each Content Area. However, in certain topics the concepts and skills are similar in two or three successive grades. The Clarification of Content in Section 3 provides guidelines on how progression should be addressed in these cases. The Specification of Content in Section 2 should therefore be read in conjunction with the Clarification of Content in Section 3.



sPeC

iFiC

atio

n o

F C

on

ten

t (P

Ha

se o

ver

vieW

)

nu

mB

ers,

oPe

rat

ion

s a

nd

rel

atio

nsH

iPs

P

rogr

essi

on in

Num

bers

, Ope

ratio

ns a

nd R

elat

ions

hips

in th

e S

enio

r Pha

se is

ach

ieve

d pr

imar

ily b

y:

-de

velo

pmen

t of c

alcu

latio

ns u

sing

who

le n

umbe

rs to

cal

cula

tions

usi

ng ra

tiona

l num

bers

, int

eger

s an

d nu

mbe

rs in

exp

onen

tial f

orm

-de

velo

pmen

t of u

nder

stan

ding

of d

iffer

ent n

umbe

r sys

tem

s fro

m n

atur

al a

nd w

hole

num

bers

to in

tege

rs a

nd ra

tiona

l num

bers

, as

wel

l as

the

reco

gniti

on o

f irr

atio

nal n

umbe

rs

-in

crea

sing

use

of p

rope

rties

of n

umbe

rs to

per

form

cal

cula

tions

-in

crea

sing

com

plex

ity o

f con

text

s fo

r sol

ving

pro

blem

s

N

umbe

rs, O

pera

tions

and

Rel

atio

nshi

ps in

the

Sen

ior P

hase

con

solid

ates

wor

k do

ne in

the

Inte

rmed

iate

Pha

se a

nd is

gea

red

tow

ards

mak

ing

lear

ners

com

pete

nt a

nd e

ffici

ent i

n pe

rform

ing

calc

ulat

ions

par

ticul

arly

with

inte

gers

and

ratio

nal n

umbe

rs.

R

ecog

nisi

ng a

nd u

sing

the

prop

ertie

s of

ope

ratio

ns fo

r diff

eren

t num

bers

pro

vide

s a

criti

cal f

ound

atio

n fo

r wor

k in

alg

ebra

whe

n le

arne

rs w

ork

with

var

iabl

es in

pla

ce o

f num

bers

and

m

anip

ulat

e al

gebr

aic

expr

essi

ons

and

solv

e al

gebr

aic

equa

tions

.

Co

nte

nt

Gr

ad

e 7

Gr

ad

e 8

Gr

ad

e 9

1.1

Who

le n

umbe

rsm

enta

l cal

cula

tions

Rev

ise

the

follo

win

g do

ne in

Gra

de 6

:

M

ultip

licat

ion

of w

hole

num

bers

to a

t lea

st 1

2 x

12

m

ultip

licat

ion

fact

s fo

r:

-un

its a

nd te

ns b

y m

ultip

les

of te

n

-un

its a

nd te

ns b

y m

ultip

les

of 1

00

-un

its a

nd te

ns b

y m

ultip

les

of 1

000

-un

its a

nd te

ns b

y m

ultip

les

of 1

0 00

0

In

vers

e op

erat

ion

betw

een

mul

tiplic

atio

n an

d di

visi

on

ord

erin

g an

d co

mpa

ring

who

le n

umbe

rs

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

-or

der,

com

pare

and

repr

esen

t num

bers

to a

t le

ast 9

-dig

it nu

mbe

rs

-re

cogn

ize

and

repr

esen

t prim

e nu

mbe

rs to

at

leas

t 100

-ro

und

off n

umbe

rs to

the

near

est 5

, 10,

100

or

1 00

0

men

tal c

alcu

latio

ns

R

evis

e m

ultip

licat

ion

of w

hole

num

bers

to a

t lea

st

12 x

12

ord

erin

g an

d co

mpa

ring

who

le n

umbe

rs

R

evis

e pr

ime

num

bers

to a

t lea

st 1

00


13CAPS

Co

nte

nt

Gr

ad

e 7

Gr

ad

e 8

Gr

ad

e 9

1.1

Who

le n

umbe

rsPr

oper

ties

of w

hole

num

bers

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

-re

cogn

ize

and

use

the

com

mut

ativ

e;

asso

ciat

ive;

dis

tribu

tive

prop

ertie

s of

who

le

num

bers

-re

cogn

ize

and

use

0 in

term

s of

its

addi

tive

prop

erty

(ide

ntity

ele

men

t for

add

ition

)

-re

cogn

ize

and

use

1 in

term

s of

its

mul

tiplic

ativ

e pr

oper

ty (i

dent

ity e

lem

ent f

or m

ultip

licat

ion)

Cal

cula

tions

usi

ng w

hole

num

bers

R

evis

e th

e fo

llow

ing

done

in G

rade

6, w

ithou

t use

of

cal

cula

tors

:

-A

dditi

on a

nd s

ubtra

ctio

n of

who

le n

umbe

rs to

at

leas

t 6-d

igit

num

bers

-M

ultip

licat

ion

of a

t lea

st w

hole

4-d

igit

by 2

-dig

it nu

mbe

rs

-D

ivis

ion

of a

t lea

st w

hole

4-d

igit

by 2

-dig

it nu

mbe

rs

-P

erfo

rm c

alcu

latio

ns u

sing

all

four

ope

ratio

ns

on w

hole

num

bers

, est

imat

ing

and

usin

g ca

lcul

ator

s w

here

app

ropr

iate

Cal

cula

tion

tech

niqu

es

U

se a

rang

e of

stra

tegi

es to

per

form

and

che

ck

writ

ten

and

men

tal c

alcu

latio

ns o

f who

le n

umbe

rs

incl

udin

g:

-lo

ng d

ivis

ion

-ad

ding

, sub

tract

ing

and

mul

tiply

ing

in c

olum

ns

-es

timat

ion

-ro

undi

ng o

ff an

d co

mpe

nsat

ing

-us

ing

a ca

lcul

ator

Prop

ertie

s of

who

le n

umbe

rs

R

evis

e:

-Th

e co

mm

utat

ive;

ass

ocia

tive;

dis

tribu

tive

prop

ertie

s of

who

le n

umbe

rs

-0

in te

rms

of it

s ad

ditiv

e pr

oper

ty (i

dent

ity

elem

ent f

or a

dditi

on)

-1

in te

rms

of it

s m

ultip

licat

ive

prop

erty

(ide

ntity

el

emen

t for

mul

tiplic

atio

n)

R

ecog

nize

the

divi

sion

pro

perty

of 0

, whe

reby

any

nu

mbe

r div

ided

by

0 is

und

efine

d

Cal

cula

tions

usi

ng w

hole

num

bers

R

evis

e ca

lcul

atio

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

Cal

cula

tion

tech

niqu

es

U

se a

rang

e of

tech

niqu

es to

per

form

and

che

ck

writ

ten

and

men

tal c

alcu

latio

ns o

f who

le n

umbe

rs

incl

udin

g:

-lo

ng d

ivis

ion

-ad

ding

, sub

tract

ing

and

mul

tiply

ing

in c

olum

ns

-es

timat

ion

-ro

undi

ng o

ff an

d co

mpe

nsat

ing

-us

ing

a ca

lcul

ator

Prop

ertie

s of

num

bers

D

escr

ibe

the

real

num

ber s

yste

m b

y re

cogn

isin

g,

defin

ing

and

dist

ingu

ishi

ng p

rope

rties

of:

-na

tura

l num

bers

-w

hole

num

bers

-in

tege

rs

-ra

tiona

l num

bers

-irr

atio

nal n

umbe

rs

Cal

cula

tions

usi

ng w

hole

num

bers

R

evis

e ca

lcul

atio

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

Cal

cula

tion

tech

niqu

es

U

se a

rang

e of

tech

niqu

es to

per

form

and

che

ck

writ

ten

and

men

tal c

alcu

latio

ns o

f who

le n

umbe

rs

incl

udin

g:

-lo

ng d

ivis

ion

-ad

ding

, sub

tract

ing

and

mul

tiply

ing

in c

olum

ns

-es

timat

ion

-ro

undi

ng o

ff an

d co

mpe

nsat

ing

-us

ing

a ca

lcul

ator



Co

nte

nt

Gr

ad

e 7

Gr

ad

e 8

Gr

ad

e 9

1.1

Who

le n

umbe

rsm

ultip

les

and

fact

ors

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

-m

ultip

les

of 2

-dig

it an

d 3-

digi

t who

le n

umbe

rs

-fa

ctor

s of

2-d

igit

and

3-di

git w

hole

num

bers

-pr

ime

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-d

igit

who

le n

umbe

rs

Fi

nd th

e LC

m a

nd H

CF

of n

umbe

rs to

at

leas

t 3-d

igit

who

le n

umbe

rs, b

y in

spec

tion

or

fact

oris

atio

n

solv

ing

prob

lem

s

S

olve

pro

blem

s in

volv

ing

who

le n

umbe

rs,

incl

udin

g

-co

mpa

ring

two

or m

ore

quan

titie

s of

the

sam

e ki

nd (r

atio

)

-co

mpa

ring

two

quan

titie

s of

diff

eren

t kin

ds (r

ate)

-sh

arin

g in

a g

iven

ratio

whe

re th

e w

hole

is g

iven

S

olve

pro

blem

s th

at in

volv

e w

hole

num

bers

, pe

rcen

tage

s an

d de

cim

al fr

actio

ns in

fina

ncia

l co

ntex

ts s

uch

as:

-pr

ofit,

loss

and

dis

coun

t

-bu

dget

s

-ac

coun

ts

-lo

ans

-si

mpl

e in

tere

st

mul

tiple

s an

d fa

ctor

s

R

evis

e:

-P

rime

fact

ors

of n

umbe

rs t

o at

lea

st 3

-dig

it w

hole

num

bers

-LC

M a

nd H

CF

of n

umbe

rs t

o at

lea

st 3

-dig

it w

hole

num

bers

, by

insp

ectio

n or

fact

oris

atio

n

solv

ing

prob

lem

s

S

olve

pro

blem

s in

volv

ing

who

le n

umbe

rs,

incl

udin

g

-co

mpa

ring

two

or m

ore

quan

titie

s of

the

sam

e ki

nd (r

atio

)

-co

mpa

ring

two

quan

titie

s of

diff

eren

t kin

ds (r

ate)

-sh

arin

g in

a g

iven

ratio

whe

re th

e w

hole

is g

iven

-in

crea

sing

or d

ecre

asin

g of

a n

umbe

r in

a gi

ven

ratio

S

olve

pro

blem

s th

at in

volv

e w

hole

num

bers

, pe

rcen

tage

s an

d de

cim

al fr

actio

ns in

fina

ncia

l co

ntex

ts s

uch

as:

-pr

ofit,

loss

, dis

coun

t and

VAT

-bu

dget

s

-ac

coun

ts

-lo

ans

-si

mpl

e in

tere

st

-hi

re p

urch

ase

-ex

chan

ge ra

tes

mul

tiple

s an

d fa

ctor

s

U

se p

rime

fact

oris

atio

n of

num

bers

to fi

nd L

CM

an

d H

CF

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

s in

volv

ing

-ra

tio a

nd ra

te

-di

rect

and

indi

rect

pro

porti

on

S

olve

pro

blem

s th

at in

volv

e w

hole

num

bers

, pe

rcen

tage

s an

d de

cim

al fr

actio

ns in

fina

ncia

l co

ntex

ts s

uch

as:

-pr

ofit,

loss

, dis

coun

t and

VAT

-bu

dget

s

-ac

coun

ts

-lo

ans

-S

impl

e in

tere

st

-hi

re p

urch

ase

-ex

chan

ge ra

tes

-co

mm

issi

on

-re

ntal

s

-co

mpo

und

inte

rest


15CAPS

Co

nte

nt

Gr

ad

e 7

Gr

ad

e 8

Gr

ad

e 9

1.2

expo

nent

sm

enta

l cal

cula

tions

D

eter

min

e sq

uare

s to

at l

east

122

and

thei

r sq

uare

root

s

D

eter

min

e cu

bes

to a

t lea

st 6

3 and

cub

e ro

ots

Com

parin

g an

d re

pres

entin

g nu

mbe

rs in

ex

pone

ntia

l for

m

C

ompa

re a

nd re

pres

ent w

hole

num

bers

in

expo

nent

ial f

orm

: ab

= a

x a

x a

x...

for b

num

ber o

f fac

tors

Cal

cula

tions

usi

ng n

umbe

rs in

exp

onen

tial f

orm

R

ecog

nize

and

use

the

appr

opria

te la

ws

of

oper

atio

ns w

ith n

umbe

rs in

volv

ing

expo

nent

s an

d sq

uare

and

cub

e ro

ots

P

erfo

rm c

alcu

latio

ns in

volv

ing

all f

our o

pera

tions

us

ing

num

bers

in e

xpon

entia

l for

m, l

imite

d to

ex

pone

nts

up to

5, a

nd s

quar

e an

d cu

be ro

ots

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

s in

volv

ing

num

bers

in

expo

nent

ial f

orm

.

men

tal c

alcu

latio

ns

R

evis

e:

-S

quar

es to

at l

east

122

and

thei

r squ

are

root

s

-C

ubes

to a

t lea

st 6

3 and

thei

r cub

e ro

ots

Com

parin

g an

d re

pres

entin

g nu

mbe

rs in

ex

pone

ntia

l for

m

R

evis

e co

mpa

re a

nd re

pres

ent w

hole

num

bers

in

expo

nent

ial f

orm

C

ompa

re a

nd re

pres

ent i

nteg

ers

in e

xpon

entia

l fo

rm

C

ompa

re a

nd re

pres

ent n

umbe

rs in

sci

entifi

c no

tatio

n, li

mite

d to

pos

itive

exp

onen

ts

Cal

cula

tions

usi

ng n

umbe

rs in

exp

onen

tial f

orm

E

stab

lish

gene

ral l

aws

of e

xpon

ents

, lim

ited

to:

-na

tura

l num

ber e

xpon

ents

-am

x a

n = a

m +

n

-am

a

n = a

m

n, i

f m>n

-(a

m)n

= am

x n

-(a

x t)

n = a

n x

tn

-a0

= 1

R

ecog

nize

and

use

the

appr

opria

te la

ws

of

oper

atio

ns u

sing

num

bers

invo

lvin

g ex

pone

nts

and

squa

re a

nd c

ube

root

s

P

erfo

rm c

alcu

latio

ns in

volv

ing

all f

our o

pera

tions

w

ith n

umbe

rs th

at in

volv

e th

e sq

uare

s, c

ubes

, sq

uare

root

s an

d cu

be 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 n

umbe

rs

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

s in

volv

ing

num

bers

in

expo

nent

ial f

orm

Com

parin

g an

d re

pres

entin

g nu

mbe

rs in

ex

pone

ntia

l for

m

R

evis

e co

mpa

re a

nd re

pres

ent i

nteg

ers

in

expo

nent

ial f

orm

-co

mpa

re a

nd r

epre

sent

num

bers

in

scie

ntifi

c no

tatio

n

E

xten

d sc

ient

ific

nota

tion

to in

clud

e ne

gativ

e ex

pone

nts

Cal

cula

tions

usi

ng n

umbe

rs in

exp

onen

tial f

orm

R

evis

e th

e fo

llow

ing

gene

ral l

aws

of e

xpon

ents

:

-am

x a

n = a

m +

n

-am

a

n = a

m

n, i

f m>n

-(a

m)n

= am

x n

-(a

x t)

n = a

n x

tn

-a0

= 1

E

xten

d th

e ge

nera

l law

s of

exp

onen

ts to

incl

ude:

-in

tege

r exp

onen

ts

-a

m=

1

am

P

erfo

rm c

alcu

latio

ns in

volv

ing

all f

our o

pera

tions

us

ing

num

bers

in e

xpon

entia

l for

m, u

sing

the

law

s of

exp

onen

ts

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

s in

volv

ing

num

bers

in

expo

nent

ial f

orm

, inc

ludi

ng s

cien

tific

nota

tion



Co

nte

nt

Gr

ad

e 7

Gr

ad

e 8

Gr

ad

e 9

1.3

inte

gers

Cou

ntin

g, o

rder

ing

and

com

parin

g in

tege

rs

C

ount

forw

ards

and

bac

kwar

ds in

inte

gers

for a

ny

inte

rval

R

ecog

nize

, ord

er a

nd c

ompa

re 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

nise

and

use

com

mut

ativ

e an

d as

soci

ativ

e pr

oper

ties

of a

dditi

on a

nd m

ultip

licat

ion

for

inte

gers

solv

ing

prob

lem

s

Sol

ve p

robl

ems

in c

onte

xts

invo

lvin

g ad

ditio

n an

d su

btra

ctio

n w

ith in

tege

rs

Cou

ntin

g, o

rder

ing

and

com

parin

g in

tege

rs

R

evis

e:

-co

untin

g fo

rwar

ds a

nd b

ackw

ards

in in

tege

rs

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 ad

ditio

n an

d su

btra

ctio

n w

ith in

tege

rs

m

ultip

ly a

nd d

ivid

e w

ith in

tege

rs

P

erfo

rm c

alcu

latio

ns in

volv

ing

all f

our o

pera

tions

w

ith in

tege

rs

P

erfo

rm c

alcu

latio

ns in

volv

ing

all f

our o

pera

tions

w

ith n

umbe

rs th

at in

volv

e th

e sq

uare

s, c

ubes

, sq

uare

root

s an

d cu

be ro

ots

of in

tege

rs

Prop

ertie

s of

inte

gers

R

ecog

nise

and

use

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

R

ecog

nize

and

use

add

itive

and

mul

tiplic

ativ

e in

vers

es fo

r int

eger

s

solv

ing

prob

lem

s

Sol

ve p

robl

ems

in c

onte

xts

invo

lvin

g m

ultip

le

oper

atio

ns w

ith 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

-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

in

tege

rs

Prop

ertie

s of

inte

gers

R

evis

e:

-C

omm

utat

ive,

ass

ocia

tive

and

dist

ribut

ive

prop

ertie

s of

add

ition

and

mul

tiplic

atio

n fo

r in

tege

rs

-ad

ditiv

e an

d m

ultip

licat

ive

inve

rses

for i

nteg

ers

solv

ing

prob

lem

s

Sol

ve p

robl

ems

in c

onte

xts

invo

lvin

g m

ultip

le

oper

atio

ns w

ith in

tege

rs


17CAPS

Co

nte

nt

Gr

ad

e 7

Gr

ad

e 8

Gr

ad

e 9

1.4

Com

mon

fr

actio

ns

ord

erin

g, c

ompa

ring

and

sim

plify

ing

frac

tions

R

evis

e th

e fo

llow

ing

done

in G

rade

6

-co

mpa

re a

nd o

rder

com

mon

frac

tions

, inc

ludi

ng

spec

ifica

lly te

nths

and

hun

dred

ths

E

xten

d to

thou

sand

ths

Cal

cula

tions

with

frac

tions

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

-ad

ditio

n an

d su

btra

ctio

n of

com

mon

frac

tions

, in

clud

ing

mix

ed n

umbe

rs, l

imite

d to

frac

tions

w

ith th

e sa

me

deno

min

ator

or w

here

one

de

nom

inat

or is

a m

ultip

le o

f ano

ther

-fin

ding

frac

tions

of w

hole

num

bers

E

xten

d ad

ditio

n an

d su

btra

ctio

n to

frac

tions

w

here

one

den

omin

ator

is n

ot a

mul

tiple

of t

he

othe

r

m

ultip

licat

ion

of c

omm

on fr

actio

ns, i

nclu

ding

m

ixed

num

bers

, not

lim

ited

to fr

actio

ns w

here

one

de

nom

inat

or is

a m

ultip

le o

f ano

ther

Cal

cula

tion

tech

niqu

es

C

onve

rt m

ixed

num

bers

to c

omm

on fr

actio

ns in

or

der t

o pe

rform

cal

cula

tions

with

them

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 b

efor

e or

afte

r ca

lcul

atio

ns

U

se k

now

ledg

e of

equ

ival

ent f

ract

ions

to a

dd a

nd

subt

ract

com

mon

frac

tions

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

s in

volv

ing

com

mon

fra

ctio

ns a

nd m

ixed

num

bers

, inc

ludi

ng g

roup

ing,

sh

arin

g an

d fin

ding

frac

tions

of w

hole

num

bers

Cal

cula

tions

with

frac

tions

R

evis

e:

-ad

ditio

n an

d su

btra

ctio

n of

com

mon

frac

tions

, in

clud

ing

mix

ed n

umbe

rs

-fin

ding

frac

tions

of w

hole

num

bers

-m

ultip

licat

ion

of c

omm

on fr

actio

ns, i

nclu

ding

m

ixed

num

bers

D

ivid

e w

hole

num

bers

and

com

mon

frac

tions

by

com

mon

frac

tions

C

alcu

late

the

squa

res,

cub

es, s

quar

e ro

ots

and

cube

root

s of

com

mon

frac

tions

Cal

cula

tion

tech

niqu

es

R

evis

e:

-co

nver

t mix

ed n

umbe

rs to

com

mon

frac

tions

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

bef

ore

or a

fter

calc

ulat

ions

-us

e kn

owle

dge

of e

quiv

alen

t fra

ctio

ns to

add

an

d su

btra

ct c

omm

on fr

actio

ns

U

se k

now

ledg

e of

reci

proc

al re

latio

nshi

ps to

di

vide

com

mon

frac

tions

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

s in

volv

ing

com

mon

fra

ctio

ns a

nd m

ixed

num

bers

, inc

ludi

ng g

roup

ing,

sh

arin

g an

d fin

ding

frac

tions

of w

hole

num

bers

Cal

cula

tions

with

frac

tions

A

ll fo

ur o

pera

tions

with

com

mon

frac

tions

and

m

ixed

num

bers

A

ll fo

ur o

pera

tions

, with

num

bers

that

invo

lve

the

squa

res,

cub

es, s

quar

e ro

ots

and

cube

root

s of

co

mm

on fr

actio

ns

Cal

cula

tion

tech

niqu

es

R

evis

e:

-co

nver

t mix

ed n

umbe

rs to

com

mon

frac

tions

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

bef

ore

or a

fter

calc

ulat

ions

-us

e kn

owle

dge

of e

quiv

alen

t fra

ctio

ns to

add

an

d su

btra

ct c

omm

on fr

actio

ns

-us

e kn

owle

dge

of re

cipr

ocal

rela

tions

hips

to

divi

de c

omm

on fr

actio

ns

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

s in

volv

ing

com

mon

fra

ctio

ns, m

ixed

num

bers

and

per

cent

ages



Co

nte

nt

Gr

ad

e 7

Gr

ad

e 8

Gr

ad

e 9

1.4

Com

mon

Fr

actio

ns

Perc

enta

ges

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 d

ecre

ase

of

who

le n

umbe

rs

S

olve

pro

blem

s in

con

text

s in

volv

ing

perc

enta

ges

equi

vale

nt fo

rms

Rev

ise

the

follo

win

g do

ne in

Gra

de 6

:

re

cogn

ize

and

use

equi

vale

nt fo

rms

of c

omm

on

fract

ions

with

1-d

igit

or 2

-dig

it de

nom

inat

ors

(frac

tions

whe

re o

ne d

enom

inat

or is

a m

ultip

le o

f th

e ot

her)

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

frac

tion,

de

cim

al fr

actio

n an

d pe

rcen

tage

form

s of

the

sam

e nu

mbe

r

Perc

enta

ges

R

evis

e:

-fin

ding

per

cent

ages

of w

hole

num

bers

-ca

lcul

atin

g th

e pe

rcen

tage

of p

art o

f a w

hole

-ca

lcul

atin

g pe

rcen

tage

incr

ease

or d

ecre

ase

C

alcu

late

am

ount

s if

give

n pe

rcen

tage

incr

ease

or

dec

reas

e

S

olve

pro

blem

s in

con

text

s in

volv

ing

perc

enta

ges

equi

vale

nt fo

rms

R

evis

e eq

uiva

lent

form

s be

twee

n:

-co

mm

on fr

actio

ns (f

ract

ions

whe

re o

ne

deno

min

ator

is a

mul

tiple

of t

he o

ther

)

-co

mm

on fr

actio

n an

d de

cim

al fr

actio

n fo

rms

of

the

sam

e nu

mbe

r

-co

mm

on fr

actio

n, d

ecim

al fr

actio

n an

d pe

rcen

tage

form

s of

the

sam

e nu

mbe

r

equi

vale

nt fo

rms

R

evis

e eq

uiva

lent

form

s be

twee

n:

-co

mm

on fr

actio

ns w

here

one

den

omin

ator

is a

m

ultip

le o

f ano

ther

-co

mm

on fr

actio

n an

d de

cim

al fr

actio

n fo

rms

of

the

sam

e nu

mbe

r

-co

mm

on fr

actio

n, d

ecim

al fr

actio

n an

d pe

rcen

tage

form

s of

the

sam

e nu

mbe

r


19CAPS

Co

nte

nt

Gr

ad

e 7

Gr

ad

e 8

Gr

ad

e 9

1.5

dec

imal

fr

actio

ns

ord

erin

g an

d co

mpa

ring

deci

mal

frac

tions

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

-co

unt f

orw

ards

and

bac

kwar

ds in

dec

imal

fra

ctio

ns to

at l

east

two

deci

mal

pla

ces

-co

mpa

re a

nd o

rder

dec

imal

frac

tions

to a

t lea

st

two

deci

mal

pla

ces

-pl

ace

valu

e of

dig

its to

at l

east

two

deci

mal

pl

aces

-ro

undi

ng o

ff de

cim

al fr

actio

ns to

at l

east

1

deci

mal

pla

ce

E

xten

d al

l of t

he a

bove

to d

ecim

al fr

actio

ns to

at

leas

t thr

ee d

ecim

al p

lace

s an

d ro

undi

ng o

ff to

at

leas

t 2 d

ecim

al p

lace

s

Cal

cula

tions

with

dec

imal

frac

tions

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

-ad

ditio

n an

d su

btra

ctio

n of

dec

imal

frac

tions

of

at le

ast t

wo

deci

mal

pla

ces

-m

ultip

licat

ion

of d

ecim

al fr

actio

ns b

y 10

and

10

0

E

xten

d ad

ditio

n an

d su

btra

ctio

n to

dec

imal

fra

ctio

ns o

f at l

east

thre

e de

cim

al p

lace

s

m

ultip

ly d

ecim

al fr

actio

ns to

incl

ude:

-de

cim

al fr

actio

ns to

at l

east

3 d

ecim

al p

lace

s by

who

le n

umbe

rs

-de

cim

al fr

actio

ns to

at l

east

2 d

ecim

al p

lace

s by

dec

imal

frac

tions

to a

t lea

st 1

dec

imal

pla

ce

D

ivid

e de

cim

al fr

actio

ns to

incl

ude

deci

mal

fra

ctio

ns to

at l

east

3 d

ecim

al p

lace

s by

who

le

num

bers

Cal

cula

tion

tech

niqu

es

U

se k

now

ledg

e of

pla

ce v

alue

to e

stim

ate

the

num

ber o

f dec

imal

pla

ces

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

che

ck re

sults

w

here

app

ropr

iate

ord

erin

g an

d co

mpa

ring

deci

mal

frac

tions

R

evis

e:

-or

derin

g, c

ompa

ring

and

plac

e va

lue

of d

ecim

al

fract

ions

to a

t lea

st 3

dec

imal

pla

ces

-ro

undi

ng o

ff de

cim

al fr

actio

ns to

at l

east

2

deci

mal

pla

ce

Cal

cula

tions

with

dec

imal

frac

tions

R

evis

e:

-ad

ditio

n, s

ubtra

ctio

n, m

ultip

licat

ion

and

of

deci

mal

frac

tions

to a

t lea

st 3

dec

imal

pla

ces

-di

visi

on o

f dec

imal

frac

tions

by

who

le n

umbe

rs

E

xten

d m

ultip

licat

ion

to 'm

ultip

licat

ion

by d

ecim

al

fract

ions

' not

lim

ited

to o

ne d

ecim

al p

lace

E

xten

d di

visi

on to

'div

isio

n of

dec

imal

frac

tions

by

deci

mal

frac

tions

'

C

alcu

late

the

squa

res,

cub

es, s

quar

e ro

ots

and

cube

root

s of

dec

imal

frac

tions

Cal

cula

tion

tech

niqu

es

U

se k

now

ledg

e of

pla

ce v

alue

to e

stim

ate

the

num

ber o

f dec

imal

pla

ces

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

che

ck re

sults

w

here

app

ropr

iate

Cal

cula

tions

with

dec

imal

frac

tions

m

ultip

le o

pera

tions

with

dec

imal

frac

tions

, usi

ng a

ca

lcul

ator

whe

re a

ppro

pria

te

m

ultip

le o

pera

tions

with

or w

ithou

t bra

cket

s, w

ith

num

bers

that

invo

lve

the

squa

res,

cub

es, s

quar

e ro

ots

and

cube

root

s of

dec

imal

frac

tions

Cal

cula

tion

tech

niqu

es

U

se k

now

ledg

e of

pla

ce v

alue

to e

stim

ate

the

num

ber o

f dec

imal

pla

ces

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

che

ck re

sults

w

here

app

ropr

iate



Co

nte

nt

Gr

ad

e 7

Gr

ad

e 8

Gr

ad

e 9

1.5

dec

imal

fr

actio

ns

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

invo

lvin

g de

cim

al

fract

ions

equi

vale

nt fo

rms

R

evis

e th

e fo

llow

ing

done

in G

rade

6:

-re

cogn

ize

equi

vale

nce

betw

een

com

mon

fra

ctio

n an

d de

cim

al fr

actio

n fo

rms

of th

e sa

me

num

ber

-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

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

invo

lvin

g de

cim

al

fract

ions

equi

vale

nt fo

rms

R

evis

e eq

uiva

lent

form

s be

twee

n:

-co

mm

on fr

actio

n an

d de

cim

al fr

actio

n fo

rms

of

the

sam

e nu

mbe

r

-co

mm

on fr

actio

n, d

ecim

al fr

actio

n an

d pe

rcen

tage

form

s of

the

sam

e nu

mbe

r

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

invo

lvin

g de

cim

al

fract

ions

equi

vale

nt fo

rms

Rev

ise

equi

vale

nt fo

rms

betw

een:

-co

mm

on fr

actio

n an

d de

cim

al fr

actio

n fo

rms

of

the

sam

e nu

mbe

r

-co

mm

on fr

actio

n, d

ecim

al fr

actio

n an

d pe

rcen

tage

form

s of

the

sam

e nu

mbe

r


21CAPS

sPeC

iFiC

atio

n o

F C

on

ten

t (P

Ha

se o

ver

vieW

)

Patt

ern

s, F

un

Cti

on

s a

nd

alG

eBr

a

P

rogr

essi

on in

Pat

tern

s, F

unct

ions

and

Alg

ebra

is a

chie

ved

prim

arily

by

-in

crea

sing

the

rang

e an

d co

mpl

exity

of:

re

latio

nshi

ps b

etw

een

num

bers

in g

iven

pat

tern

s

ru

les,

form

ulae

and

equ

atio

ns fo

r whi

curriculum and assessment policy...

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