Curriculum and Assessment Policy Statement Grades 4-6 CurriCulum and assessment PoliCy statement (CaPs) disClaimer In view of the stringent time requirements encountered by the Department

MATHEMATIC

S

Curriculum and Assessment Policy Statement

Intermediate PhaseGrades 4-6

National Curriculum Statement (NCS)

CAPS

CurriCulum and assessment PoliCy statement Grades 4-6

matHematiCs

MATHEMATICS GRADES 4-6

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: 978-1-4315-0491-6

Design and Layout by: Ndabase Printing Solution

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

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 ......................................................................................................................... 12

2.7 Specificationofcontent ............................................................................................................................... 12

Numbers, Operations and Relationships .................................................................................................. 13

Patterns, Functions and Algebra ............................................................................................................... 18

Space and Shape (Geometry) .................................................................................................................. 21

measurement ............................................................................................................................................ 26

Data handling ............................................................................................................................................ 30

seCtion 3: ClariFiCation oF Content ........................................................................................32

3.1 introduction .................................................................................................................................................. 32

3.2 allocation of teaching time ......................................................................................................................... 32

3.3 Clarificationnoteswithteachingguidelines ............................................................................................. 33

3.3.1 Clarification of content for Grade 4 ...................................................................................................... 35

Grade 4 term 1 ................................................................................................................................ 35

Grade 4 term 2 ................................................................................................................................ 66


2 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)

Grade 4 term 3 ................................................................................................................................ 86

Grade 4 term 4 .............................................................................................................................. 104

3.3.2 Clarification of content for Grade 5 .................................................................................................... 123

Grade 5 term 1 .............................................................................................................................. 123

Grade 5 term 2 .............................................................................................................................. 154

Grade 5 term 3 .............................................................................................................................. 174

Grade 5 term 4 .............................................................................................................................. 194

3.3.3. Clarification of content for Grade 6 .................................................................................................... 213

Grade 6 term 1 .............................................................................................................................. 213

Grade 6 term 2 .............................................................................................................................. 239

Grade 6 term 3 .............................................................................................................................. 257

Grade 6 term 4 .............................................................................................................................. 276

seCtion 4: assessment .................................................................................................................293

4.1 introduction ............................................................................................................................................... 293

4.2 types of assessment ................................................................................................................................. 293

4.3 informal or daily assessment .................................................................................................................... 294

4.4 Formal assessment .................................................................................................................................... 294

4.5 recording and reporting ........................................................................................................................... 296

4.6 moderation of assessment ........................................................................................................................ 297

4.7 General ................................................................................................................................................. 297


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 Intermediate 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

a spirit of curiosity and a love for mathematics

an appreciation for the beauty and elegance of mathematics

recognition that mathematics is a creative part of human activity

deep conceptual understanding 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 th at mathematics plays in real life situations including the personal development of the learner.

2.5 FoCus oF Content areas

Mathematics in the Intermediate Phase covers five 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 Intermediate Phase.



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11CAPS

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t and

app

ropr

iate

inst

rum

ents

for m

easu

ring.

The

y sh

ould

be

able

to e

stim

ate

and

verif

y re

sults

thro

ugh

accu

rate

mea

sure

men

t.

Le

arne

rs s

houl

d be

abl

e to

sel

ect a

nd c

onve

rt be

twee

n ap

prop

riate

uni

ts

of m

easu

rem

ent.

m

easu

rem

ent i

n th

is p

hase

sho

uld

also

ena

ble

the

lear

ner t

o:

-in

form

ally

mea

sure

ang

les,

are

a, p

erim

eter

and

cap

acity

/vol

ume;

-di

scus

s an

d de

scrib

e th

e hi

stor

ical

dev

elop

men

t of m

easu

ring

inst

rum

ents

an

d to

ols

M

easu

rem

ent p

rovi

des

a co

ntex

t for

lear

ners

to u

se c

omm

on fr

actio

ns a

nd

deci

mal

frac

tions

.

dat

a ha

ndlin

g

Dat

a ha

ndlin

g in

volv

es a

skin

g qu

estio

ns a

nd fi

ndin

g an

swer

s in

ord

er to

de

scrib

e ev

ents

and

the

soci

al, t

echn

olog

ical

and

eco

nom

ic e

nviro

nmen

t.

Thro

ugh

the

stud

y of

dat

a ha

ndlin

g, th

e le

arne

r dev

elop

s th

e sk

ills

to c

olle

ct,

orga

nize

, rep

rese

nt, a

naly

ze, i

nter

pret

and

repo

rt da

ta.

Th

e st

udy

of p

roba

bilit

y en

able

s th

e le

arne

r to

deve

lop

skill

s an

d te

chni

ques

for m

akin

g in

form

ed p

redi

ctio

ns, a

nd d

escr

ibin

g ra

ndom

ness

an

d un

certa

inty

. It d

evel

ops

awar

enes

s th

at

-di

ffere

nt s

ituat

ions

hav

e di

ffere

nt p

roba

bilit

ies

of o

ccur

ring

-fo

r m

any

situ

atio

ns,

ther

e ar

e a

finite

num

ber

of d

iffer

ent

poss

ible

ou

tcom

es.

Le

arne

rs s

houl

d fo

cus

on a

ll th

e sk

ills

that

ena

ble

them

to m

ove

from

co

llect

ing

data

to re

porti

ng o

n da

ta..

Le

arne

rs s

houl

d be

exp

osed

to:

-a

varie

ty o

f con

text

s fo

r col

lect

ing

and

inte

rpre

ting

data

-a

rang

e of

que

stio

ns th

at a

re p

osed

and

ans

wer

ed re

late

d to

dat

a

Le

arne

rs s

houl

d be

gin

to a

naly

se d

ata

criti

cally

thro

ugh

expo

sure

to s

ome

fact

ors

that

impa

ct o

n da

ta s

uch

as fr

om w

hom

, whe

n an

d w

here

dat

a is

co

llect

ed.

Th

e fo

cus

of p

roba

bilit

y is

to p

erfo

rm re

peat

ed e

vent

s in

ord

er to

list

, cou

nt

and

pred

ict o

utco

mes

..

L

earn

ers

are

not e

xpec

ted

to c

alcu

late

the

prob

abili

ty o

f eve

nts

occu

rrin

g



2.6 WeiGHtinG oF Content areas

The weighting of mathematics content areas serves two primary purposes:

guidance regarding the time needed to adequately address the content within each content area guidance on the spread of content in the examination (especially end- of-the year summative assessment). The weighting of the content areas is the same for each grade in this phase.

WeiGHtinG oF Content areas

Content area Grade 4 Grade 5 Grade 6

Numbers, Operations and Relationships* 50% 50% 50%

Patterns, Functions and Algebra 10% 10% 10%

Space and Shape (Geometry) 15% 15% 15%

measurement 15% 15% 15%

Data handling 10% 10% 10%

100% 100% 100%

* The weighting of Number, Operations and Relationships has been increased to 50% for all three grades. This is an attempt to ensure that learners are sufficiently numerate when they enter the Senior Phase.

2.7 sPeCiFiCation oF Content

The Specification of Content in Section 2 shows progression in terms of concepts and skills from Grade 4 to Grade 6 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.


13CAPS

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

Th

e m

ain

prog

ress

ion

in N

umbe

rs, O

pera

tions

and

Rel

atio

nshi

ps h

appe

ns in

thre

e w

ays:

-th

e nu

mbe

r ran

ge in

crea

ses

-di

ffere

nt k

inds

of n

umbe

rs a

re in

trodu

ced

-th

e ca

lcul

atio

n te

chni

ques

cha

nge.

Th

e nu

mbe

r ran

ge fo

r doi

ng c

alcu

latio

ns is

diff

eren

t fro

m th

e nu

mbe

r ran

ge fo

r ord

erin

g nu

mbe

rs a

nd fo

r find

ing

mul

tiple

s an

d fa

ctor

s.

A

s th

e nu

mbe

r ran

ge fo

r doi

ng c

alcu

latio

ns in

crea

ses

up to

Gra

de 6

, lea

rner

s sh

ould

dev

elop

mor

e ef

ficie

nt te

chni

ques

for c

alcu

latio

ns, i

nclu

ding

usi

ng c

olum

ns a

nd le

arni

ng h

ow to

us

e th

e ca

lcul

ator

. The

se te

chni

ques

how

ever

sho

uld

only

be

intro

duce

d an

d en

cour

aged

onc

e le

arne

rs h

ave

an a

dequ

ate

sens

e of

pla

ce v

alue

and

und

erst

andi

ng o

f the

pro

perti

es

of n

umbe

rs a

nd o

pera

tions

.

C

onte

xtua

l pro

blem

s sh

ould

con

side

r the

num

ber r

ange

for t

he g

rade

as

wel

l as

the

calc

ulat

ion

com

pete

ncie

s of

lear

ners

.

C

onte

xts

for s

olvi

ng p

robl

ems

shou

ld b

uild

aw

aren

ess

of o

ther

sub

ject

and

con

tent

are

as, a

s w

ell a

s so

cial

, eco

nom

ic a

nd e

nviro

nmen

tal i

ssue

s.

toPi

Cs

Gr

ad

e 4

Gr

ad

e 5

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ad

e 6

1.1

Who

le n

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men

tal c

alcu

latio

ns in

volv

ing:

A

dditi

on a

nd s

ubtra

ctio

n of

:

-un

its

-m

ultip

les

of 1

0

-m

ultip

les

of 1

00

-m

ultip

les

of 1

000

M

ultip

licat

ion

of w

hole

num

bers

to a

t lea

st 1

0 x

10

m

ultip

licat

ion

fact

s of

:

-un

its b

y m

ultip

les

of 1

0

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nits

by

mul

tiple

s of

100

men

tal c

alcu

latio

ns in

volv

ing:

A

dditi

on a

nd s

ubtra

ctio

n of

:

-un

its

-m

ultip

les

of 1

0

-m

ultip

les

of 1

00

-m

ultip

les

of 1

000

M

ultip

licat

ion

of w

hole

num

bers

to a

t lea

st 1

0 x

10

m

ultip

licat

ion

fact

s of

:

-un

its b

y m

ultip

les

of 1

0

-un

its b

y m

ultip

les

of 1

00

-un

its b

y m

ultip

les

of 1

000

-un

its b

y m

ultip

les

of 1

0 00

0

men

tal c

alcu

latio

ns in

volv

ing:

A

dditi

on a

nd s

ubtra

ctio

n of

:

-un

its

-m

ultip

les

of 1

0

-m

ultip

les

of 1

00

-m

ultip

les

of 1

000

M

ultip

licat

ion

of w

hole

num

bers

to a

t lea

st 1

2 x

12

m

ultip

licat

ion

fact

s of

:

-un

its a

nd te

ns b

y m

ultip

les

of 1

0

-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



toPi

Cs

Gr

ad

e 4

Gr

ad

e 5

Gr

ad

e 6

1.1

Who

le n

umbe

rs

num

ber r

ange

for c

ount

ing,

ord

erin

g,

com

parin

g an

d re

pres

entin

g, a

nd p

lace

val

ue o

f di

gits

C

ount

forw

ards

and

bac

kwar

ds in

2s,

3s,

5s,

10s

, 25

s, 5

0s, 1

00s

betw

een

0 an

d at

leas

t 10

000.

O

rder

, com

pare

and

repr

esen

t num

bers

to a

t le

ast 4

-dig

it nu

mbe

rs

R

epre

sent

odd

and

eve

n nu

mbe

rs to

at l

east

1

000.

R

ecog

nize

the

plac

e va

lue

of d

igits

in w

hole

nu

mbe

rs to

at l

east

4-d

igit

num

bers

R

ound

off

to th

e ne

ares

t 10,

100

, 1 0

00

num

ber r

ange

for c

alcu

latio

ns

A

dditi

on a

nd s

ubtra

ctio

n of

who

le n

umbe

rs o

f at

leas

t 4 d

igits

M

ultip

licat

ion

of a

t lea

st w

hole

2-d

igit

by 2

-dig

it nu

mbe

rs

D

ivis

ion

of a

t lea

st w

hole

3-d

igit

by 1

-dig

it nu

mbe

rs

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

-es

timat

ion

-bu

ildin

g up

and

bre

akin

g do

wn

num

bers

-ro

undi

ng o

ff an

d co

mpe

nsat

ing

-do

ublin

g an

d ha

lvin

g

-us

ing

a nu

mbe

r lin

e

-us

ing

addi

tion

and

subt

ract

ion

as in

vers

e op

erat

ions

-us

ing

mul

tiplic

atio

n an

d di

visi

on a

s in

vers

e op

erat

ions

num

ber r

ange

for c

ount

ing,

ord

erin

g,

com

parin

g, re

pres

entin

g an

d pl

ace

valu

e of

di

gits

C

ount

forw

ards

and

bac

kwar

ds in

who

le n

umbe

r

inte

rval

s up

to a

t lea

st 1

0 00

0

O

rder

, com

pare

and

repr

esen

t num

bers

to a

t le

ast 6

-dig

it nu

mbe

rs

R

epre

sent

odd

and

eve

n nu

mbe

rs to

at l

east

1

000.

R

ecog

nize

the

plac

e va

lue

of d

igits

in w

hole

nu

mbe

rs to

at l

east

6 d

igit

num

bers

.

R

ound

off

to th

e ne

ares

t 5, 1

0, 1

00 a

nd 1

000

num

ber r

ange

for c

alcu

latio

ns

A

dditi

on a

nd s

ubtra

ctio

n of

who

le n

umbe

rs o

f at

leas

t 5 d

igits

M

ultip

licat

ion

of a

t lea

st w

hole

3-d

igit

by 2

-dig

it nu

mbe

rs

D

ivis

ion

of a

t lea

st w

hole

3-d

igit

by 2

-dig

it nu

mbe

rs

Cal

cula

tion

tech

niqu

es

U

sing

a ra

nge

of te

chni

ques

to p

erfo

rm a

nd c

heck

w

ritte

n an

d m

enta

l cal

cula

tions

of w

hole

num

bers

in

clud

ing:

-es

timat

ion

-ad

ding

and

sub

tract

ing

in c

olum

ns

-bu

ildin

g up

and

bre

akin

g do

wn

num

bers

-us

ing

a nu

mbe

r lin

e

-ro

undi

ng o

ff an

d co

mpe

nsat

ing

-do

ublin

g an

d ha

lvin

g

-us

ing

addi

tion

and

subt

ract

ion

as in

vers

e op

erat

ions

-us

ing

mul

tiplic

atio

n an

d di

visi

on a

s in

vers

e op

erat

ions

num

ber r

ange

for c

ount

ing,

ord

erin

g,

com

parin

g, re

pres

entin

g an

d pl

ace

valu

e of

di

gits

O

rder

, com

pare

and

repr

esen

t num

bers

to a

t le

ast 9

-dig

it nu

mbe

rs

R

epre

sent

prim

e nu

mbe

rs to

at l

east

100

R

ecog

nizi

ng th

e pl

ace

valu

e of

dig

its in

who

le

num

bers

to a

t lea

st 9

-dig

it nu

mbe

rs

R

ound

off

to th

e ne

ares

t 5, 1

0, 1

00, 1

000

, 10

0 00

0, a

nd 1

000

000

num

ber r

ange

for c

alcu

latio

ns

A

dditi

on a

nd s

ubtra

ctio

n of

who

le n

umbe

rs o

f at

leas

t 6 d

igits

M

ultip

licat

ion

of a

t lea

st w

hole

4-d

igit

by 3

-dig

it nu

mbe

rs

D

ivis

ion

of a

t lea

st w

hole

4-d

igit

by 3

-dig

it nu

mbe

rs

m

ultip

le o

pera

tions

on

who

le n

umbe

rs w

ith o

r w

ithou

t bra

cket

s

Cal

cula

tion

tech

niqu

es

U

sing

a ra

nge

of te

chni

ques

to p

erfo

rm a

nd c

heck

w

ritte

n an

d m

enta

l cal

cula

tions

of w

hole

num

bers

in

clud

ing:

-es

timat

ion

-ad

ding

, sub

tract

ing

and

mul

tiply

ing

in c

olum

ns

-lo

ng d

ivis

ion

-bu

ildin

g up

and

bre

akin

g do

wn

num

bers

-ro

undi

ng o

ff an

d co

mpe

nsat

ing

-us

ing

addi

tion

and

subt

ract

ion

as in

vers

e op

erat

ions

-us

ing

mul

tiplic

atio

n an

d di

visi

on a

s in

vers

e op

erat

ions

-us

ing

a ca

lcul

ator


15CAPS

toPi

Cs

Gr

ad

e 4

Gr

ad

e 5

Gr

ad

e 6

1.1

Who

le n

umbe

rs

num

ber r

ange

for m

ultip

les

and

fact

ors

M

ultip

les

of 1

-dig

it nu

mbe

rs to

at l

east

100

Prop

ertie

s of

who

le n

umbe

rs

R

ecog

nize

and

use

the

com

mut

ativ

e, a

ssoc

iativ

e,

and

dist

ribut

ive

prop

ertie

s w

ith w

hole

num

bers

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

s in

volv

ing

who

le

num

bers

, inc

ludi

ng

-fin

anci

al c

onte

xts

-m

easu

rem

ent c

onte

xts

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)

-gr

oupi

ng a

nd e

qual

sha

ring

with

rem

aind

ers

num

ber r

ange

for m

ultip

les

and

fact

ors

M

ultip

les

of 2

-dig

its w

hole

num

bers

to a

t lea

st

100

Fa

ctor

s of

2-d

igit

who

le n

umbe

rs to

at l

east

100

Prop

ertie

s of

who

le n

umbe

rs

R

ecog

nize

and

use

the

com

mut

ativ

e, a

ssoc

iativ

e,

dist

ribut

ive

prop

ertie

s of

who

le n

umbe

rs

0

in te

rms

of it

s ad

ditiv

e pr

oper

ty

1

in te

rms

of it

s m

ultip

licat

ive

prop

erty

solv

ing

prob

lem

s

S

olve

pro

blem

s in

volv

ing

who

le n

umbe

rs,

incl

udin

g

-fin

anci

al c

onte

xts

-m

easu

rem

ent c

onte

xts

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)

-gr

oupi

ng a

nd e

qual

sha

ring

with

rem

aind

ers

num

ber r

ange

for m

ultip

les

and

fact

ors

M

ultip

les

of 2

-dig

it an

d 3-

digi

t num

bers

Fa

ctor

s of

2-d

igit

and

3-di

git w

hole

num

bers

P

rime

fact

ors

of n

umbe

rs to

at l

east

100

Prop

ertie

s of

who

le n

umbe

rs

R

ecog

nize

and

use

the

com

mut

ativ

e, a

ssoc

iativ

e,

dist

ribut

ive

prop

ertie

s of

who

le n

umbe

rs

0

in te

rms

of it

s ad

ditiv

e pr

oper

ty

1

in te

rms

of it

s m

ultip

licat

ive

prop

erty

solv

ing

prob

lem

s

S

olve

pro

blem

s in

volv

ing

who

le n

umbe

rs a

nd

deci

mal

frac

tions

, inc

ludi

ng

-fin

anci

al c

onte

xts

-m

easu

rem

ent c

onte

xts

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)

-gr

oupi

ng a

nd e

qual

sha

ring

with

rem

aind

ers



toPi

Cs

Gr

ad

e 4

Gr

ad

e 5

Gr

ad

e 6

1.2

Com

mon

Fr

actio

ns

des

crib

ing

and

orde

ring

frac

tions

:

C

ompa

re a

nd o

rder

com

mon

frac

tions

with

di

ffere

nt d

enom

inat

ors

(hal

ves;

third

s, q

uarte

rs;

fifth

s; s

ixth

s; s

even

ths;

eig

hths

)

D

escr

ibe

and

com

pare

com

mon

frac

tions

in

diag

ram

form

Cal

cula

tions

with

frac

tions

:

A

dditi

on o

f com

mon

frac

tions

with

the

sam

e de

nom

inat

ors

R

ecog

nize

, des

crib

e an

d us

e th

e eq

uiva

lenc

e of

di

visi

on a

nd fr

actio

ns

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

s in

volv

ing

fract

ions

, in

clud

ing

grou

ping

and

equ

al s

harin

g

equi

vale

nt fo

rms:

R

ecog

nize

and

use

equ

ival

ent f

orm

s of

com

mon

fra

ctio

ns (f

ract

ions

in w

hich

one

den

omin

ator

is a

m

ultip

le o

f ano

ther

)

des

crib

ing

and

orde

ring

frac

tions

:

C

ount

forw

ards

and

bac

kwar

ds in

frac

tions

C

ompa

re a

nd o

rder

com

mon

frac

tions

to a

t lea

st

twel

fths

Cal

cula

tions

with

frac

tions

:

A

dditi

on a

nd s

ubtra

ctio

n of

com

mon

frac

tions

with

th

e sa

me

deno

min

ator

s

A

dditi

on a

nd s

ubtra

ctio

n of

mix

ed n

umbe

rs

Fr

actio

ns o

f who

le n

umbe

rs w

hich

resu

lt in

who

le

num

bers

R

ecog

nize

, des

crib

e an

d us

e th

e eq

uiva

lenc

e of

di

visi

on a

nd 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, i

nclu

ding

gro

upin

g an

d sh

arin

g

equi

vale

nt fo

rms:

R

ecog

nize

and

use

equ

ival

ent f

orm

s of

com

mon

fra

ctio

ns (f

ract

ions

in w

hich

one

den

omin

ator

is a

m

ultip

le o

f ano

ther

)

des

crib

ing

and

orde

ring

frac

tions

:

C

ompa

re a

nd o

rder

com

mon

frac

tions

, inc

ludi

ng

tent

hs a

nd h

undr

edth

s

Cal

cula

tions

with

frac

tions

:

A

dditi

on a

nd s

ubtra

ctio

n of

com

mon

frac

tions

in

whi

ch o

ne d

enom

inat

or is

a m

ultip

le o

f ano

ther

A

dditi

on a

nd s

ubtra

ctio

n of

mix

ed n

umbe

rs

Fr

actio

ns o

f who

le n

umbe

rs

solv

ing

prob

lem

s

S

olve

pro

blem

s in

con

text

s in

volv

ing

com

mon

fra

ctio

ns, i

nclu

ding

gro

upin

g an

d sh

arin

g

Perc

enta

ges

Fi

nd p

erce

ntag

es o

f who

le n

umbe

rs

equi

vale

nt fo

rms:

R

ecog

nize

and

use

equ

ival

ent f

orm

s of

com

mon

fra

ctio

ns w

ith 1

-dig

it or

2-d

igit

deno

min

ator

s (fr

actio

ns in

whi

ch o

ne d

enom

inat

or is

a m

ultip

le

of a

noth

er)

R

ecog

nize

equ

ival

ence

bet

wee

n co

mm

on fr

actio

n an

d de

cim

al fr

actio

n fo

rms

of th

e sa

me

num

ber

R

ecog

nize

equ

ival

ence

bet

wee

n co

mm

on

fract

ion,

dec

imal

frac

tion

and

perc

enta

ge fo

rms

of

the

sam

e nu

mbe

r


17CAPS

toPi

Cs

Gr

ad

e 4

Gr

ad

e 5

Gr

ad

e 6

1.3

dec

imal

fr

actio

ns

rec

ogni

zing

, ord

erin

g an

d pl

ace

valu

e of

de

cim

al fr

actio

ns

C

ount

forw

ards

and

bac

kwar

ds in

dec

imal

fra

ctio

ns to

at l

east

two

deci

mal

pla

ces

C

ompa

re a

nd o

rder

dec

imal

frac

tions

to a

t lea

st

two

deci

mal

pla

ces

P

lace

val

ue o

f dig

its to

at l

east

two

deci

mal

pl

aces

Cal

cula

tions

with

dec

imal

frac

tions

A

dditi

on a

nd s

ubtra

ctio

n of

dec

imal

frac

tions

with

at

leas

t tw

o de

cim

al p

lace

s

M

ultip

ly d

ecim

al fr

actio

ns b

y 10

and

100

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

ecog

nize

equ

ival

ence

bet

wee

n co

mm

on fr

actio

n an

d de

cim

al fr

actio

n fo

rms

of th

e sa

me

num

ber

R

ecog

nize

equ

ival

ence

bet

wee

n co

mm

on

fract

ion,

dec

imal

frac

tion

and

perc

enta

ge fo

rms

of

the

sam

e nu

mbe

r



sPeC

iFiC

atio

n o

F C

on

ten

t (P

Ha

se o

ver

vieW

)Pa

tter

ns,

Fu

nC

tio

ns

an

d a

lGeB

ra

Th

e m

ain

prog

ress

ion

in P

atte

rns,

Fun

ctio

ns a

nd A

lgeb

ra o

ccur

s in

the

rang

e an

d co

mpl

exity

of r

elat

ions

hips

bet

wee

n nu

mbe

rs in

the

patte

rns.

In

Pat

tern

s, F

unct

ions

and

Alg

ebra

, lea

rner

s ar

e gi

ven

oppo

rtuni

ties

to:

-co

mpl

ete

and

exte

nd p

atte

rns

-re

pres

ent p

atte

rns

in d

iffer

ent f

orm

s

-id

entif

y an

d de

scrib

e pa

ttern

s.

This

pre

pare

s le

arne

rs to

des

crib

e ru

les

for p

atte

rns,

whi

ch b

ecom

e m

ore

form

aliz

ed in

alg

ebra

ic w

ork

in th

e S

enio

r Pha

se.

In

this

pha

se, t

he e

mph

asis

is o

n pr

actic

e w

ith c

ompl

etin

g an

d ex

tend

ing

num

ber p

atte

rns

as w

ell a

s re

pres

entin

g pa

ttern

s in

diff

eren

t for

ms.

P

atte

rns,

Fun

ctio

ns a

nd A

lgeb

ra a

lso

prov

ide

oppo

rtuni

ties

to d

evel

op a

n un

ders

tand

ing

of th

e pr

oper

ties

of o

pera

tions

with

who

le n

umbe

rs e

.g. c

omm

utat

ive,

dis

tribu

tive,

and

in

vers

e op

erat

ions

.

Fi

ndin

g in

put a

nd o

utpu

t val

ues

give

s le

arne

rs p

ract

ice

in th

inki

ng a

bout

and

des

crib

ing

func

tiona

l rel

atio

nshi

ps b

etw

een

num

bers

.

W

ritin

g an

d so

lvin

g nu

mbe

r sen

tenc

es p

repa

res

lear

ners

for w

ritin

g al

gebr

aic

expr

essi

ons

and

solv

ing

equa

tions

in th

e S

enio

r Pha

se. W

ritin

g an

d so

lvin

g nu

mbe

r sen

tenc

es a

lso

prov

ides

opp

ortu

nity

to c

onso

lidat

e le

arne

rs n

umbe

r kno

wle

dge.

toPi

Cs

Gr

ad

e 4

Gr

ad

e 5

Gr

ad

e 6

2.1

num

eric

pat

tern

s

inve

stig

ate

and

exte

nd p

atte

rns

In

vest

igat

e an

d ex

tend

num

eric

pat

tern

s lo

okin

g fo

r rel

atio

nshi

ps o

r rul

es o

f pat

tern

s:

-se

quen

ces

invo

lvin

g a

cons

tant

diff

eren

ce o

r ra

tio

-of

lear

ners

ow

n cr

eatio

n

D

escr

ibe

obse

rved

rela

tions

hips

or r

ules

in

lear

ners

ow

n w

ords

inpu

t and

out

put v

alue

s

D

eter

min

e in

put v

alue

s, o

utpu

t val

ues

and

rule

s fo

r pat

tern

s an

d re

latio

nshi

ps u

sing

-flo

w d

iagr

ams

-ta

bles

inve

stig

ate

and

exte

nd p

atte

rns

In

vest

igat

e an

d ex

tend

num

eric

pat

tern

s lo

okin

g fo

r rel

atio

nshi

ps o

r rul

es o

f pat

tern

s:

-se

quen

ces

not

limite

d to

a c

onst

ant

diffe

renc

e or

ratio

-of

lear

ners

ow

n cr

eatio

n

D

escr

ibe

obse

rved

rela

tions

hips

or r

ules

in

lear

ners

ow

n w

ords

inpu

t and

out

put v

alue

s

D

eter

min

e in

put v

alue

s, o

utpu

t val

ues

and

rule

s fo

r the

pat

tern

s an

d re

latio

nshi

ps u

sing

flow

di

agra

ms

-flo

w d

iagr

ams

-ta

bles

inve

stig

ate

and

exte

nd p

atte

rns

In

vest

igat

e an

d ex

tend

num

eric

pat

tern

s lo

okin

g fo

r rel

atio

nshi

ps o

r rul

es o

f pat

tern

s:

-se

quen

ces

not

limite

d to

a c

onst

ant

diffe

renc

e or

ratio

-of

lear

ners

ow

n cr

eatio

n

-re

pres

ente

d in

tabl

es

D

escr

ibe

the

gene

ral r

ules

for t

he o

bser

ved

rela

tions

hips

inpu

t and

out

put v

alue

s

D

eter

min

e in

put v

alue

s, o

utpu

t val

ues

and

rule

s fo

r the

pat

tern

s an

d re

latio

nshi

ps u

sing

:

-flo

w d

iagr

ams

-ta

bles


19CAPS

toPi

Cs

Gr

ad

e 4

Gr

ad

e 5

Gr

ad

e 6

2.1

num

eric

pat

tern

s

equi

vale

nt fo

rms

Det

erm

ine

equi

vale

nce

of d

iffer

ent d

escr

iptio

ns o

f th

e sa

me

rela

tions

hip

or ru

le p

rese

nted

ve

rbal

ly

in

a fl

ow d

iagr

am

in

a ta

ble

by

a n

umbe

r sen

tenc

e

equi

vale

nt fo

rms

Det

erm

ine

equi

vale

nce

of d

iffer

ent d

escr

iptio

ns o

f th

e sa

me

rela

tions

hip

or ru

le p

rese

nted

ve

rbal

ly

in

a fl

ow d

iagr

am

in

a ta

ble

by

a n

umbe

r sen

tenc

e

equi

vale

nt fo

rms

Det

erm

ine

equi

vale

nce

of d

iffer

ent d

escr

iptio

ns o

f th

e sa

me

rela

tions

hip

or ru

le p

rese

nted

ve

rbal

ly

in

a fl

ow d

iagr

am

in

a ta

ble

by

a n

umbe

r sen

tenc

e

2.2

Geo

met

ric

patte

rns

inve

stig

ate

and

exte

nd p

atte

rns

In

vest

igat

e an

d ex

tend

geo

met

ric p

atte

rns

look

ing

for r

elat

ions

hips

or r

ules

of p

atte

rns

-re

pres

ente

d in

phy

sica

l or d

iagr

am fo

rm

-se

quen

ces

not

limite

d to

a c

onst

ant

diffe

renc

e or

ratio

-of

lear

ners

ow

n cr

eatio

n

D

escr

ibe

obse

rved

rela

tions

hips

or r

ules

in

lear

ners

ow

n w

ords

inpu

t and

out

put v

alue

sD

eter

min

e in

put v

alue

s, o

utpu

t val

ues

and

rule

s fo

r th

e pa

ttern

s an

d re

latio

nshi

ps u

sing

flow

dia

gram

s

equi

vale

nt fo

rms

D

eter

min

e eq

uiva

lenc

e of

diff

eren

t des

crip

tions

of

the

sam

e re

latio

nshi

p or

rule

pre

sent

ed

-ve

rbal

ly

-in

a fl

ow d

iagr

am

-by

a n

umbe

r sen

tenc

e

inve

stig

ate

and

exte

nd p

atte

rns

In

vest

igat

e an

d ex

tend

geo

met

ric p

atte

rns

look

ing

for r

elat

ions

hips

or r

ules

of p

atte

rns

-re

pres

ente

d in

phy

sica

l or d

iagr

am fo

rm

-se

quen

ces

not

limite

d to

a c

onst

ant

diffe

renc

e or

ratio

-of

lear

ners

ow

n cr

eatio

n

D

escr

ibe

obse

rved

rela

tions

hips

or r

ules

in

lear

ners

ow

n w

ords

inpu

t and

out

put v

alue

sD

eter

min

e in

put v

alue

s, o

utpu

t val

ues

and

rule

s fo

r th

e pa

ttern

s an

d re

latio

nshi

ps u

sing

flow

dia

gram

s

equi

vale

nt fo

rms

D

eter

min

e eq

uiva

lenc

e of

diff

eren

t des

crip

tions

of

the

sam

e re

latio

nshi

p or

rule

pre

sent

ed

-ve

rbal

ly

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a fl

ow d

iagr

am

-by

a n

umbe

r sen

tenc

e

inve

stig

ate

and

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nd p

atte

rns

In

vest

igat

e an

d ex

tend

geo

met

ric p

atte

rns

look

ing

for r

elat

ions

hips

or r

ules

of p

atte

rns

-re

pres

ente

d in

phy

sica

l or d

iagr

am fo

rm

-se

quen

ces

not

limite

d to

a c

onst

ant

diffe

renc

e or

ratio

-of

lear

ners

ow

n cr

eatio

n

-re

pres

ente

d in

tabl

es

D

escr

ibe

the

gene

ral r

ules

for t

he o

bser

ved

rela

tions

hips

inpu

t and

out

put v

alue

sD

eter

min

e in

put v

alue

s, o

utpu

t val

ues

and

rule

s fo

r th

e pa

ttern

s an

d re

latio

nshi

ps u

sing

flo

w d

iagr

ams

ta

bles

equi

vale

nt fo

rms

D

eter

min

e eq

uiva

lenc

e of

diff

eren

t des

crip

tions

of

the

sam

e re

latio

nshi

p or

rule

pre

sent

ed

-ve

rbal

ly

-in

a fl

ow d

iagr

am

-in

a ta

ble

-by

a n

umbe

r sen

tenc

e



toPi

Cs

Gr

ad

e 4

Gr

ad

e 5

Gr

ad

e 6

2.3

num

ber

sent

ence

s

(Intro

duct

ion

to A

lgeb

raic

E

xpre

ssio

ns)

num

ber s

ente

nces

W

rite

num

ber s

ente

nces

to d

escr

ibe

prob

lem

si

tuat

ions

S

olve

and

com

plet

e nu

mbe

r sen

tenc

es b

y

-in

spec

tion

-tri

al a

nd im

prov

emen

t

C

heck

sol

utio

n by

sub

stitu

tion

num

ber s

ente

nces

W

rite

num

ber s

ente

nces

to d

escr

ibe

prob

lem

si

tuat

ions

S

olve

and

com

plet

e nu

mbe

r sen

tenc

es b

y

-in

spec

tion

-tri

al a

nd im

prov

emen

t

C

heck

sol

utio

n by

sub

stitu

tion

num

ber s

ente

nces

W

rite

num

ber s

ente

nces

to d

escr

ibe

prob

lem

si

tuat

ions

S

olve

and

com

plet

e nu

mbe

r sen

tenc

es b

y

-in

spec

tion

-tri

al a

nd im

prov

emen

t

C

heck

sol

utio

n by

sub

stitu

tion


21CAPS

sPeC

iFiC

atio

n o

F C

on

ten

t (P

Ha

se o

ver

vieW

)sP

aC

e a

nd

sH

aPe

(Geo

met

ry)

Th

e m

ain

prog

ress

ion

in S

pace

and

Sha

pe (G

eom

etry

) is

achi

eved

by

a fo

cus

on n

ew p

rope

rties

and

cha

ract

eris

tics

of 2

-D s

hape

s an

d 3-

D o

bjec

ts in

eac

h gr

ade.

Le

arne

rs a

re g

iven

opp

ortu

nitie

s to

iden

tify

and

desc

ribe

char

acte

ristic

s of

2-D

sha

pes

and

3-D

obj

ects

and

to d

evel

op th

eir a

bilit

ies

to c

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the

Sen

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Gr

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Gr

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Gr

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3.1

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R

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Cha

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pare

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ides

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R

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Cha

ract

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s

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pare

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urve

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-nu

Documents

Curriculum and Assessment Policy Statement Grades 4-6 CurriCulum and assessment PoliCy statement (CaPs) disClaimer In view of the stringent time requirements encountered by the Department