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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
MATHEMATICS GRADES 4-6
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
MATHEMATICS GRADES 4-6
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
MATHEMATICS GRADES 4-6
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
MATHEMATICS GRADES 4-6
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
MATHEMATICS GRADES 4-6
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;
MATHEMATICS GRADES 4-6
4 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
(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;
MATHEMATICS GRADES 4-6
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).
MATHEMATICS GRADES 4-6
6 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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
MATHEMATICS GRADES 4-6
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.
MATHEMATICS GRADES 4-6
8 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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
MATHEMATICS GRADES 4-6
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.
MATHEMATICS GRADES 4-6
10 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
mat
Hem
atiC
s C
on
ten
t K
no
Wle
dG
e
Con
tent
are
aG
ener
al c
onte
nt fo
cus
Interm
ediatePha
sespe
cific
con
tentfo
cus
num
bers
, ope
ratio
ns
and
rel
atio
nshi
ps
Dev
elop
men
t of n
umbe
r sen
se th
at in
clud
es:
th
e m
eani
ng o
f diff
eren
t kin
ds o
f num
bers
re
latio
nshi
p be
twee
n di
ffere
nt k
inds
of n
umbe
rs
th
e re
lativ
e si
ze o
f diff
eren
t num
bers
re
pres
enta
tion
of n
umbe
rs in
var
ious
way
s
th
e ef
fect
of o
pera
ting
with
num
bers
th
e ab
ility
to e
stim
ate
and
chec
k so
lutio
ns.
Th
e ra
nge
of n
umbe
rs d
evel
oped
by
the
end
of th
e In
term
edia
te P
hase
is
exte
nded
to a
t lea
st 9
-dig
it w
hole
num
bers
, dec
imal
frac
tions
to a
t lea
st
2 de
cim
al p
lace
s, c
omm
on fr
actio
ns a
nd fr
actio
ns w
ritte
n in
per
cent
age
form
.
In
this
pha
se, t
he le
arne
r is
expe
cted
to m
ove
from
cou
ntin
g re
liabl
y to
cal
cula
ting
fluen
tly in
all
four
ope
ratio
ns. T
he le
arne
r sho
uld
be
enco
urag
ed to
mem
oris
e w
ith u
nder
stan
ding
,mul
tiply
flue
ntly,
and
sh
arpe
n m
enta
l cal
cula
tion
skill
s.
A
ttent
ion
need
s to
be
focu
sed
on u
nder
stan
ding
the
conc
ept o
f pla
ce
valu
e so
that
the
lear
ner d
evel
ops
a se
nse
of la
rge
num
bers
and
dec
imal
fra
ctio
ns.
Th
e le
arne
r sho
uld
reco
gniz
e an
d de
scrib
e pr
oper
ties
of n
umbe
rs
and
oper
atio
ns, i
nclu
ding
iden
tity
prop
ertie
s, fa
ctor
s, m
ultip
les,
and
co
mm
utat
ive,
ass
ocia
tive
and
dist
ribut
ive
prop
ertie
s.
Patte
rns,
Fun
ctio
ns
and
alg
ebra
Alg
ebra
is
th
e la
ngua
ge
for
inve
stig
atin
g an
d co
mm
unic
atin
g m
ost
of
Mat
hem
atic
s an
d ca
n be
ext
ende
d to
the
stu
dy o
f fu
nctio
ns a
nd o
ther
re
latio
nshi
ps b
etw
een
varia
bles
. A c
entra
l par
t of t
his
cont
ent a
rea
is fo
r th
e le
arne
r to
ach
ieve
effi
cien
t m
anip
ulat
ive
skill
s in
the
use
of
alge
bra.
It
also
fo
cuse
s on
the:
de
scrip
tion
of p
atte
rns
and
rela
tions
hips
thro
ugh
the
use
of s
ymbo
lic
expr
essi
ons,
gra
phs
and
tabl
es
id
entifi
catio
n an
d an
alys
is o
f reg
ular
ities
and
cha
nge
in p
atte
rns,
and
re
latio
nshi
ps th
at e
nabl
e le
arne
rs to
mak
e pr
edic
tions
and
sol
ve p
robl
ems.
N
umer
ic a
nd g
eom
etric
pat
tern
s ar
e ex
tend
ed w
ith a
spe
cial
focu
s on
the
rela
tions
hips
:
-be
twee
n te
rms
in a
seq
uenc
e
-be
twee
n th
e nu
mbe
r of t
he te
rm (i
ts p
lace
in th
e se
quen
ce) a
nd th
e te
rm
itsel
f.
Th
e st
udy
of n
umer
ic a
nd g
eom
etric
pat
tern
s de
velo
ps th
e co
ncep
ts
of v
aria
bles
, rel
atio
nshi
ps a
nd fu
nctio
ns. T
he u
nder
stan
ding
of t
hese
re
latio
nshi
ps w
ill e
nabl
e le
arne
rs to
des
crib
e th
e ru
les
gene
ratin
g th
e pa
ttern
s.
Th
is p
hase
has
a p
artic
ular
focu
s on
the
use
of d
iffer
ent,
yet e
quiv
alen
t, re
pres
enta
tions
to d
escr
ibe
prob
lem
s or
rela
tions
hips
by
mea
ns o
f flow
di
agra
ms,
tabl
es, n
umbe
r sen
tenc
es o
r ver
bally
.
spac
e an
d sh
ape
(Geo
met
ry)
The
stud
y of
Spa
ce a
nd S
hape
im
prov
es u
nder
stan
ding
and
app
reci
atio
n of
the
pat
tern
, pr
ecis
ion,
ach
ieve
men
t an
d be
auty
in
natu
ral
and
cultu
ral
form
s. It
focu
ses
on th
e pr
oper
ties,
rel
atio
nshi
ps, o
rient
atio
ns, p
ositi
ons
and
trans
form
atio
ns o
f tw
o-di
men
sion
al s
hape
s an
d th
ree-
dim
ensi
onal
obj
ects
.
Th
e le
arne
rs e
xper
ienc
e of
spa
ce a
nd s
hape
in th
is p
hase
mov
es fr
om
reco
gniti
on a
nd s
impl
e de
scrip
tion
to c
lass
ifica
tion
and
mor
e de
taile
d de
scrip
tion
of c
hara
cter
istic
s an
d pr
oper
ties
of tw
o-di
men
sion
al s
hape
s an
d th
ree-
dim
ensi
onal
obj
ects
.
Le
arne
rs s
houl
d be
giv
en o
ppor
tuni
ties
to:
-dr
aw t
wo-
dim
ensi
onal
sha
pes
and
mak
e m
odel
s of
thr
ee-d
imen
sion
al
obje
cts
-de
scrib
e lo
catio
n, tr
ansf
orm
atio
ns a
nd s
ymm
etry
.
MATHEMATICS GRADES 4-6
11CAPS
mat
Hem
atiC
s C
on
ten
t K
no
Wle
dG
e
Con
tent
are
aG
ener
al c
onte
nt fo
cus
Interm
ediatePha
sespe
cific
con
tentfo
cus
mea
sure
men
t
mea
sure
men
t foc
uses
on
the
sele
ctio
n an
d us
e of
app
ropr
iate
uni
ts,
inst
rum
ents
and
form
ulae
to q
uant
ify c
hara
cter
istic
s of
eve
nts,
sha
pes,
ob
ject
s an
d th
e en
viro
nmen
t. It
rela
tes
dire
ctly
to th
e le
arne
rs s
cien
tific,
te
chno
logi
cal a
nd e
cono
mic
wor
lds,
ena
blin
g th
e le
arne
r to:
m
ake
sens
ible
est
imat
es
be
ale
rt to
the
reas
onab
lene
ss o
f mea
sure
men
ts a
nd re
sults
.
Le
arne
rs s
houl
d be
exp
osed
to a
var
iety
of m
easu
rem
ent a
ctiv
ities
.
Le
arne
rs s
houl
d be
intro
duce
d to
the
use
of s
tand
ardi
sed
units
of
mea
sure
men
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
MATHEMATICS GRADES 4-6
12 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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.
MATHEMATICS GRADES 4-6
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
Gr
ad
e 6
1.1
Who
le n
umbe
rs
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
-U
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
MATHEMATICS GRADES 4-6
14 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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
MATHEMATICS GRADES 4-6
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
MATHEMATICS GRADES 4-6
16 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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
MATHEMATICS GRADES 4-6
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
MATHEMATICS GRADES 4-6
18 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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
MATHEMATICS GRADES 4-6
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
-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
-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
MATHEMATICS GRADES 4-6
20 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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
MATHEMATICS GRADES 4-6
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
lass
ify s
hape
s an
d ob
ject
s in
the
Sen
ior
Pha
se toPi
Cs
Gr
ad
e 4
Gr
ad
e 5
Gr
ad
e 6
3.1
Prop
ertie
s of
2-d
sh
apes
ran
ge o
f sha
pes
R
ecog
nize
, vis
ualiz
e an
d na
me
2-D
sha
pes
in th
e en
viro
nmen
t and
geo
met
ric s
ettin
gs
-re
gula
r and
irre
gula
r pol
ygon
s
trian
gles
, sq
uare
s, re
ctan
gles
, oth
er q
uadr
ilate
rals
, pe
ntag
ons,
hex
agon
s
-ci
rcle
s
Cha
ract
eris
tics
of s
hape
s
D
escr
ibe,
sor
t and
com
pare
2-D
sha
pes
in te
rms
of -st
raig
ht a
nd c
urve
d si
des
-nu
mbe
r of s
ides
ran
ge o
f sha
pes
R
ecog
nize
, vis
ualiz
e an
d na
me
2-D
sha
pes
in th
e en
viro
nmen
t and
geo
met
ric s
ettin
g, fo
cusi
ng o
n
re
gula
r and
irre
gula
r pol
ygon
s - t
riang
les,
sq
uare
s, re
ctan
gles
, oth
er q
uadr
ilate
rals
, pe
ntag
ons,
hex
agon
s, h
epta
gons
ci
rcle
s
si
mila
ritie
s an
d di
ffere
nces
bet
wee
n sq
uare
s an
d re
ctan
gles
Cha
ract
eris
tics
of s
hape
s
D
escr
ibe,
sor
t and
com
pare
2-D
sha
pes
in te
rms
of -st
raig
ht a
nd c
urve
d si
des
-nu