study & master mathematics teacher's file grade 2
TRANSCRIPT
Teacher’s Guide 222222Grade
CAPS
MathematicsMathematicsMathematics
Gaynor Cozens • Cheryl Ann Thomas
SM_Maths_G2_TG_English.indd 1 2011/11/16 2:55 PM
Gaynor Cozens • Cheryl Ann Thomas
Study & Master
Mathematics
Grade 2Teacher’s Guide
S&M FP Maths G2 TF TP -English.indd 1 2011/08/16 11:03 AMCAPS Math Gr 2 TG.indb 1 2011/11/16 2:51 PM
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Tokyo, Mexico City
Cambridge University PressThe Water Club, Beach Road, Granger Bay, Cape Town 8005, South Africa
www.cup.co.za
© Cambridge University Press 2012
This publication is in copyright. Isifundo to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.
First published 2012
ISBN 978-1-107-38126-1
Editor: Christa Büttner-RohwerTypesetter: Laura Brecher. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
notice to teachers
The photocopy masters in this publication may be photocopied or distributed [electronically] free of charge for classroom use within the school or institution which purchases the publication. Worksheets and copies of them remain in the copyright of Cambridge University Press and such copies may not be distributed or used in any way outside the purchasing institution.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
If you want to know more about this book or any other Cambridge University Press publication, phone us at +27 21 4127800, fax us at +27 21 419-8418 or send an e-mail to [email protected]
CAPS Math Gr 2 TG.indb 2 2011/11/16 2:51 PM
ContentsPart 1 Introduction 5
The mathematics curriculum: aims and skills 5
Weekly teaching schedule 8
Phase overview 16
Part 2 Planning 49
Planning and organising your mathematics teaching 49
Allocation of teaching time 49
Resources in the classroom 49
Organising the daily mathematics period 51
Suggested structure for a mathematics period 53
Assessment 55
Photocopiable sheets 59
Part 3 Lesson-by-lesson 65
Content area/Module 1 Numbers, operations and relationships 65
1 Counting 65
2 Number names and symbols 66
3 Comparing and ordering 67
4 Fractions 69
5 Place value 71
6 Problem-solving 72
7 Calculations 74
8 Doubling and halving 79
Content area/Module 2 Patterns, functions and algebra 80
1 Number patterns 80
2 Geometric patterns 82
Content area/Module 3 Shape and space 84
1 Describing position 84
2 Position and view 85
3 Position and directions 86
4 3-D objects 87
5 Sorting 3-D objects 88
6 Constructions with 3-D objects 89
7 2-D shapes 90
8 Symmetry 91
CAPS Math Gr 2 TG.indb 3 2011/11/16 2:51 PM
Content area/Module 4 Measurement 92
1 Days, weeks and months 92
2 Calendars 93
3 Measuring time 94
4 Measuring mass 95
5 Measuring capacity 96
6 Measuring length 97
Content area/Module 5 Data handling 98
1 Concepts and skills 98
Part 4 Teaching aids 101
Part 5 Documents 119
CAPS Math Gr 2 TG.indb 4 2011/11/16 2:51 PM
5Study & Master Mathematics Grade 2 • Introduction
Part 1 IntroductionThe National Curriculum and Assessment Policy Statements (January 2011) replace the National Curriculum Statements Grades R–9 (2002) and the National Curriculum Statements Grades 10–12 (2004). The Curriculum and Assessment Policy Statement (CAPS) for Foundation Phase Mathematics (Grades R–3) comes into effect in January 2012, and replaces the Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines that were used before then.
The instructional time for subjects in the Foundation Phase is given in the table below.
Table 1: Instructional time for Foundation Phase subjects
Subject Time allocation per week (hours)
Languages (FAL and HL) 10 (11)
Mathematics 7
Life skills: 6 (7)
• Beginning knowledge 1 (2)
• Creative arts 2
• Physical education 2
• Personal and social well-being 1
The mathematics curriculum: aims and skillsThe aims of the national curriculum for Mathematics, as set out in the CAPS, are to develop the following qualities in learners:
• 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 understanding of concepts needed to make sense of
mathematics;• acquisition of specific knowledge and skills necessary for:
o the application of mathematics to physical, social and mathematical problems;
o the study of related subject matter (e.g. other subjects)o the further study of mathematics.
The CAPS lists the following specific skills that learners must acquire to develop their essential mathematical skills:
• correct use of the language of mathematics;• number vocabulary, number concept and calculation and
application skills;• ability to listen, communicate, think, reason logically and
apply the mathematical knowledge gained;
CAPS Math Gr 2 TG.indb 5 2011/11/16 2:51 PM
6 Study & Master Mathematics Grade 2 • Introduction
• ability to investigate, analyse, represent and interpret information;
• ability to pose and solve problems;• awareness of the important role that mathematics plays in
real-life situations, including the personal development of the learner.
Problem-solving and mathematics
This Study and Master Mathematics course aims to encourage learner-centred and activity-based learning through problem-solving, an approach which should be applied throughout the course.
Problem-solving is one of the unique features of learning and teaching mathematics. Learners should be able to:
• make sense of problems;• analyse, synthesise (create), determine and execute solution
strategies;• validate (confirm) and interpret the solutions appropriate to
the context.
You should realise that problem-solving does not necessarily imply solving word problems. Word problems could be examples of extending problems that test knowledge involving the use and validation of learned techniques.
In a problem-solving situation, it may be highly unlikely that learners have had previous instruction on how to tackle the problems they are facing. Learners should invent their own solution strategies using different problem-solving procedures. There are no readymade recipes or blueprints for searching for and finding problem-solving solutions.
Solutions and strategies are not as obvious in problem-solving situations as they are in word problems. In word problems it is easy to identify which operations to apply to solve the problem. Problem-solving is not a topic that can be learned. It is a process in which learners can explore situations by applying different skills. Learners construct new meaning by building on previous knowledge and experiences in an active, cooperative environment.
Learners do not learn problem-solving techniques by memorising rules or consulting checklists. You should raise consistent awareness of the different techniques suitable for different problem-solving situations. You could give the problem as a homework task, group activity or introduction to new concepts (knowledge), or deal with it in an oral or written situation that applies to all learners without gender or culture bias.
Keep in mind that it is important to acknowledge that people are fundamentally different, and experience problem situations differently. Expect learners to apply a wide range of different methods and ideas in the problem-solving process. Monitor learner groups carefully and encourage discussions and arguments while questioning learners about their progress.
CAPS Math Gr 2 TG.indb 6 2011/11/16 2:51 PM
7Study & Master Mathematics Grade 2 • Introduction
Have a class discussion on making mistakes, working well together, useful steps to keep in mind during the lesson, and enjoyment as an important part of mathematics activity. Discuss each aspect and ask learners questions like: How do you feel when you have made a mistake? Why do you feel this way? Explain, for example, what it means to work towards a common goal.
Inclusivity in the mathematics classroom
The ultimate aim of an inclusive school is to contribute towards the development of an inclusive society, where diversity is respected and used as a tool for building a stronger community.
Inclusive education is a process whereby barriers to successful learning are identified and then removed for every learner. This starts at the school level, where the physical environment should be designed to accommodate learners who are differently-abled, where the school principal, the staff and the parents/guardians work together to create a good school ethos and where specialised equipment and/or personnel are provided for the differently-abled learners.
Highlight on a day-to-day basis the aspects of mathematics that encourage cooperative learning and respect for diversity.
Plan activities on an individual, pair or group basis so that you can meet the different needs of learners.
Homogeneous groups or pairs (in which all the learners have more or less the same level of skill and knowledge) are appropriate when the purpose of the group is to assist learners who have a common special educational need. Use homogeneous groups to cope with differentiated learning, for example when learners who have completed a class activity are given an individual or group extension activity while you work with the rest of the class; or for a group that needs more intensive input from you to understand and complete an activity. The intention is not for these groups to be fixed groups, but that learners move to different groups according to their needs and progress.
Heterogeneous groups have a number of advantages. These groups consist of learners with diverse backgrounds, gender, language and ability. Heterogeneous groups expose learners to new ideas, generate more discussion, and allow explanations to be given and received more frequently, which increases understanding. Peer-tutoring, where two learners with different skills are paired, can be a mutually enriching experience.
Content areas in Foundation Phase Mathematics
Mathematics in the Foundation Phase covers five content areas: • Numbers, operations and relationships• Patterns, functions and algebra• Space and Shape (Geometry)• Measurement• Data handling
CAPS Math Gr 2 TG.indb 7 2011/11/16 2:51 PM
8 Study & Master Mathematics Grade 2 • Introduction
Weekly teaching schedule
Term 1
Week TopicContent Area/ Module
Activity LB page
1
Orientation and Baseline assessment
During this time select a few appropriate activities from Grade 1 books and
do revision and consolidation of Grade 1 work. During the teaching and
execution of these activities the educator should move around amongst the
learners to observe and record the ability levels the learners are at.
2
• Countforwardsandbackwardsinonesfromanynumberbetween0and100
• Knowandreadnumbersymbols0to50
• Placevalue:Knowwhateachdigitrepresents
• Solvewordproblemsincontextandexplainownsolutiontoproblems
involvingaddition,subtractionwithanswersupto20
• Time:knowdaysofweek
1
1
1
1
4
1
9
18
70
5
4
12
21
73
122
3
• Countforwardsandbackwards
– inonesfromanynumberbetween0and100
– infivesfromanymultipleof5between0and100
• Knowandreadnumbersymbols0to50
• Orderwholenumbersfromsmallesttobiggest,andbiggesttosmallest
• Placevalue:knowwhateachdigitrepresents
• Time:knowmonthsofyear
1
1
1
1
1
4
1
6
9
3
18
6
4
9
12
6
21
123
Each content area contributes towards the acquisition of specific skills. The table in the CAPS document (under “Documents” at the back of this file) shows the general focus of the content areas in the Mathematics curriculum for all phases, as well as the specific content focus for the Foundation Phase.
Each content area is divided into topics. All the content areas must be taught every term – see the Weekly teaching schedule below.
Please note
In Study & Master Mathematics Grade 1–3 the activities within each content area are set out in such a way that concepts and skills are scaffolded and developed progressively, allowing educators to determine progression and speed for the various ability level groups in the class.
CAPS Math Gr 2 TG.indb 8 2011/11/16 2:51 PM
9Study & Master Mathematics Grade 2 • Introduction
Term 1
Week TopicContent Area/ Module
Activity LB page
4
• Countforwardsandbackwards – inonesfromanynumberbetween0and100 – intensfromanymultipleof10between0and100• Writenumbersymbols0–50• Comparewholenumbersusingsmallerthan,greaterthan,morethan,less
than and is equal to• Solvewordproblemsincontextandexplainownsolutiontoproblems
involvingaddition,subtractionwithanswersupto20• 2-Dshapes:describe,sortandcompare• Datahandling
111
1
135
179
8
7041
41012
11
7399138
5
• Countforwardsandbackwards – inonesfromanynumberbetween0and100• Orderwholenumbersfromsmallesttobiggest,andbiggesttosmallest• Decompose2-digitnumbersintomultiplesoftensandunits/ones(TU)• Copysimplepatternsusingphysicalobjects
1112
13197
462292
6
• Countforwardsandbackwards – inonesfromanynumberbetween0and100 – fivesfromanymultipleof5between0and100• Comparewholenumbersusingsmallerthan,greaterthan,morethan,less
than and is equal to• Copysimplepatternsusingphysicalobjects
11
12
46
87
79
1192
7
• Countforwardsandbackwardsinonesfromanynumberbetween0and100
• Orderwholenumbersfromsmallesttobiggest,andbiggesttosmallest• Solvewordproblemsincontextandexplainownsolutiontoproblems
involvingaddition,subtractionwithanswersupto20• Measurement:length
11
14
43
31, 7117
76
34, 74134
8
• Countforwardsandbackwards – inonesfromanynumberbetween0and100 – intensfromanymultipleof10between0and100• Comparewholenumbersusingsmallerthan,greaterthan,morethan,less
than and is equal to• Solvewordproblemsincontextandexplainownsolutiontoproblems
involvingaddition,subtractionwithanswersupto20• Repeatedadditionleadingtomultiplication• Measurement:length
11
1
114
4 7
8
71 47 18
710
11
7450135
9
• Countforwardsandbackwardsinonesfromanynumberbetween0and100
• Decompose2-digitnumbersintomultiplesoftensandunits/ones(TU)• Solvewordproblemsincontextandexplainownsolutiontoproblems
involvingaddition,subtractionwithanswersupto20• Copysimplepatternsusingphysicalobjects
11
12
419 397
722
4292
10
• Countforwardsandbackwards – inonesfromanynumberbetween0and100 – intensfromanymultipleof10between0and100• Positionobjectsinalinefromfirsttotenthorfirsttolast,e.g.first,second,
third…tenth(ordinalnumbers)• Solvewordproblemsincontextandexplainownsolutiontoproblems
involvingaddition,subtractionwithanswersupto20• Solvemoneyproblemsinvolvingtotalsandchangeincentsupto50cor
randstoR20
11
1
1
1
47
14
41
29
710
17
44
32
CAPS Math Gr 2 TG.indb 9 2011/11/16 2:51 PM
10 Study & Master Mathematics Grade 2 • Introduction
Term 2
Week TopicContent Area/ Module
Activity LB page
1
• Countforwardsandbackwardsinonesfromanynumberbetween0
and150
• Knowandreadnumbersymbols0to150
• Comparewholenumbersusingsmallerthan,greaterthan,more
than, less than and is equal to
• Placevalue:knowwhateachdigitrepresents
• Solvewordproblemsincontextandexplainownsolution
to problems involving addition, subtraction with answers
upto20
• Copyandcompletenumberpatterns
1
1
1
1
1
2
1, 2
10
12
22
32
4
4,5
13
15
25
35
89
2
• Countforwardsandbackwardsinonesfromanynumberbetween0
and150
• Knowandreadnumbersymbols0to150
• Comparewholenumbersusingsmallerthan,greaterthan,more
than, less than and is equal to
• Decompose2-digitnumbersintomultipleoftensandones(TU)
• Solvewordproblemsincontextandexplainownsolution
to problems involving addition, subtraction with answers
upto50
• Shapeandspace:direction
1
1
1
1
1
3
1, 2
11
13
25
34
19
4,5
14
15
28
37
115
3
• Countforwardsandbackwards
– inonesfromanynumberbetween0and150
– in hundreds
• Describe,compare,ordernumbers:orderwholenumbers
• Numberbonds
• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition and subtraction
• Shapeandspace:symmetry
1
1
1
1
1
3
1, 2
5
15
23
38
10
4,5
8
18
26
41
105
4
• Countforwardsandbackwardsinonesfromanynumberbetween0
and150
• Comparewholenumbersusingsmallerthan,greaterthan,more
than, less than and is equal to
• Solvewordproblemsincontextandexplainownsolution
to problems involving addition and subtraction
• Measurement:time
1
1
1
4
1, 2, 4
9
40
1
4,5,7
12
43
118
5
• Countforwardsandbackwardsinonesfromanynumberbetween0
and150
• Solvewordproblemsincontextandexplainownsolution
to problems involving addition and subtraction
• Repeatedadditionleadingtomultiplication
• Measurement:time
1
1
1
4
1,2,4
42
48
7
4,5,7
45
51
124
CAPS Math Gr 2 TG.indb 10 2011/11/16 2:51 PM
11Study & Master Mathematics Grade 2 • Introduction
Term 2
Week TopicContent Area/ Module
Activity LB page
6
• Countforwardsandbackwards
– inonesfromanynumberbetween0and150
– infivesfromanymultipleof5between0and100
• Solveandexplainsolutionstopracticalproblemsthatinvolveequal
sharing leading to solutions that include unitary fractions, e.g. 1/2, 1/4, 1/5, etc.
• Solvemoneyproblemsinvolvingtotalsandchangeincentsupto50c
orrandstoR50
• Measurement:mass
1
1
1
1
4
4
6
16
30
13
7
9
19
33
130
7
• Countforwardsandbackwardsinonesfromanynumberbetween0
and100
• Solveandexplainsolutionstopracticalproblemsthatinvolveequal
sharing leading to solutions that include unitary fractions, e.g. 1/2, 1/4, 1/5, etc.
• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition and subtraction
• Datahandling
1
1
1
5
4
17
36
2
7
20
39
139
8
• Countforwardsandbackwardsinonesfromanynumberbetween0
and150
• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition and subtraction
• Halvingofnumbers
• Datahandling
1
1
1
5
4
43
57
3
7
46
60
140
9
• Countforwardsandbackwardsinonesfromanynumberbetween0
and150
• Decompose2-digitnumbersintomultiplesoftensandunits/ones
(TU)
• Solvewordproblemsincontextandexplainownsolutionto
problemsinvolvingaddition,subtractionwithanswersupto20
• Patterns:numberlines
• Measurement:mass
1
1
1
2
4
4
76
70,71
3
14
7
79
73, 74
88
131
10
• Countforwardsandbackwardsinonesfromanynumberbetween0
and150
• Decompose2-digitnumbersintomultiplesoftensandunits/ones
(TU)
• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition and subtraction
• Halvingofnumbers
• Solvemoneyproblemsinvolvingtotalsandchangeincentsupto50c
orrandstoR50
• 2-DShapes
• Measurement:problemsolving
• CalendarWork
1
1
1
1
1
3
4
4
4
26
27, 28
60
65
9
19
12
7
29
30,31
63
68
104
136
129
CAPS Math Gr 2 TG.indb 11 2011/11/16 2:51 PM
12 Study & Master Mathematics Grade 2 • Introduction
Term 3
Week TopicContent Area/ Module
Activity LB page
1
• Countforwardsandbackwards
• Placevalue
• Solvewordproblemsincontextandexplainownsolutionto
problemsinvolvingaddition,subtractionwithanswersupto50
• Patterns:copy,extendanddescribepatterns
• Shapeandspace:positionandview
• Measurement:telltime
1
1
1
2
3
4
1, 2
19
35
1
13
2
4,5
22
38
86
108
119
2
• Countforwardsandbackwards
• Placevalue
• Numberbonds
• Solvewordproblemsincontextandexplainownsolution
to problems involving addition and subtraction
• Repeatedadditionleadingtomultiplication
• Shapeandspace
– position and view
1
1
1
1
1
3
1, 2
21
72
20,44
49
14
4,5
24
75
23, 47
52
109
3
• Countforwardsandbackwards
• Placevalue
• Repeatedadditionleadingtomultiplication
• Patterns:copy,extendanddescribepatterns
• Shapeandspace:recogniseandname3-Dobjects
• Direction
1
1
1
2
3
3
1, 2
24
50
6
1
20
4,5
27
53
91
96
116
4
• Countforwardsandbackwards
• Repeatedadditionleadingtomultiplication
• Calculations:equalsharing(division)
• Patterns:copy,extendanddescribeanumbersequence
• Shapeandspace
– describe,sortandcompare3-Dobjects
1
1
1
2
3
1, 2, 4
51
58
10
2
4,5,7
54
61
95
97
5
• Countforwardsandbackwards
• Solvemoneyproblems
• Repeatedadditionleadingtomultiplication
• Featuresofshapes:sortedaccordingtostraight/roundedges
• Measurement:calculatelengthoftime
1
1
1
3
4
1, 2, 4
69
53
6
8
4,5,7
72
56
101
125
6
• Countforwardsandbackwardsinonesfromanynumberbetween0
and180
• Doublingandhalvingofnumbers
• Calculations:equalsharing(division)
• Measurement:tellingtime
• Measurement:calculatelengthoftime
1
1
1
4
4
4
61
59
3, 4
10
7
64
62
120,121
127
7
• Countforwardsandbackwards
• Doublingandhalvingofnumbers
• Problemsolving:equalsharing
• Shapeandspace:direction
1
1
1
3
4
77
55,62
21
7
80
58,65
117
CAPS Math Gr 2 TG.indb 12 2011/11/16 2:51 PM
13Study & Master Mathematics Grade 2 • Introduction
Term 3
Week TopicContent Area/ Module
Activity LB page
8
• Countforwardsandbackwards
• Solvewordproblemsincontextandexplainownsolutionsto
problems involving addition and subtraction
• Solvemoneyproblems
• Measurement:capacity
• Datahandling
1
1
1
4
5
4
63
64
15
4
7
66
67
132
141
9
• Countforwardsandbackwards
• Numberbonds
• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition and subtraction
• Measurement:calculatelengthoftime
• Datahandling
1
1
1
4
5
4
73
66
9
5
7
76
69
126
142
10
• Countforwardsandbackwards
• Solvemoneyproblems
• Patterns:copy,extendandexplainanumbersequence
• Symmetry
• Datahandling
1
1
2
3
5
4
68
10
12
6
7
71
95
107
143
Term 4
Week TopicContent Area/ Module
Activity LB page
1
• Countforwardsandbackwards
• Placevalue
• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition and subtraction
• Shapeandspace:sort3-Dobjects
• Revisionexercise:numberbonds
1
1
1
3
1
1, 2, 4
25
79
3
74
4,5,7
28
82
98
77
2
• Countforwardsandbackwards
• Placevalue
• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition and subtraction
• Shapeandspace:featuresofobjects
• Shapeandspace:direction
• Revisionexercise:numberbonds
1
1
1
3
3
1
1, 2
33
80
5
21
75
4,5
36
83
100
117
78
CAPS Math Gr 2 TG.indb 13 2011/11/16 2:51 PM
14 Study & Master Mathematics Grade 2 • Introduction
Term 4
Week TopicContent Area/ Module
Activity LB page
3
• Countforwardsandbackwards• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition and subtraction • Repeatedadditionleadingtomultiplication• Shapeandspace:featuresofobjectsMeasurement:calendarworkRevisionexercise
1
11341
1, 2
37 817 1178
4,5
408410212881
4
• Countforwardsandbackwards• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition and subtraction • Repeatedadditionleadingtomultiplication• Shapeandspace:buildwith2-Dshapes• Datahandling
1
1135
1, 2, 4
45828 7
4,5,7
4885103144
5
• Countforwardsandbackwards• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition and subtraction • Patterns:copy,extendanddescribepatterns• Patterns:creatinggeometricpatterns• Measurement:capacity
1
1224
1, 2, 4
46 2916
4,5,7
498794133
6
• Countforwardsandbackwards• Repeatedadditionleadingtomultiplication• Problemsolving:workingwithmoney• Patterns:copy,extendanddescribenumberpatterns• Shapeandspace:symmetry
11123
1, 2, 4 5267 511
4,5,7557090106
7
• Countforwardsandbackwards• Problemsolving:repeatedadditionleadingtomultiplication• Patterns:copy,extendanddescribegeometricpatterns• Shapeandspace:positionandview• Datahandling
11235
1, 2, 454815,168
4,5,75793110,111145
8
• Countforwardsandbackwards• Problemsolving:equalsharing• Patterns:copy,extendanddescribepatternsinnature• Shapeandspace:positionanddirection
1123
1, 2, 456917, 18
4,5,75994112, 113
9
• Countforwardsandbackwards• Solvewordproblemsincontextandexplainownsolutionto
problems involving addition/subtraction/equal sharing• Patterns:copy,extendsanddescribesnumberpatterns• Measurement:time–problemsolving• Datahandling
1
1245
1, 2, 4
571020 9
4,5,7
6095116146
10
• Itisadvisabletousethefinalweekofthetermtoconsolidate,revise,remediate and extend concepts and skills learnt during the course of the term and earlier in the year.
• Alsodofinaloral,practicalandwrittenassessmentoflearnersinneed of more attention.
CAPS Math Gr 2 TG.indb 14 2011/11/16 2:51 PM
15Study & Master Mathematics Grade 2 • Introduction
The Weekly teaching schedule shows how the content areas can be spread and revisited throughout the year. You may choose to sequence and pace the topics in each content area differently from the way the teaching schedule does this. If you do, it is important to bear in mind the relative weighting and notional hours of the content areas when you plan your teaching schedule for each topic.
Weighting of content areasMathematics content areas are weighted for two purposes: firstly the weighting gives guidance on the amount of time needed to adequately cover the content in each content area; secondly the weighting gives teachers guidance on the spread of content in the examination (especially in the end-of-year summative assessment).
The weighting of the content is not the same for each grade in the Foundation Phase. The table below shows the different weightings, per grade.
Table 2: Weighting of content areas in Foundation Phase Mathematics
Weighting of content areasContent area Grade 1 Grade 2 Grade 3Numbers, operations and relationships* 65% 60% 58%
Patterns, functions and algebra 10% 10% 10%
Space and shape (geometry) 11% 13% 13%
Measurement 9% 12% 14%
Data handling (statistics) 5% 5% 5%
100% 100% 100%
* In Grades 1–3, Numbers, operations and relationships are the main focus of mathematics. By the end of the Foundation Phase learners need to have a secure number sense and operational fluency that they can take with them into the next phase. The aim is for learners to be competent and confident with numbers and calculations. For this reason the notional time allocated to the Numbers, operations and relationships content area has been increased. Most of the work on patterns in the Patterns, functions and algebra content area should focus on Number patterns, to further consolidate learners’ ability to work with numbers. The section ‘Allocation of teaching time’ in Part 2 below gives more information about how your teaching time should be organised to cover all the content areas in the course of the year.
Progression in content areas across the Foundation PhaseIn the Foundation Phase Mathematics curriculum, links are created between the learners’ experience gained in their pre-school and home life, and the more abstract mathematics they will encounter in later grades. In Grades 1–3 they should have many mathematical experiences that give them opportunities to “do, talk and record” their mathematical thinking. Suggestions for planning and organising these types of classroom mathematical experiences are given in Part 2 of this Teacher’s Guide.
Learners develop their skills and knowledge in each content area in a careful progression from Grade R to Grade 3. The Phase overview gives an overview of this progression for the whole Foundation Phase.
CAPS Math Gr 2 TG.indb 15 2011/11/16 2:51 PM
16 Study & Master Mathematics Grade 2 • Introduction
Nu
mb
ers,
op
erat
ion
s an
d r
elat
ion
ship
s •
Nu
mb
er c
once
pt
dev
elop
men
t G
rad
e 1
Cou
nt
wit
h w
hol
e n
um
ber
sM
odTo
pic
sTe
rm 1
Term
2Te
rm 3
Term
41
Cou
nt o
bjec
tsC
oun
t con
cret
e ob
ject
sC
oun
t out
obj
ects
rel
iabl
y to
20
Cou
nt o
ut o
bjec
ts r
elia
bly
to 4
0C
oun
t out
obj
ects
rel
iabl
y to
50
Giv
e a
reas
onab
le e
stim
ate
of a
n
umbe
r of
obj
ects
th
at c
an b
e ch
ecke
d by
cou
nti
ng.
Giv
e a
reas
onab
le e
stim
ate
of a
n
umbe
r of
obj
ects
th
at c
an b
e ch
ecke
d by
cou
nti
ng.
Giv
e a
reas
onab
le e
stim
ate
of a
n
umbe
r of
obj
ects
th
at c
an b
e ch
ecke
d by
cou
nti
ng.
Giv
e a
reas
onab
le e
stim
ate
of a
n
umbe
r of
obj
ects
th
at c
an b
e ch
ecke
d by
cou
nti
ng.
1C
oun
t for
war
ds
and
back
war
dsC
oun
t for
war
ds a
nd
back
war
ds in
:•
on
es fr
om a
ny n
umbe
r be
twee
n 1
an
d 20
Cou
nt f
orw
ards
an
d ba
ckw
ards
in•
on
es fr
om a
ny n
umbe
r be
twee
n 0
- 50
Cou
nt f
orw
ards
in•
ten
s fr
om a
ny m
ulti
ple
of 1
0 be
twee
n 0
an
d 50
• f
ives
from
any
mul
tipl
e of
5
betw
een
0 a
nd
50•
tw
os fr
om a
ny m
ulti
ple
of 2
be
twee
n 0
an
d 20
Cou
nt f
orw
ards
an
d ba
ckw
ards
in•
on
es fr
om a
ny n
umbe
r be
twee
n 0
–
80C
oun
t for
war
ds in
• te
ns
from
any
mul
tipl
e of
10
betw
een
0 a
nd
80•
fiv
es fr
om a
ny m
ulti
ple
of 5
be
twee
n 0
an
d 80
• t
wos
from
any
mul
tipl
e of
2
betw
een
0 a
nd
80
Cou
nt f
orw
ards
an
d ba
ckw
ards
in•
on
es fr
om a
ny n
umbe
r be
twee
n
0-10
0C
oun
t for
war
ds in
• te
ns
from
any
mul
tipl
e of
10
betw
een
0 a
nd
100
• f
ives
from
any
mul
tipl
e of
5
betw
een
0 a
nd
100
• t
wos
from
any
mul
tipl
e of
2
betw
een
0 a
nd
100
Con
ten
tTe
rm 1
Term
2Te
rm 3
Term
4R
epre
sen
t w
hol
e n
um
ber
s1
Num
ber
sym
bols
an
d n
umbe
r n
ames
Kn
ow a
nd
rea
d n
um
ber
s•
Kn
ow a
nd
r ead
num
ber
sym
bols
0
to 2
0•
Wri
te n
umbe
r sy
mbo
ls 0
-5•
Kn
ow a
nd
r ead
num
ber
nam
es 0
-5•
Wri
t e n
umbe
r n
ames
0-5
Kn
ow a
nd
rea
d n
um
ber
s•
Kn
ow a
nd
r ead
num
ber
sym
bols
0
to 5
0•
Wri
te n
umbe
r sy
mbo
ls 0
-10
• K
now
an
d re
ad n
umbe
r n
ames
0-
10•
Wri
te n
umbe
r n
ames
0-1
0
Kn
ow a
nd
rea
d n
um
ber
s•
Kn
ow a
nd
read
num
ber
sym
bols
0
to 8
0•
Wri
t e n
umbe
r sy
mbo
ls 0
-20
• K
now
an
d re
ad n
umbe
r n
ames
0-
10•
Wri
te n
umbe
r n
ames
0-1
0
Kn
ow a
nd
rea
d n
um
ber
s•
Kn
ow a
nd
read
num
ber
sym
bols
0
to 1
00•
Wri
t e n
umbe
r sy
mbo
ls 0
-20
• K
now
an
d re
ad n
umbe
r n
ames
0-
10•
Wri
t e n
umbe
r n
ame
0-10
Ord
er a
nd
com
par
e w
hol
e n
um
ber
s1
Des
crib
e,
com
pare
, ord
er
num
bers
Ord
er a
nd
com
pare
obj
ects
.•
Com
pare
col
lect
ion
of o
bjec
ts
acco
rdin
g to
man
y, fe
w; m
ost,
le
ast;
mor
e th
an, l
ess
than
; th
e sa
me
as, j
ust a
s m
any
as, d
iffe
ren
t
Ord
er a
nd
com
pare
obj
ects
.•
Com
pare
col
lect
ion
of o
bjec
ts
acco
rdin
g to
man
y, fe
w; m
ost,
le
ast m
ore
than
, les
s th
an; t
he
sam
e as
, jus
t as
man
y as
, dif
fere
nt
Ord
er a
nd
com
pare
obj
ects
.•
Com
pare
col
lect
ion
of o
bjec
ts
acco
rdin
g to
man
y, fe
w; m
ost,
le
ast m
ore
than
, les
s th
an; t
he
sam
e as
, jus
t as
man
y as
, dif
fere
nt
Ord
er a
nd
com
pare
obj
ects
.•
Com
pare
col
lect
ion
of o
bjec
ts
acco
rdin
g to
man
y, fe
w; m
ost,
le
ast;
mor
e th
an, l
ess
than
; th
e sa
me
as, j
ust a
s m
any
as, d
iffe
ren
t•
Ord
er c
olle
ctio
n o
f obj
ects
from
m
ost t
o le
ast a
nd
leas
t to
mos
t.•
Ran
ge u
p to
5 o
bjec
ts
• O
rder
col
lect
ion
of o
bjec
ts fr
om
mos
t to
leas
t an
d le
ast t
o m
ost.
• R
ange
up
to 1
0 ob
ject
s
• O
rder
col
lect
ion
of o
bjec
ts fr
om
mos
t to
leas
t an
d le
ast t
o m
ost.
• R
ange
up
to 1
5 ob
ject
s
• O
rder
col
lect
ion
of o
bjec
ts fr
om
mos
t to
leas
t an
d le
ast t
o m
ost.
• R
ange
up
to 2
0 ob
ject
sO
rder
an
d co
mpa
re n
umbe
rs to
5O
rder
an
d co
mpa
re n
umbe
rs to
10
Ord
er a
nd
com
pare
num
bers
to 1
5O
rder
an
d co
mpa
re n
umbe
rs to
20
Phase overview
CAPS Math Gr 2 TG.indb 16 2011/11/16 2:51 PM
17Study & Master Mathematics Grade 2 • Introduction
Des
crib
e,
com
pare
, or
der
num
bers
(c
ontin
ued)
Ord
er n
umbe
rs:
• fr
om s
mal
lest
to g
reat
est a
nd
grea
test
to s
mal
lest
• n
umbe
r lin
e 1–
5D
escr
ibe
orde
r us
ing
lan
guag
e e.
g.
• b
efor
e, a
fter
, in
th
e m
iddl
e/be
twee
n
Ord
er n
umbe
rs:
• fr
om s
mal
lest
to g
reat
est a
nd
grea
test
to s
mal
lest
• b
efor
e, a
fter
, in
th
e m
iddl
e/
betw
een
• u
sin
g th
e n
umbe
r lin
e 0–
50
Ord
er n
umbe
rs:
• fr
om s
mal
les t
to g
reat
est a
nd
grea
test
to s
mal
lest
• b
efor
e, a
fter
, in
th
e m
iddl
e/be
twee
n•
usi
ng
the
num
ber
line
0–80
Ord
er n
umbe
rs:
• fr
om s
mal
lest
to g
reat
est a
nd
grea
test
to s
mal
lest
• b
efor
e, a
fter
, in
th
e m
iddl
e/be
twee
n•
usi
ng
the
num
ber
line
0–10
0
Com
pare
wh
ole
num
bers
usi
ng
lan
guag
e e.
g.•
acc
ordi
ng
to s
mal
ler
than
, gre
ater
th
an/m
ore
than
less
th
an•
num
ber
ran
ge u
p to
5
Com
pare
wh
ole
num
bers
acc
ordi
ng
to s
mal
ler
than
, gre
ater
th
an/m
ore
than
, les
s th
an, i
s eq
ual t
o•
on
e- to
on
e co
rres
pon
den
ce•
num
ber
ran
ge u
p to
10
Com
pare
wh
ole
num
bers
acc
ordi
ng
to s
mal
ler
than
, gre
ater
th
an, m
ore
than
, les
s th
an, i
s eq
ual t
o•
on
e-to
-on
e co
rres
pon
den
ce•
num
ber
ran
ge u
p to
15
Com
pare
wh
ole
num
bers
acc
ordi
ng
to s
mal
ler
than
, gre
ater
th
an, m
ore
than
, les
s th
an, i
s eq
ual t
o•
on
e-to
-on
e co
rres
pon
den
ce•
num
ber
ran
ge u
p to
20
Use
ord
inal
num
bers
to s
how
ord
er,
plac
e or
pos
itio
n•
Pos
itio
n o
bjec
ts in
a li
ne
from
fi
rst t
o te
nth
or
firs
t to
last
e.g
. fi
rst,
sec
ond
thir
d, la
st. (
ordi
nal
n
umbe
rs)
Use
ord
inal
num
bers
to s
how
ord
er,
plac
e or
pos
itio
n•
Pos
itio
n o
bjec
ts in
a li
ne
from
firs
t to
ten
th o
r fi
rst t
o la
st e
.g. f
irst
, se
con
d, t
hir
d, fo
urth
, fif
th, l
ast
(ord
inal
num
bers
)
Use
ord
inal
num
bers
to s
how
ord
er,
plac
e or
pos
itio
n•
Pos
itio
n o
bjec
ts in
a li
ne
from
firs
t to
ten
th o
r fi
rst t
o la
st e
.g. f
irst
, se
con
d, t
hir
d …
ten
th, l
ast (
ordi
nal
n
umbe
rs)
Use
ord
inal
num
bers
to s
how
ord
er,
plac
e or
pos
itio
n•
Pos
itio
n o
bjec
ts in
a li
ne
from
firs
t to
ten
th o
r fi
rst t
o la
st e
.g. f
irst
, se
con
d, t
hir
d …
ten
th, l
ast (
ordi
nal
n
umbe
rs)
Ord
inal
asp
ect o
f num
bers
in t
he
ran
ge fi
rst t
o fi
fth
Ord
inal
asp
ect o
f num
bers
in t
he
ran
ge fi
rst t
o te
nth
Ord
inal
asp
ect o
f num
bers
in t
he
ran
ge fi
rst t
o te
nth
Ord
inal
asp
ect o
f num
bers
in t
he
ran
ge fi
rst t
o te
nth
Plac
e va
lue
1Pl
ace
valu
eRe
cogn
ise
the
plac
e va
lue
of a
t lea
st
2- d
igit
num
bers
to 1
5•
Par
titi
on 2
dig
its
num
bers
into
te
ns
and
ones
to 8
0 e.
g. 1
2 is
10
and
2
Reco
gnis
e th
e pl
ace
valu
e of
at l
east
2-
dig
it n
umbe
rs to
20
• P
arti
tion
2 d
igit
s n
umbe
rs in
to
ten
s an
d on
es to
99
e.g.
19
is 1
0 an
d 9
Solv
e n
um
ber
pro
ble
ms
1Pr
oble
m s
olvi
ng
tech
niq
ues
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
s an
d ex
plai
n
solu
tion
s to
pro
blem
s:•
con
cret
e ap
para
tus
e.g.
cou
nte
rs•
pic
ture
s to
dra
w t
he
stor
y su
m•
num
ber
lines
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
s an
d ex
plai
n
solu
tion
s to
pro
blem
s:•
con
cret
e ap
para
tus
e.g.
cou
nte
rs•
pic
ture
s to
dra
w t
he
stor
y su
m•
bui
ldin
g up
an
d br
eaki
ng
dow
n
num
bers
• d
oubl
ing
and
hal
vin
g•
num
ber
lines
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
s an
d ex
plai
n
solu
tion
s to
pro
blem
s:•
con
cret
e ap
para
tus
e.g.
cou
nte
rs•
pic
ture
s to
dra
w t
he
stor
y su
m•
bui
ldin
g up
an
d br
eaki
ng
dow
n
num
bers
• d
oubl
ing
and
hal
vin
g•
num
ber
lines
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
s an
d ex
plai
n
solu
tion
s to
pro
blem
s:•
con
cret
e ap
para
tus
e.g.
cou
nte
rs•
pic
ture
s to
dra
w t
he
stor
y su
m•
bui
ldin
g up
an
d br
eaki
ng
dow
n
num
bers
• d
oubl
ing
and
hal
vin
g•
num
ber
lines
• s
har
es s
trat
egie
s w
ith
pee
rs
CAPS Math Gr 2 TG.indb 17 2011/11/16 2:51 PM
18 Study & Master Mathematics Grade 2 • Introduction
1A
ddit
ion
, su
btra
ctio
nPr
acti
cally
sol
ve w
ord
prob
lem
s in
co
nte
xt a
nd
expl
ain
ow
n s
olut
ion
to
pro
blem
s in
volv
ing
addi
tion
, su
btra
ctio
n w
ith
an
swer
s up
to 5
Solv
e w
ord
prob
lem
s in
con
text
an
d ex
plai
n o
wn
sol
utio
n to
pro
blem
s in
volv
ing
addi
tion
, sub
trac
tion
wit
h
answ
ers
up to
10
Solv
e w
ord
prob
lem
s in
con
text
an
d ex
plai
n o
wn
sol
utio
n to
pro
blem
s in
volv
ing
addi
tion
, sub
trac
tion
wit
h
answ
ers
up to
15
Solv
e w
ord
prob
lem
s in
con
text
an
d ex
plai
n o
wn
sol
utio
n to
pro
blem
s in
volv
ing
addi
tion
, sub
trac
tion
wit
h
answ
ers
up to
20.
1Re
peat
ed
addi
tion
le
adin
gto
mul
tipl
icat
ion
Solv
e w
ord
prob
lem
s in
con
text
an
d ex
plai
ns
own
sol
utio
n to
pro
blem
s in
volv
ing
repe
ated
add
itio
n w
ith
an
swer
s up
to 1
0
Solv
e w
ord
prob
lem
s in
con
text
an
d ex
plai
ns
own
sol
utio
n to
pro
blem
s in
volv
ing
repe
ated
add
itio
n w
ith
an
swer
s up
to 1
5
Solv
e w
ord
prob
lem
s in
con
text
an
d ex
plai
ns
own
sol
utio
n to
pro
blem
s in
volv
ing
repe
ated
add
itio
n w
ith
an
swer
s up
to 2
0
1G
roup
ing
and
shar
ing
lead
ing
to d
ivis
ion
Solv
e an
d ex
plai
n s
olut
ion
s to
pr
acti
cal p
robl
ems
invo
lvin
g eq
ual
shar
ing
and
grou
pin
g w
ith
wh
ole
num
bers
up
to 5
an
d w
ith
an
swer
s th
at c
an in
clud
e re
mai
nde
rs
Solv
e an
d ex
plai
n s
olut
ion
s to
pr
acti
cal p
robl
ems
invo
lvin
g eq
ual
shar
ing
and
grou
pin
g w
ith
wh
ole
num
bers
up
to 1
0 an
d w
ith
an
swer
s th
at c
an in
clud
e re
mai
nde
rs
Solv
e an
d ex
plai
n s
olut
ion
s to
pr
acti
cal p
robl
ems
invo
lvin
g eq
ual
shar
ing
and
grou
pin
g w
ith
wh
ole
num
bers
up
to 1
5 an
d w
ith
an
swer
s th
at c
an in
clud
e re
mai
nde
rs
Solv
e an
d ex
plai
n s
olut
ion
s to
pr
acti
cal p
robl
ems
invo
lvin
g eq
ual
shar
ing
and
grou
pin
g w
ith
wh
ole
num
bers
up
to 2
0 an
d w
ith
an
swer
s th
at c
an in
clud
e re
mai
nde
rs
1M
oney
Reco
gnis
e an
d id
enti
fy t
he
SA
curr
ency
•
coi
ns
5c, 1
0c, 2
0, 5
0c, R
1, R
2
Reco
gnis
e an
d id
enti
fy t
he
SA
curr
ency
•
coi
ns
5c, 1
0c, 2
0, 5
0c, R
1, R
2
Reco
gnis
es a
nd
iden
tify
th
e SA
cu
rren
cy•
coi
ns
5c, 1
0c, 2
0, 5
0c, R
1, R
2•
not
es R
10 a
nd
R20
Solv
e m
oney
pro
blem
s in
volv
ing
tota
ls a
nd
chan
ge to
R10
an
d in
ce
nts
up
to 2
0c c
ents
Solv
e m
oney
pro
blem
s in
volv
ing
tota
ls a
nd
chan
ge to
R20
an
d in
ce
nts
up
to 2
0c c
ents
• n
otes
R10
an
d R
20 So
lve
mon
ey p
robl
ems
invo
lvin
g to
tals
an
d ch
ange
in c
ents
up
to 5
0c
or r
ands
to R
20
Cal
cula
tion
s1
Met
hod
s or
st
rate
gies
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
num
ber
lines
sup
port
ed b
y co
ncr
ete
appa
ratu
s e.
g. c
oun
tin
g be
ads
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
bui
ldin
g up
an
d br
eaki
ng
dow
n
num
bers
• d
oubl
ing
and
hal
vin
g
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
bui
ldin
g up
an
d br
eaki
ng
dow
n
num
bers
• d
oubl
ing
and
hal
vin
g
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
bui
ldin
g up
an
d br
eaki
ng
dow
n
num
bers
• d
oubl
ing
and
hal
vin
g1
Add
itio
n a
nd
subt
ract
ion
Num
ber
ran
ge: 0
-5•
Add
itio
n u
p to
5•
Sub
trac
t fro
m 5
• P
ract
ise
num
ber
bon
ds to
5
Num
ber
ran
ge: 0
-10
• a
dd u
p to
10
• s
ubtr
act f
rom
10
• u
se a
ppro
pria
te s
ymbo
ls
( +,
–, =
, ×)
• p
ract
ice
num
ber
bon
ds to
7
Num
ber
ran
ge: 0
-15
• a
dd to
15
• s
ubtr
act f
rom
15
• u
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)•
pra
ctic
e n
umbe
r bo
nds
to 9
Num
ber
ran
ge: 0
-20
• a
dd to
20
• s
ubtr
act f
rom
20
• u
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)•
pra
ctic
e n
umbe
r bo
nds
to 1
01
Repe
ated
ad
diti
on
lead
ing
to
mul
tipl
icat
ion
Repe
ated
add
itio
n (
i.e. t
he
sam
e n
umbe
r) to
10
• u
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)
Repe
ated
add
itio
n (
i.e. t
he
sam
e n
umbe
r) to
10
• u
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)
Repe
ated
add
itio
n (
i.e. t
he
sam
e n
umbe
r) to
20
• u
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)
CAPS Math Gr 2 TG.indb 18 2011/11/16 2:51 PM
19Study & Master Mathematics Grade 2 • Introduction
1M
enta
l st
rate
gies
fo
r do
ing
calc
ulat
ion
s
Num
ber
con
cept
: ran
ge•
Ord
er a
giv
en s
et o
f sel
ecte
d n
umbe
rs.
• C
ompa
re n
umbe
rs to
10
and
say
wh
ich
is m
ore
or le
ss.
• K
now
wh
ich
num
ber
is 1
mor
e or
1
less
th
an a
giv
en n
umbe
r.•
Kn
ow w
hic
h n
umbe
r is
2 m
ore
or 2
le
ss t
han
a g
iven
num
ber.
Num
ber
con
cept
: ran
ge 1
0•
Ord
er a
giv
en s
et o
f sel
ecte
d n
umbe
rs.
• C
ompa
re n
umbe
rs to
10
and
say
wh
ich
is m
ore
or le
ss.
• K
now
wh
ich
num
ber
is 1
mor
e or
1 le
ss t
han
a g
iven
num
ber.
• K
now
wh
ich
num
ber
is 2
mor
e or
2
less
th
an a
giv
en n
umbe
r.
Num
ber
con
cept
: ran
ge 1
5•
Ord
er a
giv
en s
et o
f sel
ecte
d n
umbe
rs.
• C
ompa
re n
umbe
rs to
an
d sa
y w
hic
h is
mor
e or
less
.•
Kn
ow w
hic
h n
umbe
r is
1 m
ore
or 1
le
ss t
han
a g
iven
num
ber.
• K
now
wh
ich
num
ber
is 2
mor
e or
2
less
th
an a
giv
en n
umbe
r.
Num
ber
con
cept
: ran
ge 2
0•
Ord
er a
giv
en s
et o
f sel
ecte
d n
umbe
rs.
• C
ompa
re n
umbe
rs to
100
an
d sa
y w
hic
h is
mor
e or
less
.•
Kn
ow w
hic
h n
umbe
r is
1 m
ore
or 1
le
ss t
han
a g
iven
num
ber.
• K
now
wh
ich
num
ber
is 2
mor
e or
2
less
th
an a
giv
en n
umbe
r.•
Kn
ow w
hic
h n
umbe
r is
10
mor
e or
10
less
th
an a
giv
en n
umbe
r.Ra
pidl
y re
call:
• n
umbe
r bo
nds
to 5
• r
ecal
l add
itio
n a
nd
subt
r act
ion
fa
cts
to 5
Rapi
dly
reca
ll:•
num
ber
bon
ds to
10
• r
ecal
l add
itio
n a
nd
subt
ract
ion
fa
cts
to 1
0U
se c
alcu
lati
on s
trat
egie
s to
add
an
d su
btra
ctef
fici
entl
y:•
put
th
e la
rger
num
ber
firs
t in
or
der
to c
oun
t on
or
coun
t bac
k•
num
ber
line
• d
oubl
ing
and
hal
vin
g•
bui
ldin
g up
an
d br
eaki
ng
dow
n
Use
cal
cula
tion
str
ateg
ies
to a
dd a
nd
subt
ract
effi
cien
tly:
• p
ut t
he
larg
er n
umbe
r fi
rst i
n
orde
r to
cou
nt o
n o
r co
unt b
ack
• n
umbe
r lin
e•
dou
blin
g an
d h
alvi
ng
• B
uild
ing
up a
nd
brea
kin
g do
wn
Patt
ern
s, f
un
ctio
ns
and
alg
ebra
2N
umbe
r pa
tter
ns
Cop
y, e
xten
d an
d de
scri
be s
impl
e n
umbe
r se
quen
ces
to a
t lea
st 2
0C
opy,
ext
end
and
desc
ribe
sim
ple
num
ber
sequ
ence
s to
at l
east
50
Cop
y, e
xten
d an
d de
scri
be s
impl
e n
umbe
r se
quen
ces
to a
t lea
st 8
0C
opy,
ext
end
and
desc
ribe
sim
ple
num
ber
sequ
ence
s to
at l
east
100
Sequ
ence
s sh
ould
sh
ow c
oun
tin
g fo
rwar
ds a
nd
back
war
ds in
:•
on
es fr
om a
ny n
umbe
r be
twee
n 1
an
d 20
Sequ
ence
s sh
ould
sh
ow c
oun
tin
g fo
rwar
ds a
nd
back
war
ds in
:•
Oon
es fr
om a
n y n
umbe
r be
twee
n
1 an
d 50
• te
ns
from
any
mul
tipl
e of
10
betw
een
0 a
nd
50•
fiv
es fr
om a
ny m
ulti
ple
of 5
be
twee
n 0
an
d 50
• t
wos
from
any
mul
tipl
e of
2
betw
een
0 a
nd
20
Sequ
ence
s sh
ould
sh
ow c
oun
tin
g fo
rwar
ds a
nd
back
war
ds in
:•
on
es fr
om a
n y n
umbe
r be
twee
n 1
an
d 80
• te
ns
from
any
mul
tipl
e of
10
betw
een
0 a
nd
80•
fiv
es fr
om a
ny m
ulti
ple
of 5
be
twee
n 0
an
d 80
• t
wos
from
any
mul
tipl
e of
2
betw
een
0 a
nd
80
Sequ
ence
s sh
ould
sh
ow c
oun
tin
g fo
rwar
ds a
nd
back
war
ds in
:•
on
es fr
om a
ny n
umbe
r be
twee
n 1
an
d 10
0•
ten
s fr
om a
ny m
ulti
ple
of 1
0 be
twee
n 0
an
d 10
0•
fiv
es fr
om a
ny m
ulti
ple
of 5
be
twee
n 0
an
d 10
0•
tw
os fr
om a
ny m
ulti
ple
of 2
be
twee
n 0
an
d 10
0C
reat
e ow
n n
umbe
r pa
tter
ns
CAPS Math Gr 2 TG.indb 19 2011/11/16 2:51 PM
20 Study & Master Mathematics Grade 2 • Introduction
2G
eom
etri
c pa
tter
ns
Cop
y an
d ex
ten
d si
mpl
e pa
tter
ns
usin
g•
phy
sica
l obj
ects
• d
raw
ings
(e.
g. u
sin
g co
lour
s an
d sh
apes
)
Cop
y, e
xten
d an
d de
scri
be in
wor
ds•
sim
ple
patt
ern
s m
ade
wit
h
phys
ical
obj
ects
• s
impl
e pa
tter
ns
mad
e w
ith
dr
awin
gs o
f lin
es, s
hap
es o
r ob
ject
s
Cop
y, e
xten
d an
d de
scri
be in
wor
ds•
sim
ple
patt
ern
s m
ade
wit
h
phys
ical
obj
ects
• s
impl
e pa
tter
ns
mad
e w
ith
dr
awin
gs o
f lin
es, s
hap
es o
r ob
ject
s
Patt
ern
s al
l aro
und
usId
enti
fy, d
escr
ibe
in w
ords
an
d co
py
geom
etri
c pa
tter
ns
• in
nat
ure
• fr
om e
very
day
life
• fr
om o
ur c
ultu
r al h
erit
age
Ran
ge o
f p
atte
rns
Sim
ple
repe
atin
g pa
tter
ns
Ran
ge o
f p
atte
rns
Sim
ple
repe
atin
g pa
tter
ns
Ran
ge o
f p
atte
rns
Sim
ple
repe
atin
g pa
tter
ns
Cre
ate
own
geo
met
ric
patt
ern
s•
wit
h p
h ysi
cal o
bjec
ts•
by
draw
ings
lin
es, s
hap
es o
r ob
ject
s
Cre
ate
own
geo
met
ric
patt
ern
s•
wit
h p
hysi
cal o
bjec
ts•
by
draw
ings
lin
es, s
hap
es o
r ob
ject
sSu
gges
ted
seq
uen
cin
g of
act
ivit
ies
Star
t wit
h c
opyi
ng
and
exte
ndi
ng
patt
ern
s us
ing
phys
ical
obj
ects
.O
nce
lear
ner
s ar
e co
mfo
rtab
le
wit
h u
sin
g a
cray
on o
r pe
nci
l to
star
t cop
yin
g an
d ex
ten
din
g pa
tter
ns
by d
raw
ing
them
.
Shap
e an
d s
pac
e3
Posi
tion
, or
ien
tati
on
and
view
s
Lan
guag
e of
pos
itio
nD
escr
ibe
the
posi
tion
of o
ne
obje
ct
in r
elat
ion
to a
not
her
e.g
. on
top
of
, in
fron
t of ,
beh
ind,
left
, rig
ht,
up,
do
wn
, nex
t to
Ran
ge o
f ob
ject
sRe
cogn
ise
and
nam
e 3-
D o
bjec
ts in
t h
e cl
assr
oom
an
d in
pic
ture
s•
bal
l sh
apes
(sp
her
es)
• b
ox s
hap
es (
pris
ms)
Ran
ge o
f ob
ject
sR e
cogn
ise
and
nam
e 3-
D o
bjec
ts in
t h
e cl
assr
oom
an
d in
pic
ture
s•
bal
l sh
apes
(sp
her
es)
• b
ox s
hap
es (
pris
ms)
Posi
tion
an
d d
irec
tion
sFo
llow
dir
ecti
ons
to m
ove
arou
nd
the
clas
sroo
mFo
llow
inst
ruct
ions
to p
lace
one
obj
ect
in r
elat
ion
to a
noth
er e
.g. p
ut th
e pe
ncil
insi
de th
e bo
x
Feat
ure
s of
ob
ject
sD
escr
ibe,
sor
t an
d co
mpa
re 3
-D
obje
cts
in te
rms
of:
• s
ize
• c
olou
r•
obj
ects
th
at r
oll
• o
bjec
ts t
hat
slid
e
Feat
ure
s of
ob
ject
sD
escr
ibe,
sor
t an
d co
mpa
re 3
-D
obje
cts
in te
rms
of:
• s
ize
• c
olou
r•
obj
ects
th
at r
oll
• o
bjec
ts t
hat
slid
e
P osi
tion
an
d v
iew
s•
Mat
ch d
iffe
ren
t vie
ws
of t
he
sam
e ev
eryd
ay o
bjec
t
CAPS Math Gr 2 TG.indb 20 2011/11/16 2:51 PM
21Study & Master Mathematics Grade 2 • Introduction
Posi
tion
, or
ien
tati
on
and
view
s(c
ontin
ued)
Sugg
este
d fo
cus
sequ
enci
ng
of
wor
k fo
r Te
rm 1
Lang
uage
of p
osit
ion
shou
ld b
e in
trod
uced
thro
ugh
prac
tica
l ac
tivi
ties
that
invo
lve
lear
ners
in
phys
ical
mov
emen
t.
This
can
be
con
solid
ated
th
roug
h
wri
tten
rec
ordi
ng
like
draw
ing
co
lour
ing
or m
atch
ing
draw
ings
w
ith
wor
ds.
Lear
ner
s sh
ould
firs
t lea
rn s
ome
lan
guag
e of
pos
itio
n a
nd
then
app
ly
this
kn
owle
dge
wh
en fo
llow
ing
dire
ctio
ns.
Dir
ecti
ons
shou
ld b
e do
ne
thro
ugh
pra
ctic
al a
ctiv
itie
s in
wh
ich
le
arn
ers
mov
e th
emse
lves
or
obje
cts
acco
rdin
g to
inst
ruct
ion
s.
Sugg
este
d fo
cus
and
seq
uen
cin
g of
ac
tivi
ties
for
Term
3
Lear
ner
s w
ork
wit
h b
alls
an
d ob
ject
s sh
aped
like
bal
ls, a
nd
vari
ous
oxe
s an
d ot
her
obj
ects
sh
aped
like
rec
tan
gula
r pr
ism
s or
cu
bes.
Lear
ner
s in
vest
igat
e w
hic
h o
f th
e ob
ject
s ca
n r
oll,
wh
ich
slid
e, w
hic
h
can
be
stac
ked.
Lear
ner
s id
enti
fy a
nd
desc
ribe
ge
omet
ric
and
ever
yday
obj
ects
by
sayi
ng
wh
eth
er a
re s
hap
ed li
ke a
ba
ll or
th
ey a
re s
hap
ed li
ke a
box
.
Wor
k is
con
solid
ated
thro
ugh
wri
tten
exer
cise
s.
Sugg
este
d fo
cus
and
seq
uen
cin
g of
w
ork
for
Term
4
Wor
k on
pos
itio
n a
nd
dire
ctio
n c
an
be c
onso
lidat
ed t
hro
ugh
wri
tten
re
cord
ing
like
draw
ing,
col
ouri
ng
or
mat
chin
g dr
awin
gs w
ith
wor
ds.
Any
new
lan
guag
e of
pos
itio
n s
hou
ld
be in
trod
uced
th
roug
h p
ract
ical
ac
tivi
ties
th
at in
volv
e le
arn
ers
in
phys
ical
mov
emen
t.
Dir
ecti
ons
shou
ld b
e do
ne
thro
ugh
pr
acti
cal a
ctiv
itie
s in
wh
ich
le
arn
ers
mov
e th
emse
lves
or
obje
cts
acco
rdin
g to
inst
ruct
ion
s
33-
D o
bjec
tsR
ange
of
obje
cts
Reco
gnis
e an
d n
ame
3-D
obj
ects
in
the
clas
sroo
m a
nd
in p
ictu
res
• b
all s
hap
es (
sph
eres
)•
box
sh
apes
(pr
ism
s)
Ran
ge o
f ob
ject
sRe
cogn
ise
and
nam
e 3-
D o
bjec
ts in
th
e cl
assr
oom
an
d in
pic
ture
s•
bal
l sh
apes
(sp
her
es)
• b
ox s
hap
es (
pris
ms)
Ran
ge o
f ob
ject
sRe
cogn
ise
and
nam
e 3-
D o
bjec
ts in
th
e cl
assr
oom
an
d in
pic
ture
s•
bal
l sh
apes
(sp
her
es)
• b
ox s
hap
es (
pris
ms)
Feat
ure
s of
ob
ject
sD
escr
ibe,
sor
t an
d co
mpa
re 3
-D
obje
cts
in te
rms
of:
• s
ize
• c
olou
r
Feat
ure
s of
ob
ject
sD
escr
ibe,
sor
t an
d co
mpa
re 3
-D
obje
cts
in te
rms
of:
• s
ize
• c
olou
r•
obj
ects
th
at r
oll
• o
bjec
ts t
hat
slid
e
Feat
ure
s of
ob
ject
sD
escr
ibe,
sor
t an
d co
mpa
re 3
-D
obje
cts
in te
rms
of:
• s
ize
• c
olou
r•
obj
ects
th
at r
oll
• o
bjec
ts t
hat
slid
eFo
cuss
ed a
ctiv
itie
s•
Obs
erve
and
bui
ld g
iven
3-D
ob
ject
s us
ing
conc
rete
mat
eria
ls
such
as
build
ing
bloc
ks, r
e cyc
ling,
co
nstr
uctio
n ki
ts
CAPS Math Gr 2 TG.indb 21 2011/11/16 2:51 PM
22 Study & Master Mathematics Grade 2 • Introduction
3-D
obj
ects
(con
tinue
d)Su
gges
ted
focu
s an
d s
equ
enci
ng
of
acti
viti
es fo
r Te
rm 1
Lear
ner
s st
art w
ith
free
pla
y w
ith
va
riou
s 3-
D o
bjec
ts a
nd
build
ing
thin
gs o
f th
eir
own
ch
oice
usi
ng
build
ing
bloc
ks, c
onst
ruct
ion
kit
s or
rec
yclin
g. T
his
can
be
don
e in
in
depe
nde
nt t
ime.
Lear
ner
s th
en c
opy
of m
odel
of
som
eth
ing
the
teac
her
pro
vide
s. T
his
ca
n b
e do
ne
in in
depe
nde
nt t
ime.
Lear
ner
s co
mpa
re t
he
size
of s
imila
r ob
ject
s e.
g. o
rder
bal
ls a
ccor
din
g to
si
ze a
nd
use
the
lan
guag
e of
siz
e to
de
scri
be o
bjec
ts.
Lear
ner
s ta
lk a
bout
th
e co
lour
s of
obj
ects
an
d th
en s
ort o
bjec
ts
acco
rdin
g to
col
our.
Lear
ner
s id
enti
fy a
nd
desc
ribe
ge
omet
ric
and
ever
yday
obj
ects
by
sayi
ng
wh
eth
er a
re s
hap
ed li
ke a
ba
ll or
th
ey a
re s
hap
ed li
ke a
box
.
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
se.
Sugg
este
d fo
cus
and
seq
uen
cin
g of
ac
tivi
ties
for
Term
3
Lear
ner
s w
ork
wit
h b
alls
an
d ob
ject
s sh
aped
like
bal
ls, a
nd
vari
ous
boxe
s an
d ot
her
obj
ects
sh
aped
lik
e re
ctan
gula
r pr
ism
s or
cub
es.
Lear
ner
s in
vest
igat
e w
hic
h o
f th
e ob
ject
s ca
n r
oll,
wh
ich
slid
e, w
hic
h
can
be
stac
ked.
Lear
ner
s id
enti
fy a
nd
desc
ribe
ge
omet
ric
and
ever
yday
obj
ects
by
sayi
ng
wh
eth
er a
re s
hap
ed li
ke a
ba
ll or
th
ey a
re s
hap
ed li
ke a
box
.
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
ses.
Sugg
este
d fo
cus
for
Term
4
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
ses.
32-
D s
hap
esR
ange
of
shap
esRe
cogn
ise
and
nam
e 2-
D s
hap
es•
cir
cles
• t
rian
gles
• s
quar
es
Ran
ge o
f sh
apes
Reco
gnis
e an
d n
ame
2-D
sh
apes
• c
ircl
es•
tri
angl
es•
squ
ares
Feat
ure
s of
sh
apes
Des
crib
e, s
ort a
nd c
ompa
re 2
-D
shap
es in
t erm
s of
:•
siz
e•
col
our
• s
trai
ght s
ides
• r
oun
d si
des
Feat
ure
s of
sh
apes
Des
crib
e, s
ort a
nd c
ompa
re 2
-D
shap
es in
term
s of
:•
siz
e•
col
our
• s
trai
ght s
ides
• r
oun
d si
des
CAPS Math Gr 2 TG.indb 22 2011/11/16 2:51 PM
23Study & Master Mathematics Grade 2 • Introduction
2-D
sh
apes
(con
tinue
d)Su
gges
ted
focu
s an
d s
equ
enci
ng
of
acti
viti
es fo
r Te
rm 2
Lear
ner
s st
art w
ith
free
pla
y w
ith
va
riou
s sh
apes
incl
udin
g m
akin
g pi
ctur
es w
ith
cut
out g
eom
etri
c sh
apes
. Th
is c
an b
e do
ne
in
inde
pen
den
t tim
e. T
his
can
als
o be
do
ne
duri
ng
Life
Ski
lls le
sson
s.
Sugg
este
d fo
cus
and
seq
uen
cin
g of
ac
tivi
ties
for
Term
4Le
arn
ers
wor
k ci
rcle
s an
d sq
uare
s of
dif
fere
nt s
izes
, an
d tr
ian
gles
wit
h
diff
eren
t sh
apes
. Th
ey s
ort t
hem
ac
cord
ing
to w
het
her
th
ey h
ave
stra
igh
t or
roun
d si
des.
Lear
ner
s co
py o
f pic
ture
mad
e up
of
geom
etri
c sh
apes
. Th
is c
an b
e do
ne
in in
depe
nde
nt t
ime.
Th
is c
an a
lso
be d
one
duri
ng
Life
Ski
lls le
sson
s.
Lear
ner
s so
rt a
nd
grou
p sh
apes
ac
cord
ing
to w
het
her
th
ey a
re
tria
ngl
es, s
quar
es, r
ecta
ngl
es o
r ci
rcle
s.
Lear
ner
s co
mpa
re t
he
size
of s
imila
r ob
ject
s e.
g. o
rder
squ
ares
from
sm
alle
st to
big
gest
an
d us
e th
e la
ngu
age
of s
ize
to d
escr
ibe
shap
es.
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
ses
Lear
ner
s ta
lk a
bout
th
e co
lour
s of
sh
apes
an
d th
en s
ort s
hap
es
acco
rdin
g to
col
our.
Lear
ner
s w
ork
wit
h c
ircl
es a
nd
squa
res
of d
iffe
ren
t siz
es, a
nd
tria
ngl
es w
ith
dif
fere
nt s
hap
es. T
hey
so
rt t
hem
acc
ordi
ng
to w
het
her
th
ey
hav
e st
raig
ht o
r ro
und
side
s.Le
arn
ers
sort
an
d gr
oups
sh
apes
ac
cord
ing
to w
het
her
th
ey a
re
tria
ngl
es, s
quar
es, r
ecta
ngl
es o
r ci
rcle
s.W
ork
is c
onso
lidat
ed th
roug
h w
ritt
en
exer
cise
s3
Sym
met
ry•
Rec
ogn
ise
sym
met
ry in
ow
n b
ody
• R
ecog
nis
e an
d dr
aw li
ne
of
sym
met
ry in
2-D
geo
met
rica
l an
d n
on-g
eom
etri
cal s
hap
e
• R
ecog
nis
e an
d dr
aw li
ne
of
sym
met
ry in
2-D
geo
met
rica
l an
d n
on-g
eom
etri
cal s
hap
es
CAPS Math Gr 2 TG.indb 23 2011/11/16 2:51 PM
24 Study & Master Mathematics Grade 2 • Introduction
Sym
met
ry(c
ontin
ued)
Sugg
este
d fo
cus
of a
ctiv
itie
s fo
r Te
rm 3
• L
earn
ers
shou
ld lo
ok fo
r lin
es o
f sy
mm
etry
in c
oncr
ete
obje
cts
and
pict
ures
.•
Wri
tten
exe
rcis
es s
hou
ld n
ot o
nly
be
dra
w in
th
e ot
her
hal
f but
in
clud
e ex
ampl
es w
her
e le
arn
ers
draw
in t
he
line
of s
ymm
etry
.
Sugg
este
d fo
cus
of a
ctiv
itie
s fo
r Te
rm 4
Wri
tten
exe
rcis
es s
hou
ld in
clud
e ex
ampl
es w
her
e th
e lin
e of
sy
mm
etry
is n
ot a
ver
tica
l lin
e.
Mea
sure
men
t4
Tim
ePa
ssin
g of
tim
eTa
lk a
bout
pas
sin
g of
tim
e•
Ord
er r
egul
ar e
ven
ts fr
om t
hei
r ow
n li
ves.
Pass
ing
of t
ime
Talk
abo
ut p
assi
ng
of ti
me
• O
rder
reg
ular
eve
nts
from
th
eir
own
live
s.
Pass
ing
of t
ime
Talk
abo
ut p
assi
ng
of ti
me
• O
rder
reg
ular
eve
nts
from
th
eir
own
live
s.•
Com
pare
len
gth
s of
tim
e us
ing
lan
guag
e e.
g. lo
nge
r, s
hor
ter,
fa
ster
, slo
wer
• S
eque
nce
eve
nts
usi
ng
lan
guag
e su
ch a
s ye
ster
day,
toda
y, to
mor
row
• C
ompa
re le
ngt
hs
of ti
me
usin
g la
ngu
age
e.g.
lon
ger,
sh
orte
r,
fast
er, s
low
er•
Seq
uen
ce e
ven
ts u
sin
g la
ngu
age
such
as
yest
erda
y, to
day,
tom
orro
w
• C
ompa
re le
ngt
hs
of ti
me
usin
g la
ngu
age
e.g.
lon
ger,
sh
orte
r,
fast
er, s
low
er•
Seq
uen
ce e
ven
ts u
sin
g la
ngu
age
such
as
yest
erda
y, to
day,
tom
orro
w
Tell
ing
the
tim
e•
Des
crib
e w
hen
som
eth
ing
hap
pen
s us
ing
lan
guag
e e.
g. m
orn
ing,
af
tern
oon
, nig
ht,
ear
ly, l
ate
• K
now
s da
ys o
f wee
k•
Kn
ows
mon
ths
of y
ear
• P
lace
bir
t hda
ys o
n a
cal
enda
r
Tell
ing
the
tim
e•
Des
crib
e w
hen
som
eth
ing
hap
pen
s us
ing
lan
guag
e e.
g. m
orn
ing,
af
tern
oon
, nig
ht,
ear
ly, l
ate
• K
now
s da
ys o
f wee
k•
Kn
ows
mon
ths
of y
ear
• P
lace
bir
thda
ys o
n a
cal
enda
r
Tell
ing
the
tim
e•
Des
crib
e w
hen
som
eth
ing
hap
pen
s us
ing
lan
guag
e e.
g. m
orn
ing,
af
tern
oon
, nig
ht,
ear
ly, l
ate
• K
now
s da
ys o
f wee
k•
Kn
ows
mon
ths
of y
ear
• P
lace
bir
thda
ys o
n a
cal
enda
r
Plac
e w
eath
er r
ecor
din
g on
cal
enda
rPl
ace
wea
ther
rec
ordi
ng
on c
alen
dar
Plac
e w
eath
er r
ecor
din
g on
cal
enda
r
4Le
ngt
hIn
form
al m
easu
rin
g•
Com
pare
an
d or
der
the
len
gth
, h
eigh
t or
wid
th o
f tw
o or
mor
e ob
ject
s by
pla
cin
g th
em n
ext t
o ea
ch o
ther
• U
se la
ngu
age
t o ta
lk a
bout
th
e co
mpa
riso
n e
.g. l
onge
r, s
hor
ter,
ta
ller,
wid
er•
Est
imat
e, m
easu
re, c
ompa
re, o
rder
an
d re
cord
leng
th u
sing
non
-st
anda
rd m
easu
res
e.g.
han
d sp
ans,
pa
ces,
pen
cil l
engt
hs, c
ount
ers
Info
rmal
mea
suri
ng
• E
stim
ate,
mea
sure
, com
pare
, or
der
and
reco
rd le
ngt
h u
sin
g n
on-s
tan
dard
mea
sure
s e.
g. h
and
span
s, p
aces
, pe
nci
l len
gth
s,
coun
ters
CAPS Math Gr 2 TG.indb 24 2011/11/16 2:51 PM
25Study & Master Mathematics Grade 2 • Introduction
4M
ass
Info
rmal
mea
suri
ng
• E
stim
ate,
mea
sure
, com
pare
, ord
er
and
reco
rd m
ass
usin
g a
bala
nce
an
d n
on-s
tan
dard
mea
sure
s an
d e.
g. b
lock
s, b
rick
s•
Use
lan
guag
e to
talk
abo
ut t
he
com
pari
son
e.g
. lig
ht,
hea
vy,
ligh
ter,
hea
vier
Info
rmal
mea
suri
ng
• E
stim
ate,
mea
sure
, com
pare
, or
der
and
reco
rd m
ass
usin
g n
on-
stan
dard
mea
sure
s an
d a
bala
nce
e.
g. b
lock
s, b
rick
s•
Use
lan
guag
e t o
talk
abo
ut t
he
com
pari
son
e.g
. lig
ht,
hea
vy,
ligh
ter,
hea
vier
4C
apac
ity/
volu
me
Info
rmal
mea
suri
ng
• C
ompa
re a
nd
orde
r th
e am
oun
t of
liqui
d (v
olum
e) in
two
con
tain
ers
plac
ed n
ext t
o ea
ch o
ther
. Le
arn
ers
chec
k by
pou
rin
g in
to a
th
ird
con
tain
er if
nec
essa
ry.
• C
ompa
re a
nd
orde
r th
e am
oun
t of
liqu
id t
hat
two
con
tain
ers
can
h
old
if fi
lled
(cap
acit
y)•
Use
lan
guag
e t o
talk
abo
ut t
he
com
pari
son
e.g
. mor
e th
an, l
ess
than
, ful
l, em
pty
• E
stim
ate,
mea
sure
, com
pare
, or
der
and
reco
rd t
he
capa
city
of
con
tain
ers
by u
sin
g n
on-s
tan
dard
m
easu
res
e.g.
spo
ons
and
cups
Dat
a h
and
lin
g5
Col
lect
an
d so
rt
obje
cts
Col
lect
an
d or
gan
ise
obje
cts
Col
lect
an
d so
rt e
very
day
phys
ical
ob
ject
s
Col
lect
an
d or
gan
ise
obje
cts
Col
lect
an
d so
rt e
very
day
phys
ical
ob
ject
sRe
pres
ent s
orte
d co
llect
ion
of
obje
cts
Repr
esen
t sor
ted
colle
ctio
n o
f obj
ects
Dra
w a
pic
ture
of c
olle
cted
obj
ects
Repr
esen
t sor
ted
colle
ctio
n o
f obj
ects
Dra
w a
pic
ture
of c
olle
cted
obj
ects
CAPS Math Gr 2 TG.indb 25 2011/11/16 2:51 PM
26 Study & Master Mathematics Grade 2 • Introduction
Dis
cuss
an
d re
port
on
sor
ted
colle
ctio
n o
f ob
ject
s
Dis
cuss
an
d re
port
on
sor
ted
colle
ctio
n o
f obj
ects
• G
ive
reas
ons
for
how
col
lect
ion
w
as s
orte
d•
An
swer
que
stio
ns
abou
t how
th
e so
rtin
g w
as d
one
(pro
cess
)•
wh
at t
he
sort
ed c
olle
ctio
n lo
oks
like
(pro
duct
)•
Des
crib
e th
e co
llect
ion
an
d dr
awin
g•
Exp
lain
how
th
e co
llect
ion
was
so
rted
Dis
cuss
an
d re
port
on
sor
ted
colle
ctio
n o
f obj
ects
• G
ive
reas
ons
for
how
col
lect
ion
w
as s
orte
d•
An
swer
que
stio
ns
abou
t•
how
th
e so
rtin
g w
as d
one
(pro
cess
)•
wh
at t
he
sort
ed c
olle
ctio
n lo
oks
like
(pro
duct
)•
Des
crib
e th
e co
llect
ion
an
d dr
awin
g•
Exp
lain
how
th
e co
llect
ion
was
so
rted
5C
olle
ct a
nd
orga
nis
e da
taR
ecom
men
ded
Wh
ole
data
cyc
le to
mak
e cl
ass
pict
ogra
phC
olle
ct a
nd
orga
nis
e da
taC
olle
ct d
ata
abou
t th
e cl
ass
or s
choo
l to
an
swer
que
stio
n p
osed
by
the
teac
her
Re
pres
ent d
ata
Rep
rese
nt
dat
aRe
pres
ent d
ata
in p
icto
grap
hA
nal
yse
and
Inte
rpre
t dat
aA
nal
yse
and
inte
rpre
t dat
aA
nsw
er q
uest
ion
s ab
out d
ata
in
pict
ogra
ph
An
alys
e da
ta fr
om r
epre
sen
tati
ons
prov
ided
.R
ecom
men
ded
• A
t lea
s t 2
pic
togr
aph
s
CAPS Math Gr 2 TG.indb 26 2011/11/16 2:51 PM
27Study & Master Mathematics Grade 2 • Introduction
Nu
mb
ers,
op
erat
ion
s an
d r
elat
ion
ship
s •
N
um
ber
con
cep
t d
evel
opm
ent
Gra
de
2C
oun
t w
ith
wh
ole
nu
mb
ers
Mod
Top
ics
Term
1Te
rm 2
Term
3Te
rm 4
1C
oun
t obj
ects
Cou
nt t
o at
leas
t 100
eve
ryda
y ob
ject
s re
liabl
y.G
ive
a re
ason
able
est
imat
e of
a
num
ber
of o
bjec
ts t
hat
can
be
chec
ked
by c
oun
tin
g.
Cou
nt t
o at
leas
t 150
eve
ryda
y ob
ject
s re
liabl
y.G
ive
a re
ason
able
est
imat
e of
a
num
ber
of o
bjec
ts t
hat
can
be
chec
ked
by c
oun
tin
g.
Cou
nt t
o at
leas
t 180
eve
ryda
y ob
ject
s re
liabl
y.G
ive
a re
ason
able
est
imat
e of
a
num
ber
of o
bjec
ts t
hat
can
be
chec
ked
by c
oun
tin
g.
Cou
nt t
o at
leas
t 200
eve
ryda
y ob
ject
s re
liabl
y.G
ive
a re
ason
able
est
imat
e of
a
num
ber
of o
bjec
ts t
hat
can
be
chec
ked
by c
oun
tin
g.1
Cou
nt f
orw
ards
an
d ba
ckw
ards
Cou
nts
forw
ards
an
d ba
ckw
ards
in:
• o
nes
from
any
num
ber
betw
een
0
and
100
• te
ns
from
any
mul
tipl
e of
10
betw
een
0 a
nd
100
• f
ives
from
any
mul
tipl
e of
5
betw
een
0 a
nd
100
• t
wos
from
any
mul
tipl
e of
2
betw
een
0 a
nd
100
Cou
nts
forw
ards
an
d ba
ckw
ards
in:
• o
nes
from
any
num
ber
betw
een
0
and
150
• te
ns
from
any
mul
tipl
e of
10
betw
een
0 a
nd
150
• f
ives
from
any
mul
tipl
e of
5
betw
een
0 a
nd
150
• t
wos
from
any
mul
tipl
e of
2
betw
een
0 a
nd
150
• t
hre
es a
nd
four
s fr
om a
ny m
ulti
ple
of 3
an
d 4
betw
een
0 a
nd
150
Cou
nts
forw
ards
an
d ba
ckw
ards
in:
• o
nes
from
any
num
ber
betw
een
0
and
180
• te
ns
from
any
mul
tipl
e of
10
betw
een
0 a
nd
180
• f
ives
from
any
mul
tipl
e of
5
betw
een
0 a
nd
180
• t
wos
from
any
mul
tipl
e of
2
betw
een
0 a
nd
180
• t
hre
es a
nd
four
s fr
om a
ny m
ulti
ple
of 3
an
d 4
betw
een
0 a
nd
180
Cou
nt f
orw
ards
an
d ba
ckw
ards
in:
• o
nes
, fro
m a
ny n
umbe
r be
twee
n 0
an
d 20
0•
ten
s fr
om a
ny m
ulti
ple
betw
een
0
and
200
• f
ives
from
any
mul
tipl
e of
5
betw
een
0 a
nd
200
• t
wos
from
any
mul
tipl
e of
2
betw
een
0 a
nd
200
• t
hre
es fr
om a
ny m
ulti
ple
of 3
be
twee
n 0
an
d 20
0•
four
s fr
om a
ny m
ulti
ple
of 4
be
twee
n 0
an
d 20
0
Con
ten
tTe
rm 1
Term
2Te
rm 3
Term
4R
epre
sen
t w
hol
e n
um
ber
s1
Num
ber
sym
bols
an
d n
umbe
r n
ames
Kn
ow a
nd
read
num
bers
• K
now
an
d r e
ad n
umbe
r sy
mbo
ls 0
to
50
• W
rite
num
ber
sym
bols
0-5
0•
Kn
ow a
nd
r ead
s n
umbe
r n
ames
0-
25•
Wri
te n
umbe
r n
ames
0-2
5
Kn
ow a
nd
read
num
bers
• K
now
an
d re
ad n
umbe
r sy
mbo
ls 0
to
150
• W
rite
num
ber
sym
bols
0-1
50•
Kn
ow a
nd
read
s n
umbe
r n
ames
0-
50•
Wri
te n
umbe
r n
ames
0-5
0
Kn
ow a
nd
read
num
bers
• K
now
an
d re
ad n
umbe
r sy
mbo
ls 0
to
180
• W
rit e
num
ber
sym
bols
0-1
80•
Kn
ow a
nd
read
s n
umbe
r n
ames
0-
75•
Wri
te n
umbe
r n
ames
0-7
5
Kn
ow a
nd
read
num
bers
• K
now
an
d re
ad n
umbe
r sy
mbo
ls 0
to
200
• W
rit e
num
ber
sym
bols
0-2
00•
Kn
ow a
nd
read
s n
umbe
r n
ames
0-
100
• W
rit e
num
ber
nam
es 0
-100
Ord
er a
nd
com
par
e w
hol
e n
um
ber
s1
Des
crib
e,
com
pare
, ord
ern
umbe
rs
Ord
er a
nd
com
pare
num
bers
to 2
5•
Ord
er w
hol
e n
umbe
rs fr
om
smal
lest
to b
igge
st, a
nd
bigg
est t
o sm
alle
st•
Com
pare
wh
ole
num
bers
usi
ng
smal
ler
than
, gre
ater
th
an, m
ore
than
, les
s th
an a
nd
is e
qual
to.
Ord
er a
nd
com
pare
num
bers
to 5
0•
Ord
er w
hol
e n
umbe
rs fr
om
smal
lest
to b
igge
st, a
nd
bigg
est t
o sm
alle
st•
Com
pare
wh
ole
num
bers
usi
ng
smal
ler
than
, gre
ater
th
an, m
ore
than
, les
s th
an a
nd
is e
qual
to.
Ord
er a
nd
com
pare
num
bers
to 5
0•
Ord
er w
hol
e n
umbe
rs fr
om
smal
lest
to b
igge
st, a
nd
bigg
est t
o sm
alle
st•
Com
pare
wh
ole
num
bers
usi
ng
smal
ler
than
, gre
ater
th
an, m
ore
than
, les
s th
an a
nd
is e
qual
to.
Ord
er a
nd
com
pare
num
bers
to 9
9•
Ord
er w
hol
e n
umbe
rs fr
om
smal
lest
to b
igge
st, a
nd
bigg
est t
o sm
alle
st•
Com
pare
who
le n
umbe
rs u
p to
99
usin
g sm
alle
r th
an, g
reat
er th
an,
mor
e th
an, l
ess
than
and
is e
qual
to.
CAPS Math Gr 2 TG.indb 27 2011/11/16 2:51 PM
28 Study & Master Mathematics Grade 2 • Introduction
Des
crib
e,
com
pare
, ord
ern
umbe
rs(c
ontin
ued)
Use
ord
inal
num
bers
to s
how
ord
er,
plac
e or
pos
itio
n•
Pos
itio
n o
bjec
ts in
a li
ne
from
firs
t to
ten
th o
r fi
rst t
o la
st e
.g. f
irst
, se
con
d, t
hir
d …
ten
th (
ordi
nal
n
umbe
rs)
Use
ord
inal
num
bers
to s
how
ord
er,
plac
e or
pos
itio
n•
Pos
itio
n o
bjec
ts in
a li
ne
from
firs
t to
fift
een
th o
r fi
rst t
o la
st e
.g. f
irst
, se
con
d, t
hir
d …
ten
th (
ordi
nal
n
umbe
rs)
Use
ord
inal
num
bers
to s
how
ord
er,
plac
e or
pos
itio
n•
Pos
itio
n o
bjec
ts in
a li
ne
from
firs
t to
fift
een
th o
r fi
rst t
o la
st e
.g. f
irst
, se
con
d, t
hir
d …
ten
th (
ordi
nal
n
umbe
rs)
Plac
e va
lue
1Pl
ace
valu
eRe
cogn
ise
the
plac
e va
lue
at le
ast
2-di
git o
f num
bers
to 2
5•
Kn
ow w
hat
eac
h d
igit
rep
rese
nts
• D
ecom
pose
2-d
igit
num
bers
into
m
ultip
les o
f ten
s and
uni
ts/o
nes(
TU)
• I
den
tify
an
d st
ate
the
valu
e of
ea
ch d
igit
Reco
gnis
e th
e pl
ace
valu
e of
at l
east
2-
digi
t num
bers
to 5
0•
Kn
ow w
hat
eac
h d
igit
rep
rese
nts
• D
ecom
pose
2-d
igit
num
bers
into
m
ulti
ple
of te
ns
and
ones
(TU
)•
Ide
nti
fy a
nd
stat
e th
e va
lue
of
each
dig
it
Reco
gnis
e th
e pl
ace
valu
e of
at l
east
2-
digi
t num
bers
to 7
5•
Kn
ow w
hat
eac
h d
igit
rep
rese
nts
• D
ecom
pose
2-d
igit
num
bers
into
m
ulti
ple
of te
ns
and
ones
(TU
)•
Ide
nti
fy a
nd
stat
e th
e va
lue
of
each
dig
it
Reco
gnis
e th
e pl
ace
valu
e of
at l
east
2-
digi
t num
bers
to 9
9•
Kn
ow w
hat
eac
h d
igit
rep
rese
nts
• D
ecom
pose
2-d
igit
num
bers
into
m
ulti
ple
of te
ns
and
ones
(TU
)•
Ide
nti
fy a
nd
stat
e th
e va
lue
of
each
dig
it
Solv
e n
um
ber
pro
ble
ms
1Pr
oble
m s
olvi
ng
tech
niq
ues
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
s an
d ex
plai
n
solu
tion
s to
pro
blem
s:•
dra
win
gs o
r co
ncr
ete
appa
ratu
s e.
g. c
oun
ters
• b
uild
ing
up a
nd
brea
kin
g do
wn
of
num
bers
• d
oubl
ing
and
hal
vin
g•
num
ber
lines
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
an
d ex
plai
n
solu
tion
s to
pro
blem
s:•
dra
win
gs o
r co
ncr
ete
appa
ratu
s e.
g. c
oun
ters
• b
uild
ing
up a
nd
brea
kin
g do
wn
of
num
bers
• d
oubl
ing
and
hal
vin
g•
num
ber
lines
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
an
d ex
plai
n
solu
tion
s to
pro
blem
s:•
dra
win
gs o
r co
ncr
ete
appa
ratu
s e.
g. c
oun
ters
• b
uild
ing
up a
nd
brea
kin
g do
wn
of
num
bers
• d
oubl
ing
and
hal
vin
g•
num
ber
lines
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
an
d ex
plai
n
solu
tion
s to
pro
blem
s:•
dra
win
gs o
r co
ncr
ete
appa
ratu
s e.
g. c
oun
ters
• b
uild
ing
up a
nd
brea
kin
g do
wn
of
num
bers
• d
oubl
ing
and
hal
vin
g•
num
ber
lines
1A
ddit
ion
, su
btra
ctio
nSo
lve
wor
d pr
oble
ms
in c
onte
xt a
nd
expl
ain
ow
n s
olut
ion
to p
robl
ems
invo
lvin
g ad
diti
on, s
ubtr
acti
on w
ith
an
swer
s up
to 2
0.
Solv
e w
ord
prob
lem
s in
con
text
an
d ex
plai
n o
wn
sol
utio
n to
pro
blem
s in
volv
ing
addi
tion
, sub
trac
tion
wit
h
answ
ers
up to
50.
Solv
e w
ord
prob
lem
s in
con
text
an
d ex
plai
n o
wn
sol
utio
n to
pro
blem
s in
volv
ing
addi
tion
, sub
trac
tion
wit
h
answ
ers
up to
75.
Solv
e w
ord
prob
lem
s in
con
text
an
d ex
plai
n o
wn
sol
utio
n to
pro
blem
s in
volv
ing
addi
tion
, sub
trac
tion
wit
h
answ
ers
up to
100
.
1Re
peat
ed
addi
tion
le
adin
g to
m
ulti
plic
atio
n
Solv
es a
nd
expl
ain
sol
utio
ns
to
prac
tica
l pro
blem
s th
at in
volv
e eq
ual s
har
ing
and
grou
pin
g up
to
20 w
ith
an
swer
s th
at c
an in
clud
e re
mai
nde
rs.
Solv
es a
nd
expl
ain
sol
utio
ns
to
prac
tica
l pro
blem
s th
at in
volv
e eq
ual s
har
ing
and
grou
pin
g up
to
50 w
ith
an
swer
s th
at c
an in
clud
e re
mai
nde
rs.
Solv
es a
nd
expl
ain
sol
utio
ns
to
prac
tica
l pro
blem
s th
at in
volv
e eq
ual s
har
ing
and
grou
pin
g up
to
75 w
ith
an
swer
s th
at c
an in
clud
e re
mai
nde
rs.
Solv
es a
nd
expl
ain
sol
utio
ns
to
prac
tica
l pro
blem
s th
at in
volv
e eq
ual s
har
ing
and
grou
pin
g up
to
100
wit
h a
nsw
ers
that
can
incl
ude
rem
ain
ders
.
1Sh
arin
g le
adin
g to
frac
tion
sSo
lve
and
expl
ain
sol
utio
ns
to
prac
tica
l pro
blem
s th
at in
volv
e eq
ual s
har
ing
lead
ing
to s
olut
ion
s th
at in
clud
e un
itar
y fr
acti
ons
e.g.
1 _ 2, 1 _ 4, 1 _ 5 e
tc.
Solv
e an
d ex
plai
n s
olut
ion
s to
pr
acti
cal p
robl
ems
that
invo
lve
equa
l sh
arin
g le
adin
g to
sol
utio
ns
that
incl
ude
unit
ary
frac
tion
s e.
g. 1 _ 2,
1 _ 4, 1 _ 5 etc
.
Solv
e an
d ex
plai
n s
olut
ion
s to
pr
acti
cal p
robl
ems
that
invo
lve
equa
l sh
arin
g le
adin
g to
sol
utio
ns
that
incl
ude
unit
ary
frac
tion
s e.
g. 1 _ 2,
1 _ 4, 1 _ 5 etc
.
CAPS Math Gr 2 TG.indb 28 2011/11/16 2:51 PM
29Study & Master Mathematics Grade 2 • Introduction
1M
oney
• R
ecog
nis
e an
d id
enti
fy t
he
Sout
h
Afr
ican
coi
ns
(5c,
10c
, 20c
, 50c
, R
1, R
2, R
5, a
nd
ban
k n
otes
. R10
, R
20, R
50•
Sol
ve m
oney
pro
blem
s in
volv
ing
tota
ls a
nd
chan
ge in
cen
ts u
p to
50
c or
ran
ds to
R20
• R
ecog
nis
e an
d id
enti
fy t
he
Sout
h
Afr
ican
coi
ns
(5c,
10c
, 20c
, 50c
, R
1, R
2, R
5, a
nd
ban
k n
otes
. R10
, R
20, R
50•
Sol
ve m
oney
pro
blem
s in
volv
ing
tota
ls a
nd
chan
ge in
cen
ts u
p to
50
c or
ran
ds to
R50
• R
ecog
nis
e an
d id
enti
fy t
he
Sout
h
Afr
ican
coi
ns
(5c,
10c
, 20c
, 50c
, R
1, R
2, R
5, a
nd
ban
k n
otes
. R10
, R
20, R
50•
Sol
ve m
oney
pro
blem
s in
volv
ing
tota
ls a
nd
chan
ge in
cen
ts u
p to
50
c or
ran
ds to
R75
• R
ecog
nis
e an
d id
enti
fy t
he
Sout
h
Afr
ican
coi
ns
(5c,
10c
, 20c
, 50c
, R
1, R
2, R
5, a
nd
ban
k n
otes
. R10
, R
20, R
50•
Sol
ve m
oney
pro
blem
s in
volv
ing
tota
ls a
nd
chan
ge in
cen
ts u
p to
50
c or
ran
ds to
R10
0
Cal
cula
tion
s1
Tech
niq
ues
(met
hod
s or
st
rate
gies
)
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
Dra
win
gs o
r co
ncr
ete
appa
ratu
s e.
g. c
oun
ters
• B
uild
ing
up a
nd
brea
kin
g do
wn
n
umbe
rs•
Dou
blin
g an
d h
alvi
ng
• N
umbe
r lin
es
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
Dra
win
gs o
r co
ncr
ete
appa
ratu
s e.
g. c
oun
ters
• B
uild
ing
up a
nd
brea
kin
g do
wn
n
umbe
rs•
Dou
blin
g an
d h
alvi
ng
• N
umbe
r lin
es
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
Dra
win
gs o
r co
ncr
ete
appa
ratu
s e.
g. c
oun
ters
• B
uild
ing
up a
nd
brea
kin
g do
wn
n
umbe
rs•
Dou
blin
g an
d h
alvi
ng
• N
umbe
r lin
es
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
Dra
win
gs o
r co
ncr
ete
appa
ratu
s e.
g. c
oun
ters
• B
uild
ing
up a
nd
brea
kin
g do
wn
n
umbe
rs•
Dou
blin
g an
d h
alvi
ng
• N
umbe
r lin
es
1A
ddit
ion
an
d su
btra
ctio
n•
Add
to 2
0•
Sub
trac
t fro
m 2
0•
Use
app
ropr
iat e
sym
bols
(+
, –, =
, ×)
• P
ract
ice
num
ber
bon
ds to
10
• A
dd to
50
• S
ubtr
act f
rom
50
• U
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)•
Pra
ctic
e n
umbe
r bo
nds
to 1
0
• A
dd to
75
• S
ubtr
act f
rom
75
• U
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)•
Pra
ctic
e n
umbe
r bo
nds
to 1
0
• A
dd to
100
• S
ubtr
act f
rom
100
• U
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)•
Pra
ctic
e n
umbe
r bo
nds
to 1
0
1Re
peat
ed
addi
tion
le
adin
g to
m
ulti
plic
atio
n
• A
dd t
he
sam
e n
umbe
r re
peat
edly
to
20
• M
ulti
ply
num
bers
1 to
10
by ,
2, 5
, 3
and
4•
Use
app
ropr
iate
sym
bols
(+
, –, =
, ×)
• M
ulti
ply
num
bers
1 t o
10
by 2
, 5,
up to
50
• U
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)
• M
ulti
ply
num
bers
1 to
10
by 2
, 5, 4
up
to 5
0•
Use
app
ropr
iate
sym
bols
(+
, –, =
, ×)
• M
ulti
ply
num
bers
1 to
10
by 1
, 2,
5, 3
an
d 4
up to
50
• U
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)
CAPS Math Gr 2 TG.indb 29 2011/11/16 2:51 PM
30 Study & Master Mathematics Grade 2 • Introduction
Div
isio
n1
Men
tal
stra
tegi
es
for
doin
g ca
lcul
atio
ns
Num
ber
con
cept
: ran
ge 2
5•
Ord
er a
giv
en s
et o
f sel
ecte
d n
umbe
rs.
• C
ompa
re n
umbe
rs to
100
an
d sa
y w
hic
h is
mor
e or
less
• K
now
wh
ich
num
ber
is 1
mor
e or
1
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
2 m
ore
or 2
le
ss t
han
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 1
0 m
ore
or
10 le
ss t
han
a g
iven
num
ber
Num
ber
con
cept
: ran
ge 2
5•
Ord
er a
giv
en s
et o
f sel
ecte
dn
umbe
rs.
• C
ompa
re n
umbe
rs to
100
an
d sa
y w
hic
h is
mor
e or
less
• K
now
wh
ich
num
ber
is 1
mor
e or
1
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
2 m
ore
or 2
le
ss t
han
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 1
0 m
ore
or
10 le
ss t
han
a g
iven
num
ber
Num
ber
con
cept
: ran
ge 9
9•
Ord
er a
giv
en s
et o
f sel
ecte
d n
umbe
rs.
• C
ompa
re n
umbe
rs to
200
an
d sa
y w
hic
h is
mor
e or
less
• K
now
wh
ich
num
ber
is 1
mor
e or
1
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
2 m
ore
or 2
le
ss t
han
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 3
mor
e or
3
less
th
an a
giv
en n
umbe
r.•
Kn
ow w
hic
h n
umbe
r is
4 m
ore
or 4
le
ss t
than
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 5
mor
e or
5
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
10
mor
e or
10
less
th
an a
giv
en n
umbe
r.
Num
ber
con
cept
: ran
ge 9
9•
Ord
er a
giv
en s
et o
f sel
ecte
d n
umbe
rs.
• C
ompa
re n
umbe
rs to
200
an
d sa
y w
hic
h is
mor
e or
less
• K
now
wh
ich
num
ber
is 1
mor
e or
1
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
2 m
ore
or 2
le
ss t
han
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 3
mor
e or
3
less
th
an a
giv
en n
umbe
r.•
Kn
ow w
hic
h n
umbe
r is
4 m
ore
or 4
le
ss t
than
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 5
mor
e or
5
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
10
mor
e or
10
less
th
an a
giv
en n
umbe
r.Ra
pidl
y re
call:
• R
ecal
l add
itio
n a
nd
Subt
ract
ion
fa
cts
to 1
0
Rapi
dly
reca
ll:•
Rec
all a
ddit
ion
an
d Su
btra
ctio
n
fact
s to
10
Rapi
dly
reca
ll:•
Rec
all a
ddit
ion
an
d su
btra
ctio
n
fact
s to
15
• A
dd o
r su
btra
ct m
ultip
les
of 1
0 fr
om
0 to
50
Rapi
dly
reca
ll:•
Rec
all a
ddit
ion
an
d su
btra
ctio
n
fact
s to
20
• A
dd o
r su
btra
ct m
ultip
les
of 1
0 fr
om
0 to
100
Men
tal s
trat
egie
s U
se c
alcu
lati
on s
trat
egie
s to
add
an
d su
btra
ct e
ffic
ien
tly:
• P
ut t
he
larg
er n
umbe
r fi
rst i
n
orde
rto
cou
nt o
n o
r co
unt b
ack
• M
enta
l num
ber
line
• D
oubl
ing
and
hal
vin
g•
Bui
ldin
g up
an
d br
eaki
ng
dow
n•
Use
th
e re
lati
onsh
ip b
etw
een
ad
diti
on a
nd
subt
ract
ion
Men
tal s
trat
egie
s U
se c
alcu
lati
on s
trat
egie
s to
add
an
d su
btra
ct e
ffic
ien
tly:
• P
ut t
he
larg
er n
umbe
r fi
rst i
n
orde
rto
cou
nt o
n o
r co
unt b
ack
• M
enta
l num
ber
line
• D
oubl
ing
and
hal
vin
g•
Bui
ldin
g up
an
d br
eaki
ng
dow
n•
Use
th
e re
lati
onsh
ip b
etw
een
ad
diti
on a
nd
subt
ract
ion
Men
tal s
trat
egie
sU
se c
alcu
lati
on s
trat
egie
s to
add
an
d su
btra
ct e
ffic
ien
tly:
• P
ut t
he
larg
er n
umbe
r fi
rst i
n
orde
r to
cou
nt o
n o
r co
unt b
ack
• U
se t
he
rela
tion
ship
bet
wee
nad
diti
on a
nd
subt
ract
ion
• N
umbe
r lin
e•
Dou
blin
g an
d h
alvi
ng
• B
uild
ing
up a
nd
brea
kin
g do
wn
Men
tal s
trat
egie
sU
se c
alcu
lati
on s
trat
egie
s to
add
an
d su
btra
ct e
ffic
ien
tly:
• P
ut t
he
larg
er n
umbe
r fi
rst i
n
orde
r to
cou
nt o
n o
r co
unt b
ack
• U
se t
he
rela
tion
ship
bet
wee
nad
diti
on a
nd
subt
ract
ion
• N
umbe
r lin
e•
Dou
blin
g an
d h
alvi
ng
• B
uild
ing
up a
nd
brea
kin
g do
wn
1Fr
acti
ons
• U
se a
nd
nam
e fr
acti
ons
in
fam
iliar
con
text
s in
clud
ing
hal
ves,
qu
arte
rs, t
hir
ds a
nd
fift
hs.
• R
ecog
nis
e fr
acti
ons
in
diag
ram
mat
ic fo
rm•
Wri
te fr
acti
ons
as 1
hal
f, 2
th
irds
• U
se a
nd
nam
e fr
acti
ons
in
fam
iliar
con
text
s in
clud
ing
hal
ves,
qu
arte
rs, t
hir
ds a
nd
fift
hs.
• R
ecog
nis
e fr
acti
ons
in
diag
ram
mat
ic fo
rm•
Wri
t e fr
acti
ons
as 1
hal
f, 2
th
irds
• U
se a
nd
nam
e fr
acti
ons
in
fam
iliar
con
text
s in
clud
ing
hal
ves,
qu
arte
rs, t
hir
ds a
nd
fift
hs.
• R
ecog
nis
e fr
acti
ons
in
diag
ram
mat
ic fo
rm•
Wri
te fr
acti
ons
as 1
hal
f, 2
th
irds
CAPS Math Gr 2 TG.indb 30 2011/11/16 2:51 PM
31Study & Master Mathematics Grade 2 • Introduction
Shap
e an
d s
pac
e3
Posi
tion
, or
ien
tati
on a
nd
view
s
Lan
guag
e of
pos
itio
nD
escr
ibe
the
posi
tion
of o
ne
obje
ct
in r
elat
ion
to a
not
her
e.g
. on
top
of
, in
fron
t of,
beh
ind,
left
, rig
ht,
up,
do
wn
, nex
t to
Posi
tion
an
d vi
ews
• M
atch
dif
fere
nt v
iew
s of
th
e sa
me
ever
yday
obj
ect
Posi
tion
an
d v
iew
s•
Mat
ch d
iffe
ren
t vie
ws
of t
he
sam
e ev
eryd
ay o
bjec
t
Posi
tion
an
d d
irec
tion
sFo
llow
dir
ecti
ons
to m
ove
arou
nd
the
clas
sroo
m
Posi
tion
an
d d
irec
tion
sFo
llow
dir
ecti
ons
to m
ove
arou
nd
the
clas
sroo
m3
3D o
bjec
tsR
ange
of o
bjec
tsRe
cogn
ise
and
nam
e 3-
D o
bjec
ts in
th
e cl
assr
oom
and
in p
ictu
res
• b
all s
hape
s, (
sphe
res)
• b
ox s
hape
s (p
rism
s)
Ran
ge o
f ob
ject
sR e
cogn
ise
and
nam
e 3-
D o
bjec
ts in
th
e cl
assr
oom
an
d in
pic
ture
s•
bal
l sh
apes
, (sp
her
es)
• b
ox s
hap
es (
pris
ms)
• c
ylin
ders
Ran
ge o
f ob
ject
sRe
cogn
ise
and
nam
e 3-
D o
bjec
ts in
th
e cl
assr
oom
an
d in
pic
ture
s•
bal
l sh
apes
, (sp
her
es)
• b
ox s
hap
es (
pris
ms)
• c
ylin
ders
Feat
ures
of o
bjec
tsD
escr
ibe,
sor
t and
com
pare
3-D
ob
ject
s in
term
s of
:•
siz
e•
obj
ects
that
rol
l•
obj
ects
that
slid
e
Feat
ure
s of
ob
ject
sD
escr
ibe,
sor
t an
d co
mpa
re 3
-D
obje
cts
in te
rms
of:
• s
ize
• o
bjec
ts t
hat
rol
l•
obj
ects
th
at s
lide
Feat
ure
s of
ob
ject
sD
escr
ibe,
sor
t an
d co
mpa
re 3
-D
obje
cts
in te
rms
of:
• s
ize
• o
bjec
ts t
hat
rol
l•
obj
ects
th
at s
lide
Focu
ssed
act
ivit
ies
• O
bser
ve a
nd b
uild
giv
en 3
D o
bjec
ts
usin
g co
ncre
te m
ater
ials
suc
h as
cu
t-ou
t 2D
sha
pes,
bui
ldin
g bl
ocks
, re
cycl
ing,
con
stru
ctio
n ki
ts, o
ther
3D
geo
met
ric
obje
cts
Sugg
este
d fo
cus
and
sequ
enci
ng o
f ac
tivi
ties
for
Term
1Le
arne
rs c
opy
of m
odel
of s
omet
hing
th
e te
ache
r pr
ovid
es. M
odel
s or
con
stru
ctio
ns c
an b
e m
ade
usin
g bu
ildin
g bl
ocks
, rec
yclin
g,
cons
truc
tion
kit
s, o
ther
3D
geo
met
ric
obje
cts,
cut
-out
2D
sha
pes.
Thi
s ca
n
be d
one
in in
depe
nden
t tim
e.
Sugg
este
d fo
cus
and
sequ
enci
ng
of
acti
viti
es fo
r Te
rm 2
Lear
ner
s w
ork
wit
h•
bal
ls a
nd
obje
cts
shap
ed li
ke b
alls
,•
cyl
inde
rs a
nd
obje
cts
shap
ed li
ke
cylin
ders
• v
ario
us b
oxes
an
d ot
her
obj
ects
sh
aped
like
rec
tan
gula
r pr
ism
s or
cu
bes.
Sugg
este
d fo
cus
or T
erm
4
CAPS Math Gr 2 TG.indb 31 2011/11/16 2:51 PM
32 Study & Master Mathematics Grade 2 • Introduction
3D o
bjec
ts(c
ontin
ued)
Lear
ners
com
pare
and
des
crib
e th
e si
ze o
f sim
ilar
obje
cts
e.g.
sta
ck b
oxes
fr
om b
igge
st to
sm
alle
stLe
arne
rs w
ork
wit
h
• b
alls
and
obj
ects
sha
ped
like
balls
,•
var
ious
bo x
es a
nd o
ther
obj
ects
sh
aped
like
rec
tang
ular
pri
sms
or
cube
s.Le
arne
rs in
vest
igat
e w
hich
of t
he
obje
cts
can
roll,
whi
ch s
lide,
whi
ch
can
be s
tack
ed.
Lear
ners
iden
tify
and
des
crib
e ge
omet
ric
and
ever
yday
obj
ects
by
sayi
ng w
heth
er a
re s
hape
d lik
e a
ball,
sha
ped
like
a bo
x, s
hape
d lik
e a
cylin
der.
Lear
ner
s in
vest
igat
e w
hic
h o
f th
e ob
ject
s ca
n r
oll,
wh
ich
slid
e, w
hic
h
can
be
stac
ked.
Lear
ner
s id
enti
fy a
nd
desc
ribe
ge
omet
ric
and
ever
yday
obj
ects
by
sayi
ng
wh
eth
er a
re s
hap
ed li
ke a
ba
ll, s
hap
ed li
ke a
box
, sh
aped
like
a
cylin
der.
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
ses
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
ses
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
ses
32-
D s
hap
esR
ange
of
shap
esRe
cogn
ise
and
nam
e 2D
sh
apes
• c
ircl
es•
tri
angl
es•
squ
ares
• r
ecta
ngl
es
Ran
ge o
f sh
apes
Reco
gnis
e an
d n
ame
2D s
hap
es•
cir
cles
• t
rian
gles
• s
quar
es•
rec
tan
gles
Ran
ge o
f sh
apes
Reco
gnis
e an
d n
ame
2D s
hap
es•
cir
cles
• t
rian
gles
• s
quar
es•
rec
tan
gles
Feat
ure
s of
sh
apes
Des
crib
e, s
ort a
nd
com
pare
2-D
sh
apes
in te
rms
of:
• s
ize
• c
olou
r•
sh
ape
• s
trai
ght s
ides
• r
oun
d si
des
Feat
ure
s of
sh
apes
Des
crib
e, s
ort a
nd
com
pare
2-D
sh
apes
in te
rms
of:
• s
ize
• c
olou
r•
sh
ape
• s
trai
ght s
ides
• r
oun
d si
des
Feat
ure
s of
sh
apes
Des
crib
e, s
ort a
nd
com
pare
2-D
sh
apes
in te
rms
of:
• s
ize
• c
olou
r•
sh
ape
• s
trai
ght s
ides
• r
oun
d si
des
Sugg
este
d fo
cus
and
seq
uen
cin
g of
ac
tivi
ties
for
Term
1Le
arn
ers
star
t wit
h fr
ee p
lay
wit
h
vari
ous
shap
es in
clud
ing
mak
ing
pict
ures
wit
h c
ut-o
ut g
eom
etri
c sh
apes
. Th
is c
an b
e do
ne
in
inde
pen
den
t tim
e. T
his
can
als
o be
do
ne
duri
ng
Life
Ski
lls le
sson
s.
Sugg
este
d fo
cus
and
seq
uen
cin
g of
ac
tivi
ties
for
Term
3Le
arn
ers
wor
k ci
rcle
s an
d sq
uare
s of
dif
fere
nt s
izes
, an
d tr
ian
gles
an
d re
ctan
gles
wit
h d
iffe
ren
t sh
apes
. Th
ey s
ort t
hem
acc
ordi
ng
to w
het
her
th
ey h
ave
stra
igh
t or
roun
d si
des.
Sugg
este
d fo
cus
and
seq
uen
cin
g of
ac
tivi
ties
for
Term
4Le
arn
ers
wor
k ci
rcle
s an
d sq
uare
s of
dif
fere
nt s
izes
, an
d tr
ian
gles
an
d re
ctan
gles
wit
h d
iffe
ren
t sh
apes
. Th
ey s
ort t
hem
acc
ordi
ng
to w
het
her
th
ey h
ave
stra
igh
t or
roun
d si
des.
CAPS Math Gr 2 TG.indb 32 2011/11/16 2:51 PM
33Study & Master Mathematics Grade 2 • Introduction
2-D
sh
apes
(c
ontin
ued)
Lear
ner
s co
py o
f pic
ture
mad
e up
of
geom
etri
c sh
apes
. Th
is c
an b
e do
ne
in in
depe
nde
nt t
ime.
Th
is c
an a
lso
be d
one
duri
ng
Life
Ski
lls le
sson
s.Le
arn
ers
com
pare
th
e si
ze o
f sim
ilar
shap
es e
.g. o
rder
rec
tan
gles
from
sm
alle
st to
big
gest
an
d us
e th
e la
ngu
age
of s
ize
to d
escr
ibe
shap
es.
Lear
ner
s ta
lk a
bout
th
e co
lour
s of
sh
apes
an
d th
en s
ort s
hap
es
acco
rdin
g to
col
our.
Lear
ner
s w
ork
circ
les
and
squa
res
of d
iffe
ren
t siz
es, a
nd
tria
ngl
es a
nd
rect
angl
es w
ith
dif
fere
nt s
hap
es.
They
sor
t th
em a
ccor
din
g to
wh
eth
er
they
hav
e st
raig
ht o
r ro
und
side
s.Le
arne
rs s
ort a
nd g
roup
s sh
apes
ac
cord
ing
to w
heth
er th
ey a
re
tria
ngle
s, s
quar
es, r
ecta
ngle
s or
cir
cles
.
Lear
ners
sor
t and
gro
ups
shap
es
acco
rdin
g to
whe
ther
they
are
tr
iang
les,
squ
ares
, rec
tang
les
or c
ircl
es.
Lear
ners
sor
t and
gro
ups
shap
es
acco
rdin
g to
whe
ther
they
are
tr
iang
les,
squ
ares
, rec
tang
les
or c
ircl
esW
ork
is c
onso
lidat
ed th
roug
h w
ritt
en
exer
cise
sW
ork
is c
onso
lidat
ed th
roug
h w
ritt
en
exer
cise
sW
ork
is c
onso
lidat
ed th
roug
h w
ritt
en
exer
cise
s3
Sym
met
ryRe
cogn
ise
and
draw
lin
e of
sy
mm
etry
in 2
- D g
eom
etri
cal a
nd
non
- geo
met
rica
l sh
apes
Reco
gnis
e an
d dr
aw li
ne
of
sym
met
ry in
2- D
geo
met
rica
l an
d n
on- g
eom
etri
cal s
hap
esSu
gges
ted
focu
s of
act
ivit
ies
for
Term
2Le
arn
ers
shou
ld lo
ok fo
r lin
es o
f sy
mm
etry
in c
oncr
ete
obje
cts
and
pict
ures
Wri
tten
exe
rcis
es s
hou
ld in
clud
e ex
ampl
es w
her
e th
e lin
e of
sy
mm
etry
is n
ot a
ver
tica
l lin
e
Sugg
este
d fo
cus
of a
ctiv
itie
s fo
r Te
rm 2
Lear
ner
s sh
ould
look
for
lines
of
sym
met
ry in
con
cret
e ob
ject
s an
d pi
ctur
esW
ritt
en e
xerc
ises
sh
ould
incl
ude
exam
ples
wh
ere
the
line
of
sym
met
ry is
not
a v
erti
cal l
ine
Mea
sure
men
t4
Tim
eTe
llin
g th
e ti
me
• K
now
s da
ys o
f wee
k•
Kn
ows
mon
ths
of y
ear
• P
lace
bir
thda
ys, r
elig
ious
fest
ival
s,
publ
ic h
olid
ays,
his
tori
cal e
ven
ts,
sch
ool e
ven
ts o
n a
cal
enda
r•
Tel
l 12-
hou
r ti
me
in h
ours
on
an
alog
ue c
lock
s
Telli
ng
the
tim
e•
Kn
ows
days
of w
eek
• K
now
s m
onth
s of
yea
r•
Pla
ce b
irth
days
, rel
igio
us fe
stiv
als,
pu
blic
hol
iday
s, h
isto
rica
l eve
nts
, sc
hoo
l eve
nts
on
a c
alen
dar
• T
ell 1
2-h
our
tim
e in
hou
rs o
n
anal
ogue
clo
cks
Telli
ng
the
tim
e•
Kn
ows
days
of w
eek
• K
now
s m
onth
s of
yea
r•
Pla
ce b
irth
days
, rel
igio
us fe
stiv
als,
pu
blic
hol
iday
s, h
isto
rica
l eve
nts
, sc
hoo
l eve
nts
on
a c
alen
dar
• T
ell 1
2-h
our
tim
e in
hou
rs o
n
anal
ogue
clo
cks
Tell
12-h
our
tim
e in
hou
rs, h
alf
hou
rs a
nd
quar
ter
hou
rs o
n
anal
ogue
clo
cks
CAPS Math Gr 2 TG.indb 33 2011/11/16 2:51 PM
34 Study & Master Mathematics Grade 2 • Introduction
Tim
e(c
ontin
ued)
Cal
cula
te le
ngt
hs
of ti
me
and
pass
ing
of ti
me
• U
se c
lock
s t o
cal
cula
te le
ngt
hs
of
tim
e in
hou
rs o
r h
alf h
ours
Cal
cula
te le
ngt
hs
of ti
me
and
pass
ing
of ti
me
• U
se c
alen
dars
to c
alcu
late
an
d de
scri
be le
ngt
hs
of ti
me
in d
ays
or
wee
ks•
Use
clo
cks
to c
alcu
late
len
gth
s of
ti
me
in h
ours
or
hal
f hou
rs
4Le
ngt
hIn
form
al m
easu
rin
g•
Est
imat
e, m
easu
re, c
ompa
re,
orde
r an
d re
cord
len
gth
usi
ng
non
sta
nda
rd m
easu
res
e.g.
han
d sp
ans,
pac
es, p
enci
l len
gth
s,
coun
ters
•
Des
crib
e th
e le
ngt
h o
f obj
ects
by
coun
tin
g an
d st
atin
g h
ow m
any
info
rmal
un
its
lon
g it
is•
Use
lan
guag
e to
talk
abo
ut t
he
com
pari
son
e.g
. lon
ger,
sh
orte
r,
talle
r, w
ider
Intr
odu
cin
g fo
rmal
mea
suri
ng
Esti
mat
e, m
easu
re, o
rder
an
d re
cord
le
ngt
h u
sin
g m
etre
s (e
ith
er m
etre
st
icks
or
met
re lo
ng
len
gth
s of
str
ing)
as
th
e st
anda
rd u
nit
of l
engt
h.
Intr
odu
cin
g fo
rmal
mea
suri
ng
Esti
mat
e, m
easu
re, c
ompa
re, o
rder
an
d re
cord
len
gth
usi
ng
met
res
(eit
her
met
re s
tick
s or
met
re lo
ng
len
gth
s of
str
ing)
as
the
stan
dard
un
it o
f len
gth
4M
ass
Info
rmal
mea
suri
ng
• E
stim
ate,
mea
sure
, com
pare
, ord
er
and
reco
rd m
ass
usin
g a
bala
nce
an
d n
on s
tan
dard
mea
sure
s e.
g.
bloc
ks, b
rick
s et
c•
Use
lan
guag
e t o
talk
abo
ut t
he
com
pari
son
e.g
. lig
ht,
hea
vy,
ligh
ter,
hea
vier
CAPS Math Gr 2 TG.indb 34 2011/11/16 2:51 PM
35Study & Master Mathematics Grade 2 • Introduction
Mas
s (c
ontin
ued)
Intr
odu
cin
g fo
rmal
mea
suri
ng
• C
ompa
re, o
rder
an
d re
cord
th
e m
ass
of c
omm
erci
ally
pac
kage
d ob
ject
s w
hic
h h
ave
thei
r m
ass
stat
ed in
kilo
gram
s e.
g. 2
ki
logr
ams
of r
ice
and
1 ki
logr
am o
f fl
our
• W
her
e ba
thro
om s
cale
s ar
e av
aila
ble,
lear
ner
s ca
n m
easu
re
thei
r ow
n m
ass
in k
ilogr
ams
usin
g a
bat
hro
om s
cale
.
Intr
odu
cin
g fo
rmal
mea
suri
ng
Lear
ner
s do
wri
tten
task
s to
co
nso
lidat
e th
e fo
llow
ing,
incl
udin
g re
adin
g pi
ctur
es o
f•
pro
duct
s w
ith
mas
s w
ritt
en o
n
them
,•
pic
ture
s of
mas
s on
bat
hro
om
scal
es w
her
e th
e n
eedl
e po
ints
to a
n
umbe
red
grad
atio
n li
ne.
The
expe
ctat
ion
is t
hat
lear
ner
s on
ly r
ead
to t
he
nea
rest
num
bere
d gr
adat
ion
lin
e. T
hey
des
crib
e th
eir
mas
s as
alm
ost/
nea
rly/
clos
e to
/a b
it
mor
e th
an/m
ore
or le
ss/
or e
xact
ly
the
num
ber
(of k
ilogr
ams)
th
ey r
ead
off t
he
mas
s m
eter
.
4C
apac
ity/
volu
me
Info
rmal
mea
suri
ng
Esti
mat
e, m
easu
re, c
ompa
re, o
rder
an
d re
cord
th
e am
oun
t th
e ca
paci
ty
of c
onta
iner
s (i
.e. t
he
amou
nt t
he
con
tain
er c
an h
old
if fi
lled)
by
usin
g n
on-s
tan
dard
mea
sure
s e.
g. s
poon
s an
d cu
ps D
escr
ibe
the
capa
city
of
th
e co
nta
iner
by
coun
tin
g an
d st
atin
g h
ow m
any
of t
he
info
rmal
un
its
it ta
kes
to fi
ll th
e co
nta
iner
e.g
. Th
e bo
ttle
has
th
e ca
paci
ty o
f 4 c
ups.
CAPS Math Gr 2 TG.indb 35 2011/11/16 2:51 PM
36 Study & Master Mathematics Grade 2 • Introduction
Cap
acit
y/vo
lum
e(c
ontin
ued)
Intr
odu
cin
g fo
rmal
mea
suri
ng
• E
stim
ate,
mea
sure
, com
pare
, ord
er
and
reco
rd t
he
capa
city
of o
bjec
ts
bym
easu
rin
g in
litr
es u
sin
go
usin
g bo
ttle
s w
ith
aca
paci
ty o
f 1 li
tre
o a
mea
suri
ng
jug
wh
ich
has
num
bere
d ca
libra
tion
lines
in li
tres
• C
ompa
re, o
rder
an
d re
cord
th
e ca
paci
ty o
f com
mer
cial
ly p
acka
ges
obje
cts
wh
ose
capa
city
is s
tate
d in
lit
res
e.g.
2 li
tres
of m
ilk, 1
litr
e of
co
ol d
rin
k, 5
litr
es o
f pai
nt
Intr
odu
cin
g fo
rmal
mea
suri
ng
Lear
ner
s do
wri
tten
task
s to
co
nso
lidat
e th
e fo
llow
ing,
incl
udin
g re
adin
g pi
ctur
es o
f•
pro
duct
s w
ith
th
eir
capa
city
w
ritt
en o
n t
hem
in o
rder
to
sequ
ence
in o
rder
• p
ictu
res o
f jug
s whe
re th
e vo
lum
e is
ne
ar to
a n
umbe
red
1 lit
re o
r 2 li
tre
grad
atio
n lin
e. T
he e
xpec
tatio
n is
th
at le
arne
rs o
nly
read
to th
e ne
ares
t nu
mbe
red
grad
atio
n lin
e. D
escr
ibe
thei
r vol
ume
as a
lmos
t/ne
arly
/clo
se
to/a
bit
mor
e th
an/m
ore
or le
ss/o
r ex
actly
the
num
ber (
of li
tres
) th
ey
read
off
the
jug
Dat
a h
and
lin
g5
Col
lect
an
d or
gan
ise
data
Reco
mm
ende
d:W
hol
e da
ta c
ycle
to m
ake
clas
s pi
ctog
raph
Reco
mm
ende
d:M
ake
indi
vidu
al p
icto
grap
hs fr
om d
ata
prov
ided
in e
ither
pic
ture
form
or t
able
.
Repr
esen
t dat
aC
olle
ct a
nd
org
anis
e d
ata
Col
lect
dat
a ab
out t
he
clas
s or
sch
ool
to a
nsw
er q
uest
ion
pos
ed b
y th
e
teac
her
Rep
rese
nt
dat
aRe
pres
ent d
ata
in p
icto
grap
h
Col
lect
an
d o
rgan
ise
dat
aC
olle
ct d
ata
abou
t th
e cl
ass
or s
choo
l to
an
swer
que
stio
n p
osed
by
the
te
ach
erR
epre
sen
t d
ata
Repr
esen
t dat
a in
pic
togr
aph
An
alys
e an
d in
terp
ret d
ata
An
alys
e an
d in
terp
ret
dat
aA
nsw
er q
uest
ion
s ab
out d
ata
in
pict
ogra
ph
An
alys
e da
ta fr
om r
epre
sen
tati
ons
prov
ided
.Re
com
men
ded:
• A
t lea
st 1
pic
togr
aph
An
alys
e an
d in
terp
ret
dat
aA
nsw
er q
uest
ion
s ab
out d
ata
in
pict
ogra
ph
An
alys
e da
ta fr
om r
epre
sen
tati
ons
prov
ided
.Re
com
men
ded
to•
At l
east
1 p
icto
grap
h
CAPS Math Gr 2 TG.indb 36 2011/11/16 2:51 PM
37Study & Master Mathematics Grade 2 • Introduction
Nu
mb
ers,
op
erat
ion
s an
d r
elat
ion
ship
s •
N
um
ber
con
cep
t d
evel
opm
ent
Gra
de
3C
oun
t w
ith
wh
ole
nu
mb
ers
Mod
Top
ics
Term
1Te
rm 2
Term
3Te
rm 4
1C
oun
t obj
ects
Cou
nt t
o at
leas
t 200
eve
ryda
y ob
ject
s re
liabl
y.C
oun
t to
at le
ast 5
00 e
very
day
obje
cts
relia
bly.
Cou
nt t
o at
leas
t 750
eve
ryda
y ob
ject
s re
liabl
y.C
oun
t to
at le
ast 1
000
eve
ryda
y ob
ject
s re
liabl
y.G
ive
a re
ason
able
est
imat
e of
a
num
ber
of o
bjec
ts t
hat
can
be
chec
ked
by c
oun
tin
g.
Giv
e a
reas
onab
le e
stim
ate
of a
n
umbe
r of
obj
ects
th
at c
an b
e ch
ecke
d by
cou
nti
ng.
Giv
e a
reas
onab
le e
stim
ate
of a
n
umbe
r of
obj
ects
th
at c
an b
e ch
ecke
d by
cou
nti
ng.
Giv
e a
reas
onab
le e
stim
ate
of a
n
umbe
r of
obj
ects
th
at c
an b
e ch
ecke
d by
cou
nti
ng.
1C
oun
t for
war
ds
and
back
war
dsC
oun
t for
war
ds a
nd
back
war
ds in
:•
the
inte
rval
s sp
ecif
ied
in g
rade
2
wit
h in
crea
sed
num
ber
ran
ges
• 10
0s to
at l
east
500
Cou
nt f
orw
ards
an
d ba
ckw
ards
in:
• th
e in
t erv
als
spec
ifie
d in
gra
de 2
w
ith
incr
ease
d n
umbe
r ra
nge
s•
50s,
100
s to
at l
east
1 0
00
Cou
nt f
orw
ards
an
d ba
ckw
ards
in:
• th
e in
terv
als
spec
ifie
d in
gra
de 2
w
ith
incr
ease
d n
umbe
r ra
nge
s•
20s,
25s
, 50s
, 100
s to
at l
east
1 0
00
Cou
nt f
orw
ards
an
d ba
ckw
ards
in:
• th
e in
terv
als
spec
ifie
d in
gra
de 2
w
ith
incr
ease
d n
umbe
r ra
nge
s•
20s,
25s
, 50s
, 100
s to
at l
east
1 0
00
Con
ten
tTe
rm 1
Term
2Te
rm 3
Term
4R
epre
sen
t w
hol
e n
um
ber
s1
Num
ber
sym
bols
an
dn
umbe
r n
ames
Kn
ow a
nd
rea
d n
um
ber
s•
Kn
ow a
nd
read
num
ber
sym
bols
0
to 5
00•
Wri
tes
num
ber
sym
bols
0-5
00•
Kn
ows
and
read
s n
umbe
r n
ames
0-
250
• W
rite
s n
umbe
r n
ames
0-1
00
Kn
ow a
nd
rea
d n
um
ber
s•
Kn
ow a
nd
read
num
ber
sym
bols
0
to 1
000
• W
rite
s n
umbe
r sy
mbo
ls 0
–1 0
00•
Kn
ows
and
read
s n
umbe
r n
ames
0-
250
• W
rite
s n
umbe
r n
ames
0-2
50
Kn
ow a
nd
rea
d n
um
ber
s•
Kn
ow a
nd
read
num
ber
sym
bols
0
to 1
000
• W
rit e
s n
umbe
r sy
mbo
ls 0
–1 0
00•
Kn
ows
and
read
s n
umbe
r n
ames
0-
500
• W
rite
s n
umbe
r n
ames
0-5
00
Kn
ow a
nd
rea
d n
um
ber
s•
Kn
ow a
nd
read
num
ber
sym
bols
0
to 1
000
• W
rite
s n
umbe
r sy
mbo
ls 0
-1 0
00•
Kn
ows
and
read
s n
umbe
r n
ames
0-
1 00
0•
Wri
tes
num
ber
nam
es 0
-1 0
00
Ord
er a
nd
com
par
e w
hol
e n
um
ber
s1
Des
crib
e,
com
pare
, ord
er
num
bers
Ord
er a
nd
com
pare
num
bers
to 9
9•
Ord
er w
hol
e n
umbe
rs u
p t o
99
from
sm
alle
st to
big
gest
, an
d bi
gges
t to
smal
lest
• C
ompa
re w
hol
e n
umbe
rs u
p to
99
usin
g sm
alle
r th
an, g
reat
er t
han
, m
ore
than
, les
s th
an a
nd
is e
qual
to
.
Ord
er a
nd
com
pare
num
bers
to 5
00•
Ord
er w
hol
e n
umbe
rs u
p to
500
fr
om s
mal
lest
to b
igge
st, a
nd
bigg
est t
o sm
alle
st•
Com
pare
wh
ole
num
bers
up
to
500
usin
g sm
alle
r th
an, g
reat
er
than
, mor
e th
an, l
ess
than
an
d is
eq
ual t
o.
Ord
er a
nd
com
pare
num
bers
to 7
50•
Ord
er w
hol
e n
umbe
rs u
p to
750
fr
om s
mal
lest
to b
igge
st, a
nd
bigg
est t
o sm
alle
st•
Com
pare
wh
ole
num
bers
up
to
750
usin
g sm
alle
r th
an, g
reat
er
than
, mor
e th
an, l
ess
than
an
d is
eq
ual t
o.
Ord
er a
nd
com
pare
num
bers
to 9
99•
Ord
er w
hol
e n
umbe
rs u
p to
999
fr
om s
mal
lest
to b
igge
st, a
nd
bigg
est t
o sm
alle
st•
Com
pare
wh
ole
num
bers
up
to
999
usin
g sm
alle
r th
an, g
reat
er
than
, mor
e th
an, l
ess
than
an
d is
eq
ual t
o.U
se o
rdin
al n
umbe
rs to
sho
w o
rder
, pl
ace
or p
osit
ion
• U
se, r
ead
and
wri
te o
rdin
al
num
bers
, in
clud
ing
abbr
evia
ted
form
up
to 3
1.
Use
ord
inal
num
bers
to s
how
ord
er,
plac
e or
pos
itio
n•
Use
, rea
d an
d w
rite
ord
inal
n
umbe
rs, i
ncl
udin
g ab
brev
iate
d fo
rm u
p to
31.
Use
ord
inal
num
bers
to s
how
ord
er,
plac
e or
pos
itio
n•
Use
, rea
d an
d w
rite
ord
inal
n
umbe
rs, i
ncl
udin
g ab
brev
iate
d fo
rm u
p to
31.
Plac
e va
lue
1Pl
ace
valu
e
CAPS Math Gr 2 TG.indb 37 2011/11/16 2:51 PM
38 Study & Master Mathematics Grade 2 • Introduction
Solv
e n
um
ber
pro
ble
ms
1Pr
oble
m s
olvi
ng
tech
niq
ues
Reco
gnis
e th
e pl
ace
valu
e of
n
umbe
rs to
99
• K
now
wh
at e
ach
dig
it r
epre
sen
ts•
Dec
ompo
se 2
-dig
it n
umbe
rs u
p t o
99
into
mul
tipl
es o
f ten
s an
d on
es
(TU
).•
Iden
tify
an
d st
ate
the
valu
e of
ea
ch d
igit
Reco
gnis
e th
e pl
ace
valu
e of
n
umbe
rs to
500
• K
now
wh
at e
ach
dig
it r
epre
sen
ts•
Dec
ompo
se 3
-dig
it n
umbe
rs u
p to
50
0 in
to m
ulti
ples
of h
undr
eds,
te
ns
and
ones
(H
TU).
• Id
enti
fy a
nd
stat
e th
e va
lue
of
each
dig
it
Reco
gnis
e th
e pl
ace
valu
e of
n
umbe
rs to
750
• K
now
wh
at e
ach
dig
it r
epre
sen
ts•
Dec
ompo
se 3
-dig
it n
umbe
rs u
p t o
750
into
mul
tipl
e of
hun
dred
s,
ten
s an
d on
es (
HTU
).•
Iden
tify
an
d st
ate
the
valu
e of
ea
ch d
igit
Reco
gnis
e th
e pl
ace
valu
e of
n
umbe
rs to
999
• K
now
wh
at e
ach
dig
it r
epre
sen
ts•
Dec
ompo
se 3
-dig
it n
umbe
rs u
p to
999
into
mul
tipl
e of
hun
dred
s,
ten
s an
d on
es (
HTU
)•
Iden
tify
an
d st
ate
the
valu
e of
ea
ch d
igit
1A
ddit
ion
, su
btra
ctio
nU
se t
he
follo
win
g te
chn
ique
s w
hen
so
lvin
g pr
oble
m:
• bu
ildin
g up
an
d br
eaki
ng
dow
n
num
bers
• do
ublin
g an
d h
alvi
ng
• n
umbe
r lin
es
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
:•
build
ing
up a
nd
brea
kin
g do
wn
n
umbe
rs•
doub
ling
and
hal
vin
g•
num
ber
lines
• ro
undi
ng
off i
n te
ns
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
: •
build
ing
up a
nd
brea
kin
g do
wn
n
umbe
rs•
doub
ling
and
hal
vin
g•
num
ber
lines
• ro
undi
ng
off i
n te
ns
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
solv
ing
prob
lem
s up
to 9
99 a
nd
expl
ain
sol
utio
ns
topr
oble
ms:
• bu
ildin
g up
an
d br
eaki
ng
dow
n
num
bers
• do
ublin
g an
d h
alvi
ng
• n
umbe
r lin
es•
roun
din
g of
f in
ten
s
1Re
peat
ed
addi
tion
le
adin
g to
m
ulti
plic
atio
n
Solv
e n
umbe
r pr
oble
ms
in c
onte
xt
and
expl
ain
ow
n s
olut
ion
to
prob
lem
s in
volv
ing
mul
tipl
icat
ion
w
ith
an
swer
s up
to 5
0.
Solv
e n
umbe
r pr
oble
ms
in c
onte
xt
and
expl
ain
ow
n s
olut
ion
to
prob
lem
s in
volv
ing
mul
tipl
icat
ion
w
ith
an
swer
s up
to 7
5.
Solv
e n
umbe
r pr
oble
ms
in c
onte
xt
and
expl
ain
ow
n s
olut
ion
to
prob
lem
s in
volv
ing
mul
tipl
icat
ion
w
ith
an
swer
s up
to 7
5.
Solv
e n
umbe
r pr
oble
ms
in c
onte
xt
and
expl
ain
ow
n s
olut
ion
to
prob
lem
s in
volv
ing
mul
tipl
icat
ion
w
ith
an
swer
s up
to 1
00.
1G
roup
ing
and
shar
ing
lead
ing
to d
ivis
ion
Solv
e an
d ex
plai
n so
luti
ons
to
prac
tica
l pro
blem
s th
at in
volv
e eq
ual
shar
ing
and
grou
ping
up
to 5
0 w
ith
an
swer
s th
at c
an in
clud
e re
mai
nder
s
Solv
e an
d ex
plai
n so
luti
ons
to
prac
tica
l pro
blem
s th
at in
volv
e eq
ual
shar
ing
and
grou
ping
up
to 7
5 w
ith
an
swer
s th
at c
an in
clud
e re
mai
nder
s
Solv
e an
d ex
plai
n so
luti
ons
to
prac
tica
l pro
blem
s th
at in
volv
e eq
ual
shar
ing
and
grou
ping
up
to 7
5 w
ith
an
swer
s th
at c
an in
clud
e re
mai
nder
s
Solv
e an
d ex
plai
n so
luti
ons
to
prac
tica
l pro
blem
s th
at in
volv
e eq
ual
shar
ing
and
grou
ping
up
to 1
00 w
ith
an
swer
s th
at c
an in
clud
e re
mai
nder
1Sh
arin
g le
adin
g to
frac
tion
sSo
lve
and
expl
ain
sol
utio
ns
to
prac
tica
l pro
blem
s th
at in
volv
e eq
ual s
har
ing
lead
ing
to s
olut
ion
s th
at in
clud
e un
itar
y an
d n
on-u
nit
ary
frac
tion
s e.
g. ½
, ¼, ¾
, etc
.
Solv
e an
d ex
plai
n s
olut
ion
s to
pr
acti
cal p
robl
ems
that
invo
lve
equa
l sh
arin
g le
adin
g to
sol
utio
ns
that
incl
ude
unit
ary
and
non
-un
itar
y fr
acti
ons
e.g.
½, ¼
, ¾, e
tc.
Solv
e an
d ex
plai
n s
olut
ion
s to
pr
acti
cal p
robl
ems
that
invo
lve
equa
l sh
arin
g le
adin
g to
sol
utio
ns
that
incl
ude
unit
ary
and
non
-un
itar
y fr
acti
ons
e.g.
½, ¼
, ¾, e
tc.
Solv
e an
d ex
plai
n s
olut
ion
s to
pr
acti
cal p
robl
ems
that
invo
lve
equa
l sh
arin
g le
adin
g to
sol
utio
ns
that
incl
ude
unit
ary
and
non
-un
itar
y fr
acti
ons
e.g.
½, ¼
, ¾, e
tc.
1M
oney
• Re
cogn
ise
and
iden
tify
th
e So
uth
A
fric
an c
oin
s an
d ba
nk
not
es•
Solv
e m
oney
pro
blem
s in
volv
ing
tota
ls a
nd
chan
ge in
ran
ds o
r ce
nts
.
• Re
cogn
ise
and
iden
tify
th
e So
uth
A
fric
an c
oin
s an
d ba
nk
not
es•
Solv
e m
oney
pro
blem
s in
volv
ing
tota
ls a
nd
chan
ge in
ran
ds o
r ce
nts
.
• Re
cogn
ise
and
iden
tify
th
e So
uth
A
fric
an c
oin
s an
d ba
nk
not
es•
Solv
e m
oney
pro
blem
s in
volv
ing
tota
ls a
nd c
hang
e in
ran
ds o
r ce
nts.
• C
onve
rt b
etw
een
ran
ds a
nd
cen
ts.
• Re
cogn
ise
and
iden
tify
th
e So
uth
A
fric
an c
oin
s an
d ba
nk
not
es•
Solv
e m
oney
pro
blem
s in
volv
ing
tota
ls a
nd c
hang
e in
ran
ds o
r ce
nts.
• C
onve
rt b
etw
een
ran
ds a
nd
cen
ts.
CAPS Math Gr 2 TG.indb 38 2011/11/16 2:51 PM
39Study & Master Mathematics Grade 2 • Introduction
Cal
cula
tion
s1
Tech
niq
ues
(met
hod
s or
st
rate
gies
)
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
build
ing
up a
nd
brea
kin
g do
wn
n
umbe
rs•
doub
ling
and
hal
vin
g•
num
ber
lines
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
build
ing
up a
nd
brea
kin
g do
wn
n
umbe
rs•
doub
ling
and
hal
vin
g•
num
ber
lines
• ro
undi
ng
off i
n te
ns
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
build
ing
up a
nd
brea
kin
g do
wn
n
umbe
rs•
doub
ling
and
hal
vin
g•
num
ber
lines
• ro
undi
ng
off i
n te
ns
Use
th
e fo
llow
ing
tech
niq
ues
wh
en
perf
orm
ing
calc
ulat
ion
s:•
build
ing
up a
nd
brea
kin
g do
wn
n
umbe
rs•
doub
ling
and
hal
vin
g•
num
ber
lines
• ro
undi
ng
off i
n te
ns
1A
ddit
ion
an
d su
btra
ctio
n•
Add
up
to 9
9•
Subt
ract
from
99
• U
se a
ppro
pria
te s
ymbo
ls
(+, –
, =, ×
)•
Prac
tice
num
ber
bon
ds t o
20
• A
dd u
p to
400
• Su
btra
ct fr
om 4
00•
Use
app
ropr
iate
sym
bols
(+
, –, =
, ×)
• Pr
acti
ce n
umbe
r bo
nds
to 3
0
• A
dd u
p to
800
• Su
btra
ct fr
om 8
00•
Use
app
ropr
iate
sym
bols
(+
, –, =
, ×)
• Pr
acti
ce n
umbe
r bo
nds
to 3
0
• A
dd u
p to
999
• Su
btra
ct fr
om 9
99•
Use
app
ropr
iate
sym
bols
(+
, –, =
, ×)
• Pr
acti
ce n
umbe
r bo
nds
to 3
0
1Re
peat
ed
addi
tion
le
adin
g to
m
ulti
plic
atio
n
• M
ulti
ply
num
bers
1 to
10
by 2
, 5,
10•
Use
app
ropr
iate
sym
bols
(+,
=, ×
)
• M
ulti
ply
num
bers
1 to
10
by 2
, 4,
5, 1
0•
Use
app
ropr
iate
sym
bols
(+,
=, ×
)
• M
ulti
ply
num
bers
1 to
10
by 2
, 3,
4, 5
, 10
• U
se a
ppro
pria
te s
ymbo
ls (
+, =
, ×)
• M
ulti
ply
num
bers
1 to
10
by 2
, 3,
4, 5
, 10
• U
se a
ppro
pria
te s
ymbo
ls (
+, =
, ×)
1D
ivis
ion
• D
ivid
e n
umbe
rs to
50
by 2
, 5, 1
0•
Use
app
ropr
iate
sym
bols
(÷,
=, ×
)•
Div
ide
num
bers
to 5
0 by
2, 4
, 5,
10, 4
• U
se a
ppro
pria
te s
ymbo
ls (
÷, =
, ×)
• D
ivid
e n
umbe
rs to
99
by 2
, 4, 5
, 10
, 3•
Use
app
ropr
iate
sym
bols
(÷,
=, ×
)
• D
ivid
e n
umbe
rs to
99
by 2
, 3, 4
, 5,
10•
Use
app
ropr
iate
sym
bols
(÷,
=, ×
)
1M
enta
l st
rate
gies
fo
r do
ing
calc
ulat
ion
s
Num
ber
con
cept
: ra
nge
200
• O
rder
a g
iven
set
of s
elec
ted
num
bers
. Ran
ge -2
00•
Com
pare
num
bers
to 2
00 a
nd
say
wh
ich
is m
ore
or le
ss•
Kn
ow w
hic
h n
umbe
r is
1 m
ore
or 1
le
ss to
num
bers
. Ran
ge –
till
200
• K
now
wh
ich
num
ber
is 2
mor
e or
2
less
to n
umbe
rs. R
ange
– ti
ll 20
0•
Kn
ow w
hic
h n
umbe
r is
3 m
ore
or 3
le
ss to
num
bers
. Ran
ge –
till
200
• K
now
wh
ich
num
ber
is 4
mor
e or
4
less
to n
umbe
rs. R
ange
– ti
ll 20
0•
Kn
ow w
hic
h n
umbe
r is
5 m
ore
or
Kn
ow w
hic
h n
umbe
r is
10
mor
e or
le
ss to
num
bers
. Ran
ge –
till
200
Num
ber
con
cept
: ra
nge
500
• O
rder
a g
iven
set
of s
elec
ted
num
bers
. Ran
ge -5
00•
Com
pare
num
bers
to 5
00 a
nd
say
wh
ich
is m
ore
or le
ss•
Kn
ow w
hic
h n
umbe
r is
1 m
ore
or 1
le
ss to
num
bers
. Ran
ge –
till
500
• K
now
wh
ich
num
ber
is 2
mor
e or
2
less
to n
umbe
rs. R
ange
– ti
ll 50
0•
Kn
ow w
hic
h n
umbe
r is
3 m
ore
or 3
le
ss to
num
bers
. Ran
ge –
till
500
• K
now
wh
ich
num
ber
is 4
mor
e or
4
less
to n
umbe
rs. R
ange
– ti
ll 50
0•
Kn
ow w
hic
h n
umbe
r is
5 m
ore
or
less
to c
erta
in n
umbe
rs. R
ange
–
till
500
• K
now
wh
ich
num
ber
is 1
0 m
ore
or
less
to n
umbe
rs. R
ange
– ti
ll 50
0
Num
ber
con
cept
: ra
nge
750
• O
rder
a g
iven
set
of s
elec
ted
num
bers
.•
Com
pare
num
bers
to 2
00 a
nd
say
wh
ich
is m
ore
or le
ss•
Kn
ow w
hic
h n
umbe
r is
1 m
ore
or 1
le
ss t
han
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 2
mor
e or
2
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
3 m
ore
or 3
le
ss t
han
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 4
mor
e or
4
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
5 m
ore
or 5
le
ss t
han
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 1
0 m
ore
or
less
th
an a
giv
en n
umbe
r
Num
ber
con
cept
: ra
nge
999
• O
rder
a g
iven
set
of s
elec
ted
num
bers
.•
Com
pare
num
bers
to 1
000
an
d sa
y w
hic
h is
mor
e or
less
th
an a
gi
ven
num
ber
• K
now
wh
ich
num
ber
is 1
mor
e or
1
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
2 m
ore
or 2
le
ss t
han
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 3
mor
e or
3
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
4 m
ore
or 4
le
ss t
han
a g
iven
num
ber
• K
now
wh
ich
num
ber
is 5
mor
e or
5
less
th
an a
giv
en n
umbe
r•
Kn
ow w
hic
h n
umbe
r is
10
mor
e or
10
less
th
an a
giv
en n
umbe
r
CAPS Math Gr 2 TG.indb 39 2011/11/16 2:51 PM
40 Study & Master Mathematics Grade 2 • Introduction
Men
tal
stra
tegi
es
for
doin
g ca
lcul
atio
ns
(con
tinue
d)
Rapi
dly
reca
ll:•
Reca
ll ad
diti
on a
nd
subt
ract
ion
fa
cts
to 2
0•
Add
or
subt
ract
mul
tipl
es o
f 10
from
0 to
100
Rapi
dly
reca
ll:•
Reca
ll ad
diti
on a
nd
subt
r act
ion
fa
cts
to 2
0•
Add
or
subt
ract
mul
tipl
es o
f 10
from
0 to
100
Rapi
dly
reca
ll:•
Reca
ll ad
diti
on a
nd
subt
ract
ion
fa
cts
to 2
0•
Add
or
subt
r act
mul
tipl
es o
f 10
from
0 to
100
Rapi
dly
reca
ll:•
Reca
ll ad
diti
on a
nd
subt
ract
ion
fa
cts
to 2
0•
Add
or
subt
ract
mul
tiple
s of
10
from
0
to 1
00•
mul
tipl
icat
ion
an
d di
visi
on fa
cts
for
the:
–
two
tim
es ta
ble
up to
2 ×
10
–
ten
tim
es ta
ble
up to
10 ×
10M
enta
l str
ateg
ies
Use
cal
cula
tion
str
ateg
ies:
• P
ut t
he
larg
er n
umbe
r fi
rst i
n
orde
r to
cou
nt o
n o
r co
unt b
ack
• N
umbe
r lin
e•
Dou
blin
g an
d h
alvi
ng
• B
uild
ing
up a
nd
brea
kin
g do
wn
• U
se t
he
rela
tion
ship
bet
wee
n
addi
tion
an
d su
btra
ctio
n
Men
tal s
trat
egie
sU
se t
he
follo
win
g ca
lcul
atio
n
stra
tegi
es•
Put
th
e la
rger
num
ber
firs
t in
or
der
to c
oun
t on
or
coun
t bac
k•
Num
ber
line
• D
oubl
ing
and
hal
vin
g•
Bui
ldin
g up
an
d br
eaki
ng
dow
n•
Use
th
e re
lati
onsh
ip b
etw
een
ad
diti
on a
nd
subt
ract
ion
Men
tal s
trat
egie
sU
se t
he
follo
win
g ca
lcul
atio
n
stra
tegi
es:
• P
ut t
he
lar g
er n
umbe
r fi
rst i
n
orde
r to
coun
t on
or
coun
t bac
k•
Num
ber
line
• D
oubl
ing
and
hal
vin
g•
Bui
ldin
g up
an
d br
eaki
ng
dow
n•
Use
th
e re
lati
onsh
ip b
etw
een
ad
diti
on a
nd
subt
ract
ion
• U
se t
he
rela
tion
ship
bet
wee
n
mul
tipl
icat
ion
an
d di
visi
on
Men
tal s
trat
egie
sU
se t
he
follo
win
g ca
lcul
atio
n
stra
tegi
es•
Put
th
e la
rger
num
ber
firs
t in
or
der
to c
oun
t on
or
coun
t bac
k•
Num
ber
line
• D
oubl
ing
and
hal
vin
g•
Bui
ldin
g up
an
d br
eaki
ng
dow
n•
Use
th
e re
lati
onsh
ip b
etw
een
ad
diti
on a
nd
subt
ract
ion
• U
se t
he
rela
tion
ship
bet
wee
n
mul
tipl
icat
ion
an
d di
visi
on
1Fr
acti
ons
• U
se a
nd
nam
e fr
acti
ons
in
fam
iliar
con
text
s in
clud
ing
hal
ves,
qu
arte
rs, t
hir
ds, f
ifth
s,•
Rec
ogn
ise
frac
tion
s in
di
agra
mm
atic
form
• W
rite
frac
tion
s as
1 h
alf,
1 t
hir
d
• U
se a
nd
nam
e fr
acti
ons
in
fam
iliar
con
text
s in
clud
ing
hal
ves,
qu
arte
rs, e
igh
ths,
th
irds
, six
ths,
fi
fth
s•
Rec
ogn
ise
frac
tion
s in
di
agra
mm
atic
form
• W
rite
frac
tion
s as
1 h
alf,
1 t
hir
d
• U
se a
nd
nam
e fr
acti
ons
in
fam
iliar
con
text
s in
clud
ing
hal
ves,
qu
arte
rs, e
igh
ths,
th
irds
, six
ths,
fi
fth
s,•
Rec
ogn
ise
frac
tion
s in
di
agra
mm
atic
form
• B
egin
to re
cogn
ise
that
two
halv
es
or th
ree
thir
ds m
ake
one
who
le a
nd
that
one
hal
f and
two
quar
ters
are
eq
uiva
lent
• W
rite
frac
tion
s as
1 h
alf,
1 t
hir
d
• U
se a
nd
nam
e fr
acti
ons
in
fam
iliar
con
text
s in
clud
ing
hal
ves,
qu
arte
rs, e
igh
ths,
th
irds
, six
ths,
fi
fth
s,•
Rec
ogn
ise
frac
tion
s in
di
agra
mm
atic
form
• B
egin
to r
ecog
nis
e th
at tw
o h
alve
s or
th
ree
thir
ds m
ake
one
wh
ole
and
that
on
e h
alf a
nd
two
quar
ters
are
equ
ival
ent
Patt
ern
s, f
un
ctio
ns
and
alg
ebra
2N
umbe
r pa
tter
ns
Cop
y, e
xten
d an
d de
scri
beC
opy,
ext
end
and
desc
ribe
sim
ple
num
ber
sequ
ence
s to
at l
east
100
Cop
y, e
xten
d an
d de
scri
beC
opy,
ext
end
and
desc
ribe
sim
ple
num
ber
sequ
ence
s to
at l
east
150
Cop
y, e
xten
d an
d de
scri
beC
opy,
ext
end
and
desc
ribe
sim
ple
num
ber
sequ
ence
s to
at l
east
180
Cop
y, e
xten
d an
d de
scri
beC
opy,
ext
end
and
desc
ribe
sim
ple
num
ber
sequ
ence
s to
at l
east
1 0
00
CAPS Math Gr 2 TG.indb 40 2011/11/16 2:51 PM
41Study & Master Mathematics Grade 2 • Introduction
Num
ber
patt
ern
s(c
ontin
ued)
Sequ
ence
s sh
ould
sh
ow c
oun
tin
g fo
rwar
ds a
nd
back
war
ds in
:•
th
e in
terv
als
spec
ifie
d in
gra
de 2
w
ith
incr
ease
d n
umbe
r ra
nge
s•
100
s to
at l
east
500
Sequ
ence
s sh
ould
sh
ow c
oun
tin
g fo
rwar
ds a
nd
back
war
ds in
:•
th
e in
terv
als
spec
ifie
d in
gra
de 2
w
ith
incr
ease
d n
umbe
r ra
nge
s•
50s
, 100
s to
at l
east
1 0
00
Sequ
ence
s sh
ould
sh
ow c
oun
tin
g fo
rwar
ds a
nd
back
war
ds in
:•
th
e in
t erv
als
spec
ifie
d in
gra
de 2
w
ith
incr
ease
d n
umbe
r ra
nge
s•
20s
, 25s
, 50s
, 100
s to
at l
east
1 0
00
Sequ
ence
s sh
ould
sh
ow c
oun
tin
g fo
rwar
dsan
d ba
ckw
ards
in:
Cre
ate
own
num
ber
patt
ern
sC
reat
e ow
n n
umbe
r pa
tter
ns
• t
he
int e
rval
s sp
ecif
ied
in g
rade
2
wit
h in
crea
sed
num
ber
ran
ges
• 2
0s,2
5s, 5
0s,1
00s
to a
t lea
st 1
000
2G
eom
etri
c Pa
tter
ns
Cop
y, e
xten
d an
d de
scri
beC
opy,
ext
end
and
desc
ribe
in w
ords
• s
impl
e pa
tter
ns
mad
e w
ith
ph
ysic
al o
bjec
ts•
sim
ple
patt
ern
s m
ade
wit
h
draw
ings
of l
ines
, sh
apes
or
obje
cts
Cop
y, e
xten
d an
d de
scri
beC
opy,
ext
end
and
desc
ribe
in w
ords
• s
impl
e pa
tter
ns
mad
e w
ith
ph
ysic
al o
bjec
ts•
sim
ple
patt
ern
s m
ade
wit
h
draw
ings
of l
ines
, sh
apes
or
obje
cts
Cop
y, e
xten
d an
d de
scri
beC
opy,
ext
end
and
desc
ribe
in w
ords
• s
impl
e pa
tter
ns
mad
e w
ith
ph
ysic
al o
bjec
ts•
sim
ple
patt
ern
s m
ade
wit
h
draw
ings
of l
ines
, sh
apes
or
obje
cts
Patt
ern
s al
l aro
un
d u
s Id
enti
fy, d
escr
ibe
in w
ords
an
d co
py
geom
etri
c pa
tter
ns
• in
nat
ure
• fr
om e
very
day
life
• fr
om o
ur c
ultu
r al h
erit
age
Ran
ge o
f p
atte
rns
Sim
ple
repe
atin
g pa
tter
ns
Ran
ge o
f p
atte
rns
Sim
ple
repe
atin
g pa
ttern
sPa
tter
ns in
whi
ch th
e nu
mbe
r of
sha
pes
in e
ach
stag
e ch
ange
s in
a p
redi
ctab
le w
ay i.
e. r
egul
ar
incr
easi
ng p
atte
rns
Ran
ge o
f p
atte
rns
Patt
ern
s in
wh
ich
th
e n
umbe
r of
sh
apes
in e
ach
sta
ge c
han
ges
in
a p
redi
ctab
le w
ay i.
e. r
egul
ar
incr
easi
ng
patt
ern
s
Cre
ate
own
geo
met
ric
patt
ern
s•
wit
h p
hysi
cal o
bjec
ts•
by
draw
ings
lin
es, s
hap
es o
r ob
ject
s
Cre
ate
own
geo
met
ric
patt
ern
s•
wit
h p
hysi
cal o
bjec
ts•
by
draw
ings
lin
es, s
hap
es o
r ob
ject
s
Cre
ate
own
geo
met
ric
patt
ern
s•
wit
h p
hysi
cal o
bjec
ts•
by
draw
ings
lin
es, s
hap
es o
r ob
ject
s
Shap
e an
d s
pac
e3
Posi
tion
, or
ien
tati
on a
nd
view
s
Posi
tion
an
d v
iew
s•
Mat
ch d
iffe
ren
t vie
ws
of t
he
sam
e ev
eryd
ay o
bjec
t•
Nam
e an
eve
ryda
y ob
ject
wh
en
show
n a
n u
nus
ual v
iew
of i
t
Posi
tion
an
d v
iew
s•
Rea
ds, i
nt e
rpre
t an
d dr
aw
info
rmal
map
s, o
r to
p vi
ews
of a
co
llect
ion
of o
bjec
ts.
• F
ind
obje
cts
on m
aps
Posi
tion
an
d d
irec
tion
sFo
llow
dir
ecti
ons
to m
ove
arou
nd
the
clas
sroo
m, a
nd
sch
ool.
Giv
e di
rect
ion
s to
mov
e ar
oun
d th
e cl
assr
oom
an
d sc
hoo
l
Posi
tion
an
d d
irec
tion
sFo
llow
dir
ecti
ons
from
on
e pl
ace
to
anot
her
on a
n in
form
al m
ap
CAPS Math Gr 2 TG.indb 41 2011/11/16 2:51 PM
42 Study & Master Mathematics Grade 2 • Introduction
33D
obj
ects
Ran
ge o
f ob
ject
sRe
cogn
ise
and
nam
e 3-
D o
bjec
ts in
th
e cl
assr
oom
an
d in
pic
ture
s•
bal
l sh
apes
(sp
her
es)
• b
ox s
hap
es (
pris
ms)
• c
ylin
ders
Ran
ge o
f ob
ject
sRe
cogn
ise
and
nam
e 3-
D o
bjec
ts in
th
e cl
assr
oom
an
d in
pic
ture
s•
bal
l sh
apes
(sp
her
es)
• b
ox s
hap
es (
pris
ms)
• c
ylin
ders
Ran
ge o
f ob
ject
sRe
cogn
ise
and
nam
e 3-
D o
bjec
ts in
th
e cl
assr
oom
an
d in
pic
ture
s•
bal
l sh
apes
(sp
her
es)
• b
ox s
hap
es (
pris
ms)
• c
ylin
ders
Feat
ure
s of
ob
ject
sD
escr
ibe,
sor
t an
d co
mpa
re 3
-D
obje
cts
in te
rms
of:
• 2
D s
hap
es t
hat
mak
e up
th
e fa
ces
of 3
D o
bjec
ts•
fla
t or
curv
ed s
urfa
ces
Feat
ure
s of
ob
ject
sD
escr
ibe,
sor
t an
d co
mpa
re 3
-D
obje
cts
in te
rms
of:
• 2
D s
hap
es t
hat
mak
e up
th
e fa
ces
of 3
D o
bjec
ts•
fla
t or
curv
ed s
urfa
ces
Feat
ure
s of
ob
ject
sD
escr
ibe,
sor
t an
d co
mpa
re 3
-D
obje
cts
in te
rms
of:
• 2
D s
hap
es t
hat
mak
e up
th
e fa
ces
of 3
D o
bjec
ts•
fla
t or
curv
ed s
urfa
ces
Focu
ssed
act
ivit
ies
• O
bser
ve a
nd
build
giv
en 3
D
obje
cts
usin
g co
ncr
ete
mat
eria
ls
such
as
cuto
ut 2
D s
hap
es, c
lay,
to
oth
pick
s, s
traw
s, o
ther
3D
ge
omet
ric
obje
cts
Focu
ssed
act
ivit
ies
• O
bser
ve a
nd
build
giv
en 3
D
obje
cts
usin
g co
ncr
ete
mat
eria
ls
such
as
cuto
ut 2
D s
hap
es, c
lay,
to
oth
pick
s, s
traw
s, o
ther
3D
ge
omet
ric
obje
cts
Sugg
este
d fo
cus
and
seq
uen
cin
g of
ac
tivi
ties
for
Term
2Le
arn
ers
wor
k w
ith
sph
eres
, pri
sms
and
cylin
ders
as
they
did
in G
rade
2.
They
nam
e th
em a
nd
grou
p th
em.
Lear
ner
s fo
cus
on t
he
kin
d of
su
rfac
es o
n e
ach
type
of o
bjec
t. T
hey
di
stin
guis
hsu
rfac
es a
ccor
din
g to
wh
eth
er t
hey
ar
e cu
rved
or
flat
.Le
arn
ers
use
cut-
out c
ardb
oard
sq
uare
s to
mak
e a
box.
Th
en le
arn
ers
talk
abo
ut t
he
flat
sur
face
s on
pr
ism
s an
d cy
linde
rs a
nd
desc
ribe
th
em a
ccor
din
g to
wh
eth
er t
hey
are
ci
rcul
ar, s
quar
e or
rec
tan
gula
r
Sugg
este
d fo
cus
and
seq
uen
cin
g of
ac
tivi
ties
for
Term
3
Lear
ner
s w
ork
wit
h s
pher
es,
pris
ms,
cyl
inde
rs, p
yram
ids
and
con
es. L
earn
ers
focu
s on
th
e ki
nd
of s
urfa
ces
on e
ach
type
of o
bjec
t.
They
dis
tin
guis
h s
urfa
ces
acco
rdin
g to
wh
eth
er t
hey
are
cur
ved
or f
lat.
Th
en le
arn
ers
talk
abo
ut t
he
flat
su
rfac
es o
n p
rism
s an
d cy
linde
rs a
nd
desc
ribe
th
em a
ccor
din
g to
wh
eth
er
they
are
cir
cula
r, s
quar
e, r
ecta
ngu
lar
or tr
ian
gula
r.Le
arn
er n
ame
and
grou
p th
e ge
omet
ric
obje
cts
abov
e.Le
arn
ers
use
toot
hpi
cks,
str
aws,
or
rolle
d pa
per
to m
ake
a py
ram
id.
Sugg
este
d fo
cus
and
seq
uen
cin
g of
ac
tivi
ties
for
Term
4
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
ses
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
ses
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
ses
CAPS Math Gr 2 TG.indb 42 2011/11/16 2:51 PM
43Study & Master Mathematics Grade 2 • Introduction
32-
D s
hap
esR
ange
of
shap
es•
cir
cles
• t
rian
gles
• s
quar
es•
rec
t an
gles
Feat
ure
s of
sh
apes
Des
crib
e, s
ort a
nd
com
pare
2-D
sh
apes
in te
rms
of:
• s
hap
e•
str
aigh
t sid
es•
rou
nd
side
s
Ran
ge o
f sh
apes
• c
ircl
es•
tri
angl
es•
squ
ares
• r
ecta
ngl
esFe
atu
res
of s
hap
esD
escr
ibe,
sor
t an
d co
mpa
re 2
-D
shap
es in
term
s of
:•
sh
ape
• s
trai
ght s
ides
• r
oun
d si
des
Sugg
este
d fo
cus
of a
ctiv
itie
s fo
r Te
rm 1
Lear
ner
s n
ame
them
an
d gr
oup
shap
esLe
arn
ers
focu
s on
th
e ki
nd
of s
ides
th
at e
ach
sh
ape
has
Th
ey d
isti
ngu
ish
sh
apes
by
talk
ing
abou
t wh
eth
er
thei
r si
des
are
roun
d or
str
aigh
tD
raw
cir
cles
, squ
ares
, rec
tan
gles
an
d tr
ian
gles
Wor
k is
con
solid
ated
thro
ugh
wri
tten
ex
erci
ses
Sugg
este
d fo
cus
of a
ctiv
itie
s fo
r Te
rm 3
Lear
ner
s n
ame
and
grou
p sh
apes
Lear
ner
s fo
cus
on t
he
kin
d of
sid
es
that
eac
h s
hap
e h
as T
hey
dis
tin
guis
h
shap
es b
y ta
lkin
g ab
out w
het
her
th
eir
side
s ar
e ro
und
or s
trai
ght
Dra
w c
ircl
es, s
quar
es, r
ecta
ngl
es a
nd
tria
ngl
esW
ork
is c
onso
lidat
ed th
roug
h w
ritt
en
exer
cise
s
3Sy
mm
etry
• D
eter
min
e lin
e of
sym
met
ry
thro
ugh
pape
r fo
ldin
g an
d re
flec
tion
• R
ecog
nis
e an
d dr
aw li
ne
of
sym
met
ry in
2-D
geo
met
rica
l an
d n
onge
omet
rica
l sh
apes
Sugg
este
d fo
cus
of T
erm
2Pa
per
fold
ing
acti
viti
es t
hat
dev
elop
an
un
ders
tan
din
g of
sym
met
ry
incl
ude:
• a
ctiv
itie
s in
wh
ich
wet
pai
nt i
s pl
aced
on
th
e pa
ge b
efor
e fo
ldin
g•
act
ivit
ies
in w
hic
h p
aper
is c
ut o
r to
rn fr
om t
he
fold
lin
eTh
ese
activ
ities
can
be
done
bot
h in
th
e M
aths
less
on a
nd th
e Li
fe S
kills
le
sson
s
Sugg
este
d fo
cus
of T
erm
4W
ritt
en e
xerc
ises
sh
ould
incl
ude
exam
ples
wh
ere
• t
he
line
of s
ymm
etry
is n
ot a
ve
rtic
al li
ne
• t
her
e is
mor
e th
an o
ne
line
of
sym
met
ry in
th
e sh
ape
or o
bjec
t
CAPS Math Gr 2 TG.indb 43 2011/11/16 2:51 PM
44 Study & Master Mathematics Grade 2 • Introduction
Mea
sure
men
t4
Tim
eTe
llin
g th
e ti
me
• R
ead
date
s on
cal
enda
rs•
Pla
ce b
irth
days
, rel
igio
us fe
stiv
als,
pu
blic
hol
iday
s, h
isto
rica
l eve
nts
, sc
hoo
l eve
nts
on
a c
alen
dar
Telli
ng
the
tim
e•
Rea
d da
tes
on c
alen
dars
• P
lace
bir
thda
ys, r
elig
ious
fest
ival
s,
publ
ic h
olid
ays,
his
tori
cal e
ven
ts,
sch
ool e
ven
ts o
n a
cal
enda
r
Telli
ng
the
tim
e•
Rea
d da
tes
on c
alen
dars
• P
lace
bir
thda
ys, r
elig
ious
fest
ival
s,
publ
ic h
olid
ays,
his
tori
cal e
ven
ts,
sch
ool e
ven
ts o
n a
cal
enda
r
Telli
ng
the
tim
e•
Rea
d da
tes
on c
alen
dars
• P
lace
bir
thda
ys, r
elig
ious
fest
ival
s,
publ
ic h
olid
ays,
his
tori
cal e
ven
ts,
sch
ool e
ven
ts o
n a
cal
enda
r
Tell
12-h
our
tim
e in
• h
ours
• h
alf h
ours
• q
uart
er h
ours
• m
inut
eson
an
alog
ue c
lock
s an
d di
gita
l cl
ocks
an
d ot
her
dig
ital
inst
rum
ents
th
at s
how
tim
e e.
g. c
ell p
hon
es
Tell
12-h
our
tim
e in
• h
ours
• h
alf h
ours
• q
uart
er h
ours
• m
inut
eson
an
alog
ue c
lock
s an
d di
gita
l cl
ocks
an
d ot
her
dig
ital
inst
rum
ents
th
at s
how
tim
e e.
g. c
ell p
hon
es
Tell
12-h
our
tim
e in
• h
ours
• h
alf h
ours
• q
uart
er h
ours
• m
inut
eson
an
alog
ue c
lock
s an
d di
gita
l cl
ocks
an
d ot
her
dig
ital
inst
rum
ents
th
at s
how
tim
e e.
g. c
ell p
hon
es
Tell
12-h
our
tim
e in
• h
ours
• h
alf h
ours
• q
uart
er h
ours
• m
inut
eson
an
alog
ue c
lock
s an
d di
gita
l cl
ocks
an
d ot
her
dig
ital
inst
rum
ents
th
at s
how
tim
e e.
g. c
ell p
hon
es
Cal
cula
te le
ngt
hs
of ti
me
and
pass
ing
of ti
me
Cal
cula
te le
ngt
hs
of ti
me
and
pass
ing
of ti
me
Cal
cula
te le
ngt
hs
of ti
me
and
pass
ing
of ti
me
Use
cal
enda
rs to
cal
cula
te a
nd
desc
ribe
len
gth
s of
tim
e in
day
s or
w
eeks
or
mon
ths
incl
udin
g
Use
cal
enda
rs to
cal
cula
te a
nd
desc
ribe
len
gth
s of
tim
e in
day
s or
w
eeks
or
mon
ths
incl
udin
g•
con
vert
ing
betw
een
day
s an
d w
eeks
• c
onve
rtin
g be
twee
n w
eeks
an
d m
onth
Use
cal
enda
rs to
cal
cula
te a
nd
desc
ribe
len
gth
s of
tim
e in
day
s or
w
eeks
or
mon
ths
incl
udin
g•
con
vert
ing
betw
een
day
s an
d w
eeks
• c
onve
rtin
g be
twee
n w
eeks
an
d m
onth
s•
Use
clo
cks
to c
alcu
late
len
gth
s of
ti
me
in h
ours
or
hal
f hou
rsU
se c
lock
s to
cal
cula
te le
ngt
hs
of ti
me
in h
ours
, hal
f hou
rs a
nd
quar
ter
hou
rs
Use
clo
cks
to c
alcu
late
len
gth
s of
tim
e in
hou
rs, h
alf h
ours
an
d qu
arte
r h
ours
4Le
ngt
hIn
form
al m
easu
rin
g•
Est
imat
e, m
easu
re, c
ompa
re,
orde
r an
d re
cord
len
gth
usi
ng
non
-sta
nda
rd m
easu
res
e.g.
han
d sp
ans,
pac
es, p
enci
l len
gth
s,
coun
ters
•
Des
crib
e th
e le
ngt
h o
f obj
ects
by
coun
tin
g an
d st
atin
g h
ow m
any
info
rmal
un
its
lon
g it
is•
Use
lan
guag
e to
talk
abo
ut t
he
com
pari
son
e.g
. lon
ger,
sh
orte
r,
talle
r, w
ider
CAPS Math Gr 2 TG.indb 44 2011/11/16 2:51 PM
45Study & Master Mathematics Grade 2 • Introduction
Len
gth
(c
ontin
ued)
Intr
odu
cin
g fo
rmal
mea
suri
ng
• E
stim
ate,
mea
sure
, ord
er a
nd re
cord
le
ngth
usi
ng m
etre
s (e
ither
met
re
stic
ks o
r m
etre
leng
ths
of st
ring
) as
th
e st
anda
rd u
nit o
f len
gth.
• E
stim
ate
and
mea
sure
len
gth
s in
ce
nti
met
res
usin
g a
rule
r.N
o co
nve
rsio
ns
betw
een
met
res
and
cen
tim
etre
s re
quir
ed
Intr
odu
cin
g fo
rmal
mea
suri
ng
• E
stim
ate,
mea
sure
, com
pare
, ord
er
and
reco
rd le
ngt
h u
sin
g m
etre
s (e
ith
er m
etre
sti
cks
or m
etre
le
ngt
hs
of s
trin
g) a
s th
e st
anda
rd
unit
of l
engt
h.
• E
stim
ate,
mea
sure
and
rec
ord
leng
ths
in c
enti
met
res
usin
g a
rule
r.
4M
ass
Info
rmal
mea
suri
ng
• E
stim
ate,
mea
sure
, com
pare
, ord
er
and
reco
rd m
ass
usin
g a
bala
nce
an
d n
on-s
tan
dard
mea
sure
s e.
g.
bloc
ks, b
rick
s et
c•
Use
lan
guag
e to
talk
abo
ut t
he
com
pari
son
e.g
. lig
ht,
hea
vy,
ligh
ter,
hea
vier
In
trod
uci
ng
form
al m
easu
rin
g•
Com
pare
, ord
er a
nd r
ecor
d th
e m
ass
of c
omm
erci
ally
pac
kage
d ob
ject
s w
hich
hav
e th
eir
mas
s st
ated
in k
ilogr
ams
e.g.
2 k
ilogr
ams
of r
ice
and
1 ki
logr
am o
f flo
ur o
r in
gr
ams
e.g.
500
gra
ms
of s
alt
• W
her
e ba
thro
om s
cale
s ar
e av
aila
ble,
lear
ner
s ca
n m
easu
re
thei
r ow
n m
ass
in k
ilogr
ams
usin
g a
bath
room
sca
le.
Intr
oduc
ing
form
al m
easu
rin
gLe
arn
ers
do w
ritt
en ta
sks
to
con
solid
ate
the
follo
win
g, in
clud
ing
read
ing
pict
ures
of
• p
rodu
cts
wit
h m
ass
wri
tten
on
th
em,
• p
ictu
res
of m
ass
on b
ath
room
sc
ales
wh
ere
the
nee
dle
poin
ts to
a
num
bere
d gr
adat
ion
lin
es
The
expe
ctat
ion
is t
hat
lear
ner
s on
ly r
ead
to t
he
nea
rest
num
bere
d gr
adat
ion
lin
e. T
hey
des
crib
e th
eir
mas
s as
alm
ost/
nea
rly/
clos
e to
/a b
it
mor
e th
an/m
ore
or le
ss/o
r ex
actl
y th
e n
umbe
r (o
f kilo
gram
s) t
hey
rea
d of
f th
e m
ass
met
er.
• W
her
e ba
lan
cin
g sc
ales
wit
h m
ass
piec
es c
alib
rate
d in
gra
ms
are
avai
labl
e, le
arn
ers
can
mea
sure
m
ass
or d
iffe
ren
t obj
ects
.N
o co
nve
rsio
ns
betw
een
gra
ms
and
kilo
gram
s re
quir
ed
CAPS Math Gr 2 TG.indb 45 2011/11/16 2:51 PM
46 Study & Master Mathematics Grade 2 • Introduction
4C
apac
ity/
volu
me
Info
rmal
mea
suri
ng
• E
stim
ate
and
mea
sure
, com
pare
an
d or
der
the
amou
nt t
he
capa
city
of
con
tain
ers
(i.e
. th
e am
oun
t th
e co
nta
iner
can
hol
d if
fille
d) b
y us
ing
non
-sta
nda
rd m
easu
res
e.g.
sp
oon
s an
d cu
ps•
Des
crib
e th
e ca
paci
ty o
f th
e co
nta
iner
by
coun
tin
g an
d st
atin
g h
ow m
any
of t
he
info
rmal
un
its
it
take
s to
fill
the
con
tain
er e
.g. T
he
bott
le h
as t
he
capa
city
of 4
cup
s.In
trod
ucin
g fo
rmal
mea
suri
ng
Esti
mat
e, m
easu
re, c
ompa
re, o
rder
an
d re
cord
the
capa
city
of o
bjec
ts b
y m
easu
ring
in li
tres
, hal
f lit
res
and
quar
ter
litre
s•
usi
ng b
ottl
es w
ith
a ca
pa ci
ty o
f 1
litre
, or
cont
aine
rs w
hose
cap
a cit
y is
sta
ted
in m
illili
tres
e.g
. coo
l dri
nk
cans
• m
easu
ring
jugs
in w
hich
num
bere
d ca
libra
tion
line
s sh
ow li
tres
, hal
f lit
res
and
quar
ter
litre
s•
mea
suri
ng ju
gs w
hich
hav
e nu
mbe
red
calib
rati
on li
nes
for
mill
ilitr
es. L
earn
ers
are
not
expe
cted
to r
ead
volu
mes
at
unnu
mbe
red
calib
rati
on li
nes
• m
easu
ring
cup
s an
d te
aspo
ons
whi
ch in
dica
te th
eir
capa
city
• c
ompa
r e, o
rder
and
rec
ord
the
capa
city
of c
omm
erci
ally
pac
kage
s ob
ject
s w
hose
cap
acit
y is
sta
ted
in li
tres
e.g
. 2 li
tres
of m
ilk, 1
litr
e of
coo
l dri
nk, 5
litr
es o
f pai
nt o
r in
mill
ilitr
es e
.g. 5
00 m
l of m
ilk,
340
mill
ilitr
es o
f coo
l dri
nk, 7
50
mill
ilitr
es o
f oil
• k
now
that
a s
tand
ard
cup
is 2
50
mill
ilitr
es•
kno
w th
at a
teas
poon
is 5
mill
ilitr
es
Intr
odu
cin
g fo
rmal
mea
suri
ng
Lear
ner
s do
wri
tten
task
s to
co
nso
lidat
e th
e fo
llow
ing,
incl
udin
g re
adin
g pi
ctur
es o
f•
pro
duct
s w
ith
th
eir
capa
city
w
ritt
en o
n t
hem
in o
rder
to
sequ
ence
in o
rder
• p
ictu
res
of ju
gs w
here
the
volu
me
is n
ear
to a
num
bere
d 1
litre
or
2 lit
re g
rada
tion
line
or
half
litre
s or
qua
rter
litr
e•
pic
ture
s of
jugs
wh
ere
the
volu
me
is n
ear
to a
num
bere
d m
illili
tres
gr
adat
ion
lin
e Th
e ex
pect
atio
n
is t
hat
lear
ner
s on
ly r
ead
to t
he
nea
rest
num
bere
d gr
adat
ion
lin
e. T
he
desc
ribe
th
eir
volu
me
as a
lmos
t / n
earl
y/ c
lose
to/
a bi
t mor
e th
an/
mor
e or
less
/ or
ex
actl
y th
e n
umbe
r (o
f lit
res)
th
ey
read
off
th
e ju
g
CAPS Math Gr 2 TG.indb 46 2011/11/16 2:51 PM
47Study & Master Mathematics Grade 2 • Introduction
Cap
acity
/vol
ume
(con
tinue
d)N
o co
nve
rsio
ns
betw
een
mill
ilitr
es
and
litre
s re
quir
edN
o co
nve
rsio
ns
betw
een
mill
ilitr
es
and
litre
s re
quir
ed4
Peri
met
erIn
vest
igat
e th
e di
stan
ce a
roun
d 2D
sh
apes
an
d 3D
obj
ects
usi
ng
stri
ng
4A
rea
Inve
stig
ate
the
area
usi
ng
tilin
g
Dat
a h
and
lin
g5
Col
lect
an
dor
gan
ise
data
Rec
omm
end
ed:
Wh
ole
data
cyc
le to
mak
e ba
r gr
aph
Col
lect
an
d or
gan
ise
data
Col
lect
dat
a ab
out t
he
clas
s or
sch
ool
to a
nsw
er q
uest
ion
pos
ed b
y th
e te
ach
er. U
se ta
llies
to r
ecor
d da
ta in
ca
tego
ries
pro
vide
d.
Rec
omm
end
ed:
Re-o
rgan
ise
data
pro
vide
d in
a li
st o
r ta
lly o
r ta
ble
into
a b
ar g
raph
Col
lect
an
d or
gan
ise
data
Col
lect
dat
a ab
out t
he
clas
s or
sch
ool
to a
nsw
er q
uest
ion
pos
ed b
y th
e te
ach
er
Repr
esen
t dat
aRe
pres
ent d
ata
in•
tabl
e•
bar
gra
ph
Repr
esen
t dat
a in
bar
An
alys
e an
d In
terp
ret d
ata
An
alys
e an
d in
terp
ret d
ata
An
swer
que
stio
ns
abou
t dat
a in
bar
An
alys
e da
ta fr
om r
epre
sen
tati
ons
prov
ided
.Re
com
men
ded
• a
t lea
st 1
pic
togr
aph
• a
t lea
st 1
tabl
e
An
alys
e an
d in
terp
ret d
ata
An
swer
que
stio
ns
abou
t dat
a in
bar
An
alys
e da
ta fr
om r
epre
sen
tati
ons
prov
ided
.Re
com
men
ded
• a
t lea
st 1
pic
t ogr
aph
• a
t lea
st 1
tabl
e
CAPS Math Gr 2 TG.indb 47 2011/11/16 2:51 PM
CAPS Math Gr 2 TG.indb 48 2011/11/16 2:51 PM
49Study & Master Mathematics Grade 2 • Planning
Part 2 PlanningPlanning and organising your mathematics teachingThe Teacher’s Guide is an essential component of this series. It gives clear instructions on how to teach the concepts the learners need to master in Grade 2. It also provides guidance on how to use the Learner’s Book and Workbook so that learners can practise the concepts learnt.
Use this Teacher’s Guide as a starting point and then refer to the Learner’s Book and Workbook when the Teacher’s Guide instructs you to do so. For the Workbook activities the learners should write their answers in the Workbook. Provide the learners with sheets of paper or exercise books to complete their activities for the Learner’s Book.
In the Teacher’s Guide a section is dedicated to each concept the learners have to grasp. At the beginning of the content area (called “Modules” in the Learner’s Book) you will see the topics you are dealing with.
Allocation of teaching timeThe CAPS allocates teaching time for mathematics as follows:
• 10 weeks per term for 4 terms, with 7 hours for mathematics per week: 10 × 4 × 7 = 280 hours per year
• 5 lessons per week for 10 weeks each term• 1 lesson per day of 1 hour 24 minutes• Allow one week at the start of each term for orientation
and consolidation, to help children who have forgotten a lot of the content during the holidays.
• Allow a further week at the beginning of each term to consolidate concepts and knowledge that will be a baseline for the next phase of teaching and learning during the term.
• This leaves 4 terms of 8 weeks each with 5 lessons per week: 4 × 8 × 5 = 160 lessons.
• In the Foundation Phase about 3 lessons every week should be focused on Numbers, operations and relationships. The remaining 2 lessons can be used to focus on other content areas. Shape and space and Measurement will need more time than Data handling and Number patterns.
Resources in the classroomBesides the resources listed for each unit, you will need to have these items in your classroom at all times:
• number charts from 1–100 and 101–200• vertical and horizontal number lines• a counting frame• counters of the same colour and kind• counters of different colours• counting objects such as stones, blocks, beads, buttons,
bottle tops, pegs and sticks, ice-cream sticks, shells
CAPS Math Gr 2 TG.indb 49 2011/11/16 2:51 PM
50 Study & Master Mathematics Grade 2 • Planning
• number symbol cards (1, 2, 3, and so on)• number name cards (one, two, three, and so on)• ordinal number cards (first, second, third, and so on)• value cards• a set of Flard cards (expanding cards)• building blocks• modelling clay• chalk• crayons• koki pens• pencils• paper• newspapers• magazines• scissors• glue• Prestik• sticky tape• drawing pins• rulers• tape measures• a balance scale• thermometers• analogue clocks• old and new calendars• measuring jugs• height charts• boxes and containers of different shapes and sizes• spheres, balls, cones, cylinders and pyramids• squares, rectangles, circles and different triangles, all of
different sizes• other quadrilaterals, also pentagons and hexagons• empty containers, including bottles (plastic)• match boxes• empty toilet rolls• egg boxes or trays• string, wool, rope• paint• dice• playing cards,• mathematical games such as Ludo, dominoes, puzzles,
tangrams, snakes and ladders• climbing and balancing equipment• play money (notes and coins)• a play-shop with items that can be bought and sold.
Under the heading Learning experiences you will find a step-by-step breakdown suggesting what you should do to teach the concepts relating to each topic. Once the learners have understood the concepts, they can practise and reinforce what they have learnt by doing the activities in their Learner’s Books and the worksheets in the Workbooks.
CAPS Math Gr 2 TG.indb 50 2011/11/16 2:51 PM
51Study & Master Mathematics Grade 2 • Planning
Organising the daily mathematics periodAccording to the CAPS, ‘all the time allocated to mathematics on a single day should be considered as one period’. The daily mathematics period should include all of the following:
Whole class activity
• Mental mathematics• Consolidation of concepts• Classroom management (allocation of independent
activities, etc.)
Small group teaching
• Counting• Concept development (oral and practical activities)• Problem-solving (oral and practical activities)• Written recording of mathematical thinking• Developing calculating strategies (oral and practical
activities)
Independent work
• Learners practise and consolidate concepts developed in whole class and small group activities.
More details about these different aspects of daily classroom activity are given in the CAPS under Documents in this file.
Counting activities
Learners need to understand mathematics and therefore they need to experience it and make sense of it through their own thinking and doing activity. A learner’s understanding of numbers is the basis of his or her understanding of mathematics. Counting should therefore always be the starting point in mathematics, as it forms part of an essential process in the development of an understanding of number. Involve the learners daily in counting activities and encourage them to count as far as they can. At the same time, allow the learners to develop at their own pace and at their own level. Learners can do their daily counting activities individually, in pairs, in groups or as a class.
Learners need to go through different stages of progression to develop their understanding of number. Guide them to progress from one level of counting to the next. These levels are:
• Counting all numbers: The learners count all the numbers. When they add numbers they will start counting from 1 every time.
• Counting on: The learners count on from a given number. When adding numbers they will start counting from the given number and continue. For example, if the learners add 7 + 3 they will start counting from 7 and then count 8, 9, 10.
• Decomposing numbers: The learners break down numbers and develop their understanding of the value of numbers.
CAPS Math Gr 2 TG.indb 51 2011/11/16 2:51 PM
52 Study & Master Mathematics Grade 2 • Planning
They will know the number components (parts) of a number and therefore they will not have to count. For example, 4 and 3 are number components of 7.
In Grade 2 the learners should do counting activities every day. As part of these daily counting activities they should identify the numbers on the number chart or number lines and write the number symbols and the number names. Here are a few suggestions for activities:
Count concrete objects such as stones, blocks, beads, buttons, bottle tops, plastic bottle rings, pegs, sticks, match sticks, books, pencils, crayons, tables, chairs, windows, bricks, eyes, ears, feet, legs, hands, toes and fingers.
• Count counters.• Count things in pictures, magazines, books and
newspapers.• Count from 0–10.• Count from 0–15.• Count from 0–20.• Count from 0–50.• Count in ones from 0–80.• Count in tens from 0–100.• Count forwards.• Count backwards.• Count even numbers.• Count odd numbers.• Count from given numbers.• Count in twos.• Count in fives.
When doing counting activities make use of the number chart, number lines or a counting frame. Counting is not about memorising or chanting numbers, but about understanding numbers. The learners need to touch or move concrete objects when counting, or point to the numbers on the number chart or number lines.
Mental mathematics
The CAPS states that mental mathematics plays a very important role in the mathematics curriculum. Learners must know and be able to recall number bonds and multiplication table facts, as listed in the CAPS content area and topic tables for each grade at the back of this Teacher’s Guide. They must also use this skill in a range of skip counting and ‘chain’ calculation activities. Mental mathematics is an important part of the Counting and number concept sections relating to Number and patterns, and is also sometimes used in Measurement and Data handling activities.
When doing mental mathematics, it is important never to force the learners to do mental calculations that they cannot manage. They should have writing materials and/or counters available to help them with the calculations, if they can’t do them entirely by mental methods.
CAPS Math Gr 2 TG.indb 52 2011/11/16 2:51 PM
53Study & Master Mathematics Grade 2 • Planning
A teaching strategy that builds conceptual and social skills
The learning experiences in this course are designed for group work, pair work, individual work and for the whole class to do together. This cultivates an ethos of cooperation and working together. Letting learners work together is a very useful and successful teaching strategy. It helps the learners develop social skills such as cooperating in teams, taking turns, showing respect and responsibility, as well as listening and communicating effectively through interactive learning.
Helping learners overcome barriers to learning mathematics
Learners who experience barriers to learning mathematics should be given many opportunities for activity-based learning, to help them overcome their barriers at the pace that works for them. They should be given more time to do practical examples, using concrete objects and practical experiences, than other learners. Moving too soon to abstract work may make these learners feel frustrated, and lead to them losing any mathematical understanding and skills they have developed.
When organising daily classroom activities, allow more time for these learners to complete tasks, use their own strategies to develop their thinking skills, and do assessment activities. You may also need to reduce the number of activities you give to these learners, without leaving out any of the concepts and skills that need to be introduced and consolidated.
Suggested structure for a mathematics periodThe flow diagram on the next page presents a possible structure for a mathematics period. As suggested earlier, do counting activities with the learners daily. Learners can do these activities individually, in pairs, in groups or as a class. After the counting activities, do mat work to teach concepts (knowledge) and skills. You can do mat work with groups of four, six or eight learners, and the groups can be mixed groups or ability groups. The concepts taught in these learning experiences will cover topics in Content areas 1 to 5.
Keep in mind that you do not necessarily have to cover a whole topic on any single day. It might take your learners much longer to grasp a concept in that topic, and you can spread the learning experiences for the topic over a few days.
CAPS Math Gr 2 TG.indb 53 2011/11/16 2:51 PM
54 Study & Master Mathematics Grade 2 • Planning
Suggested f low for the mathematics periodTime allocation: Grade 2
Tidy up
±15 minutes
±10 minutes
±5 minutes
±1 hour
Whole class
Pairs
Groups
Individuals
CountingMental mathematics
Patterns: Numbers Shapes
DA
ILy
Whole class instruction/activity
On the mat
Concepts
Knowledge
Skills
Values
Remedial
Groups of 4, 6 or 8
Ability groups
Mixed groups
CAPS Math Gr 2 TG.indb 54 2011/11/16 2:51 PM
55Study & Master Mathematics Grade 2 • Planning
AssessmentThe purpose of assessment is to inform you, the learners and their parents or guardians about their performance. Assessment also serves as a tool for you to reflect on and analyse your own teaching practice, as this impacts on the learners’ performance. You can use your assessment to see whether you need to provide more opportunities for some or all of the learners to develop a particular skill or master a concept in a given topic.
You should develop a well planned process to identify, record and interpret the performance of your learners throughout the year, using both informal and formal assessment methods. Keep a record of the learners’ performance on assessment sheets, and summarise this information on a report form or card to give the learners and their parents or guardians at certain times of the year. You may photocopy the various assessment sheets provided in this Teacher’s Guide to use in your classroom.
Assessment methods
You can use various methods to assess the learners’ progress during the year. Any assessment method involves four steps:
• generate and collect evidence of learners’ achievement;• evaluate this evidence;• record your findings;• use this information to understand learners’ development
and help them improve the process of learning, and also to improve your teaching.
Before you undertake any assessment of learners’ work, decide on a set of criteria or standards for what they should be able to understand and do, and base your assessment on these criteria. It is important that you give the learners clear instructions on what you expect of them, so that they can complete the assessment tasks correctly and honestly. Once an assessment task has been completed, discuss your assessment with the learners and give them feedback to help them increase their ability to do the task successfully.
In the Foundation Phase assessment is a continuous process. In the course of the year, your continuous assessment plan should include informal and formal assessment. These are some of the methods you can use:
• Observation is your main assessment method for informal and formal assessment. Try to observe a few learners at a time. Select an observation sheet from the photocopiable assessment sheets in this Teacher’s Guide and record your observations for these learners. For informal assessment purposes you should also keep an observation book in which you record notes on each learner’s achievement in daily activities. For formal assessment, you will use checklists and rubrics to write down your observations while learners are performing set tasks.
CAPS Math Gr 2 TG.indb 55 2011/11/16 2:51 PM
56 Study & Master Mathematics Grade 2 • Planning
• Performance-based assessment consists of tasks in which learners must create, produce or demonstrate something. You need to assess both the process learners use to complete the task, and the end product they produce.
• Written work to be assessed can include worksheets and tests. A test is a written task completed individually by learners within a set time span. Tests should consist of questions and tasks similar to those that learners have already done in class, with the support of the teacher and other learners. A test should not include new types of questions or tasks that learners have not encountered before. w Standardisation exercises provided to schools should
not be used as tests in Grades 1 and 2, as they are not intended to assess individual learners; rather, their purpose is to help teachers reflect on their own teaching practice.
w Written assessments on their own don’t provide the teacher with enough information to understand why learners are making errors. These tests should therefore always be used together with observation and other informal assessment methods (such as interviews with learners) to find out what learners are thinking when they do a mathematics activity.
You should practise continuous assessment by monitoring all the written work done by learners. All written work should be kept as evidence of learners’ progress, and to identify their needs.
Further details are given below about informal and formal assessment methods specified in the CAPS.
Informal assessment
Informal assessment is done on a daily basis, as learners work on their learning activities. It should not be seen as a separate activity from learning and teaching.
Due to the fact that learners assimilate content at a varied pace makes it important that the educator continuously record informal assessments as learners interact with the content.
You can do this assessment by observing the learners as they work, by asking them to demonstrate a particular skill, or by talking to a learner about his or her thinking during an activity. Learners can also assess each other’s skills and understanding as they do a shared activity. This encourages them to reflect on their own performance and recognise where they need help.
The information you gather in this informal assessment need not be recorded, unless you find this useful. The results of this assessment are not counted for promotion purposes.
CAPS Math Gr 2 TG.indb 56 2011/11/16 2:51 PM
57Study & Master Mathematics Grade 2 • Planning
Formal assessment
Formal assessment consists of the tasks that you mark and formally record during the year for progression and certification purposes. These tasks are subject to moderation, to ensure that they maintain the appropriate quality and standards. Formal assessment provides you with a systematic way to evaluate how well the learners are progressing.
There are no examinations in the Foundation Phase. All formal assessment tasks are conducted using continuous assessment methods.
Examples of formal assessment tasks are: tests, practical tasks, projects, oral presentations, demonstrations, etc. At regular intervals the educator should conduct a formal assessment from extracts of the content that has been taught to and practiced by the learners.
Assessing learners who experience barriers to learning
Learners who experience barriers to learning should be given opportunities to demonstrate their competence in ways that suit their needs. You may have to consider using some or all of the following methods when assessing these learners:
• Allow these learners to use concrete apparatus for a longer time than other learners in the class.
• Break up assessment tasks (especially written tasks) into smaller sections for learners who have difficulty concentrating for long periods, or give them short breaks during the task.
• Learners who are easily distracted may need to do their assessment tasks in a separate venue.
• Use a variety of assessment methods, as some learners may not be able to demonstrate what they can do using certain types of assessment. For example, a learner may be able to explain a concept orally but have difficulty writing it down.
• In the Foundation Phase the inability to read should not prevent learners from demonstrating their mathematical competence.
Reporting learners’ performance
Reporting is the process of communicating learners’ performance to the learners themselves, and to parents and guardians, schools and other stakeholders. You can use report cards, parent meetings, school visitation days, parent-teacher conferences, phone calls, letters and other appropriate methods to make your reports.
Records of learner performance should provide evidence of the learner’s conceptual progression within a grade and her/his readiness to progress to the next grade.
Formal assessment is reported in all grades using percentages.
CAPS Math Gr 2 TG.indb 57 2011/11/16 2:51 PM
58 Study & Master Mathematics Grade 2 • Planning
The table below sets out the national codes and descriptors to be used for recording and reporting levels of competence in the Foundation Phase. You should also use comments to describe learners’ performance, as appropriate.
Table 5: Codes and descriptors for recording and reporting in Grades R–3
Achievement level
Achievement description Marks (%)
7 Outstanding achievement 80–1006 Meritorious achievement 70–795 Substantial achievement 60–694 Adequate achievement 50–593 Moderate achievement 40–492 Elementary achievement 30–391 Not achieved 0–29
CAPS Math Gr 2 TG.indb 58 2011/11/16 2:51 PM
59Study & Master Mathematics Grade 2 • Planning
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Teacher assessmentTask
Date Learners Observations
Photocopiable sheets
CAPS Math Gr 2 TG.indb 59 2011/11/16 2:51 PM
60 Study & Master Mathematics Grade 2 • Planning
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Teacher assessment
Learner:
Date Observations and comments
CAPS Math Gr 2 TG.indb 60 2011/11/16 2:51 PM
61Study & Master Mathematics Grade 2 • Planning
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Teacher assessmentTask:
Learners exceptional competence
progress is fast
progress is consistent
progress is slow
unable to do task
CAPS Math Gr 2 TG.indb 61 2011/11/16 2:51 PM
62 Study & Master Mathematics Grade 2 • Planning
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Parent/guardian assessment
Date:
I am assessing the work of:
Please tick (3) yes no
He/she struggled.
He/she understood what to do.
He/she could work on his/her own.
He/she needed my help.
He/she completed the task.
Any other comments:
Signature:
CAPS Math Gr 2 TG.indb 62 2011/11/16 2:51 PM
63Study & Master Mathematics Grade 2 • Planning
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Parent/guardian assessment
Date:
I am assessing the work of:
Comments:
Signature:
CAPS Math Gr 2 TG.indb 63 2011/11/16 2:51 PM
64 Study & Master Mathematics Grade 2 • Planning
CAPS Math Gr 2 TG.indb 64 2011/11/16 2:51 PM
65Study & Master Mathematics Grade 2 • Content area/Module 1
Part 3 Lesson-by-lesson
Content area/Module 1Numbers, operations and relationships
1 CountingLearning experiences
Lesson focus
• Do counting with the learners as a whole class or with small groups on a mat. Use a variety of concrete objects and counters, such as buttons, sticks, stones, and so on.
• Vary the daily counting:w Count from number charts or the number line and
identify the numbers.w Count forwards or backwards in ones, tensw Count forwards or backwards from a given numberw Skip-count in multiplesw Count odd or even numbersw Count objectsw Count objects in a picturew Count four people or five animals from a magazinew Draw ten balls and five batsw Heap up counters and count in groups, e.g. in twos, fives,
tens, fifteens.• Do one counting exercise each day. Refer to the Counting
term planning schedule to see how the learners should progress in the number range.
Give the learners practice in counting by doing:Learner’s Book: Module 1, Activities 1–8 Workbook: Worksheets 1–3
Skillscounting, reading, matching and recognising
Resourcesnumber chart; number line; counters; concrete objects such as sticks or buttons; crayons; pencils; paper
Conceptscounting
Vocabularycount, forwards, backwards, more, less, before, after, between
CAPS Math Gr 2 TG.indb 65 2011/11/16 2:51 PM
66 Study & Master Mathematics Grade 2 • Content area/Module 1
2 Number names and symbolsLearning experiences
Lesson focus
• The learners work in pairs on a mat. • Ask the learners to compare numbers. For example, ask:
Which number is more than . . . ? Which number is less than . . . ? Which number is bigger than . . . ? Which number is smaller than . . . ? Which number is between . . . and . . . ? Which number comes before . . . ? Which number comes after . . . ? Let the learners identify the numbers on the number chart each time.
• The focus in this lesson is on larger numbers and their number names. Revise the concepts of more and less from Grade 1.
• Give each pair of learners an envelope with number symbol and number name cards in it. The numbers should be in groups of ten and range from 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90 and 90–100.
• The pairs read the number symbols and the number names and match them. They must put the cards in sequence, and then write the number symbols and the number names in the correct order.
• The learners put the cards back into the envelopes and swap with another pair. They follow the same procedure with the second set of number symbols and name cards.
Give the learners practice in number symbols and number names by doing:Learner’s Book: Module 1, Activities 9–11 Workbook: Worksheets 4–5
• Learners will not be able to complete all these activities in one lesson. They can complete some tasks for homework or during group work in the next lesson. Discuss the instructions for each activity with the learners so that they understand what to do.
Skillscounting, writing, reading, matching and recognising
Resourcesnumber chart; number line; counters; concrete objects such as sticks or buttons; envelopes or small packets or boxes with number symbol and number name cards ranging from 20–100; crayons; pencils; paper
Conceptsnumber
Vocabularynumber names from 34 to 100, more, less, before, after
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 66 2011/11/16 2:51 PM
67Study & Master Mathematics Grade 2 • Content area/Module 1
3 Comparing and orderingLearning experiences
• Set up four work areas beforehand.
Lesson focus
Work area 1• Prepare a set of greater than and less than symbol cards, a
set of number symbol cards and a set of number name cards for each work area.
• Place each group of cards face down in this order: number, symbol and number name.
• Learners take turns to choose a card from each group, read it aloud and state if it is true or false, for example: 145 < eighty is false.
Work area 2• Prepare a set of before and after cards, a set of number
symbol cards (with an order range of e.g. 320 to 340), a set of number name cards and sheets of paper with before, after and between written on them.
• Place the cards face down in their sets.• Learners take turns to choose a card from each group of
cards and place them in the correct column on the before, after and between sheets.
• Let the learners move the cards around until they have the correct answer.
Work area 3• Prepare a set of number cards and these instruction cards:
w Arrange from the biggest to the smallestw Arrange from the highest to the lowestw Arrange from the smallest to the biggestw Arrange from the lowest to the highest
• The group chooses one instruction card at a time and arranges the numbers accordingly.
• They repeat the activity for all the instruction cards.
Work area 4• Prepare a set of more and less cards (i.e. 10 more, 20 more,
50 more, 100 less, 40 less, 30 less), a set of number cards and sheets to write on.
• The learners choose a number card and a more and less card. They write their answers on the sheet provided.
• The group discusses the answer and then passes the sheet to the next learner.
• The learners continue until all the number cards have been done.
• Make four groups of four learners to work in the work areas.
Skillscounting, reading, matching, recognising
Resourcesnumber chart; number line; counters; concrete objects such as sticks or buttons; envelopes or small packets or boxes with number symbol and number name cards ranging from 20–100; crayons; pencils; paper
Conceptsordering, greater than, less than, bigger, higher, smaller, lower
Vocabularygreater than, less than, before, after, between, larger, smaller, highest, lowest
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 67 2011/11/16 2:51 PM
68 Study & Master Mathematics Grade 2 • Content area/Module 1
• Allow each group 15 minutes at the most at each work area. Give each group a turn at all the work areas.
• Move around the groups and give help where necessary. • The remainder of the class do activities from the Learner’s
Book and Workbook.• Make sure that each learner has a turn at each work area.
Give the learners practice in comparing and ordering numbers by doing:Learner’s Book: Module 1, Activities 12–15 Workbook: Worksheets 6–7 and 22–24
CAPS Math Gr 2 TG.indb 68 2011/11/16 2:51 PM
69Study & Master Mathematics Grade 2 • Content area/Module 1
4 FractionsLearning experiences
Lesson focus
• Divide the learners into pairs and give each pair a slice of bread, fruit or a sheet of paper. Ask them to talk about how they could share the object so that each one has an equal piece. Give them time to discuss the problem and to decide what should be done and how.
• Make sure the learners understand that two halves are equal parts of a whole and should therefore be the same size. If one piece is bigger or smaller, it is not a half; it is just a piece.
• Let each pair cut their slice of bread, fruit or paper in half using a plastic knife. Point out that they now each have half a slice of bread. Ask them how many halves they have in total, and whether they are the same size. Ask learners: How many halves do you get from one whole?
• Then ask the learners how many halves they would get from five slices of bread. Encourage them to work out the solution with their partners.
• Give each learner an envelope with cut-out shapes (see photocopiable page 111 at the back of this book). They take out one shape and halve it by folding it in half. Show the learners how to fold and then unfold the shape. Ask them how many halves they see. They colour in one half of the shape. Write the fraction on the board.
• The learners take another shape and halve it by first folding it, and then drawing a line down the fold, and finally cutting the shape in half.
• Ask them how many halves they have, and how they know that each piece is a half. Encourage the learners to give their own explanations. Make sure they understand that both parts are equal. Let them colour one half of the shape blue and the other half yellow.
• Ask the learners how many halves they would get from two circles and from four circles. Learners who do not know the answer should work it out practically.
• Give the learners two sheets of paper. They fold one sheet in half, unfold it and draw a line down the fold. Ask them how many halves they have. They cut the sheet in half so that they have two halves.
• Ask the learners to fold the other sheet of paper in half as they did for the first. They then fold the half in half again. Let them unfold the paper and draw a line on the new fold. Ask them how many parts they see, and whether they are equal.
• Say that each part is called a quarter. Write the fraction on the board. Say that it means one equal part of four parts. Ask the learners to count the number of quarters they have. They write the fraction on each quarter. Then ask them to colour in a quarter red and two quarters green. Ask how
Skillsidentifying, problem-solving, explaining, drawing, communicating
Resourcesnumber chart; number line; number cards; counters; concrete objects; bread; fruit; plastic knives; cut-out cardboard or paper shapes (see page 111) envelopes or packets; crayons; pencils; paper; scissors
Conceptshalves, quarters, equal
Vocabularyhalf, quarter
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 69 2011/11/16 2:51 PM
70 Study & Master Mathematics Grade 2 • Content area/Module 1
many quarters they have coloured in, and what fraction is not coloured in. Let them cut out their quarters.
• Ask how many quarters fit into a half, how many quarters fit into a whole, and how many halves fit into a whole. They do this practically using their cut-out halves, quarters and whole shapes.
• Divide the learners into pairs. Give each pair a set of counters. One learner in each pair takes four counters and gives half of them to a partner. Ask how many counters they each have. Point out that half of 4 is 2. They repeat the activity a number of times using different numbers of counters.
Give the learners practice with fractions by doing:Learner’s Book: Module 1, Activities 16–17 Workbook: Worksheets 8–14
CAPS Math Gr 2 TG.indb 70 2011/11/16 2:51 PM
71Study & Master Mathematics Grade 2 • Content area/Module 1
5 Place valueLearning experiences
Lesson focus
• The learners work in groups on a mat. Ask them to take ten sticks each. Explain that they are going to exchange their ten loose sticks for one whole ten. Show them how to tie an elastic band around the ten loose sticks to make one whole ten. Explain that they now have 1 ten. Show the number card 10 and point to the one (meaning one 10) and to the zero (meaning no or zero ones).
• The learners work in pairs. Ask how many tens each pair has. Explain that two tens are equal to 20, meaning two tens and zero ones. Show the number card 20.
• Let learners repeat the activity by having one learner join each pair until the group has nine tens. Put down the number card each time.
• Ask the learners to choose any number between 10 and 20. Encourage them to think carefully about how many tens and how many ones there are in the number they have chosen. Give them time to do this before asking individual learners to explain their numbers.
• Use the number cards to help the learners, for example, 15 is one ten and five ones, or 10 + 5. Show the number cards 10 and 5, and put the 5 over the 0.
• Ask the learners to choose any number between 10 and 99. They use the sticks and the number cards to explain and write out the number, for example:
Give the learners practice in place value by doing:Learner’s Book: Module 1, Activities 18–28 Workbook: Worksheets 15–21
Skillscounting, recognising, explaining
Resourcesnumber chart; number line; number cards; counters; concrete objects; number cards for 100, 10 and 1; 100 sticks (ask the learners to each bring a few sticks to class); elastic bands; interlocking cubes; blocks; crayons; pencils; paper
Conceptsplace value
Vocabularyhundreds, tens, ones
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
10 4010 + 51 ten + 5 ones
40 + 34 tens + 3 ones5 3
CAPS Math Gr 2 TG.indb 71 2011/11/16 2:51 PM
72 Study & Master Mathematics Grade 2 • Content area/Module 1
6 Problem-solvingLearning experiences
Lesson focus
• The learners work in groups of four on a mat. Give each group a problem written on a card or a large sheet of paper. For example:
Nina has 15 cents. Anne gives her 9 cents more. How many cents does Nina have altogether?
Xoli has 50 cents. He buys an orange for 25 cents. How much money does he have left?
• The groups read their problem at least once (two or three learners in each group could take turns to read the problem aloud) and then discuss it. They need to interpret the problem and understand what it is about.
• Encourage each learner to draw a picture of their own interpretation and understanding of the problem.
• Group members then take turns to explain how they think the problem can be solved – that is, what operation they will use and how they will do the problem.
• Ask them to estimate the answer and to write it down.• Learners then work out the problem on paper using their
own methods. They describe how they reached their solutions. Group members check each other’s solutions to make sure they are correct.
• Encourage the learners to compare their answers to the estimated answer and talk about the different methods that were used by the learners in their group.
• Repeat the activity with more problems.• It is important for the learners to: (1) read the problem,
(2) draw a picture of their interpretation and understanding of the problem, (3) solve the problem using their methods, (4) explain how they came to their solutions, and (5) check their solutions to the problem, as well as the solutions of their peers. Expose learners to different kinds of problems.
• Do problem-solving activities daily to give the learners enough opportunity to develop their problem-solving and reasoning skills. Try to give the learners one word problem to solve each day. Introduce different types of problems gradually to prevent confusion and a dislike or fear of word problems.
• If the learners can’t read well or struggle to understand and interpret story sums, help them by integrating reading in the Mathematics lessons. Write out the word problem on a large sheet of newsprint and put it up in the classroom. Select specific vocabulary from the word problem (for example, altogether, each, same, share, sweets, marbles, bananas, names) and make flashcards. Teach these words to the learners. Put them up in the classroom for the learners to read at any time during the day. Use these same words to formulate more word problems, and slowly introduce new words.
Skillscounting, reading, interpreting, problem-solving, estimating, calculating, explaining, communicating, reasoning, logical thinking, checking, cooperating in a group, taking turns
Resourcesnumber chart; number line; number cards; counters; concrete objects; crayons; pencils; large sheets of paper such as newsprint; calculators; cards with word problems
Conceptsaddition, subtraction, equal sharing, grouping, multiplication
Vocabularyrands, cents, total cost, change, calculate, check, solve, solution
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 72 2011/11/16 2:51 PM
73Study & Master Mathematics Grade 2 • Content area/Module 1
• Encourage the learners to write their own word problems too. Let them look at pictures and talk about what they think is happening. Help them to write appropriate words to label items in pictures. Ask each learner to write a word problem based on a picture. They should use the labels to help them.
• Let the learners read their problems aloud to their groups. The learners work out the problems on paper, using their own methods. Ask them to describe to their groups how they reached their solutions. Group members should check each other’s solutions to make sure they are correct. If there is time, let the learners swap and solve each other’s word problems.
• Repeat the activity using other pictures.
Give the learners practice in problem-solving by doing:Learner’s Book: Module 1, Activities 29, 30, 38, 41, 53, 54, 62–69Workbook: Worksheets 25, 26, 37, 38, 39, 43 and 48
CAPS Math Gr 2 TG.indb 73 2011/11/16 2:51 PM
74 Study & Master Mathematics Grade 2 • Content area/Module 1
7 CalculationsLearning experiences
Lesson focus
Addition• Divide the learners into pairs and give each pair a set of the
cards you prepared for this lesson. Your cards should look like this:
15 + 8 23 Front Back
• Ask the learners to shuffle the cards. One learner in each pair then takes a card and shows it to the partner. The partner works out the answer in their head. If the partner answers correctly the card goes back into the deck, and if they answer incorrectly they keep the card.
• Learners take turns to show a card and work out the answer. At the end of the game each learner takes the cards they answered incorrectly and works out the correct answers using counters and objects. Ask them to draw and write out the problem.
• Divide learners into groups of four and give each group two or three dice. Ask them to take turns to throw the dice and add the numbers. The learner throwing the dice works out the answer in their head. The other three learners check to confirm if the answer is correct. If the answer is incorrect, another learner in the group can answer.
• You could use wooden blocks to make your own dice and write the numbers with a koki pen.
• The learners remain in groups of four. Give each learner five blank cards and ask them to write a one-digit number on each card. Then ask them to place all the cards face down in the middle of the group. The learners take turns to pick up any two cards. The learner who picks up the cards should add the two numbers in their head.
If the answer is correct they keep the cards and if incorrect another learner in the group can give the correct answer and keep the cards. At the end of the game the learner with the most cards wins.
• You could add another set of blank cards on which the learners write two-digit numbers. Combine both sets of cards, shuffle them, and then place them face down and start the game over.
• Give the learners plenty practice with adding small numbers before moving on to bigger numbers. It is difficult to count out concrete objects for bigger numbers, so allow the learners to work out the answer in the way they are
Skillscounting, recognising, calculating, problem-solving, estimating, communicating, explaining, reading, reasoning, logical thinking, critical
Resourcesnumber chart; number line; number cards; counters; concrete objects; crayons; pencils; paper
Conceptsaddition
Vocabularycalculation, calculate, add, equals, solve, solution, estimate, check
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 74 2011/11/16 2:51 PM
75Study & Master Mathematics Grade 2 • Content area/Module 1
most comfortable. Allow them to use paper, place value cards, and so on, to help them. For example:
84 + 11 = 95 8 + 1 and 4 + 1
Give the learners practice with addition by doing:Learner’s Book: Module 1, Activities 31–37 Workbook: Worksheets 27–33
Learning experiences
Lesson focus
Subtraction• Prepare flashcards for the words take away, minus and
subtraction and for the subtraction sign (–) and the addition sign (+).
• Ensure that each learner has a few counters, for example, stones, buttons, matchsticks or bottle tops.
• Ask each learner to count 20 counters and place them in front of them in a straight line. They point to each counter and count aloud. Now ask the learners to count eight counters and to keep them in their hands. They then count the remaining counters on the desk. Ask the learners to check their partner’s counters. Ask learners to explain what they think was done with the counters? Explain that they had 20 counters on the table, they took eight away by keeping them in their hands and had 12 left on the desk. Now show the flashcards with the words subtraction, take away and minus one at a time, allowing the learners to read the words after you. Explain to the learners that they have now done a subtraction problem. Show the learners the flashcard with the subtraction sign. Explain that this is the sign we use for subtraction problems. Show the learners the flashcard with the addition sign on it and see if they can identify it. Place the two flashcards next to each other and ask the learners to explain the difference (for example, one is a cross and the other is a straight line).
• Draw the problem on the board and write the number sentence below it:
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
20 – 8 = 12 • Point to the number sentence and read it aloud. Remind
the learners what the equals sign (=) means. Ask learners to read the problem aloud. Do a few more examples with learners using their counters. Let learners check each other’s counters. Now draw and write each number sentence, and then ask the learners to read each part as you point to it.
• Ask learners to work in pairs. They combine their 20 counters and put them in a line in front of them. Ask them to point to each counter and count aloud. Ask the learners to construct a problem with their counters on the board.
Skillsproblem-solving, explaining, calculating, communicating, working with numbers
Resourcesnumber chart; number line; number cards; concrete objects; flashcards; crayons; pencils; paper
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
Conceptssubtraction
Vocabularysubtract, minus, take away, equals, solve, solution, calculate, difference, check
CAPS Math Gr 2 TG.indb 75 2011/11/16 2:51 PM
76 Study & Master Mathematics Grade 2 • Content area/Module 1
• Draw and write the number sentence for all the counters: 20 + 20 = 40 • Ask the learners to read the problem aloud. Get one learner
in each pair to take back their counters. Ask learners to explain what has happened. Guide the learners towards their answer. First, they add their 20 counters together to make 40 (addition sum) and then take away 20 from 40 to get 20 (subtraction problem). Ask one pair of learners to draw the problem on the board.
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
• The learners write the number sentence 40 – 20 = 20.
Give the learners practice in subtraction by doing:Learner’s Book: Module 1, Activities 39–40, 70–75 Workbook: Worksheets 34–36
Learning experiences
Lesson focus
Multiplication• To teach the concept of grouping/equal amounts, select
eight learners to stand in front of the class in a straight line, shoulder to shoulder and facing the class. Point at them one at a time and ask the seated learners to count aloud the number of standing learners. Ask the standing learners to arrange themselves into four equal groups.
• Ask the seated learners to think of and discuss a solution among themselves, but not to help the standing learners. If they do not find the correct solution, ask the learners to repeat the original instruction. Give the seated learners an opportunity to give suggestions. Emphasise the four groups, so start with four learners in separate areas. Then ask the four remaining learners to hold the hand of one of the other four learners. Guide the learners to understand that we can only work with what we are given. That is why we started with four separate groups and then added to them in equal parts. Ask learners what the number was, how many groups there are and how many in each group.
● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● • Get different learners to repeat the exercise. Help any
learners who have difficulty with the concept. Explain that equal means the same as. When they seem familiar with the concept, ask the standing learners to arrange themselves into two equal groups. Allow the seated learners to give opinions and suggestions. Guide the learners by arranging the standing learners into two groups of four. Ask learners what number you used, how many groups there are and how many in each group.
● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ●
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
Skillsproblem-solving, logical thinking, explaining, calculating, cooperating in a group
Resourcesnumber chart; number line; number cards; counters; concrete objects; crayons; pencils; paper; flashcards
Conceptsgrouping
Vocabularygroup, same, equal amounts, divide
CAPS Math Gr 2 TG.indb 76 2011/11/16 2:51 PM
77Study & Master Mathematics Grade 2 • Content area/Module 1
• Take the learners outside and divide them into teams of 10. Ask the teams to discuss the solution within the team before rearranging themselves. Ask the learners to get into two equal groups. There should be a few extra learners who do not fit into any team; keep them as your assistants and checkers. Make sure that the teams are grouped into two groups of five. Ask learners what number they used, how many groups there are and how many in each group.
● ● ● ● ● ● ● ● ● ●
● ● ● ● ● ● ● ● ● ● • Go back inside and ask each learner to count six counters
and to place them in a row in front of them. Ask the partners to check that they have the correct number of counters. Ask learners to make three equal groups. Get partners to verify each other’s work. There should be three groups of two; circulate, help and guide where required. Ask learners what number they used, how many groups there are and how many in each group.
• Explain that if we count the groups of two, we get six. Write the number problem 2 + 2 + 2 = 6 on the board. Tell the learners to read it aloud. Once again, ask learners what number was used, how many groups there are and how many in each group. Draw this example on the board. Get the learners to write the example in their exercise books:
● ● ● ● ● ●
● ● ● ● ● ● 2 + 2 + 2 = 6 • Explain that we can do this activity with 3s, 4s, 5s, and
so on. Repeat the activity with different numbers to give learners plenty practice at this skill.
• Work with small groups to identify any confusion or misconception that the learners may have on the grouping concept.
Give the learners practice in multiplication by doing:Learner’s Book: Module 1, Activities 47–52 Workbook: Worksheets 37–40
Note: Multiplication and division go hand in hand. It is important for the learners to master these operations. Make sure the learners understand multiplication well so that they can master division.
Learning experiences
Lesson focus
Dividing equally• Divide the learners into groups. Give each group a
container and a set of counters.• To teach the concept of dividing equally (equal amounts/
groups of equal amounts), ask each learner to take, say, 20 counters. It does not matter if they have the wrong number
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 77 2011/11/16 2:51 PM
78 Study & Master Mathematics Grade 2 • Content area/Module 1
of counters the first time. If they do, repeat the instruction and explain that each learner in the group must have the same number of counters (20). Give them time to regroup and recount their counters.
• Ask the learners to divide their 20 counters into five equal piles. Explain that each pile must have the same number of counters.
• Ask the learners how many counters they have in each pile (4).
• Explain that we can say: 20 divided by 5 equals 4. Then say: ‘We can write it like this: 20 ÷ 5 = 4.’
• Ask the learners to draw the 20 counters, then the five equal piles and then to write out the problem and the answer. Their sums may look like this:
20
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
142
43 ●●●●●●●●●● 4 4 4 4 4
20 ÷ 5 = 4
• The learners also need to be able to identify that 4 × 5 = 20.• The learners must understand that division is the opposite
of multiplication. • Ask the learners to take 20 counters and divide them
equally into four piles. Let them tell you how many counters in each pile. Let them say the problem and the answer.
• They now draw the whole, the equal parts and then write the problem with the answer.
• Say to the learners: ‘We can also write out the dividing problem like this:’
4 5 20
• Repeat the activity with more numbers to divide equally. Ask the learners to put out the counters, then to draw and write the problems with the answers.
• Encourage the learners to explain how they did their problems and got their answers.
• Give the learners division problems to work out in the same way. You could write the word problems on cards and give each group a card to solve, after which they can explain how they found their answer.
• Make sure the learners understand the process well before working with bigger numbers that need to be broken down.
Give the learners practice in dividing equally by doing:Learner’s Book: Module 1, Activities 55–59 Workbook: Worksheets 41–48
Skillscounting, identifying, drawing, explaining, cooperating in a group
Resourcesnumber chart; number line; counters; concrete objects; crayons; pencils; paper
Conceptsdividing, sharing
Vocabularyequal, equally, share, divide
CAPS Math Gr 2 TG.indb 78 2011/11/16 2:51 PM
79Study & Master Mathematics Grade 2 • Content area/Module 1
8 Doubling and halvingLearning experiences
Lesson focus
• Divide the learners into pairs and give each pair counters in a container. One learner in each pair takes out a few counters and says how many they have taken out. The second learner takes out the same number of counters.
• Point out that each pair of learners has two numbers that are exactly the same. Tell the learners that when we have two numbers that are exactly the same, we say the number is double. Write the word double on the board. Explain that double means two of the same number, or the same number times two. Ask the pairs to work out the total of their two numbers.
• The learners complete this word sentence for their number of counters: Double . . . is . . . .
• Each pair of learners now takes out 15 counters and then doubles the number of counters. Explain that double 15 is 30. This is the same as 15 + 15 = 30, or 15 × 2 = 30. The learners draw the number of counters they took out and write the word sentence (double 15 is 30) and the number sentences 15 + 15 = 30 and 15 × 2 = 30.
• The learners take more counters to double their number. They draw and write the new problem. They must be able to identify the pattern and recognise that doubling is adding the same number or multiplying it by 2.
• Learners can also practise doubling with dice. They take turns to throw the dice and double the number.
• While developing the concept of doubling, the learners need to practise halving. Halving is taking away the same number. For example, tell the learners to take out 10 counters, and then to halve the number. They should take away five counters. Ask them what half of 10 is. Let the learners draw a picture. Then show them how to write ‘half of 10 is 5’.
• The learners repeat the halving activity with numbers of their choice. They should be able to double a number and halve it.
Give the learners practice in doubling and halving numbers by doing:Learner’s Book: Module 1, Activities 60–61 Workbook: Worksheets 49–51
Skillsidentifying, problem-solving, explaining, drawing, counting, communicating, cooperating with others
Resourcesnumber chart; number line; number cards; counters; concrete objects; containers such as margarine tubs; crayons; pencils; paper
Conceptsdouble, half of
Vocabularydouble, half of, halve
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 79 2011/11/16 2:51 PM
80 Study & Master Mathematics Grade 2 • Content area/Module 2
Contents area/Module 2 Patterns, functions and algebraIn this module we have set out activities for you to choose from. The pattern activities provided in the Learner’s Book and Workbook are not meant to be done in isolation, but as a part of the Mathematics lessons.
Patterns provide a means for developing manipulation skills. They also teach learners how to investigate, sequence and analyse to help them make sense of a situation. Patterns enable the learners to see relationships and use mathematical language to communicate those relationships. Working with patterns also sets a basis for generalising, drawing conclusions and for problem-solving. These are all important processes in mathematics.
In this module you will be given step-by-step guidelines on how to teach the concepts covered in this module.
1 Number patternsLearning experiences
Lesson focus
Copy, extend and describe number patterns• Put out number cards to form a simple number pattern.
2 4 6 8 10 or
• • • •• • • • •• • • • • • •• • • • ••••••••••
• Ask the learners to identify the patterns.• Let them talk about the two patterns – what is different,
what is the same.• Ask them to copy the pattern onto a sheet of paper.• Repeat the process by doing more number patterns.• Next put out only the start of a number pattern.
1 3 5
or
• •• •
• ••• •
• Ask the learners to identify the pattern by looking at given numbers at the beginning of the pattern.
• Let them talk about the pattern and describe it.• Ask them to complete and extend the pattern.• Let them do the patterns on a sheet of paper.
Skillsdescribing, identifying, recognising, sequencing, creating, drawing, copying, interpreting, analysing, observing, explaining, thinking
Starting offDo a variety of counting activities with the class.
Resourcesnumber chart; number line; number cards; counters; concrete objects; beads; blocks; cut-out shapes from the back of this book (pages 111–113); sticks; matches; crayons; pencils; paper; scissors
CAPS Math Gr 2 TG.indb 80 2011/11/16 2:51 PM
81Study & Master Mathematics Grade 2 • Content area/Module 2
Create own number patterns• Have the learners work in groups on a mat. Ask them to use
their number cards and the counters to create their own patterns.
• Encourage them to put out the cards or counters in building their own patterns.
• Have them look at the different patterns and describe each pattern to the group.
• Let them draw or write their own patterns on a sheet of paper.
Create own patterns• Divide the learners into pairs. Give each pair a variety
of objects and ask them to create their own patterns. Encourage them to talk about and describe their patterns as they create them.
• Let the learners draw their patterns and colour them in.
Give the learners practice with patterns by doing:Learner’s Book: Module 2, Activities 3–5, 10 Workbook: Worksheets 54–56
Conceptspattern
Vocabularycopy, sequence, complete, describe
CAPS Math Gr 2 TG.indb 81 2011/11/16 2:51 PM
82 Study & Master Mathematics Grade 2 • Content area/Module 2
2 Geometric patternsLearning experiences
Lesson focus
• Arrange beads or shapes into a specific pattern. Make sure all the learners can see the pattern.
• Give each learner a selection of beads or shapes similar to the ones you used. Ask them to copy your pattern by arranging their beads or shapes in the same way you did.
• Encourage them to talk about the pattern and to discuss the colours, the shapes, the objects, the sizes and the flow of the pattern. Ask them to describe how they arranged the pattern, in other words, the sequence.
• Let the learners draw the pattern on a sheet of paper and colour it in.
• Learners should always first copy patterns practically, using concrete objects.
• Arrange beads, shapes, blocks or matchsticks to start a pattern that has a specific sequence, but leave the pattern incomplete. Make sure all the learners can see the pattern.
• Work with the class as a whole. Encourage the learners to talk about the pattern’s sequence by asking questions like: What shape is first in the sequence? What shape comes next? What colour does the pattern begin with?
• Now ask a few learners to complete the pattern you started.• Encourage them to talk about and describe the pattern as
they are building.• Once they have built a few repetitions of your pattern, the
learners draw the completed pattern and colour it in.
Patterns all around us• The learners work in groups.• Take the learners outside and ask them to find a leaf or a
flower petal.• When the learners are back in the classroom, divide them
into groups of four.• Ask each learner to examine their leaf or petal carefully
and to take note of the pattern, shape, colour, size and the texture.
• Now ask the learners to show and describe their leaves and flower petals to their group.
• Each learner has a turn. • Explain that they will be making leaf patterns or flower
patterns. • Tell them to put their leaf/flower petal flat on a sheet of
paper and then to place another sheet of paper over it.• Show learners how to colour the top sheet of paper lightly
with a crayon until the pattern of the leaf/flower petal underneath starts showing through.
Skillsdescribing, identifying, recognising, sequencing, creating, drawing, copying, interpreting, analysing, observing, explaining, thinking
Starting offDo a variety of counting activities with the class.
Resourcesnumber chart; number line; number cards; counters; concrete objects; beads; blocks; cut-out shapes from the back of this book (pages 111–113); sticks; matches; crayons; pencils; paper; scissors
Conceptspattern
Vocabularycopy, sequence, complete, describe
CAPS Math Gr 2 TG.indb 82 2011/11/16 2:51 PM
83Study & Master Mathematics Grade 2 • Content area/Module 2
• Encourage the learners to talk about their leaf patterns and to compare them to real ones.
• Display their work in the classroom.
Give the learners practice with patterns by doing:Learner’s Book: Module 2, Activities 1–2 and 6–9 Workbook: Worksheets 52–53 and 57–59
CAPS Math Gr 2 TG.indb 83 2011/11/16 2:51 PM
84 Study & Master Mathematics Grade 2 • Content area/Module 3
Contents area/Module 3Shape and spaceEach of the following units gives you step-by-step guidelines on how to teach the concepts covered in this module.
1 Describing positionLearning experiences
Lesson focus
• Divide the learners into pairs and give each pair one or two objects. Ask one learner in each pair to place the object in a specific position. The other learner must describe the object’s position. Learners should take turns to place the object and to describe its position. For example, the shoe is on top of the desk, or the book is behind the cupboard.
• Now ask one learner in each pair to tell their partner to move to a specific position in the classroom. For example: Stand behind the door. Sit on the chair. Stand next to the cupboard. After following the instruction, the partner must describe their position. Learners should take turns to give and follow instructions.
Give the learners practice in describing position by doing:Learner’s Book: Module 3, Activities 16–18 Workbook: Worksheets 70–72
Skillsfollowing instructions, listening, describing, taking turns
Resourcesnumber chart; number line; number cards; counters; a variety of concrete objects; crayons; pencils; paper
Conceptspositional relationships
Vocabularynext to, underneath, middle, in front, under, top, bottom, left, right, behind
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 84 2011/11/16 2:51 PM
85Study & Master Mathematics Grade 2 • Content area/Module 3
2 Position and viewLearning experiences
Lesson focus
• Divide the learners into pairs. Ask each pair to choose an object.
• Ask the learners in each pair to take turns to look at and draw their object from different positions. For example, they draw what they see when they view the object from the top, the bottom, the side, the front, from behind, the left and the right. Each time they should describe what they see to their partners. If there is time, the learners could do this with more than one object.
Give the learners practice in position and views by doing:Learner’s Book: Module 3, Activities 13–15 Workbook: Worksheets 68–69
Skillsobserving, describing, drawing, labelling, cooperating with others, taking turns
Resourcesnumber chart; number line; number cards; counters; concrete objects; a variety of 3-D objects, for example, washing powder boxes, cool drink cans, books; crayons; pencils; paper
Conceptsrecognising 3-D objects and position
Vocabularyin front, behind, on top, bottom, under, left, right, side
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 85 2011/11/16 2:51 PM
86 Study & Master Mathematics Grade 2 • Content area/Module 3
3 Position and directionsLearning experiences
Lesson focus
• Play the game Hide and seek.• Select one object which will be used as the hidden object.• Ask one learner to leave the classroom and wait outside the
door.• The rest of the class remains and sees where the object
will be hidden. Everyone should know the position of the object as they will be giving directions to the learner who is to find it.
• Call the learner to come inside.• Tell the learner to listen to the directions and to find the
hidden object.• The other learners have turns to give directions to help the
learner find the hidden object.• Once the hidden object is found, that learner describes the
position where the object was fouind.• Another option would be to blindfold the learner and then
to help him or her find the object with directions on where to move.
• When giving directions, the learners should use words such as left, right, turn right, turn left, walk straight ahead, opposite, backwards, forwards.
Give the learners practice in directions by doing:Learner’s Book: Module 3, Activities 19–21
Skillsfollowing instructions, listening, describing, counting, taking turns
Resourcesnumber chart; number line; counters; concrete objects; crayons; pencils; paper
Conceptsleft, right, forwards, backwards
Vocabularyleft, right, forwards, backwards, straight
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 86 2011/11/16 2:51 PM
87Study & Master Mathematics Grade 2 • Content area/Module 3
4 3-D objectsLearning experiences
Lesson focus
• Divide the learners into groups of four or six and give each group 3-D objects.
• Ask each learner to name the shapes of their objects and to describe the, e.g. This is a ball. It is a sphere, it is round, and so on. Let them describe the shapes in their own languages.
• Hold up one of the objects and explain that it is called a 3-D (three-dimensional) object, because it has height, depth and width.
• Point to each feature as you mention it.• Ask the learners to put the box-like objects (the prisms)
together, the ball-like objects (the spheres) togher and the cylinders together. They have three piles.
• Use flashcards with the words prism, sphere, cylinder.• Ask the learners to find prisms, spheres and cylinders in the
classroom and outside, as well as in magazines.
Give the learners practice in identifying and recognising 3-D objects by doing:Learner’s Book: Module 3, Activities 1–3 Workbook: Worksheets 60–61
Skillsidentifying, recognising, describing, comparing, drawing, matching, taking responsibility, taking turns, cooperating in a group
Resourcesnumber chart; number line; number cards; concrete objects; a variety of boxes of different shapes and sizes; containers such as jars, cans or icecream tubs; magazines; crayons; pencils; paper; cardboard; scissors; glue
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
Concepts3-D objects
Vocabulary3-D, prism, sphere, cylinder
CAPS Math Gr 2 TG.indb 87 2011/11/16 2:51 PM
88 Study & Master Mathematics Grade 2 • Content area/Module 3
5 Sorting 3-D objectsLearning experiences
Lesson focus
• Let the learners work in groups on a mat. Give each group different 3-D objects. Use the photocopiable sheets at the back of this book if you need to.
• Ask the learners to compare the objects and to sort them into sizes, for example, all the small objects into a set, all the big objects into a set. The groups will probably sort their objects differently.
• Then give each group an opportunity to describe to the class how they sorted their objects.
• Once they have all reported back, ask the learners to draw their sorted sets.
• Ask the groups to investigate which objects can roll and which objects can slide, and to sort them into two groups – objects that roll and objects that slide.
• Help the learners describe the objects by asking them questions like: Why do you think this object rolls? Why do you think this object can’t roll? Why do you think this object slides? Encourage them to give their opinions.
• Ask the learners to draw the objects that roll and the objects that slide.
• Give each group a few old magazines. Ask them to look at the pictures and to identify and discuss objects that roll and/or slide, as well as shapes and objects that have round and/or straight edges. Let them cut out the pictures to make a poster.
Give the learners practice in identifying features by doing:Learner’s Book: Module 3, Activities 5–6 Workbook: Worksheets 64–65
Skillsdescribing, sorting, comparing, observing
Resourcesnumber chart; number line; number cards; concrete objects; objects such as boxes, tins or icecream tubs; wooden blocks; 3-D objects; magazines; pictures; crayons; pencils; paper; scissors; glue
Conceptsphysical features of objects
Vocabularyroll, slide, straight edges, round edges
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 88 2011/11/16 2:51 PM
89Study & Master Mathematics Grade 2 • Content area/Module 3
6 Constructions with 3-D objectsLearning experiences
Lesson focus
• Let the learners work in groups on the mats. • Give each group the equipment they will need to construct
something three-dimensional.• Explain that they need to construct something specific such
as an animal, a house or a vehicle.• Once they have completed their constructions, ask each
group to describe to the class what they used, for example, how many cylinders.
• Then ask the learners to draw an picture of their construction.
Skillsobserving, building, describing, drawing
Resourcesblocks; interlocking blocks; concrete objects; prisms of different sizes; cylinders of different sizes; cellotape; string; wool; Prestik; paper; scissors
Concepts3-D objects
Vocabulary3-D construction
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 89 2011/11/16 2:51 PM
90 Study & Master Mathematics Grade 2 • Content area/Module 3
7 2-D shapesLearning experiences
Lesson focus
Identify 2-D shapes• Have a variety of cylinders, prisms and spheres in the
classroom.• Let the learners work in small groups.• Each group has each of the 3-D objects on the mat.• Give each learner a sheet of paper.• Ask the learners to trace around the open edge of the
cylinder, and to trace around a variety of prisms.• Refresh their memory by reminder them that the shapes on
their sheets of paper are 2-D shapes.• Ask them to identify the 2-D shapes.• Have the names circle, rectangle, square and triangle on
flashcards to put on the board as you mention the shapes.• Let the learners identify 2-D shapes in magazines.
Build with 2-D shapes• Divide the learners into pairs. Give each pair a number of
triangles, rectangles, squares and circles, as well as cards with instructions on them for the learners to follow, for example: Use triangles to make a square. Use rectangles to make a square. Use squares to make a rectangle. Draw or trace around each new shape you have made.
• Ask the pairs to read and carry out the instructions on their cards.
• Once they have all completed the activity, ask a few pairs to tell the class what they did and to describe how many and what shapes they used to create the new shapes.
• Draw animals and other objects that the learners can make using cardboard shapes. Give each learner a card. Ask them to use shapes to build whatever they see on the cards.
• Let them describe the constructions in the group.
Give the learners practice in 2-D shapes by doing:Learner’s Book: Module 3, Activities 4 and 7–9 Workbook: Worksheets 62–63 and 66
Skillsbuilding, describing, drawing, following instructions, creating
Resourcesnumber chart; number line; number cards; counters; concrete objects; instruction cards; cut-out 2-D shapes of various sizes, for example, triangles, rectangles and squares; crayons; pencils; paper
Conceptsshapes
Vocabularytriangle, rectangle, square
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 90 2011/11/16 2:51 PM
91Study & Master Mathematics Grade 2 • Content area/Module 3
8 SymmetryLearning experiences
Lesson focus
• Give each learner a sheet of paper. Ask them to fold the sheet in half and to cut out shapes or patterns on the fold. Then let them unfold the sheet to see the design they have made.
• Explain that the folded line is the line of symmetry. Encourage the learners to look at their designs and to talk about what is on the left of their symmetry line and what is on the right of their symmetry line.
• Now ask the learners to fold their sheet of paper into quarters and to cut shapes or patterns on the new folded line. Then let them unfold the sheet to see the new design they have made. They should see that the left and right sides are symmetrical, i.e. one side is a reflection of the other side.
• Give each learner a new sheet of paper. Ask them to fold the sheet in half, unfold it again and draw a shape on the left of the fold (symmetry line). Then let them draw the matching part on the right side of the symmetry line.
• Ask learners to look for symmetrical objects in the school yard or at home. They can then talk about these objects to a partner or someone at home.
Give the learners practice with symmetry by doing:Learner’s Book: Module 3, Activities 10–12 Workbook: Worksheet 67
Skillscutting, drawing, describing, recognising
Resourcesnumber chart; number line; number cards; counters; concrete objects; a mirror; crayons; pencils; paper; scissors
Conceptssymmetry
Vocabularysymmetry, symmetrical, line of symmetry
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 91 2011/11/16 2:51 PM
92 Study & Master Mathematics Grade 2 • Content area/Module 4
Content area/Module 4Measurement
1 Days, weeks and monthsLearning experiences
Lesson focus
• Revise the days of the week.• Let the learners cut out letters from old magazines to build
the names of the days of the week. They paste the names on paper in order.
• The learners do the same for the months of the year.• Ask the learners to read aloud the names of the days of the
week and the months of the year.• Ask the learners to tell you when their birthdays are.• Let the learners discuss what they do during weekends.
Give the learners practice in days, weeks and months by doing:Learner’s Book: Module 4, Activities 5–9 and 20 Workbook: Worksheets 75–76
Skillscounting, reading, ordering, cutting, pasting
Resourcesnumber chart; number line; counters; concrete objects; paper; cardboard; crayons; pencils; old magazines; scissors; glue
Conceptsdays of the week, months of the year
Vocabularyday, week, month, year, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, January, February, March, April, May, June, July, August, September, October, November, December
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 92 2011/11/16 2:51 PM
93Study & Master Mathematics Grade 2 • Content area/Module 4
2 CalendarsLearning experiences
Lesson focus
• Divide the learners into pairs or small groups. Give each pair or group a current calendar. Ask them to point to the names of the months and to read them aloud.
• Draw the learners’ attention to the details on a calendar by asking questions about a specific month. For example: How many days are there in January? How many weeks are there in January? On what day does the 1st of January fall? What day is the 31st of January? Ask the questions one by one, and give the learners time to work out and discuss the answers with their partners.
• Now ask the learners if there are any special days in January. Explain that special days are days that the whole nation celebrates, such as public holidays; or days that people from particular cultures and religions celebrate, such as Jewish or Muslim religious holidays; or days that are special to individuals, such as birthdays and anniversaries.
• Let the learners find and discuss all the special days in the rest of the year. (Research all the special days so that you can explain them in more detail to the learners. For example, 16 June, Youth Day, commemorates the sacrifices made by the youth of South Africa.) These days will also be discussed in detail in the Life skills lessons at the appropriate time.
• Then let the learners ask their partners questions about the calendar. Learners should take turns to ask and answer questions. Move around the classroom while they are working, and encourage and assist where necessary.
• On another day, divide the learners into pairs and give each pair a current calendar.
• Ask questions about the calendar to draw the learners’ attention to the concept of time (days, weeks and months). For example: How many months are there from June to January? Turn to the month we are currently in. How many months from now to Christmas? School closes for the holidays on . . . ? How many weeks from now to the end of term? How many days to the weekend? Ask the questions one by one, and give the learners time to work out and discuss the answers with their partners.
• Then let the learners use their calendars to ask their partners questions about time. Learners should take turns to ask and answer questions.
Give the learners practice with using calendars by doing:Learner’s Book: Module 4, Activities 10–12
Skillscounting, reading, questioning, sequencing
Resourcesnumber chart; number line; number cards; counters; concrete objects; calendars; crayons; pencils; paper; calendars
Conceptsimportant dates
Vocabularyday, week, month, year
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 93 2011/11/16 2:51 PM
94 Study & Master Mathematics Grade 2 • Content area/Module 4
3 Measuring timeLearning experiences
Lesson focus
• Draw a large circle on the board. Point to the top of the circle and say top. Repeat with left, right and bottom.
• Now give the learners paper plates to make clock faces.• Point to the top of the circle you have drawn on the board.
Ask the learners to write the number 12 in the same place on their plates. After checking that they have written the number in the correct place, ask them to write a 6 at the bottom of the plate, opposite the 12. They then write a 3 on the right-hand side and a 9 on the left-hand side, opposite the 3.
• Explain that they are making the face of a clock without the hands. Ask them to fill in the remaining numbers. Move around checking and correcting the learners where necessary.
• Now give each learner a long strip of cardboard, a short strip of cardboard, and a thumbtack or pin. Show them how to pin the two cardboard strips to the centre of the paper plate clock.
• Before the learners practise telling the time, quickly revise the terms o’clock, quarter to, quarter past and half past.
• Then call out a time and ask the learners to move the hands on their paper clocks to the appropriate positions. Once they have done this, draw the hands in the correct positions on your clock on the board. Ask the learners to check if the hands of their clocks are in the correct positions.
• Learners need plenty practice in moving the hands of their clocks and telling the time.
• While the learners are completing this activity, take those who are struggling to a mat and reinforce the concepts.
Give the learners practice in measuring time by doing:Learner’s Book: Module 4, Activities 1–4 Workbook: Worksheets 73–74, and 77
Skillscounting, counting in fives, reading time
Resourcesnumber chart; number line; number cards; counters; concrete objects; a paper plate; cardboard strips; thumbtacks; straight pins; crayons; pencils; paper
Conceptstime
Vocabularytime, digital, analogue, opposite
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 94 2011/11/16 2:51 PM
95Study & Master Mathematics Grade 2 • Content area/Module 4
4 Measuring mass Learning experiences
Lesson focus
• Display a few containers in the classroom. Ask questions such as: Do you see any numbers printed on the containers? What are these? What do the letters in each measurement stand for?
• Write the abbreviations and the full words for all the units of measurement on the board. For example, g = gram, kg = kilogram.
• Call out different masses one at a time.For example, 250 g and 5 kg. Ask the learners to check if they have containers with that measurement.
• Divide the learners into groups and give each group a variety of containers. Ask them to place their containers in ascending order from the smallest mass to the largest mass.
• Let the groups draw their containers and record the units of measurement.
• Show the learners how to use a bathroom scale, a kitchen scale and a balancing scale. Work with a small group of learners on a mat and show the learners these three different scales. Ask the learners to select the scale they would use to measure their mass. Allow the learners to explain their choices. Ask the learners to select something in the classroom that they would weigh using one of the other scales. Once again, allow them to explain their choices. Now give the group an opportunity to weigh different objects in the classroom, for example, the board duster. Show them how to read the measurement. Then ask them to measure the mass of a school bag.
Give the learners practice in measuring mass by doing:Learner’s Book: Module 4, Activities 13–14 Workbook: Worksheet 78
Skillsestimating, measuring, comparing, reading
Resourcesnumber chart; number line; number cards; counters; concrete objects; empty containers which have different units of measure for mass, such as grams or kilograms; advertisements that show different units of measure for mass/weight; cups; teaspoons; crayons; pencils; paper; empty containers
Conceptsmeasurement, heavy, light, heavier, lighter
Vocabularygram, kilogram, mass, heavy, light, heavier, lighter
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 95 2011/11/16 2:51 PM
96 Study & Master Mathematics Grade 2 • Content area/Module 4
5 Measuring capacityLearning experiences
Lesson focus
• Display a few containers in the classroom. Draw the learners’ attention to the measurements on the containers. Ask questions such as: What do these measurements show? What do the numbers indicate? What do the letters stand for?
• Write the abbreviations and the full words for the units of measurement on the board. For example: ml = millilitre.
• Divide the learners into groups of about eight and give each group a variety of containers. Ask them to arrange their containers in order, from the one that should hold the smallest quantity to the one that should hold the largest quantity.
• Take the groups outside and give each group a teaspoon, a cup, a 500-ml container, a 2-litre container and a container with water.
• Ask the learners to measure how many teaspoons of water will fill the cup, and how many 500-ml containers of water will fill the 2-litre container. Each group should choose one learner to record the results.
• Once the learners have completed the activity, ask them to give you feedback on their results, using spoons and cups as units of measurement.
Give the learners practice in measuring capacity by doing:Learner’s Book: Module 4, Activities 15–16 Workbook: Worksheet 79
Skillsestimating, measuring, following instructions, reading
Resourcescounters; number cards; number chart; number lines; 500-ml container; 2-litre container; teaspoon; cup; crayons; pencils; paper
Conceptsmeasurement
Vocabularymore, less, most, least, full, half full, empty
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 96 2011/11/16 2:51 PM
97Study & Master Mathematics Grade 2 • Content area/Module 4
6 Measuring lengthLearning experiences
Lesson focus
Handspans• Explain to the learners that in the old days there were no
rulers and tape measures, so people had to work out other ways to measure objects. Ask the learners to suggest ways in which we can measure without instruments.
• Show the learners how to measure using handspans. (A handspan is from the tip of the little finger to the tip of the thumb when the hand is extended.)
• Now ask the learners to estimate the height of their desks in handspans. Once they have done this, let them measure the height in handspans and compare the difference between the estimate and the actual measurement.
• Divide the learners into pairs and let them practise measuring different objects in the classroom using handspans.
Give the learners practice in measuring with handspans by doing:Learner’s Book: Activity 18 Workbook: Worksheets 80–81
Foot lengths• Show the learners how to measure using their feet.
Demonstrate by placing one foot in front of the other, heel to toe, and counting as you take each step.
• Let the learners work with their partners to practise measuring using their feet. They could measure the length of the classroom or the distance from their desks to the classroom door.
• Introduce the learners to paces or steps as another informal form of measurement. Paces are the normal-sized steps people take when they walk. Demonstrate by pacing from one side of the classroom to the other, counting as you take each step.
• Let the learners practise outside by measuring the number of paces they take from the classroom to the school gate.
• The learners will probably get different answers when they measure in this way. Explain that handspans, feet and paces are not accurate forms of measurement. These measurements will differ from learner to learner, depending on hand-size, foot-size and the length of their steps.
Give the learners practice in measuring with foot lengths by doing:Learner’s Book: Module 4, Activities 17 and 19Workbook: Worksheet 82
Skillsestimating, measuring, counting
Resourcesnumber chart; number line; number cards; counters; concrete objects; ruler; tape measure; crayons; pencils; paper
Conceptsmeasurement, length
Vocabularyarm, leg, back, shoulder, body, foot, handspan, foot lengths
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 97 2011/11/16 2:51 PM
98 Study & Master Mathematics Grade 2 • Content area/Module 5
Content area/Module 5Data handling
Learning experiences
Do the activities one at a time over a few lessons. Discuss the content, questions and topics of the activities in groups or as a class. Ensure that the learners understand the information they are dealing with. Give them short, clear instructions before they start the activities.
We have described the Learning experiences under Concepts and skills.
1 Concepts and skills
Lesson focus
Sorting• The learners work in small groups on a mat. Give them a
variety of objects. Explain to the learners that the objects in front of them are mixed up. Ask the learners to sort the objects into groups that belong together. Explain that after they have finished sorting or grouping the objects, they can name the groups. Let the learners name the groups and explain why they chose a particular name.
Data• Explain to the learners that all the information they have in
front of them (the sorted groups) is called data. Tell them that data is another word for information. We collect data when we gather information. Tell the learners that we can collect data by asking questions, looking in books, magazines, newspapers and by looking around us. Explain to the learners that in the previous lessons they sorted their data into specific groups and named the groups according to specific characteristics.
Recording• Explain that we can write down or record data. Show the
learners how we can record data in different ways. We can use pictures, ticks, strokes, crosses, dots or colours to represent data. Show the learners that each symbol that we record represents one item, for example: we can write a 3 to represent 1 child.
Skillsobserving, sorting, classifying, counting, questioning, answering questions, recording, interpreting, reasoning, discussing
Resourcesnumber chart; counters; concrete objects; crayons; pencils; paper; flashcards
Conceptssorting, recording, data
Vocabularysorting, recording, data
Starting offDo a variety of counting activities with the class.Choose a pattern activity from Module 2 for the learners to do.
CAPS Math Gr 2 TG.indb 98 2011/11/16 2:51 PM
99Study & Master Mathematics Grade 2 • Content area/Module 5
Reading and interpreting data• Explain to the learners that it is important to read all the
data they have in front of them. When they look at data and read the information, they need to understand what it is and what it says. The data will inspire the learners to think of questions as they will want to know more about the data. They will ask ‘why?’ and ‘why not?’ questions. Learners must be able to read and interpret data so they can answer questions about the data or to make decisions about it. Choose one activity in the Learner’s Book to do as a class exercise so the learners can practise reading and interpreting data.
Give the learners practice in collecting, sorting, representing and interpreting data by doing:Learner’s Book: Module 5, Activities 1–9Workbook: Worksheets 83–86
CAPS Math Gr 2 TG.indb 99 2011/11/16 2:51 PM
blankCAPS Math Gr 2 TG.indb 100 2011/11/16 2:51 PM
101Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Part 4 Teaching aids: photocopiable sheets
Number symbol cards
10 10020 20030 30040 40050 500
CAPS Math Gr 2 TG.indb 101 2011/11/16 2:51 PM
102 Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Number symbol cards
60 60070 70080 800901 2 3 4 5
900
CAPS Math Gr 2 TG.indb 102 2011/11/16 2:51 PM
103Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Number symbol cards
Flashcards
6 7 8 9
Sunday 1st
Monday 2nd
Tuesday 3rd
Wednesday 4th
CAPS Math Gr 2 TG.indb 103 2011/11/16 2:51 PM
104 Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Flashcards
Thursday 5th
Friday 6th
Saturday 7th
8th 9th
11th
12th
10th
CAPS Math Gr 2 TG.indb 104 2011/11/16 2:51 PM
105Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Flashcards
first second
third fourth
fifth sixth
seventh eighth
ninth tenth
eleventh twelfth
CAPS Math Gr 2 TG.indb 105 2011/11/16 2:51 PM
106 Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Number chart
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
101 102 103 104 105 106 107 108 109 110
111 112 113 114 115 116 117 118 119 120
CAPS Math Gr 2 TG.indb 106 2011/11/16 2:51 PM
107Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Number chart
121 122 123 124 125 126 127 128 129 130
131 132 133 134 135 136 137 138 139 140
141 142 143 144 145 146 147 148 149 150
151 152 153 154 155 156 157 158 159 160
161 162 163 164 165 166 167 168 169 170
171 172 173 174 175 176 177 178 179 180
181 182 183 184 185 186 187 188 189 190
191 192 193 194 195 196 197 198 199 200
201 202 203 204 205 206 207 208 209 210
211 212 213 214 215 216 217 218 219 220
221 222 223 224 225 226 227 228 229 230
231 232 233 234 235 236 237 238 239 240
CAPS Math Gr 2 TG.indb 107 2011/11/16 2:51 PM
108 Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Shapes
CAPS Math Gr 2 TG.indb 108 2011/11/16 2:51 PM
109Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Shapes
CAPS Math Gr 2 TG.indb 109 2011/11/16 2:51 PM
110 Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Shapes
CAPS Math Gr 2 TG.indb 110 2011/11/16 2:51 PM
111Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Shapes
CAPS Math Gr 2 TG.indb 111 2011/11/16 2:51 PM
112 Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Shapes
CAPS Math Gr 2 TG.indb 112 2011/11/16 2:51 PM
113Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
2-D shapes
rectangle
rectanglesquare square
circle
circle
triangles
CAPS Math Gr 2 TG.indb 113 2011/11/16 2:51 PM
114 Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Dotted paper
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
CAPS Math Gr 2 TG.indb 114 2011/11/16 2:51 PM
115Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Squared paper
CAPS Math Gr 2 TG.indb 115 2011/11/16 2:52 PM
116 Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Counters
CAPS Math Gr 2 TG.indb 116 2011/11/16 2:52 PM
117Study & Master Mathematics Grade 2 • Teaching aids: photocopiable sheets
You may photocopy this sheet for use with Study & Master Mathematics Grade 2 Learner’s Book and Workbook.
Money
CAPS Math Gr 2 TG.indb 117 2011/11/16 2:52 PM
CAPS Math Gr 2 TG.indb 118 2011/11/16 2:52 PM
119Study & Master Mathematics Grade 2 • Documents
Part 5 DocumentsAdd your own documents and notes, for example the CAPS document for Foundation Phase Mathematics, here.
CAPS Math Gr 2 TG.indb 119 2011/11/16 2:52 PM
I S BN 978-1-107-65630-7
9 7 8 1 1 0 7 6 5 6 3 0 7
Mathematics English TG
www.cup.co.za
222222Grade
MathematicsMathematicsMathematicsStudy & Master Mathematics has been specially developed by an experienced author team for the Curriculum and Assessment Policy Statement (CAPS). This new and easy-to-use course not only helps learners to master essential content and skills in the subject, but gives them the best possible foundation on which to build their Mathematics knowledge.
Study & Master Mathematics Grade 2 is made up of these core components:
The comprehensive Learner’s Book provides:• graded activities that develop learners’ skills and understanding
in each of the content areas specifi ed by the CAPS document• examples and activities based on learners’ own experiences.
The substantial Workbook provides:• ample worksheets to consolidate the activities dealt with in
the Learner’s Book• activities to enhance fi ne motor skills.
The innovative Teacher’s Guide includes:• additional classroom activities to introduce and consolidate
work done in the Learner’s Book and Workbook• teaching tips and support for all the activities in the
learner material• guidance on whole class activities, small group teaching
and independent work• photocopiable record sheets and templates.
SM_Maths_G2_TG_English.indd 2 2011/11/16 2:55 PM