mathematics teachers’ manual mathematics teachers’ …€¦ · guide for grade 1 is...

REPUBLIC OF NAMIBIA

MINISTRY OF EDUCATION

FOR IMPLEMENTATION: 2015

Mathematics Teachers’ Manual

Grade 2

MATHEMATICS TEACHERS’ MANUAL

GRADE 2

Supported by:

Ministry of Education National Institute for Educational Development (NIED) Private Bag 2034 Okahandja Namibia

© Copyright NIED, Ministry of Education, 2014 Mathematics Teachers’ Manual Grades 2

ISBN 978-99945-2-137-1

Printed by NIED

Website: http://www.nied.edu.na Publication date: 2014

http://www.nied.edu.na/

ACKNOWLEDGEMENTS This manual was developed under the support of the Rössing Foundation. The following people are acknowledged:

1. Teun Hanemaaijer – Rössing Foundation, Namibia 2. Jaap Griffioen - Amsterdam University, Holland 3. Jaap Waard - Amsterdam University, Holland 4. Alina Niipare – NIED, Namibia 5. Junior Primary Co-Group of 2013/14 6. Junior Primary Panel members of 2013/15

Table of Content

Week Theme/Topic Page

Introduction 1

Overview 2

1-3 Family 4

4 Summer 11

5-7 Customs and cultural events 15

8 Building materials 22

9 Public Transport 25

10 Local Media 28

11-12 Local business 32

13 Autumn 37

14-15 Cleanliness 40

16-17 Function of the 5 senses 45

18 Winter 51

19 Caring for friends 54

20-21 Being safe 57

22 Food Hygiene 62

23 Road safety 65

24 Properties and uses of materials 68

25 Clean up 71

26-27 Plants and growth 74

28 Parts of plants and uses 79

29 Spring 83

30-31 Habits and products 86

32 Life cycle 91

33-34 Saving water 94

35 Change in the sky 99

36 Uses of energy 102

Dice 105

Clock Face 106

Coin & bank notes 107

Sun Game 108

Twenty frame 112

Introduction In front of a new Teacher’s Guide, written on a weekly bases aligned with the Scheme of Work as provided by NIED. Although the new syllabus may not have changed much as compared with the previous syllabus; the proposed approach in this teacher’s guide is rather different. The new approach aims to get learners away from counting. The new approach is a much smarter approach; using ten frames and empty number lines. A calculation like 18 + 7 cannot be solved by putting up 18 lines; then 7 lines and count all the lines again. This procedure takes too long. Learners are given tools in the form of ten frames and are challenged to set up smart procedures themselves. The solution that is acceptable can look like: 8 + 7 = 8 + 2 + 5 = 10 + 5 = 15 therefore 18 + 7 = 20 + 5 = 25. Some learners may need support from the ten frames:

For this reason all learners should have 2 ten frames with 20 bottle tops on their desk when doing mathematics. They have already some experience with the two ten frames from grade 1. The ten frames are not the only way; another way of showing 18 +7 is with the empty number line:

Learners are to be stimulated to find there own ways to calculate sums. Ones they are given the means (the ten frames) they will start performing the calculations in their own way. Constructing their own knowledge. Less time is to be spend on counting; more on practicing basic computations. Counting is based on the small sequence (1-10) and the big sequence (10 20 …100). All counting is based on these two sequences. If the learners know these two sequences then they will be able to count up to a 1000 and beyond without any problems. Counting needs short practice (5 minutes), on very regular bases. The mathematics curriculum in grade 2 should be spending for 80% of the time on Number Concept Development. (NCD). The other topics: Geometry; measurements and data handling occupy the 20% remaining time.

A weekly worksheet consisting of 2 pages can be copied freely for use in

class.

0 18 20 25

+2 +5

8 + 7 = 15

1

Overview

Term 1 Term 2 Term 3

1-100 1-100 1-500

Counting, repeat, maintainance

Orientation and counting Counting in 2’s up to 20, in 5’s up to 50 repeat counting in 3’s up to 30, in 10’s up to 100 repeat

counting

Rounding off to tens - ROT Rounding off to fives - ROF Doubling and halving – DH Place value - PC

ROT

PV

ROF

PV

DH

DH

1 2 3 4 5 R 7 8 9 10

11

R 13

14

15

16

17

R 19

20

21

22

23

R 25

26

27

28

29

R 31

32

33

34

35 R

Computation, repeat, maintenance 1-20. Pay attention to all previous phases!

Computation 1-100+ Computation 1-100 Computation 1-100

P1

P2

P3

P4

P5

P6

P28

P1

P2

P3

P4

P5

P6

P7

1 2 3 4 5 R 7 8 9 10

11

R 13 14

15

16

17

R 19

20

21

22

23

R 25

26

27

28 29

R 31

32

32

34

35 R

Computation X (TT means times table) TT2 (1-10 times), TT10 (1-10 times), TT5 (1-10 tim.

Computation X TT3 (1-10 times), TT1 (1-10 times), TT4 (1-10 times)

TT2

TT10

TT5

TT 3

TT4

1 2 3 4 5 R 7 8 9 10

11

R 13

14

15

16

17

R 19

20

21

22

23

R 25 26

27

28

29

R 31

32

33

34

35 R

Computation: 2, :10, :5, :3

:2 :10

:5 : 1

1 2 3 4 5 R 7 8 9 10

11

R 13 14

15

16

17

R 19

20

21

22

23

R 25

26

27

28 29

R 31

32

32

34

35 R

Fractions

F F

13

14

15

16

17

R 19

20

21

22

23

R

2

Numbers: numbers of the week during the year R: revision Phases:

P1+ decades 40 + 20 P1- decades – decades 40 – 20

P2+ decade + digit 30 + 6 P2- decade – digit 40 – 6

P3+ 2 digits + 1 digit, not bridging 10 32 + 6 P3- 2 digits – 1 digit, not bridging 10 37 – 4

P4+ 2 digits + 1 dgit, bridging 10 37 + 5 P4- 2 digits – decades 42 – 20

P5+ 2 digits + decade(s) 37 + 20 P5- 2 digits – 1 digit, bridging 10 37 -9

P6+ 2 digits + 2 digits, not bridging 10 32 + 24 P6- 2 digits – 2 digits, not bridging 10 37 – 23

P7+ 2 digits + 2 digits, bridging 10 37 + 28 P7- 2 digits – 2 digits, bridging 10 52 - 15

Addition / Subtraction <100

In the IPM, you will find the weeks in which the different phases will be introduced.

Teachers won’t stop to repeat all these phases. So while introducing (e.g.) phase 3, the teacher will pay attention and repeat phase 1 and 2

as well.

Times tables

Repeating the times tables during grades 2, 3, 4, 5, 6, 7 is really a ‘must’

If you find a time table in the week of a term, this means the moment the time table will be introduced.

Strategies:

Stepwise addition / Stringing (=counting in tens and ones) 47 + 28 = 47 + 3 + 20 + 5

or

47 + 28 = 47 + 20 + 3 + 5 or more possibilities

3

Week 1-3; Term 1 Theme: Family NCD Many suggestions given for counting; all Counting is based on the small and the big sequence; every day one can start with the small (1-10) and the big sequence: (10-20-30…100) and furthermore concentrate on the counting as stipulated in the Scheme of Work. Important topics of these 3 weeks: Friends of ten. How much to add to 8 to get ten. It is important that the learners practice this often so that it is a ‘fact’ to them. When they see 8 + . = 10 they know it is 2; if you ask: how? Learners cannot say much, they just know it. To visualize this you can use a ten frame: 5 + 3 are filled (no counting!); 2 are open so 8 and 2 are friends. Of course the friend of 8 can be

found as well using the subtraction 10 8 = 2. A mobile as described on page 24 in Teacher’s Guide for grade 1 is recommendable to display in your classroom permanently. Analogue problems. In stead of counting with sticks or drawing lines, a ten frame offers a fast way to calculate 14 + 3. On top of that the ten frame offers a mental ‘guide line’ to perform calculations. In grade 1 there was an attempt to internalize 4 + 3 = 7. If this is still known, then it can be used to work out 14 + 3. Of course not all learners will know all the additions under 10 by heart after a long holiday. So it has to be revised often, until the majority in your class is fluent in all addition fact up to 10. The problems are analogue can be seen using the ten frames:

4 + 3 14 + 3 Number bonds up to 9 If you want to add 17 + 8 one must instantly be able to split 8 favourably; in this case: 8 = 3 + 5 since the friend of 7 is three.

Again the 10 frame can help. C of course counting is not allowed. Halves and doubles. Halves of the even numbers up to 20 have to be internalised, as well as all the doubles from 1-10. The verbs learners should get used to is to halve and to double. Once more the two ten frames can help out but in the end all learners must know them by heart as basic calculation fact which are instantly available when asked for.

Possible lesson objectives wk 1-3 At the end of the week learners will be able to:

Count forward and backward in

selected intervals up to 100.

Count in 2’s up to 20; in 3’s up to 30

Count in 5’s and 10’s up to 100

Decompose numbers from 10-100;

identify correct place values.

Add a single digit number to a number

between 10-20 using known number

facts.

Split numbers 2-9 in all possible

ways.

Identify friends of 10 [Add and subtr.]

Double all no1-10

Half all even number from 2 up to 20

Subtract a single digit no from a

number between 10-20 using known

number facts

Subtract 10 [Range 10-20]

Mention days of the week.

8 = . + .

4 bottle tops up; 3 down, altogether 7.

14 bottle tops up; 3 down; altogether 17.

4

Name:………… Class…. Wk 1 Gr2

Write the numbers on the dots.

Friends of 10 [No counting!]

One friend is missing! Draw it.

What is more? Draw a circle.

5 or 19 13 or 12 5 or 8 14 or 17 12 or 11

16 or 8 13 or 14 1 or 11 6 or 16 4 or 17

1 or 12 4 or 10 11 or 10 8 or 17 3 or 12

3 or 13 17 or 6 12 or 10 4 or 20 9 or 8

If you use the number line, what do you notice?

. . . . . . . . . . . . . . . . . . . . . .

10 20 . . . . . . . . . . . . . . 100

. + . = 10

10 . = .

4 + 6 = 10

10 6 = 4

. + . = 10

10 . = .

. + . = 10

10 . = .

. + . = 10

10 . = .

. + . = 10

10 . = .

. + . = 10

10 . = .

. + . = 10

10 . = .

. + . = 10

10 . = .

……………………………………………………………………………………………………..

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

5

Use the bottle tops and the 10 frame(s).

5 + 3 = 8

15 + 3 = 18

7 + 1 = 8

17 + 1 = . .

2 + 6 = 8

12 + 6 = . .

9 + 1 = 10

19 + 1 = . .

4 + 4 = 8

14 + 4 = . .

6 + 1 = .

16 + 1 = . .

1 + 8 = .

11 + 8 = . .

3 + 5 = .

13 + 5 = . .

4 + 5 = .

14 + 5 = . .

3 + 6 = .

13 + 6 = . .

7 + 2 = .

17 + 2 = . .

6 + 3 = .

16 + 3 = . .

5 + 2 = .

15 + 2 = . .

8 + 2 = . .

18 + 2 = . .

1 + 5 = .

11 + 5 = . .

3 + 2 = .

13 + 2 = . .

2 + 7 = .

12 + 7 = . .

4 + 1 = .

14 + 1 = . .

3 + 5 = . .

13 + 5 = . .

2 + 2 = .

12 + 2 = . .

Fill in, ask the teacher: what is the date for Sunday.

Mixed exercise; use the bottle tops and ten frames.

4 + 4 = . 9 7 = . 3 + 6 = . 8 6 = . 5 + 4 = .

7 4 = . 2 + 6 = . 3 + 4 = . 10 9 = . 2 + 4 = .

7 + 3 = . 7 6 = . 9 9 = . 3 + 5 = . 8 + 2 = . .

6 + 7 = . 19 2 = . . 8 + 9 = . . 18 9 = . . 10 + 8 = .

12 7 = . 8 + 6 = . . 14 8 = . . 8 + 8 = . . 15 7 = . .

What do you do on:

Friday.

…………………………

Saturday.

…………………………

Sunday

…………………………

Monday

…………………………

Sunday

. . January

Monday

. . January

Tuesday

. . January

Wednesday

. . January

Thursday

. . January

Friday

. . January

Saturday

. . January

One

week

6


Count in five’s:

Take half: (Use your ten frames)


12 + 5 = . 13 9 = . 10 + 6 = . 15 7 = . 8 + 12 = .

19 17 = . 7 + 6 = . 14 + 4 = . 13 9 = . 13 + 6 = .

16 + 3 = . 9 6 = . 19 6 = . 18 + 1 = . 15 + 4 = .

8 + 7 = . 19 4= . 17 9 = . 16 9 = . 11 + 8 = .

15 + 1 = . 10 + 8 = . 12 + 6 = . 17 + 3 = . 14 + 5 = .

18 7 = . 13 4= . 11 4 = . 13 9 = . 10 + 9 = .

12 + 3 = . 14 + 2 = . 13 + 5 = . 18 + 2 = . 10 + 5 = .

Half of 16 is 8

× × ×

× × ×

× ×

Half of 14 is . Half of 18 is . Half of 12 is .

Half of 20 is . .

Use one ten frame to find half of:

Number Half Number Half

8 . 10 .

4 . 2 .

6 . 0 .

. . . . . . . . . . . . . . . . 5 15

10 20 . . . . . . . . . . . . . . 100

7

Double the number. Use your ten frame(s).

Double 7 Put 7 on the ten frame:

Number: 7 2 5 9 1 3 4 6 8 10

Double: 14 . . . . . . . . .

Name the shapes and color them.

Use the bottle tops and the 10 frame(s).

5 3 = 2

15 3 = 12

6 4 = 2

16 4 = . .

6 2 = 4

16 4 = . .

9 3 = 6

19 3 = . .

4 4 = 0

14 4 = . .

6 1 = .

16 1 = . .

3 2 = .

13 2 = . .

7 5 = .

17 5 = . .

8 5 = .

18 5 = . .

7 5 = .

17 5 = . .

7 2 = .

17 2 = . .

6 3 = .

16 3 = . .

5 1 = .

15 1 = . .

8 2 = . .

18 2 = . .

4 3 = .

14 3 = . .

5 2 = .

15 2 = . .

2 1 = .

12 1 = . .

4 2 = .

14 2 = . .

9 7 = . .

19 7 = . .

7 3 = .

17 3 = . .

3 1 = .

13 1 = . .

6 6 = .

16 6 = . .

7 1 = .

17 1 = . .

4 1 = . .

14 1 = . .

5 5 = .

15 5 = . .

8 6 = .

18 6 = . .

9 6 = .

19 6 = . .

8 8 = .

18 8 = . .

9 5 = . .

19 5 = . .

6 5 = .

16 5 = . .

……………. ……………. ……………. …………….

……………. ……………. …………….

Together 14 again

:

8


Count in two’s.

Count in three’s.

Write the number; NO COUNTING. Is the number odd or even?

Friends of 10. Use a ten frame.

. + 5 = 10 10 . = 2 1 + . = 10 10 7 = . 8 + . = 10

10 . = 3 . + 6 = 10 7 + . = 10 10 2 = . 3 + . = 10

10 . = 4 5 + 5 = . . . + 4 = 10 . . 8 = 2 5 + . = 10

Write down all the friends of 10.

. + . = 10 . + . = 10 . + . = 10 . + . = 10 . + . = 10

. + . = 10 . + . = 10 . + . = 10 . + . = 10 . + . . = 10

13 odd

13 = 10 + 3 . . . . . . . . = 10 + .

. . . . . .

. . = 10 + . . . . . . .

. . = . . + .

. . . . . .

. . = . . + .

. . . . . .

. . = . . + .

. . . . . .

. . = . . + .

. . . . . .

. . = . . + .

. . . . . .

. . = . . + .

. . . . . .

. . = . . + .

2 . . . . . . . . . . . . . 20

3 . . . . . . . . . . . . . . 30

9

What is less? Draw a circle.

5 or 19 13 or 12 5 or 8 14 or 17 12 or 11

16 or 8 13 or 14 1 or 11 6 or 16 4 or 17

1 or 12 4 or 10 11 or 10 8 or 17 3 or 12

2 or 7 12 or 17 10 or 20 18 or 16 13 or 4

Write the number; NO COUNTING.

8 . . . . . . . . . .

Use your ten frame only once per box.

5 + 3 = 8 15 + 3 = 18 7 6 = . 17 6 = . . 5 + 3 = . 15 + 3 = . .

9 5 = . 19 5 = . . 2 + 6 = . 12 + 6 = . . 4 4 = . 14 4 = . .

4 + 5 = . 14 + 5 = . . 8 3 = . 18 3 = .

. 1 + 7 = . 11 + 7 = . .

5 3 = . 15 3 = . . 7 + 3 = . . 17 + 3 = .

. 9 7 = . 19 7 = . .

6 + 3 = . 16 + 3 = . . 3 2 = . 13 2 = .

. 2 + 7 = . 12 + 7 = . .

8 1 = . 18 1 = . . 3 + 4 = . 13 + 4 = .

. 7 7 = . 17 7 = . .

4 + 2 = . 14 + 2 = . . 8 5 = . 18 5 = . . 5 + 5 = . . 15 + 5 = . .

Odd Even

Odd Even

Odd Even

Odd Even

Odd Even

Odd Even

Odd Even

Odd Even

Odd Even

Odd Even

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

10

Week 4; Term 1 Theme: Summer Counting The basis of counting is the small and the big sequence. If your class is not too big one can make individual learners count the small and the big sequence: All learners stand up and the teacher starts with 1 and points at a learner who says 2; the teacher points at the next learner, who says 3. Etc. The learner who fails to say correct sits down. This can be done as well with the big sequence:10… This week bridging the 10 is practiced, both in addition and subtraction. Crucial is that learners are not allowed to count. 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13. As a sum this isn’t easy for most grade 2 learners, that is why they have two ten frames on their table. Put 8 on the first ten frame and 5 on the other ten frame. (If you like you may put the first 8 bottle tops, top down and the 3 top up, though in my eyes not that crucial.) Fill up the first ten frame and read the answer. It will look like this: It is important that the 2 from the 5 are used to complete the 8. Subtractions that bridge the ten are done as well in 2 stages:

14 6 = 14 4 2 = 10 2 = 8. The two ten frames come in handy here as well. First put the 14 bottle tops on the frames, all having the top facing upwards; turn 6 around or take away 6 which is better but not that easily shown on paper. Read the answer. Remark: learners have a tendency of putting the bottle tops disorderly; the teacher have to see to it that the bottle tops are put properly. The turning of the 6 bottle tops is still very close to counting 6. So very soon the 6 bottle tops that are to be subtracted are not any more turned around, but the learner only looks at the 14 bottle tops and decides to subtract 4. In the work sheet the following notation will be followed:

14 6 = 14 4 2 = 10 2 = 8.

Possible lesson objectives wk 4 At the end of the week learners will be able to:



Count in 2’s up to 20; in 3’s up to

30


Identify number images for 1-20 in

various ways.

Add and subtract numbers in the

range 1-20, bridging the 10.

Apply the commutative law for

add.

Work out subtraction in the range

1-20 for numbers that are ‘close’.

Use correctly vocabulary for mass.

Identify odd & even numbers in the

range 1-100.

What happened? In written form: 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13.

So 14 6 = 8 In written expanded form:

14 6 = 14 4 2 = 10 2 = 8. So the subtraction is done in two phases.

11

4 2 It is likely that all learners need the ten frames, but if a learner can work it out without the ten frames; the learner is allowed to do so as long as there is no counting involved. For both addition and subtraction the numbers are split. If learners are not fluent in this splitting extra work has to be done. In this week there is an exercise for this practice of splitting numbers. In order for your learners to practise addition more often one can introduce the game: Make 15. It is a highly competitive game; learners can be encouraged to play it at home with their parents or sisters and brothers. It is played on a card that looks as drawn below:

Name: 1 2 3 4 5 6 7 8 9

Player 1 5

Player 2 3

Player 1 one has picked number 5; if it is crossed it cannot be picked again. Player 2 has picked 3 and wrote it on his row. Now it is player 1 again to pick a number; the aim is to make 15 using exactly 3 numbers. As soon as one player has 15 with three numbers he/she is the winner. If none of the players gets 15, the game ends in a draw. There are forced choices, for instance if player 1 gets 8 as a second number; player 2 is forced to take the 2, to avoid player 1 taking the 2 in the next round and win the game. [A short analyses of the game shows that there are eight favourable triplets to get 15: (1,5,9); (1,6,8); (2,4,9); (2,5,8) ; (2,6,7); (3,4,8); (3,5,7) and (4,5,6) if you order the triplets. The only number that appears 4 times is the number 5, so if you play it yourself, try to get 5 if it is not yet taken. It will give you a higher chance of winning]

12


Count in threes.

Put the right numbers on the dots.

2 1 + .

3 1 + 2 2 + 1

4 1 + . . + . . + .

5 . + . . + . . + . . + .

6 . + . . + . . + . . + . . + .

7 . + . . + . . + . . + . . + . . + .

8 . + . . + . . + . . + . . + . . + . . + .

9 . + . . + . . + . . + . . + . . + . . + . . + .

Friends of ten.

Use your ten frames to add.

Example: 6 + 7 So 6 + 7 = 13

8 + 3 = . . 7 + 9 = . . 6 + 8 = . . 4 + 8 = . . 9 + 6 = . .

8 + 8 = . . 6 + 5 = . . 6 + 7 = . . 9 + 4 = . . 5 + 9 = . .

7 + 5 = . . 5 + 6 = . . 9 + 6 = . . 3 + 8 = . . 6 + 6 = . .

4 + 9 = . . 3 + 7 = . . 7 + 7 = . . 7 + 6 = . . 5 + 5 = . .

3 . . . . . . . . . . . . . . 30

10 =

. . + 0 10 =

8 + 2 10 =

. + . 10 =

. + . 10 =

. + . 10 =

. + . 10 =

. + . 10 =

. + . 10 =

. + . 10 =

. + .

No Counting or fingers!

13

Just look at the ten frame, and answer:

Friends of ten.

10 3 = . 10 6 = . 10 5 = . 10 7 = . 10 9 = .

10 0 = . . 10 1 = . 10 4 = . 10 2 = . 10 8 = .

Subtract using the ten frames.

18 9 = . 14 5 = . 16 8 = . 11 8 = . 13 6 = .

15 7 = . 11 6 = . 14 9 = . 12 3 = . 11 4= .

13 9 = . 14 7 = . 11 2 = . 16 7 = . 12 4 = .

17 7 = . 16 9 = . 17 9 = . 15 8 = . 13 5 = .

Subtract; the numbers are close!

Example 12 11

19 17 = . 14 12 = . 16 16 = . 11 10 = .

15 13 = . 11 11 = . 14 13 = . 18 17 = .

13 12 = . 14 14 = . 19 18 = . 16 15 = .

17 16 = . 16 14 = . 17 17 = . 15 14 = .

20 19 = . 13 11 = . 11 9 = . 20 18 = .


7 or 12 3 or 11 15 or 18 12 or 7 7 or 8

20 or 19 15 or 9 13 or 12 16 or 15 17 or 19

15 or 12 14 or 13 18 or 19 17 or 14 3 or 10

5 or 7 19 or 12 16 or 9 14 or 12 16 or 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

One step so 12 11 = 1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

14

Week 5-7; Term 1 Theme: Customs and cultural events

NCD Subitizing is seeing how many objects are shown at a glance. It means: no counting. This can be done by showing flash cards with a ten frame with some dots on it. Counting is part of NCD but when it comes to computations, it is not a very smart approach. Subitizing plays an important role in smart computations. The mental image learners must have for 18 is: The learners are supposed to conclude 18 not by Counting one by one but reasoning: a full ten frame stands for 10; on the other ten frame there is one full column, that is 5; and still another three so altogether 10 + 5 + 3 = 18. Other ways are of course as well acceptable 3 × 5 = 15 and 3 make 18 as well. The number images are very important for mental calculations. Learners first learn computations up to 20 with the 2 ten frames by actually moving the bottle tops on the 10 frames; after doing this for quite some time the ten frames are not needed any more learners will perform such calculations mentally. Of course learners have different abilities so the moment the ten frames are not needed anymore will be different for individual learners. Usually they will themselves see the ten frame as a waste of time if they can do a calculations faster mentally. Other important aspects in addition and subtraction from 1-20 are:

Friends of 10. (6 needs a 4 to make ten but as well 10 take away 3 is seven)

Addition of a single digit number plus a multiple of 10: 10 + 4 = 14.

The way the numbers 1-9 can be split: 7 = 2 + 5 should be instantaneously

available when you add 8 + 7. (Subtraction as well demands suitable splitting of

numbers)

Addition is commutative: somehow 8 + 3 is easier than 3 + 8, yet they have the

same answer.

When it comes to subtraction: If the numbers are close to each other it is easier to

figure out how far apart the numbers are on the number line: 19 18 = 1

Doubles and halves can as well play an important role in fast mental calculations. If

you know 8 + 8 = 16 then you can as well answer 8 + 9 = 17. (Line of thinking: 8 +

9 = 8 + 8 + 1 = 16 + 1 = 17)

Analogy sums if 3 + 4 = 7 then 13 + 4 = 17. The same applies for subtraction 8 3

= 5 then 18 3 = 15.

All these aspects are practiced in the 3 work sheets for the 3 weeks.

Possible lesson objectives wk5-7 At the end of the week learners will be able to:





Count with steps of 10 starting

anywhere in the range 1-100.

Add and subtract any two numbers in

the range 1-20 using the 10 frame(s),

at reasonable speed and accuracy.

Mention the months of the year.

Identify the day of a certain date, given

a calendar.

Identify all coins used in Namibia as

legal tender.

Identify basic geometric shapes as they

occur around us.

15


Put the numbers on the dots.

Write the sum. NO COUNTING!

Use your ten frame only once per box.

6 + 1 = 7 16 + 1 = 17 9 3 = . 19 3 = .

. 2 + 7 = . 12 + 7 = . .

7 4 = . 17 4 = . . 3 + 3 = . 13 + 3 = .

. 6 2 = . 16 2 = . .

3 + 7 = . . 13 + 7 = . . 9 8 = . 19 8 = .

. 2 + 5 = . 12 + 5 = . .

8 5 = . 18 5 = . . 5 + 3 = . . 15 + 3 = .

. 8 6 = . 18 6 = . .

7 + 6 = 13 . + . = . . . + . = . . . + . = . . . + . = . .

. + . = . . . + . = . . . + . = . . . + . = . . . + . = . .

. . . . . . . . . . . . . . . . . . . . . .

10 20 . . . . . . . . . . . . . . 100

16

Friends of 10. Write the numbers on the dots.

Answer fast:

10 + 3 = . 10 + 6 = . 10 + 5 = . 10 + 7 = . 10 + 9 = .

10 + 0 = . . 10 + 1 = . 10 + 4 = . 10 + 2 = . 10 + 8 = .

Split the numbers:

Fill in the neighbors:

1 + 1

2 =

. + .

3 =

. + .

. + .

5 =

. + .

. + .

. + .

. + .

6 =

. + . . + .

. + .

. + .

. + .

4 =

. + .

. + .

. + .

7 =

. + .

. + .

. + .

. + .

. + . . + .

8 =

. + . . + .

. + .

. + . . + .

. + .

. + .

9 =

. + . . + .

. + .

. + .

. + .

. + .

. + .

6 + 4 = 10 0 1 2 3 4 5 6 7 8 9 10

. + . =10 0 1 2 3 4 5 6 7 8 9 10

. + . =10 0 1 2 3 4 5 6 7 8 9 10

. + . =10 0 1 2 3 4 5 6 7 8 9 10

. + . =10 0 1 2 3 4 5 6 7 8 9 10

. + . =10 0 1 2 3 4 5 6 7 8 9 10

. + . =10 0 1 2 3 4 5 6 7 8 9 10

. + . =10 0 1 2 3 4 5 6 7 8 9 10

. + . =10 0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

. + . =10

55 . . . . 49 . . . . 70 . . . .

68 . . . . 41 . . . . . . 99 . . .

17



Rewrite and use your ten frames.

3 + 8 = 8 + 3 = 11 4 + 7 = . + . = . . 2 + 9 = . + . = . .

6 + 7 = . + . = . . 5 + 6 = . + . = . . 4 + 8 = . + . = . .

5 + 8 = . + . = . . 1 + 9 = . + . = . . 3 + 7 = . + . = . .

3 + 9 = . + . = . . 7 + 8 = . + . = . . 4 + 9 = . + . = . .

1 + 8 = . + . = . 3 + 8 = . + . = . . 5 + 7 = . + . = . .

Subtract; the numbers are close!

Example 14 12

16 14 = . 13 12 = . 18 17 = . 12 10 = .

18 16 = . 14 13 = . 17 15 = . 18 18 = .

13 10 = . 16 13 = . 19 17 = . 16 16 = .

17 16 = . 15 14 = . 17 17 = . 15 13 = .

19 18 = . 10 9 = . 14 12 = . 18 15 = .

13 11 = . 14 14 = . 19 19 = . He he, one line to go

12 11 = . 11 10 = . 16 15 = . 13 13 = .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 20 . . . . . . . . . . . . . . 100

Two steps so 14 12 = 2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

18

Double the numbers. Cut off the strip drawn at the bottom of the page.

To find double of 7 put the extra number line

with the zero at 7 and read the number on the top: 14; so

double of 7 is 14.

In the same way find:

Double of 6 is: . . Double of 8 is: . . Double of 5 is: . .

Double of 9 is: . . Double of 4 is: . Double of 3 is: .

Double of 2 is: . Double of 10 is: . . Double of 7 is: . .

Use your ten frames to find half.

Example : half of 12? so half of 12 is 6.

Half of 16 is: . . Half of 18 is: . . Half of 10 is: . .



Use the ten frame for the first sum only.

4 + 3 = 7

14 + 3 = 17

8 4 = .

18 4 = . .

7 + 1 = .

17 + 1 = . .

2 1 = .

12 1 = . .

6 + 4 = . .

16 + 4 = . .

4 3 = .

14 3 = . .

4 + 5 = .

14 + 5 = . .

9 6 = .

19 6 = . .

3 + 7 = . .

13 + 7 = . .

2 + 2 = .

12 + 2 = . .

2 + 7 = .

12 + 7 = . .

3 3 = .

13 3 = . .

4 + 2 = .

14 + 2 = . .

7 5 = .

17 5 = . .

3 + 3 = . .

13 + 3 = . .

8 2 = .

18 2 = . .

1 + 1 = .

11 + 1 = . .

5 4 = .

15 4 = . .

4 + 4 = . .

14 + 4 = . .

9 2 = .

19 2 = . .

5 + 4 = .

15 + 4 = . .

9 7 = .

19 7 = . .

3 + 6 = .

13 + 6 = . .

7 3 = .

17 3 = . .

4 + 4 = . .

14 + 4 = . .

0 1 2 3 4 5 6 7 8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

19



Friends of 10.

. + 3 = 10 . + 9 = 10 . + 1 = 10 . . + 0 = 10 . + 7 = 10

. + 5 = 10 . + 2 = 10 . + 4 = 10 . + 6 = 10 . + 8 = 10

10 4 = . 10 3 = . 10 9 = . 10 5 = . 10 8 = .

10 6 = . 10 2 = . 10 1 = . 10 7 = . 10 0 = . .


11 or 19 5 or 17 10 or 8 14 or 19 1 or 3

8 or 7 14 or 5 16 or 6 12 or 4 9 or 19

2 or 6 17 or 9 20 or 19 18 or 16 3 or 5

12 or 2 13 or 19 14 or 17 12 or 6 13 or 3

How much money?

5 + 5 + 1 = N$ 11 . + . + . + . = . . + . = .

. + . + . = . . + . + . + . = . . + . + . = . .

. . . . . . . . . . . . . . . . . . . . . .

10 20 . . . . . . . . . . . . . . 100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

20

Split the numbers:

4 + . = 7 6 + . = 9 1 + . = 6 5 + . = 6 2 + . = 5

1 + . = 5 2 + . = 8 3 + . = 8 7 + . = 8 3 + . = 5

3 + . = 9 1 + . = 7 2 + . = 9 5 + . = 9 1 + . = 3

2 + . = 4 2 + . = 3 1 + . = 4 3 + . = 6 6 + . = 7

Answer fast:

10 + 4 = . . 10 + 2 = . . 10 + 8 = . . 10 + 0 = . . 10 + 9 = . .

10 + 7 = . . 10 + 9 = . . 10 + 3 = . . 10 + 6 = . . 10 + 5 = . .

Write the number; NO COUNTING!

8 . . . . . . . . . .


18 + 1 = . . 14 8 = . 13 + 5 = . . 20 7 = . . 2 + 17 = . .

13 5 = . 7 + 7 = . . 18 + 2 = . . 11 9 = . 13 + 4 = . .

12 + 4 = . . 7 6 = . 19 9 = . . 7 + 5 = . . 13 + 2 = . .

6 + 2 = . . 19 7 = . . 3 + 9 = . . 17 9 = . 11 + 8 = . .

11 7 = . 9 + 9 = . . 14 + 5 = . . 16 8 = . 12 + 2 = . .

Fill in the neighbors:

76 . . . . 53 . . . . 80 . . . .

29 . . . . 51 . . . . . . 99 . . .

Odd

Even

Odd

Even

Odd

Even

Odd

Even

Odd

Even

Odd

Even

Odd

Even

Odd

Even

Odd

Even

Odd

Even

21

Week 8; Term 1 Theme: Building materials.

NCD This week we start with computation beyond 1-20. The new range is 0-100. It is carefully set up, so That the knowledge build up so far is used all the time. For instance addition in the range 1-10 are used to perform additions on tens: 5 + 2 = 7 then 50 + 20 = 70. By now the expectation is that some of the learners do not use anything else than their mind to get the answer for 5 + 2. If they use counting on the fingers the teacher has to encourage faster methods. So I do not say no fingers but: no counting on the fingers. Learners are supposed to know at this stage that you have 5 fingers on one hand and 2 extra fingers give 7. That should run smoothly somehow. To internalize the basic additions under 10, it is better to use the ten frame. After using it very often; one time they can imagine the ten frame and make the step to mental calculations rather then putting lines or counting with fingers. [It is a bit more cumbersome to look for the 10 frame; to put the bottle tops up and to get the answer. Compared to fingers, they are always available so kids will not easily do away with using fingers to perform basic calculations.] So with the ten frame learners are urged to come to short cuts as compared to fingers. That is the main reason for looking more critical to the use of fingers. A learner who puts up any number under 10 on the fingers and adds and subtract without counting is on the right way; after a lot of practice the fingers will be one time a bygone station. However learners who keep on counting with fingers or pencil lines should be told to use the 10 frame.

At this stage it is important to have the numbers 1, 2, 3,….98, 99, 100 exposed in your class room! The multiples of 10 (10, 20, …,100) should be different then the other numbers. (maybe on a different background colour)






Identify even and odd no in the range

1-100

Add multiples of 10 in the range 1-100

using known number facts.

Subitize items up to five; estimate

groups of items up to 20.

Add and subtract numbers in the range

1-20, bridging the ten.

Use appropriate vocabulary when

comparing lengths.

22



Add, you may use the 10 frame.

5 + 3 = 8 50 + 30= 80 1 + 2 = . 10 + 20= . . 2 + 2 = . 20 + 20 = . .

3 + 2 = . 30 + 20= . . 4 + 1 = . 40 + 10= . . 6 + 2 = . 60 + 20= . .

4 + 5 = . 40 + 50= . . 8 + 1 = . 80 + 10= . . 1 + 1 = . 10 + 10= . .

4 + 3 = . 40 + 30= . . 7 + 2 = . 70 + 20= . . 6 + 3 = . 60 + 30= . .

5 + 2 = . 50 + 20= . . 3 + 3 = . 30 + 30= . . 7 + 2 = . 70 + 20= . .

Connect; which sum can help?

11 + 7 5 + 2 10 + 70 6 + 3

30 + 50 4 + 6 18 + 1 2 + 3

40 + 60 3 + 5 20 + 30 1 + 7

15 + 2 1 + 7 16 + 3 8 + 1


15 or 17 11 or 9 15 or 7 6 or 16 15 or 14

12 or 9 3 or 4 4 or 3 5 or 6 14 or 16

18 or 12 5 or 9 14 or 19 12 or 13 10 or 20

7 or 15 5 or 9 6 or 7 14 or 11 18 or 8

. . . . . . . . . . . . . . . . . . . . . .

10 . . . . . . . . . . . . . . . . 100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

23

Revision: use your ten frames or by heart.

11 + 7 = . . 14 8 = . 12 + 5 = . . 16 8 = . 8 + 8 = . .

17 16 = . 8 + 5 = . . 14 + 4 = . . 17 9 = . 14 + 3 = . .

16 + 3 = . . 9 6 = . 19 6 = . . 8 + 7 = . . 16 + 4 = . .

7 + 7 = . . 17 4= . . 16 7 = . . 15 9 = . 12 + 8 = . .

11 + 1 = . . 10 + 7 = . . 11 + 5 = . . 12 + 3 = . . 14 + 5 = . .

13 6 = . 13 4= . 11 4 = . 11 9 = . 7 + 6 = . .

Find the total length:

Look at: ,...

Which two ropes are the shortest together? Answer: …..

Which two ropes are the longest together? Answer: …..

The friends of 10.

10 = 3 + . 10 = 1 + . 10 = 5 + . 10 = 7 + . 10 = 8 + .

10 = 2 + . 10 = 4 + . 10 = 6 + . 10 = 9 + . 10 = 0 + . .

60 mm 20 mm

60 + 20 = 80 mm

30 mm 70 mm

30 + 70 = . . .

mm

20 mm 70 mm

. . + . . = . . mm

30 mm 60 mm

. . + . . = . . mm

40 mm 30 mm

. . + . . = . . mm

20 mm 40 mm

. . + . . = . . mm

24

Week 9; Term 1 Theme: Public transport.

NCD Counting is done in short exercises verbally in class. Make sure the small sequence (1-10) and the big sequence (10, 20 , …,100) is completely internalized. Only after internalising these two sequences one can count any interval between 0 and 100. Suggestions for counting from easy to more difficult: Small sequence Big sequence 31-32-…-39-40 or any other ten numbers under 100. Bridging a ten: 54-55-…..-64 etc. Counting in tens: 22-32-42-…..-92 Downwards: first the small and big sequence in reverse order. Then & in reverse order. in reverse order. Counting should be done in every lesson but short, maybe only a few minutes. Computation. This is the first time we are to work on multi step problems like 8 + 3 + 2 = ?; as well in a later stage:

12 + 2 7 = ? For learners to build up a practical understanding of addition and subtraction one can use the idea of passengers getting in and out of a minibus. Schematically it can be shown as follows: One can have a nice role play in class with this set up. Appoint a driver and some passengers; when you are part of the minibus you keep both hands on the shoulders of another passenger (first passenger on the driver’s shoulders). In this way you form a “train” of passengers that can move through the class. It stops at certain places and lets passengers out and in. The learners have to translate what they see into mathematical statements.

The requested statement for the diagram drawn above is: 12 + 2 3 = 11 so there will be 11 passengers in the minibus. The worksheet of this week has some activities as well on the minibus. It is very important that the role play is actually done in class before they get the worksheet. (If this is the first time to come across this role play do not hesitate to do it in class; learners will love it).





Count with steps of 10 in the range 1-

100..

Solve multi step problems on addition

and subtraction using a clear context.

Add multiples of 10 in the range 1-100


Associate addition under 10 correctly

with addition of multiples of 10.

Use correct terminology when comparing

c capacity of containers used in daily

life.

12

12 passengers in the bus

2

3 2 passengers get in the bus

3 passengers get out of the bus

25



Fill in the right numbers on the dots. Use your twenty frame

Sum: 12 + 2 = 14 Sum: 9 4 = 5

Sum: . . = . Sum: . . + . = . .

Sum: . . . + . = . . Sum: . . . + . = .

Sum: . . . + . = . . Sum: …………….......= 9


6 or 10 14 or 8 6 or 7 8 or 10 12 or 16

3 or 5 9 or 2 7 or 6 19 or 11 4 or 13

5

7 9

11

1 8

16

2

14

8 5

12

2

12 9

2

8

4

10

. . . . . . . . . . . . . . . . . . . . . .

10 . . . . . . . . . . . . . . . . 100

4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

26

Use your ten frame to work out the first sum.

4+5 = 9 40+50 = 90 3+5 = . 30 + 50 =. . 4+2 = . 40 + 20 = . .

9+1 = . . 90+10 = . .

. 5+2 = . 50 + 20 . . 7+1 = . 70 + 10 = . .

3+6 = . 30 + 60 = . . 1+8 = . 10 + 80 = . . 1+6 = . 10 + 60 = . .

1+1 = . 10 + 10 = . . 4+4 = . 40 + 40 = . . 6+3 = . 60 + 30 = . .

2+7 = . 20 + 70 = . . 2+2 = . 20 + 20 = . . 3+2 = . 30 + 20 = . .

What is the biggest container? How much is it together?

7 + 6 = 13 ℓ

. + . = . . ℓ

. + . = . . ℓ

. + . = . . ℓ

. + . = . . ℓ

. + . = . . ℓ

. + . = . . ℓ

. + . = . . ℓ

. + . = . . ℓ

Revision: use your ten frames or by heart.

5 + 7 = . . 12 8 = . 6 + 5 = . . 17 8 = . 7 + 8 = . .

17 16 = . 7 + 6 = . . 8 + 4 = . 15 9 = . 8 + 3 = . .

6 + 9= . . 16 9 = . 18 12 = . 7 + 7 = . 8 + 6 = . .

6 + 6 = . . 18 9= . 16 7 = . 14 9 = . . 5 + 8 = . .

11 + 6 = . . 10 + 9 = . . 7 + 5 = . . 3 + 9 = . . 14 5 = . .

12 5 = . 17 4 = . . 16 7 = . 14 9 = . . 5 + 8 = . .

7ℓ 6ℓ biggest 8ℓ 9ℓ biggest 5ℓ 8ℓ biggest



27

Week 10; Term 1 Theme: Local media. NCD After adding tens in the previous week, the next stage is adding single digits to multiples of 10. This is to be repeated over and over . One speaks about internalizing this addition, it means that it can be done correctly without the need to think deeply. It is like recognizing a pattern. The reason for doing this type of addition is to build up capacity for mental calculations later on: 38 +17 = 38 + 2 + 15 = 40 + 10 + 5 = 50 + 5 = 55 For these last additions 50 + 5 = 55 there is no need for a number line or ten frame. They can all be done just like that. Of course the issue of place values appears here. It is a must for learners to compare the following additions: 30 + 40 = 70 30 + 4 = 34 In the worksheet of this week 2 different exercises on place value will be given.To discuss the issue of place value one can ask questions like what is more 32 or 23? In the follow up discussion place value tables should appear on the board: Exercises like: 47 = 40 + 7 have limited effect on the level of understanding place values. Often the learners follow the example blindly so that the exercise contributes not much to understanding of our decimal number system. One can challenge a learner by asking 3 tens and 12 ones is which number? A suitable task on 2D shapes can be the following: Give learners up to four identical shapes (triangles; squares and rectangles). Task for the learners: what can you form using several of the given shapes? Some outcome: 2 rectangles: 4 triangles: 4 squares: 2 or 3 squares: as well with right angled triangles: or:


Count forward and backward in selected

intervals up to 100.



Count with steps of 10 in the range 1-100

forwards and backwards starting anywhere

Add a multiple of 10 to a single digit

number speedily.

Use correct terminology when comparing

masses with a simple balance.

Compare 2 or 3 different objects using a

simple balance.

Draw basic geometric shapes like square;

rectangle etc.

Add and subtract numbers in the range 1-20,

bridging the ten.

What is the difference?

TENS UNITS

3 2 2 3

32:

23:

28

A very good game one can play even with grade 2 kids is tangram:

7 shapes that can be put in various ways to show something. On the internet you can easily get more information; these are just a few of the shapes you can form:

These are just but a few examples of shapes you can make with tangram. There are many more easier and more challenging shapes one can make with the 7 basic shapes shown above. For many learners, using all 7 shapes is difficult, one can form as well shapes with less pieces. Tangram is very suitable to challenge fast learners who usually need less time than the average learner to do all the exercises.

29



Form the numbers:

4 Tens; 7 Ones 47 5 Tens; 3 Ones . . 3 Ones; 8 Tens . . !

2 Tens; 9 Ones . . 2 Ones; 7 Tens . . ! 8 Tens; 3 Ones . .

1 One; 7 Tens . . ! 2 Tens; 2 Ones . . 6 Ones; 2 Tens . .

5 Ones; 5 Tens . . 9 Tens; 6 Ones . . 7 Ones; 4 Tens . .

Write down the answer quickly:

40 + 3 = 43 70 + 8 = . . 3 + 70 = . . 50 + 9 = . .

80 + 7 = . . 3 + 60 = . . 30 + 5 = . . 4 + 30 = . .

20 + 9 = . . 6 + 80 = . . 9 + 40 = . . 30 + 5 = . .

70 + 6 = . . 7 + 80 = . . 20 + 8 = . . 8 + 90 = . .

What is the number? Is it odd or even?

. . . . . . . . . . . . . . . . . . . . . .

10 . . . . . . . . . . . . . . . . 100

Number is: . . …… Number is: . .

………. Number is: 43odd

30

Draw the circles in the two ten frames:

Revision: Use your ten frames or by heart.

6 + 8 = . . 13 9 = . 7 + 9 = . . 13 5 = . 6 + 6 = . .

19 13 = . 8 + 7 = . . 9 + 2 = . . 15 9 = . 3 + 9 = . .

5 + 7= . . 12 9 = . 17 11 = . 8 + 8 = . . 4 + 9 = . .

7 + 7 = . . 15 9= . 16 7 = . 17 9 = . . 6 + 9 = . .

14 + 6 = . . 3 + 9 = . . 5 + 5 = . . 4 + 8 = . . 16 8 = .

What is it? Colour all the triangles and the squares.

18 Even

Odd 13

Even

Odd 19

Even

Odd 16

Even

Odd 12

Even

Odd 15

Even

Odd

Number is: . . …….. Number is: . . ……..

…….. ……..

31

Week 11-12; Term 1 Theme: Local business.

NCD Counting in twos is done up to 20; counting in three’s up to 30; counting in five’s up to 50 and counting in ten’s is done up to 100; all this is done in preparation of learning the multiplication tables for 2; 3; 5 and 10. Counting in twos in the interval 20 – 100 is not necessary; it is not a skill that contributes significantly to Number Concept Development. The point is there are better things to do to increase NCD. For addition we repeat what has been done before; learners are to answer swiftly additions like: 50 + 6 = 56. No fingers; no ten frame is needed; it is more a visual thing: the 6 replaces the 0 in 50. Very important is as well bridging the 10 in addition and subtraction. Learners are to internalize additions like 3 + 4; but when it comes to 8 + 7 we expect some steps to be taken. For 8 + 7 first find a proper number bond for 7 (here 7 = 2 + 5) Notation is very important; if the book you are using does not suggest a suitable notation one can use: 8 and 2 are friends of 10.

Learners have more difficulties with: 8 + 7 = 8 + 2 + 5 = 10 + 5 = 15, since that is quite long. In the worksheets some questions will be given that look like the above notation.


Count forward and backward in selected

intervals up to 100.



Count with steps of 10 in the range 1-100

forwards and backwards starting

anywhere

Recognize number images using hands;

ten frames and tallies up to 20.[No

counting]

Mention the correct number bonds for 2-

9.

Identify the friends of 10 through addition

& subtraction.

Add a multiple of 10 to a single digit

number speedily.

Identify N$10 and N$20 notes.

Make correct payments with coins up to

N$5 correctly [No change]

2 + 5

8 + 7 = 10 + 5 = 15

32


Fill in the numbers on the dots:

The friends of 10.

8 + . = 10 6 + . = 10 7 + . = 10 1 + . = 10 3 + . = 10

2 + . = 10 4 + . = 10 9 + . = 10 5 + . = 10

Cross the ten. Use your ten frames.

Subtract from 10.

10 3 = . 10 9 = . 10 5 = . 10 2 = . 10 8 = .

10 6 = . 10 4 = . 10 1 = . 10 7 = . 10 0 = .

What is more? How much more? Subtract!

5 or 7 ? 8 or 3 ? 2 or 9 ? 5 or 6 ? 10 or 14?

7 is 2 more

than 5

. is . more

than .

. is . more

than .

. is . more

than .

. . is . more

than . .

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2 + 5

8 + 7 = 10 + 5 = 15

. + .

3 + 9 = 10 + . = . .

. + .

5 + 6 = 10 + . = . .

. + .

7 + 6 = 10 + . = . .

. + .

4 + 7 = 10 + . = . .

. + .

7 + 5 = 10 + . = . .

. + .

9 + 2 = 10 + . = . .

. + .

8 + 5 = 10 + . = . .

. + .

6 + 9 = 10 + . = . .

. + .

8 + 4 = 10 + . = . .

. + .

9 + 5 = 10 + . = . .

. + .

5 + 7 = 10 + . = . .

. 2 4 . 20 . . . . . . . . . .

3 6 30 . . . . . . . . . . . . .

33

Subtraction across the ten. You may use your ten frames.

16 7 = 10 1 = 9

6 + 1

17 9 = 10 . = .

. + .

14 8 = 10 . = .

. + .

12 5 = 10 . = .

. + .

13 6 = 10 . = .

. + .

11 4 = 10 . = .

. + .

17 8 = 10 . = .

. + .

11 8 = 10 . = .

. + .

16 7 = 10 . = .

. + .

13 4 = 10 . = .

. + .

15 6 = 10 . = .

. + .

18 9 = 10 . = .

. + .

How can I pay?

Money: Article:

none

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

N$ 8

. . . . . .

N$ 12

N$ 18

N$ 9

N$ 19

N$16

N$ 17

34


Fill in the numbers on the dots:

Subtract: no ten frames are needed.

13 3 = . . 19 9 = . . 15 5 = . . 12 2 = . . 18 8 = . .

16 6 = . . 14 4 = . . 11 1 = . . 17 7 = . . 10 0 = . .

Add or subtract, across the 10. You can use the 10 frames.

12 8 = 10 . = .

. + .

7 + 6 = 10 + . = . .

. + .

15 9 = 10 . = .

. + .

9 + 2 = 10 + . = . .

. + .

14 7 = 10 . = . .

. + .

3 + 8 = 10 + . = . .

. + .

18 9 = 10 . = .

. + .

4 + 7 = 10 + . = . .

. + .

13 5 = 10 . = .

. + .

6 + 5 = 10 + . = . .

. + .

11 4 = 10 . = .

. + .

5 + 6 = 10 + . = . .

. + .

13 7 = 10 . = .

. + .

8 + 8 = 10 + . = . .

. + .

16 7 = 10 . = .

. + .

7 + 7 = 10 + . = . .

. + .

17 9 = 10 . = .

. + .

4 + 9 = 10 + . = . .

. + .

15 6 = 10 . = .

. + .

9 + 9 = 10 + . = . .

. + .

13 4 = 10 . = .

. + .

5 + 9 = 10 + . = . .

. + .

12 5 = 10 . = .

. + .

2 + 9 = 10 + . = . .

. + .

15 7 = 10 . = .

. + .

4 + 8 = 10 + . = . .

. + .

16 8 = 10 . = .

. + .

12 6 = 10 . = .

. + .

5 + 7 = 10 + . = . .

. + .

14 5= 10 . = .

. + .

. 3 6 30 . . . . . . . . . . . .

5 . . . . . . . . . . . . . . . . 50

10 . . . . . . . . . . . . . . . . 100

35

Add quickly; look at the pattern.

60 + 5 = . . 50 + 3 = . . 9 + 60 = . . 20 + 4 = . .

20 + 5 = . . 1 + 10 = . . 40 + 4 = . . 2 + 90 = . .

40 + 7 = . . 3 + 20 = . . 6 + 70 = . . 20 + 8 = . .

80 + 2 = . . 5 + 60 = . . 30 + 5 = . . 7 + 70 = . .

30 + 9 = . . 7 + 50 = . . 40 + 8 = . . 2 + 80 = . .

The 10 dollar note: The 20 dollar note: How many five’s?

N$ 10 = ……….. N$ 20 = ………………….

Use your ten frames to find half.

Half of 16 is: . Half of 20 is: . . Half of 8 is: .

Half of 6 is: . Half of 12 is: . Half of 18 is: .

Half of 10 is: . Half of 4 is: . Half of 14 is: .

Double the numbers. Use your ten frames:

Double of 6 is: 12 Double of 9 is: . . Double of 7 is: . .

Double of 4 is: . Double of 5 is: . . Double of 10 is: . .

Double of 3 is: . Double of 2 is: . Double of 8 is: . .

36

Week 13; Term 2. Theme: Autumn.

NCD. Counting with steps of 10 is important for addition and subtraction in the range of 0-100. In the worksheet some exercises will be given for this skill. Slowly the computational skills are expanded; step by step; always using what has been learnt in the past. Phase 3 is concerning addition within a ten like: 34 + 5 = 39. This addition will be linked to 4 + 5 = 9 For obvious reasons. For how many learners is the addition in the range 1-10 fully automatic? [It means they just know the answer of 3 + 6; if you ask them: how did you get it, they are taken aback, because it is just a fact to them] If there is a substantial part of the learners that uses a paper putting lines or counts fingers; more practice is needed. The practice can be done in different ways. Flashcards with additions on it is one way, although it does not offer much structure; better is two ten frames with circles on them that represent numbers. Like this: answer: 5 + 3 = 8. Number recognition plays an important role here. If learners recognize the two configurations for 8 quickly: and it helps addition a lot in adding numbers. The addition in the range of 0-10 I as well directly linked with the number bonds. An exercise will be given in the worksheet of this week.



selected intervals up to 100



Count with steps of 10 forward

backward, any starting point. <100

Name parts of a whole: halves and

quarters.

Add within a decade, using known

number facts.

Use vocabulary correct when

comparing mass and capacity.

Mention the friends of ten.

Mention the number bonds of 2-9.

Add numbers below 10 mechanically.

+

37


Count with steps of ten:

What number is it? Do not count!

Write on the dots if it is even or odd.

Odd ……. ……… ………

……. ……. ……… ………

……. ……. ……… ………

Use the first sum to answer the second sum.

3 + 4 = 7

23 + 4 = . .

6 + 2 = 8

46 + 2 = . .

3 + 2 = 5

63 + 2 = . .

5 + 2 = 7

55 + 2 = . .

5 + 3 = .

75 + 3 = . .

1 + 7 = .

91 + 7 = . .

8 + 1 = .

48 + 1 = . .

4 + 4 = .

84 + 4 = . .

3 + 3 = .

33 + 3 = . .

5 + 4 = .

65 + 4 = . .

6 + 3 = .

66 + 3 = . .

7 + 2 = .

37 + 2 = . .

6 + 1 = .

46 + 1 = . .

5 + 5 = . .

75 + 5 = . .

6 + 4 = . .

26 + 4 = . .

5 + 1 = .

55 + 1 = . .

6 + 1 = .

46 + 1 = . .

4 + 2 = . .

54 + 2 = . .

3 + 7 = . .

63 + 7 = . .

2 + 1 = .

82 + 1 = . .

. . . .

. . . .

. . . .

10 . . . . . . . . . . . . . . 100 . .

. . . . . . . . . . . . . . 16 26

38

How big is this part? Color one quarter

:

Color one

half: ………………

………………

Friends of ten.

4 + . = 10 7 + . = 10 3 + . = 10 2 + . = 10 6 + . = 10

1 + . = 10 8 + . = 10 9 + . = 10 5 + . = 10

Jump the 10. Use your 10 frames. No counting!

17 – 9 = . 4 + 7 = . . 14 – 6 = . 5 + 8 = . .

9 + 2 = . . 11 – 4 = . 7 + 5 = . . 13 – 6 = .

14 – 5 = . 6 + 5 = . . 15 – 6 = . 3 + 7 = . .

6 + 6 = . . 14 – 7 = . 6 + 9 = . . 12 – 5 = .

Use your ten frame(s) Cross the wrong option: even or odd.

Half of 16 is 8 odd

Half of 12 is . odd

Half of 10 is . odd

even even even

Half of 14 is . odd

Half of 20 is . odd

Half of 8 is . odd

even even even

Half of 6 is . odd

Half of 18 is . odd

Half of 4 is . odd

even even even

What is more? How much more? Subtract: 8 – 3 = 5

3 or 8 ? 4 or 7 ? 1 or 6 ? 8 or 2 ? 12 or 18?

8 is 5 more

than 3

. is . more

than .

. is . more

than .

. is . more

than .

. . is . more

than . .

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

39

Week 14-15; Term 2 Theme: Cleanliness.

NCD This week the multiplication time table of 2 is to be introduced. Objects that usually appear in pairs are to be used. Like a pair of shoes or couples. The worksheet will have an exercise on the time table of 2. Addition and subtraction are taken to the next level. Addition is done within a decade; not crossing to the next 10. Learners are suppose to be very fluent in addition under 10, (no fingers; no lines on a paper by now) this knowledge is to be transferred to addition within a decade.

4 + 5 = 9 54 + 5 = 59. Subtraction with tens is as well compared to subtraction of numbers between 1-10. What can be done if learners are not fluent in adding and subtracting under ten? More practice is the obvious answer; how can it be done? Below a few suggestions: Show an empty ten frame and point which ones will be covered when adding 4 + 3 which other 3 will be covered? [Of course one can start with the bottle tops if learners are not responsive] A number line: starting at 4, counting on with 3. Fingers: put 4 at one hand and 3 on the other hand. [Fingers are somehow associated with counting one by one, so the use of fingers can block further internalization of basic addition and subtraction] The key to internalization is repetition; by doing it over and over again it will in the end be automatic. But it is knowledge which needs maintenance. After a holiday this knowledge needs to be brought to the front of the memory. This week all the coins will be introduced; the relation of cents and dollars are not yet to be revealed, it is all money, you can buy things with money; that is about it. If learners ask for the relation one can say 100 cents make a dollar, no exercises yet.




Count in 2’s up to 20 using the ×

sign.




Write correctly number names for 1-

10.

Add within a decade, using known

number facts.

Subtract multiples of 10 in the range

1-100 using known number facts.

Measure capacity using the liter

notation (ℓ).

Name & identify all Namibian coins

and the 20 and 50 dollar bank notes.

Determine change in coins for

payments up to N$20.

Identify and name basic geometric

shapes.

40



Subtract; use the first one to do the second one.

7 5 = 2 70 50 = 20

8 3 = . 80 30 = . .

6 1 = . 60 10 = . . 4 1 = . 40 10 = . .

6 4 = . 60 40 = . . 9 2 = . 90 20 = . .

5 3 = . 50 30 = . . 7 4 = . 70 40 = . .

8 7 = . 80 70 = . . 3 2 = . 30 20 = . .

9 8 = . 90 80 = . . 5 4 = . 50 40 = . .

4 2 = . 40 20 = . . 6 5 = . 60 50 = . .


5 + 1 = 6

75 + 1 = . .

7 + 1 = .

57 + 1 = . .

6 + 3 = .

46 + 3 = . .

4 + 4 = .

84 + 4 = . .

8 + 1 = .

78 + 1 = . .

5 + 2 = .

25 + 2 = . .

4 + 2 = .

94 + 2 = . .

3 + 3 = .

33 + 3 = . .

6 + 1 = .

36 + 1 = . .

5 + 4 = .

85 + 4 = . .

2 + 7 = .

42 + 7 = . .

7 + 2 = .

97 + 2 = . .

4 + 3 = .

74 + 3 = . .

5 + 5 = . .

65 + 5 = . .

2 + 6 = . .

32 + 6 = . .

7 + 3 = .

77 + 3 = . .

9 + 1 = . .

99 + 1 = . . .

2 + 3 = .

42 + 3 = . .

2 + 4 = .

52 + 4 = . .

4 + 1 = .

44 + 1 = . .

1 + 5 = .

81 + 5 = . .

4 + 3 = . .

54 + 3 = . .

6 + 2 = . .

36 + 2 = . .

1 + 2 = .

61+ 2 = . .

10 . . . . . . . . . . . . . . 100 . .

. . . . . . . . . . . . . . 11 21

41

Jump the 10. Use your 10 frames. No counting!

14 7 = . 6 + 9 = . . 12 4 = . 3 + 8 = . .

7 + 7 = . . 13 6 = . 2 + 9 = . . 17 9 = .

14 7 = . 6 + 9 = . . 12 4 = . 3 + 8 = . .

6 + 8 = . . 15 8 = . 5 + 5 = . . 13 4 = .

11 3 = . 9 + 8 = . . 13 8 = . 4 + 7 = . .

How many wheels?

Bicycles Wheels Coins

1 × 2 = 2

2 × 2 = .

3 × 2 = .

. × 2 = .

. × 2 = . .

. × 2 = . .

. × 2 = . .

. × 2 = . .

. × 2 = . .

. . × 2 = . .

What is more; how much more? Subtract: 6 – 2 = 4

2 or 6 ? 8 or 6 ? 2 or 7 ? 4 or 5 ? 11 or 14?

6 2 = .

. more.

. . = .

. more.

. . = .

. more.

. . = .

. more.

. . . . = .

. more.

3 or 12 ? 7 or 5 ? 1 or 10 ? 5 or 8 ? 17 or 12?

. . . = .

. more.

. . = .

. more.

. . . = .

. more.

. . = .

. more.

. . . . = .

. more.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

42



Times table of 2.

3 × 2 = 6

shoes

. × 2 = . .

shoes

. × 2 = . .

shoes

. × 2 = . .

shoes

. × 2 = .

shoes

10 . . . . . . . . . . . . . .

. . . . . . . . . . . .

. . 100

. . 144

24

. . × 2 = . .

shoes

. × 2 = .

shoes

. × 2 = . .

socks

. × 2 = . .

shoes

. × 2 = . .

shoes

43


7 2 = 5

70 20 = 50

8 6 = 2

80 60 = . .

4 3 = .

40 30 = . .

6 5 = .

60 50 = . .

3 2 = .

30 20 = . .

8 2 = .

80 20 = . .

9 7 = .

90 70 = . .

5 4 = .

50 40 = . .

6 4 = .

60 40 = . .

7 3 = .

70 30 = . .

5 3 = .

50 30 = . .

6 1 = .

60 10 = . .

5 2 = .

50 20 = . .

9 4 = .

90 40 = . .

4 2 = .

40 20 = . .

7 4 = .

70 40 = . .

Use your ten frames.

18 9 = . 4 + 7 = . . 13 8 = . 5 + 7 = . .

6 + 7 = . . 11 8 = . 3 + 8 = . . 16 8 = .

13 4 = . 8 + 8 = . . 15 7 = . 1 + 9 = . .

Use the first sum to do the other sum.

4 + 3 = 7 24 + 3 = 27

2 + 6 = . 52 + 6 = . .

5 + 1 = . 85 + 1 = . . 7 + 2 = . 47 + 2 = . .

3 +3 = . 63 + 3 = . . 4 + 5 = . 74 + 5 = . .

2 + 6 = . 32 + 6 = . . 1 + 7 = . 91 + 7 = . .

6 + 3 = . 46 + 3 = . . 8 + 1 = . 88 + 1 = . .

What is more; how much more?

12 or 5 ? 11 or 9 ? 17 or 7 ? 8 or 9 ? 19 or 17?

12 5 = .

. more.

. . . = .

. more.

. . . = . .

. . more.

. . = .

. more.

. . . . = .

. more.

8 or 15 ? 13 or 10 ? 6 or 12 ? 15 or 8 ? 20 or 12?

12 5 = .

. more.

. . . = .

. more.

. . . = . .

. . more.

. . = .

. more.

. . . . = .

. more.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

44

Week 16-17; Term 2 Theme: Function of the 5 senses This two weeks important new additions and subtraction are done. The problem with: 38 + 6 = 38 + 2 + 4 = 40 + 4 = 44 is, that it is too long for many learners. Of course one can shorten the notation: 38 + 6 = 40 + 4 = 44 if that doesn’t help one better analyses what is difficult for the learners. Different steps are taken and all these steps should go smoothly before an addition like this can be done in the proper way. Check if your learners can do all these steps separately. Step friend of 8 is 2. Step the 6 is split into 2 and 4. Step Which 10 follows the 30 because the 8 + 2 Make another 10. Step the left over number has to be added to 40. Quite helpful can be the empty number line: (empty is relative here, I give 2 examples.) Possible class discussion on this topic 38 + 6 = 44:

Drawn on the board: Questions asked: Comments:

What numbers can be put in the boxes?

Distances between the boxes is equal. Numbers are filled in.

Where is 38? If the learner points half way between 30 and 40 the next question is: closer to 30 than to 40?

If we add 6 to 38, will we pass the 40?

If learners say no, go back to 8 + 6. Is it more or less than 10?

How much do we add to 38 to reach 40?

If this is difficult one can ask what number is between 38 and 40? So 38 + . = 40 ( analogy 8 and 10) The answer 2 is obtained. (Friends of ten!)




Count in 2’s up to 20 using the ×

sign.




Add a single digit number to a two

digit number, bridging a multiple of

10, using known number facts.

Subtract a single digit from a

multiple of 10 <100, using known

number facts.

Order numbers in the range of 1-

20and work out the difference using

a number line.

Mention days of the week and

months of a year.

Distract relevant information from a

calendar page.

2 4

0 10 . . . . . . . .

0 10 20 30 40 50

0 10 20 30 40 50

38

0 10 20 30 40 50

38

0 38 30 10

+ 2

+ 4

20 40 50 44

0 38 40 44

+2 + 4

45

Drawn on the board: Questions asked: Comments:

If we get 2 out 6, how much is left?

Learners may use the ten frame if they have difficulties in answering this question.

38 + 6 = 38 + . + . = 40 + 4 = . . Fill in the numbers on the dots.

The addition can be done as well on the number line; the number line drawn here is a bit small to show it nicely

For the subtraction of these weeks the friends of 10 have to be revised.

0 10 20 30 40 50

38 39

46



Friends of 10, fill in the number on the dots.

7 + . = 10 5+ . = 10 3 + . = 10 1 + . = 10 8 + . = 10

2 + . = 10 6 + . = 10 9 + . = 10 4 + . = 10

Split the numbers.

6 = 4 + . 7 = 2 + . 5 = 4 + . 6 = 3 + . 3 = 2 + .

8 = 4 + . 9 = 1 + . 7 = 1 + . 8 =2 + . 4 = 3 + .

5 = 2 + . 7 = 3 + . 3 = 1 + . 9 = 8 + . 8 = 7 + .

9 = 2 + . 8 = 3 + . 9 = 3 + . 5 = 3 + . 9 = 7 + .

6 = 5 + . 4 = 2 + . 5 = 1 + . 7 = 4 + . 8 = 1 + .

8 = 5 + . 7 = 6 + . 9 = 4 + . 8 = 6 + . 6 = 2 + .

Write the next number:

Answer fast; no fingers; no ten frame.

30 + 5 = . . 40 + 2 = . . 70 + 1 = . . 60 + 9 = . . 20 + 4 = . .

50 + 6 = . . 30 + 3 = . . 10 + 7 = . . 40 + 5 = . . 90 + 9 = . .

60 + 8 = . . 70 + 7 = . . 40 + 1 = . . 90 + 7 = . . 10 + 2 = . .

10 + 4 = . . 50 + 5 = . . 70 + 6 = . . 20 + 2 = . . 80 + 0 = . .

40 + 3 = . . 40 + 6 = . . 30 + 1 = . . 40 + 5 = . . 80 + 7 = . .

30 . . 20 50 . . 40 80 . . 70

60 . . 50

0 20 . . 10 40 . . 30

10 . . . . . . . . . . . . . .

. . . . . . . . . . . .

. . 100

. . 124

22

47

Fill in the right numbers on the dots.

Use the number line to add.

Put the days in the right order:

Days One week

Friday Sunday

Tuesday

Saturday

Sunday

Wednesday

Thursday

Monday

28 + 6 = 34

20 30 40

28

+2

34

+ 4

35 + 7 = . .

30 40 50

. .

+ .

. .

+ .

77 + 5 = . .

. . . . 90

53 + 9 = . .

50 60 70 . .

+ .

. .

+ .

28 + 7 = 30 + 5 =

35 2 5

34 + 7 = . . + . = .

. . .

46 + 5 = 50 + . =

51 . .

37 + 4 = . . + . = .

. . . 25 + 9 = . . + . = .

. . .

59 + 2 = . . + . = .

. . .

66 + 8 = . . + . = .

. . . 63+ 8 = . . + . = . .

. .

88 + 3 = . . + . = . .

. . 38+ 4 = . . + . = . .

. .

57 + 5 = . . + . = .

. . .

27 + 5 = . . + . = .

. . .

22 + 9 = . . + . = .

. . .

75 + 7 = . . + . = .

. . .

49 + 6 = . . + . = .

. . .

48



Friends of ten

10 3 = . 10 5 = . 10 2 = . 10 9 = . 10 7 = .

10 6 = . 10 8 = . 10 4 = . 10 1 = .

Use the 1st subtraction to do the 2nd.

10 8 = 2 40 8 = 32

10 4 = . 70 4 = . .

10 5 = . 80 5 = . . 10 6 = . 30 6 = . .

10 3 = . 60 3 = . . 10 1 = . 20 1 = . .

10 7 = . 90 7 = . . 10 2 = . 50 2 = . .

10 9 = . 80 9 = . . 10 10 = . 60 10 = . .

10 6 = . 40 6 = . . 10 3 = . 20 3 = . .

10 2 = . 60 2 = . . 10 8 = . 70 8 = . .

What is more; how much more?

6 or 16 ? 18 or 7 ? 10 or 2 ? 4 or 16 ? 18 or 14?

16 6 = . .

. . more.

. . . = . .

. . more.

. . . = .

. more.

. . . = . .

. . more.

. . . . = .

. more.

3 or 11 ? 14 or 9 ? 10 or 20 ? 16 or 5 ? 12 or 13?

. . . = . .

. more.

. . . = .

. more.

. . . . =. .

. . more.

. . . = . .

. . more.

. . . . = .

. more.

2 or 7 ? 19 or 18 ? 15 or 5 ? 6 or 10 ? 4 or 17?

16 6 = . .

. . more.

. . . = . .

. more.

. . . = .

. . more.

. . . = .

. more.

. . . = . .

. . more.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

10 . . . . . . . . . . . . . .

. . . . . . . . . . . .

. . 100

. . 174

27

49

Put the months in order, draw the arrows.

February 1. January

October 7. July

March 2. August 8.

January 3. December 9.

April 4. November 10.

June 5. July 11.

May 6. September 12.

What is the day?

June 18 Wednesday

June 9 ……………..

June 28 ……………..

June 13 ……………..

June 5 ……………..

Revision, you may use your frames.

20 + 30 = . . 70 20 = . . 34 + 5 = . . 50 + 8 = . .

80 40 = . . 81 + 6 = . . 40 + 7 = . . 71 + 6 = . .

80 + 10 = . . 90 60 = . . 62 + 6 = . . 40 + 3 = . .

70 10 = . . 42 + 3 = . . 20 + 2 = . . 33 + 5 = . .

77 + 1 = . . 30 + 9 = . . 40 + 40 = . . 60 50 = . .

90 + 6 = . . 52 + 2 = . . 40 30 = . . 66 + 3 = . .

55 + 3 = . . 70 + 3 = . . 30 + 30 = . . 80 70 = . .

20 + 5 = . . 83 + 4 = . . 60 60 = . . 42 + 7 = . .

42 + 6 = . . 90 + 5 = . . 30 + 60 = . . 90 20 = . .

40 + 9 = . . 74 + 2 = . . 70 10 = . . 43 + 6 = . .

50

Grade 2 week 18; Term 2 Theme: Winter.

NCD The concept of place values can be discussed in class. One can write on the board: 23 and 32 and ask questions like: Are they the same? What is the difference? You will discuss place values in this way. One can ask again questions like: Given a 2 and a 5, form the biggest possible number, using each digit once. [The answer is 52.] Or a bit more challenging: given the digits 2; 5 and 7, how many different numbers under 100 can you form, using each digit once? [They are: 25 and 52; 27 and 72 and lastly: 75 and 57.] For Phase 4 (P+4) it is necessary that the addition up to ten goes very fluently. If this is not the case practice with the ten frame(s). 2 + 6 for instance can be done as follows: Or it can be done with two frames: Learners are stimulated to find there own ways of calculating sums, as long as counting one by one is not done.

For subtraction the friends of 10 are used, revise them first before phase (P2 ) is started.

This revision can be done by using flashcards: learners mention 10 3 = 7. Repetition is the key, by doing things over and over again they enter a part of the brain with facts that are directly available, just like your name, the name of your sister etc. The friends of ten give one addition and two subtractions.

For instance 2 and 8 are friends of 10 so 2 + 8 = 10; 10 8 = 2 and 10 2 = 8. There will be an exercise on this in the worksheets. A big clock face is available in the appendices for grade 2. The hands of the clock are drawn as well, they can be cut out and fixed with a pin to the centre of the clock face. To make it more durable one can stick this sheet on a carton. Make sure the small hand is nicely half way between two numbers on the clock face when it is half past the hour.

Possible lesson objectives wk 18

At the end of the week learners will be able to:



Count in 2’s up to 20 using the × sign.

Count in 5’s and 10’s up to 100.


backward, any starting point. <100.

Mention all possible number bonds for

all number between 2-9.

Mention the friends of ten speedily.

Add a single digit number to a two digit

number, bridging a multiple of 10,


Subtract a single digit from a multiple

of 10 that is less than 100, using

known number facts.

Read the time correctly from a clock

face (whole hours and half hours)

51



Count with steps of five:

Number bonds.

2 3 4 5 6 7 8 9

1 + 1 1 + 2 1 + . . + . . + . . + . . + . . + .

2 + 1 2 + . . + . . + . . + . . + . . + .

. + . . + . . + . . + . . + . . + .

. + . . + . . + . . + . . + .

. + . . + . . + . . + .

. + . . + . . + .

. + . . + .

. + .

Make a number.

Digits: 4; 3 5; 9 7; 2 8; 1 6; 9 4; 5 0; 1

Place Values: T U T U T U T U T U T U T U

Biggest number: 4 3 . . . . . . . . . . . .

Smallest

number:

3 4 . . . . . . . . . . . .

Expand:

14 = 10 + . 36 = 30 + . 45 = . . + . 89 = . . + . 78 = . . + .

26 = . . + . . . = 50 + 7 83 = . . + . . . = 30 + 5 21 = . . + .

. 1 = 30 + . 54 = . . + . . . = 40 + 4 90 = . . + . . . = 60 + 6

10 . . . . . . . . . . . . . .

. . . . . . . . . . . .

. . 100

. . 194

29

5 10 . . . . . . . . . . . . . . . .

52

Use the 1st addition to do the 2nd.

8 + 4 = 12 28 + 4 = 32

7 + 6 = 13 47 + 6 = . .

9 + 3 = . . 69 + 3 = . . 6 + 5 = . . 86 + 5 = . .

5 + 7 = . . 55 + 7 = . . 4 + 9 = . . 14 + 9 = . .

3 + 8 = . . 73 + 8 = . . 9 + 2 = . . 59 + 2 = . .

6 + 6 = . . 46 + 6 = . . 7 + 8 = . . 87 + 8 = . .

8 + 2 = . . 28 + 2 = . . 7 + 4 = . . 77 + 4 = . .

5 + 9 = . . 35 + 9= . . 8 + 6 = . . 28 + 6 = . .

Use the first one to do the second sum.

10 7 = 3

50 7 = 43

10 2 = .

70 2 = . .

10 1 = .

40 1 = . .

10 9 = .

30 9 = . .

10 4 = .

60 4 = . .

10 7 = .

20 7 = . .

10 5 = .

90 5 = . .

10 6 = .

80 2 = . . .

10 8 = .

40 8 = . .

10 1 = .

30 1 = . .

10 7 = .

70 7 = . .

10 4 = .

50 4 = . . .

10 3 = .

60 3 = . .

10 5 = .

50 5 = . .

10 6 = .

100 6 = . .

10 2 = .

40 2 = . . .

10 9 = .

30 9 = . .

10 7 = .

20 7 = . .

10 4 = .

80 4 = . .

10 8 = .

70 8 = . ..

10 7 = .

60 7 = . .

10 4 = .

80 4 = . .

10 5 = .

60 4 = . .

10 2 = .

40 8 = . ..

What is the time?

. o’clock . o’clock . o’clock . . . . . . . . . .

53

Week 19; Term 2. Theme: Caring for friends

NCD. This week the new addition is adding a multiple of ten to any number like 21 + 30 = 51. Some learners with understanding of place value may be able to perform this addition on an abstract level; but many learners will be understanding this better if concrete material is used. In class you have to work with sticks and elastic bands or with beans and a small transparent plastic sacks (Banks provide these free of charge if you tell them that you want to deposit many coins). You put ten beans in a sack or bundle 10 sticks to represent a ten. 21 + 30 = 51 can be visualized as follows:

+ = 51 The learners will get a deeper understanding what the 1; 2; 3 and the 5 stand for. Learners should be given the opportunity to work with beans/sticks themselves or in groups. In the worksheet some exercises with ten frames will be given. The role play on buying and selling can best be done using articles up to N$ 50, not mixing dollars and cents. To make things look very realistic some specimen of coins and paper money is included in the appendix of year 2 teacher’s guide. They can be glued to thick paper or carton and used more than once. The two times table can be practiced in a more abstract form. In the worksheets there is one exercise on this.







backward, any starting point. (<100)

Add 2 digits and a multiple of 10

(decade) in the interval 1-100.

Participate in a role play on selling and

buying articles, including finding

change.

Collect relevant information and

represent the info in a suitable way.

Bridging the 10 with addition &

subtraction (revision)

54



Write the sum and add.

Or . . + . . = . .

Or . . + . . = . .

Or . . + . . = . .

Or . . + . . = . .

Now without the ten frames.

4 + 2 = 6 46 + 20 = 66 2 + 6 = . 21 + 60 = . .

3 + 1 = . 37 + 10 = . . 6 + 3 = . 64 + 30 = . .

5 +4 = . 51 + 40 = . . 5 + 2 = . 52 + 20 = . .

4 + 5 = . 43 + 50 = . . 1 + 7 = . 14 + 70 = . .

7 + 2 = . 76 + 20 = . . 4 + 4 = . 43 + 40 = . .

3 + 3 = . 34 + 30 = . . 3 + 5 = . 38 + 50 = . .

4 + 3 = . 46 + 30 = . . 3 + 2 = . 37 + 20 = . .

2 + 5 = . 29 + 50 = . . 6 + 2 = . 65 + 20 = . .

88

10 . . . . . . . . . . . . . . 100 . .

. . . . . . . . . . . . 98 . .

= . . +

+ = . .

+ = . .

+ = . .

55

Buying and selling.

Lucy has in her shop: bread N$9; sugar N$6 and milk N$13.

Bought: Paid with: Change

Sugar N$ 10 10 6 = N$ 4

Bread N$ 10 10 . = N$ .

Milk N$ 15 . . . . = N$ .

Milk N$ 20 . . . . = N$ . .

Sugar and bread N$ 20 6 + 9 = 15 20 15 = N$ 5

Sugar and milk N$ 20 6 + . . = . . 20 . . = N$ .

Milk and bread N$ 30 . . + . . = . . . . . . = N$ . .

Groups of 2; no counting!

● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

3 × 2 = 6 . × 2 = . . × 2 = . . × 2 = . . × 2 = .

● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

. × 2 = . . . × 2 = . . . × 2 = . . . × 2 = . . . × 2 = . .

Use the 20 frame.

14 7 = . 8 + 3 = . . 15 8 = . 17 + 3 = . .

9 + 6 = . . 11 9 = . 7 + 8 = . . 13 4 = .


5 or 12 ? 2 or 11 ? 12 or 16 ? 7 or 17 ? 10 or 20?

12 is 7 more

than 5

. is . more

than .

. is . more

than .

. is . more

than .

. . is . more

than . .

13 or 7 ? 8 or 12 ? 14 or 15 ? 10 or 14 ? 18 or 17?

12 is 7 more

than 5

. is . more

than .

. is . more

than .

. is . more

than .

. . is . more

than . .

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

56

Week 20-21; Term 2 Theme: Being Safe.

NCD. The time table of ten is scheduled for this week. It will not be a problem since the learners have been counting in tens before.

The subtraction that are new is looking like: 38 2. At this stage we are not yet bridging the ten. The sentence used in the syllabus is: using known number facts. It means here

8 2 = 6 38 2 = 36. So you have to make sure that these basic number facts as they are called are revised first. This week learners are going to measure lengths in cm. The activity is best done with rulers looking like: The white and black parts of the ruler have a length of exactly 1cm. The learners have actually to count the cm one by one. At this stage this is better, the ruler with mm and numbers on them is too sophisticated. If your class is ready for it bring a hanger for clothes into the classroom.










Subtract a single digit from any number

less than 100, not bridging the ten.

Measure length of short objects correct

to the nearest cm.

Use the correct vocabulary when

comparing lengths of objects.

Cut squares; rectangles and triangles

from recycled materials

Recite the times table of 10.

Identify halves and quarters.

A B

C

What is shorter? The distance from A to B or the distance from A to C plus the distance from C to B? The distances can be put on the board or one can use ropes to establish that AB is slightly shorter. This will establish the rule that the shortest distance between two points is the straight line between these two points.

57



Work out by heart, no fingers. You may look at your 10

frame.

6 4 = . 4 3 = . 8 5 = . 2 1 = . 8 1 = .

7 7 = . 9 2 = . 5 3 = . 4 1 = . 9 5 = .

4 2 = . 5 1 = . 7 4 = . 6 5 = . 5 4 = .

Use the first sum to do the second.

8 3 = 5 so…. 48 3 = 45 7 4 = . so…. 77 4 = . .

6 4 = . so…. 56 4 = . . 9 2 = . so…. 29 2 = . .

7 5 = . so…. 67 5 = . . 8 4 = . so…. 38 4 = . .

5 2 = . so…. 55 2 = . . 4 3 = . so…. 44 3 = . .

9 6 = . so…. 89 6 = . . 6 3 = . so…. 56 3 = . .

5 3 = . so…. 75 3 = . . 2 1 = . so…. 72 1 = . .

7 1 = . so…. 57 1 = . . 3 3 = . so…. 93 3 = . .

How big is this part? Color one quarter: Color one

half: ………………

………………

10 . . . . . . . . . . . . . . 100 . .

. . . . . . . . . . 84 . . 94 . .

58

Cut off the strip above. Measure the ropes.

How long is the shortest rope? The shortest rope is . cm

Use the first sum to answer the second.

3 + 4 = 7

36 + 40 =

76

2 + 6 = .

25 + 60 = .

.

4 + 5 = .

41 + 50 = .

.

3 + 3 = .

39 + 30 = .

. 7 + 2 = .

73 + 20 = .

.

1 + 5 = .

18 + 50 = .

.

2 + 5 = .

21 + 50 = .

.

4 + 2 = .

47 + 20 = .

. 3 + 6 = .

32 + 60 = .

.

7 + 1 = .

77 + 10 = .

.

5 + 3 = .

53 + 30 = .

.

3 + 5 = .

38 + 50 = .

. 1 + 8 = .

14 + 80 = .

.

6 + 1 = .

69 + 10 = .

.

2 + 8 = .

20 + 80 = .

.

4 + 4 = .

46 + 40 = .

. 2 + 2 = .

27 + 20 = .

.

3 + 2 = .

38 + 20 = .

.

5 + 5 = .

50 + 50 = .

.

1 + 3 = .

14 + 30 = .

.

The time table of ten.

6 × 10 = 60 . × 10 = . . . × 10 = . . . × 10 = . .

1 2 3 4 5 6 7 The length of the rope is 7 cm.

The length of the rope is . cm.





59


Count in three’s:

Count in five’s:

The friends of 10

10 . = 8 10 . = 5 10 . = 3 10 . = 1 10 . = 9

10 . = 2 10 . = 6 10 . = 4 10 . = 7

Number bonds. No Counting!


4 or 13 ? 12 or 7 ? 2 or 9 ? 6 or 18 ? 15 or 20?

13 is 9 more

than 4

. is . more

than .

. is . more

than .

. . is . .

more than .

. . is . more

than . .

. . . . . . . . . . . . . . . . . 50

3 . . . . . . . . . . . . . . 30

4 = 3 + 1 . = . + . . = . + . . = . + . . = . + .

. = . + . . = . + . . = . + . . = . + . . = . + .

. = . + . . = . + . . = . + . . = . + . . = . + .

. = . + . . = . + . . = . + . . = . + . . = . + .

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

60

Use the first sum to do the second.

4 + 5 = 9 so… 42 + 50 = 92 3 + 2 = . so… 36 + 20 = . .

7 + 1 = . so… 77 + 10 = . . 2 + 2 = . so… 28 + 20 = . .

6 + 2 = . so… 62 + 20 = . . 1 + 5 = . so… 17 + 50 = . .

4 + 3 = . so… 41 + 30 = . . 3 + 3 = . so… 32 + 30 = . .

8 + 1 = . so… 84 + 10 = . . 5 + 2 = . so… 59 + 20 = . .

7 + 2 = . so… 70 + 20 = . . 2 + 5 = . so… 27 + 50 = . .

4 + 2 = . so… 45 + 20 = . . 6 + 3 = . so… 66 + 30 = . .

Use the first subtraction for the second subtraction.

7 2 = 5

87 2 = 85

3 1 = .

43 1 = . .

8 5 = .

68 5 = . .

9 7 = .

59 7 = . .

8 3 = .

58 3 = . .

6 4 = .

76 4 = . .

4 2 = .

94 2 = . .

7 7 = .

37 7 = . .

7 6 = .

57 6 = . .

9 2 = .

89 2 = . .

8 4 = .

38 4 = . .

6 3 = .

66 3 = . .

5 4 = .

75 4 = . .

4 3 = .

54 3 = . .

10 2 = .

40 2 = . .

6 1 = .

36 1 = . .

5 2 = .

95 2 = . .

8 2 = .

58 2 = . .

6 2 = .

86 2 = . .

8 1 = .

88 1 = . .

2 1 = .

32 1 = . .

7 5 = .

67 5 = . .

8 6 = .

78 6 = . .

9 3 = .

89 3 = . .

Measure the lengths. Cut the measuring stick below.





The length of the rope is . . cm.

61

Week 22; Term 2 Theme: Food Hygiene. NCD It is high time to introduce the idea of the empty number line in class, if you haven’t already done so. It is important that learners get used to the empty number line because it is the only tool available for more difficult calculations like: 47 + 35 and

6128. This week we are adding decades to any number, It will look like this for 24 + 60 = 84 For subtraction we make jumps to the left.

For instance 56 40 will look like: Jumping with 10 forwards and backwards will not be a big problem because at the start of

the lesson learners have often counted like: 6 16 26 36 46 56 66 76

86 96 and as well: 94 84 …4 In the worksheet there will be some exercises, but they are not enough; the learners need more practice in their exercise book. Comparing ½ kg and 1 kg needs some preparation. If you do not have a scale to measure ½ kg and 1 kg, you can use water in a plastic bottle. Half a liter of water has a mass of ½ kg and a liter of water in a 1 liter bottle. [The mass of the plastic bottle can be neglected, it is very little] In class it is not the idea to show bottles for mass because volume and mass are different. You use the water bottles to prepare two small bags/containers of sand of ½ kg and one of 1 kg. Then they can be compared:










Subtract 2 digits and a multiple of 10


Compare objects of ½ kg and 1 kg

correctly.

Describe objects around us using

terms like edge, top surface etc.

10

0 16 26 36 46 56

10 10 10

Remark: it is important that the arcs have arrows. So learners get used:

to the right addition;

to the left subtraction.

0 24 34 44 54 64 74 84

+10 +10 +10 +10 +10 +10

½ kg

½ kg 1 kg

Since ½ + ½ = 1 the balance is flat. Or the mass of two ½ kg’s is the same as 1kg.

62


Where is the number?


34 + 20 = 54 22 + 40 = . .

57 + 30 = . . 72 + 20 = . .

46 + 40 = . . 18 + 50 = . .

66 + 20 = . . 23 + 60 = . .

Now add without a number line:

26 + 70 = . . 21 + 50 = . . 53 + 20 = . . 87 + 10 = . .

64 + 30 = . . 19 + 80 = . . 22 + 40 = . . 45 + 50 = . .

38 + 60 = . . 44 + 40 = . . 12 + 80 = . . 66 + 30 = . .

32 + 20 = . . 26 + 70 = . . 49 + 50 = . . 33 + 30 = . .

47 + 40 = . . 31 + 20 = . . 17 + 60 = . . 54 + 10 = . .

56 + 30 = . . 39 + 40 = . . 89 + 10 = . . 44 + 50 = . .

0

0 0

0 0

0 0

0 34 44 54

+10 +10

8 16 5 24 31 37 49 62 66 73 78 87 96 99

63

Use the number line to subtract.

67 30 = 37 69 50 = . .

34 20 = . . 72 20 = . .

52 50 = . . 81 60 = . .

63 20 = . . 95 70 = . .

Now subtract without a number line:

54 30 = . . 38 20 = . . 62 50 = . . 89 70 = . .

73 10 = . . 44 40 = . . 71 60 = . . 55 50 = . .

66 60 = . . 57 10 = . . 99 90 = . . 87 60 = . .

23 10 = . . 67 50 = . . 81 70 = . . 94 80 = . .

34 20 = . . 81 60 = . . 74 40 = . . 75 20 = . .

43 40 = . . 93 60 = . . 55 50 = . . 86 40 = . .

Time table of 2 and 10. Connect to the right answer.

0

0 0

0 0

0 0

0 37 47 57

10 10 10

67

3 × 2 =

7 × 2 =

4 × 2 =

9 × 2 =

5 × 2 =

10

18

8

6

14

8 × 10 =

6 × 10 =

2 × 10 =

9 × 10 =

4 × 10 =

80

90

20

60

40

64

Week 23; Term 2 Theme: Road safety.

NCD This week further practice on addition and subtraction. Learners should know how to do this with and without the number line. Attention should be given to the arrows on the number line.

To the right addition; to the left subtraction. The learners should draw arcs with arrows. Step by step the additions and subtractions are becoming more difficult so teachers should insist on using the number line. Counting in 5’s and tens is one of the objectives this week . I hope you did not only count the big sequence: 10-20-30….100 but as well: 23-33-43…..93 and 97-87-77….7. The purpose of the counting exercises are designed to assist learning computations. [This should be the case with many activities in class when it comes to mathematics] One can say the basic computations skills are to be learnt in grade 1-3; just as reading and writing are the domain of junior primary. The worksheet has a task to compare lines that are drawn in a way that you cannot easily compare them; the idea is to use any piece of paper to compare the various lines: Conclusion: Line is the shortest line and line is the longest line. I think you have to give a demonstration on the blackboard of this action. Estimation is part of the exercise as well; explain first before you give the worksheet!








Subtract 2 digits and a multiple of 10


Add and subtract numbers bridging the

10.

Recite the time table of five.

Determine the longest and shortest

distance given a set of lengths.

Identify commonly known geometrical

shapes from a set of shapes.

Piece of paper

Start

Start

Start

65



Use the number line to add or subtract.

14 + 50 = 64 83 20 = . .

41 30 = . . 28 + 60 = . .

16 + 40 = . . 75 50 = . .

63 50 = . . 25 + 75 = . .

Now add or subtract without a number line:

34 + 20 = . . 88 60 = . . 55 + 10 = . . 69 30 = . .

37 20 = . . 42 + 50 = . . 93 70 = . . 21 + 60 = . .

62 + 30 = . . 59 20 = . . 77 + 20 = . . 44 40 = . .

51 + 40 = . . 55 50 = . . 78 50 = . . 53 + 40 = . .

62 + 30 = . . 59 20 = . . 77 + 20 = . . 44 40 = . .

51 + 40 = . . 55 50 = . . 78 50 = . . 53 + 40 = . .

0

0 0

0 0

0 0

0 14 24 34

+10 +10 +10

44

+10 +10

54 64

9 17 2 26 33 39 46 61 67 72 77 88 95 98

66

Which line is the shortest? Use a piece of paper.

. is the shortest . is the shortest

For the other two first estimate, then measure

Estimate: . is the shortest

Measure: . is the shortest

Estimate: . is the shortest

Measure: . is the shortest

Mixed exercise.

20 + 9 = . . 50 7 = . . 70 + 20 = . . 45 3 = . .

48 + 6 = . . 90 70 = . . 28 + 8 = . . 70 9 = . .

40 5 = . . 65 + 7 = . . 89 6 = . . 40 + 40 = . .

80 80 = . . 70 + 5 = . . 44 + 4 = . . 44 4 = . .

88 + 6 = . . 37 + 2 = . . 70 7 = . . 66 + 6 = . .

80 30 = . . 77 7 = . . 56 + 5 = . . 33 + 3 = . .

78 + 5 = . . 48 6 = . . 40 + 40 = . . 87 + 4 = . .

70 6 = . . 30 + 8 = . . 52 + 6 = . . 77 5 = . .

a b

c d

e

f

g

h

i j k

l

67

Week 24; Term 2 Theme: Properties and uses of materials.

NCD This week is even numbers in the range 1-100 and adding two digits to two digits, not yet bridging the ten.When halving numbers, there are the easy ones:half of 64 is 32. (Both the tens and the units canbe halved separately) There are as well the difficult ones: half of 74. (The tens appear in an odd number) This last case needs special attention. I suggest to split the number favorably: The last splitting is not really necessary, one can as well work as shown: There will be some exercises on this topic in the worksheet, using the first approach. The addition of 2 two digit numbers will be practiced again with the number line. Although some people like splitting the units and the tens for both numbers, I will only split the second number. The reason is: I want to stay as close as possible to the mental process when adding such numbers. Fact is that the human mind is not keen to remember so many different numbers. It is more a matter of replacing one calculation with another one, which is getting closer and closer to the answer. An example: Of course very few learners in grade 2 can work this out mentally, but later on, one can expect many to be able to calculate this by heart. Another argument not to split the first number is the counting you have hopefully practiced often with your class: 36, 46, 56, 66, 76….. followed by 6 + 2.




Count forward and backward in tens

starting anywhere in the range 1-100.

Add a two digit number to another two

digit number, not bridging the ten.

Identify odd and even numbers in the

range 1-100.

Half any even number in the range 1-

100.

Measure volumes in liters correctly.

Recite the time tables of 2; 5 and 10

Add and subtract in the range 1-20

bridging the ten (revision)

Interpret data correctly.

74 = 60 + 10 + 4 Half Half Half

30 + 5 + 2 = 37

74 = 60 + 14 Half Half

30 + 7 = 37

36 + 42 byreplacedis

76 + 2 byreplacedis

78

68

Name:………… Class… Wk 24 Gr2


36 + 23 = 59 42 + 45 = . .

37 + 51 = . . 22 + 56 = . .

76 + 12 = . . 51 + 47 = . .

33 + 25 = . . 18 + 21 = . .

Add without a number line.

42 + 36 = 72 + 6 =

78

51 + 38 = . . + 8 = .

.

37 + 21 = . . + 1 = .

. 76 + 21 = . . + 1 = .

.

65 + 24 = . . + 4 = .

.

22 + 22 = . . + 2 = .

. 53 + 45 = . . + . = .

.

83 + 16 = . . + . = .

.

46 + 33 = . . + . = .

. 77 + 12 = . . + . = .

.

41 + 28 = . . + . = .

.

62 + 37 = . . + . = .

. 43 + 15 = . . + . = .

.

56 + 43 = . . + . = .

.

44 + 44 = . . + . = .

. 32 + 44 = . . + . = . . 47 + 22 = . . + . = . . 73 + 15 = . . + . = . ..

0

0 0

0 0

0 0

0 36 46 56 59

+10 +10 +3


7 14 4 19 27 36 45 53 61 72 78 87 92 97

69

Half the number.

Half; in a short way.

Half other numbers.

86 sohalf of 86 is 43

40 40 3

3

62 sohalf of 48 is . .

. . . . .

.


. . . . .

.


. . . . .

.


. . . . .

.


. . . . .

.

H H

36 = 20 + 16

10 8

Half of 36 is 18 H H

58 = 40 + . .

. . .

Half of 58 is . .

H H

94 = 80 + . .

. . .

Half of 94 is . . H H

72 = 60 + . .

. . .

Half of 72 is . .

H H

56 = . . + . .

. . .

Half of 55 is . . H H

32 = . . + . .

. . .

Half of 32 is . .

Half 42 21

Half 84 . .

Half 46 . .

Half 20 . .

Half 88 . .

Half 44 . . Half 60 . .

Half 64 . . Half 26 . .

Half 80 . .

Half 28 . . Half 40 . .

Half 66 . . Half 22 . .

Half 10 .

Half 24 . .

Half 62 . .

Half 86 . .

Half 48 . .

Half 68 .

70

Week 25; Term 3. Theme: Clean up

NCD This week we start with orientation on the Numbers 1-500. The first sequence to concentrate on is: 100-200-300-400-500. These counting numbers are based on the small sequence 1-5. To emphasize that counting between 0 and 100 is very similar to counting between 100 and 200 for instance, one can do exercises like: count from 50 to 60. count from 150 to 160 learners will notice The similarity between the two sequences. On addition the work scheduled for this week is as previous term: addition of two 2 digit numbers, not bridging the 10. Before this is practiced a revision exercise of addition of numbers not bridging the 10 may be very necessary. At this stage one cannot expect all learners to have internalised the additions below 10. Remember in junior primary, the big majority of the learners should know addition and subtraction up to 10 and the friends of ten by heart. This means if you ask a learner what

is 72 the immediate answer is 5; if you ask how did you get this, the learner says something like: I know. In the worksheet there will be a revision exercise on those additions. If learners are slow or if they have a tendency to use their fingers, let them just look at an empty ten frame, on which they imagine the numbers. Orientation on the numbers 1-100 Suggested activities one can do to orient learners on the numbers 1-100. Learners throw one die and add this to the previous number. The number is put on the number snake (see appendix). Above the number snake there is a more or less empty number line. At first maybe only multiples of 10 are shown. A learner is called to the front; she/he throws the die; adds the number to the previous number already obtained by all the throws done before and puts the result on the snake and on the number line.


Count in 100’s up to 500.

Count in tens between any two

consecutive hundreds in the range 1-

500.

Add a two digit number to another two

digit number, not bridging the ten.

Compare and order numbers in the

range 1-100.

Mention the number bonds for numbers

between 1 and 10 and the friends of 10.

Recite the tables of 2;5 and 10.

Tell the time correct to the nearest half

hour from a clock face.

Indicate how long an event lasts; only in

whole hours.

71


Which number is more? [Numbers are from exercise.]

23 or 79 94 or 82 44 or 56 33 or 23 51 or 16 11 or 74

79 is more . . is more . . is more . . is more . . is more . . is more

Add , you can use the number snake from .

31 + 42 = 71 + 2 =

73

36 + 32 = . . + . = .

.

13 + 46 = . . + . = . .

. 62 + 37 = . . + . = . . 44 + 34 = . . + . = .

. 25 + 43 = . . + . = . . .

48 + 41 = . . + . = . . 72 + 27 = . . + . = . . 33 + 33 = . . + . = . ..

57 + 32 = . . + . = . . 25 + 63 = . . + . = . . 28 + 51 = . . + . = . .

34 + 34 = . . + . = . . 42 + 55 = . . + . = . . 12 + 62 = . . + . = . .

Friends of ten. Answer quickly, no fingers!

4 + . = 10 7 + . = 10 2 + . = 10 5 + . = 10 6 + . = 10

1 + . = 10 3 + . = 10 9 + . = 10 8 + . = 10

Count in tens.

9 11 2 16 23 33 44 51 56 74 79 82 85 94


100 50 200 150 300 250 400 350 500 450

7

0

. .

.

. .

.

. .

. . .

.

. .

. . .

.

. .

.

. .

.

72

Add the numbers on the number line.

28 + 31= 59 63 + 26 = . .

42 + 35 = . . 21 + 38 = . .

63 + 36 = . . 42 + 24 = . .

Add. Answer quickly, no fingers!

5 + 3 = . 8 + 1 = . 7 + 2 = . 3 + 3 = . 1 + 7 = .

4 + 4 = . 6 + 2 = . 2 + 3 = . 3 + 6 = . 2 + 5 = .

3 + 1 = . 4 + 5 = . 6 + 1 = . 2 + 4 = . 1 + 1 = .

How long?

……… ……

……… ………

0

0 0

0 0

0 28 48 58 59

+10 +10

+1

38

+10

It lasted for 2 hours (5 3 = 2)

3 o’clock 5 o’clock

It lasted for . hours

. o’clock

Begin:

End: Begin: End:

. . o’clock


. o’clock

Begin: End:

. . o’clock


. . o’clock

Begin: End:

. o’clock

73

Week 26-27; Term 3 Theme: Plants and growth.

NCD These two weeks we are bridging the 10 by subtracting a single digit from a two digit number.

Like 43 8. If learners can do it correctly in a Limited time span using any method apart from counting one by one, it is acceptable.

However on the board a subtraction like 43 8 Has to be shown as follows: With the (empty) number line: The 8 splits in 3 and 5, not in 2 and 6 for instance.

43 2 6 is more difficult so it should be avoided.

As a sum: 43 8 = 43 3 5 = 40 5 = 35. If you find this notation too long one can shorten it

a bit by writing: 43 8 = 40 5 = 35 The times table of 3 is introduced this week; in the worksheet there will be an exercise on the time table of 3 using tricycles. One can consider 3 stages learning the times tables: [A] Multiplication as repeated addition. [B] Recognizing multiplication in a rectangular grid (examples crates with bottles; trays of eggs etc.) [C] Smart strategies to know the times table (doubling; halving; take one more or one less etc.) This week we concentrate on repeated addition and the × symbol which is rather abstract for most learners so it will take time before learners fully understand ×. Make sure you follow a fixed interpretation of ×: 4 × 3 = 3 + 3 + 3 + 3. [Of course 3 × 4 = 4 × 3, that will come later.] Another skill mentioned is rounding off. The best approach is the number line and asking questions like: is 28 nearer to 30 or to 20, after the learners as found the approximate place for 28 on the number line. Make sure the learners estimate the position more or less correctly. They have to develop a feeling for the placement of the numbers on the number line. This is OK: This is not OK





500.

Subtract a single digit from a two digit

number, bridging the 10. (32 6)

Recite the time table of 3

Take 10 more or take 10 less than a

given number in the range up to 100.

Estimate and measure lengths less than

20 cm using an improvised ruler.

Compare the capacity of various

containers using liters

Identify well known 3D shapes.

43 40 35

3 5

0

5 3

90 95 100

Where is 91?

So 91 is nearer to . .

60 65 70

Where is 67?


67 must be closer to 65!

74


Time table of 3. (A tricycle has 3 wheels.)


. + 2 = 10 . + 6 = 10 . + 9 = 10 . + 5 = 10 . + 3 = 10

. + 4 = 10 . + 1 = 10 . + 7 = 10 . + 8 = 10

8 13 4 19 24 31 46 52 58 66 77 85 89 97


9 × 3 = . .

2 × 3 = .

3 × 3 = .

7 × 3 = . .

8 × 3 = . .

4 × 3 = . .

5 × 3 = . .

6 × 3 = . .

1 × 3 = 3

10 × 3 = . .

75

Subtract.

Find the nearest 10. Put the dot first.

What is more? How much more? Subtract: 70 50 = 20.

50 or 70 ? 90 or 60 ? 10 or 60 ? 70 or 40 ? 30 or 80?

70 is 20 more

than 50

. . is . . more

than . .

. . is . . more

than . .

. . is . . more

than . .

. . is . . more

than . .

20 or 40 ? 40 or 80 ? 90 or 30 ? 80 or 50 ? 10 or 20?

. . is . . more

than . .

. . is . . more

than . .

. . is . . more

than . .

. . is . . more

than . .

. . is . . more

than . .

5 3

43 8 = 40 5 = 35

. 4

54 7 = 50 . = . .

. 2

72 3 = 70 . = . .

. .

37 9 = . . . = . .

. .

61 4 = . . . = . .

. .

25 6 = . . . = . .

. .

42 4 = . . . = . .

. .

96 8 = . . . = . .

. .

33 5 = . . . = . .

. .

56 7 = . . . = . .

. .

42 6 = . . . = . .

. .

85 7 = . . . = . .

. .

78 9 = . . . = . .

. .

26 8 = . . . = . .

. .

43 5 = . . . = . .

20 25 30

Where is 28?

So 28 is nearer to 30.

50 55 60

Where is 52?


30 35 40

Where is 36?


. . . 5 . .

Where is 89?


. . . . . .

Where is 44?


70 75 80

Where is 73?


. . . . . .

Where is 67?


. . . . . .

Where is 88?


. . . . . .

Where is 91?


90 100 10 20 30 40 50 60 70 80

76


Count in tens.

Take ten more or ten less.


10 2 = . 10 7 = . 10 5 = . 10 1 = . 10 8 = .

10 3 = . 10 9 = . 10 4 = . 10 6 = .

7 17 3 22 26 37 43 48 55 68 71 82 94 99


100 50 200 150 300 250 400 350 500 450

6

0

. . . . . . . . . . . . . . . . . . . . . . . .

46 Ten more 56

Ten less 36 37

Ten more . .

Ten less . .

72 Ten more

. . Ten less

. . 65 Ten more

. . Ten less

. .

88 Ten more

. . Ten less

. . 23 Ten more

. . Ten less

. .

54 Ten more

. . Ten less

. . 71 Ten more

. . Ten less

. .

22 Ten more

. . Ten less

. . 59 Ten more

. . Ten less

. .

77

Subtract.

Time table of 3. Fill in the right number in the box.

4 × 3 = . . 2 × 3 = . 7 × 3 = . . 1 × 3 = . 5 × 3 = . .

10 × 3 = . . 6 × 3 = . . 9 × 3 = . . 3 × 3 = . 8 × 3 = . .

Estimate first, then measure. Cut the strip below.

3 . . . . . . . . . . . . . . . .

The length of the stick is 9 cm.

2 4 6 8 10 12 14 16

2 4 6 8 10 12 14 16

I estimate the stick is . . cm long. When measured, I find . .

cm.

I estimate the stick is . cm long. When measured, I find . cm.


cm.


cm.

2 6

86 8 = 80 2 = 78

. 5

35 9 = 30 . = . .

. 2

62 5 = 60 . = . .

. .

75 6 = . . . = . .

. .

51 3 = . . . = . .

. .

75 7 = . . . = . .

. .

41 2 = . . . = . .

. .

33 5 = . . . = . .

. .

55 6= . . . = . .

. .

94 8 = . . . = . .

. .

23 4 = . . . = . .

. .

98 9 = . . . = . .

. .

45 7= . . . = . .

. .

713 = . . . = . .

. .

33 4 = . . . = . .

. .

44 7 = . . . = . .

. .

65 9= . . . = . .

. .

846 = . . . = . .

78

Week 28; Term 3 Theme: Parts of plants and uses.

NCD This week we start with the most advanced addition s o far: the sum of 2, two digital numbers, bridging the 10. Like 43 + 28. It is important that these additions are visualized on the number line. If this is done seriously, it lays the ground work for later abilities in the field of mental calculations. Since a lot of time has been spend on learning the friends of ten and the number bonds, the ideal method to work it out is as follows: 43 + 29 = If learners do the tens in one step; that is fine, good for them. The number line will look like: With numbers only: 43 + 29 = 43 + 20 + 9 = 63 + 7 + 2 = 70 + 2 = 72. This is the long version. If you want to shorten this (5 steps is quite long) it looks like: An example *: or 72 straight away. This method is fine although a bit cumbersome if you have to do it mentally. As stated before a mental process works more along the line: replace the original addition with another addition. In example* the brain is tasked a bit more since it has to remember more things. Of course if a learner comes up with such a strategy, you welcome it very much and you do not force the learner to use another strategy.





500.

Subtract a single digit from a two digit

number, bridging the 10. (32 6)

Add 2 two digit numbers in the range of

1-100; bridging the ten.

Put numbers in the range 1-100 in

ascending and descending order.

Round off numbers to the nearest 10.

Compare masses of ½ and 1 kg.

Analyze data and draw relevant

conclusions

Recite time table of 2; 3; 5 and 10.

2 7

43 + 29 = 63 + 9 = 72

0 43 63

70

72

+20 +7

+2

0 43 53 63

70

72

+10 +10 +7

+2

43 + 29 = 40 + 20 = 60

3 + 9 = 12 So 43 + 29 = 60 + 12 = 72

79

A very suitble game can be played now in groups of 4-6. Additions bridging the 10 has been practised already in class. The sun game is a game in which these additions are practised. The board on which the sun game is played looks like: they become very durable. The first throw is easy: a 3 and a 4 is thrown the player moves his/her pawn to 7 on the board. The next player throws the dice. If he/she throws a 2 and a 5, which is 7 as well it will force the first player one step back to the circle with number 6. If all players have thrown the dice and moved their pawns the first player throws again. He/she is not allowed to count out the steps on the board but has to calculate where he/she will come. Suppose the first player who is at 6 throws a 5 and a 6 which is 11 together, the learners has to calculate by heart 6 + 11 = 17. As a check the 11 steps are taken one by one on the board. If the learner made a mistake for instance he/she said 18; the 11 steps have to be taken in the reverse direction counting backwards as a punishment.(In this case the learner has to start afresh). The game ends if a player reaches 100 who is then declared the winner. If you want to make it a bit more challenging for your learners; one can make two dice with the numbers 1; 3; 5; 7; 9 and 11 on it. The game will go faster but the additions to be made are more difficult. As a teacher you should not miss this chance to make your maths lessons more lively.

A black and white copy of a bigger size of this game is found in the appendices of this teacher guide or one can download this board from the NIED website. Rules of the game: All players are represented by a different colored pawn/paper or anything available. Two dice are thrown together by a player and the number thrown is the number of steps you make on the board. The net of a die is as well included in the appendices; you need a thick paper; cello tape and some old plastics or old news papers to fill the dice, so that

80

http://www.google.nl/url?sa=i&source=images&cd=&cad=rja&docid=oclDZzWfx48RvM&tbnid=94gHU4RJGNVtRM:&ved=0CAgQjRwwAA&url=http://webwinkel.edumat.nl/Zonnespel-set-van-5-spelborden-enkelzijdig&ei=Z0JNUpu3IumQ1AWD9IDAAg&psig=AFQjCNF6p1afhVV5AvlmEU3hocJzFiX6iQ&ust=1380881383637758


Find the numbers in between.

Split the number.


3 + . = 10 1 + . = 10 4 + . = 10 9 + . = 10 6 + . = 10

8 + . = 10 2 + . = 10 5 + . = 10 7 + . = 10

9 14 4 23 27 33 44 46 55 66 77 88 94 99


100 50 200 150 300 250 400 350 500 450

220 . . . . . . . . . . . . 225 . . . . . . . . . . . . 230

2 . + . 3 . + .

. + .

. + .

. + .

5 . + .

. + .

. + .

. + .

4 . + .

. + .

. + .

. + .

. + .

. + .

. + .

. + .

. + .

. + .

. + .

. + .

. + .

9 . + .

. + .

. + .

. + .

. + .

. + .

. + .

. + .

6 . + . 7 . + .

. + .

. + .

. + .

8 . + .

81

Add on the number line.

43 + 29 = 72 27 + 45 = . .

66 + 18 = . . 55 + 37 = . .

72 + 19 = . . 48 + 33 = . .

38 + 54 = . . 27 + 46 = . .

Add you may use the number snake if you want.

From small to big. [18 is the smallest; 56 the biggest.]

Numbers Ordered Numbers Ordered 29 56 18 18 29 56 89 52 75 . . . . . .

34 21 76 . . . . . . 23 67 8 . . . . . .

55 41 39 . . . . . . 100 38 49 . . . . . .

63 85 91 . . . . . . 77 73 75 . . . . . .

29 17 48 . . . . . . 25 36 47 . . . . . .

68 70 69 . . . . . . 52 74 63 . . . . . .

0 43 53 63 70 72

+10 +10 +7 +2

0

0

0

0 0

0

0

1 4

36 + 35 = 66 + 5 = 71

. .

28 + 46 = 68 + 6 = . .

. .

23 + 48 = . . + . = . .

. .

57 + 37 = . . + . = . .

. .

48 + 17 = . . + . = . .

. .

66 + 25 = . . + . = . .

. .

37+ 56 = . . + . = . .

. .

75 + 19 = . . + . = . .

. .

44 + 57 = . . + . = . .

. .

38 + 54 = . . + . = . .

. .

27 + 47 = . . + . = . .

. .

79 + 12 = . . + . = . .

82

Week 29; Term 3 Theme: Spring.

NCD This week a new phase for subtraction: two digits minus two digits not bridging the ten. As has been done before; it is worked out on the (empty) number line and as a sum. Crucial here is the subtractions under ten; after revising them many, many times learners have at this stage internalized these subtraction.

8 6 = 2 should be “automatic”. If learners still take time, let them look at an empty ten frame. How does 8 look like? If I take 6 away; how many left? By thinking of number images learners are to come up with 2.

8 6 8 take away 6: left over 2. Only the weaker learners are allowed to use their bottle tops in combination with their ten frame. Grouping in twos and fives are scheduled as well this week; these are the first preparing activities for the operation division. Remainders are avoided in this initial stage. So only even numbers when grouping in twos and multiples of fives for grouping in fives. Although counting is important, one should always be keen on short cuts when it comes to counting. Suppose the following set of dots is given and the task is: form groups of 5.

::::: Learners can use their subitizing skills by combining 3 and 2 as a group of 5. So they should not be allowed to count all 5 groups on their own.



Count in tens bridging hundreds in the

range 1-500.

Subtract a two digit number from a two

digit number, not bridging the 10. (3816)

Add 2 two digit numbers in the range of 1-

100; bridging the ten.

Break up numbers in tens and units.

Round off numbers to the nearest 10.

Group numbers in two’s up to 20; in five’s

up to 50.

Tell time from a clock face in hours and

half hours correctly.

Use a calendar to gather information

about dates.

8 stars form 4 groups of 2.

83


Fill in the right number on the dots.

Subtract. No fingers! If you do not know, look at:

8 3 = . 5 1 = . 7 4 = . 9 2 = . 4 3 = .

9 7 = . 6 5 = . 8 5 = . 3 1 = . 8 7 = .

6 4 = . 4 2 = . 9 5 = . 5 4 = . 9 3 = .

8 2 = . 5 3 = . 6 1 = . 9 4 = . 7 7 = .

9 6 = . 2 1 = . 8 8 = . 6 2 = . 8 1 = .

7 5 = . 3 2 = . 4 1 = . 5 2 = . 6 3 = .

8 4 = . 5 5 = . 8 6 = . 9 8 = . 7 2 = .

9 0 = . 9 1 = . 7 3 = . 9 9 = . 7 6 = .

Subtract on the number line. Look at the first row for

examples.

68 35 = 33 68 35 = 33

47 24 = . . 83 52 = . .

76 45 = . . 39 22 = . .

56 14 = . . 95 72 = . .

10

0

50 . . . 15

0 . . . 25

0 . . . 35

0 . . . 45

0

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

68 0 38 33

30

0 38 48 58 33

10 10 5 10 5

0

68

0 0

0

0

0

84

Subtract.

Add, draw your own number line.

What time is it?

. o’clock ……………………… . o’clock ……………………

37 + 44 = . . + . = .

.

65 + 26 = . . + . = . .

69 + 23 = . . + . = . .

76 + 15 = . . + . = . . 47 + 38 = 77 + 8 = 85

. .

58 + 23 = 78 + 3 = . .

5 3

. .

. .

54 + 37 = . . + . = . .

. .

39 + 32 = . . + 2 = . .

. .

79 + 13 = . . + . = . .

. .

28 + 53 = . . + . = . .

. .

. .

72 + 19 = . . + . = . .

. .

48 + 38 = . . + . = . .

. .

. .

64 42 = 24 2 = 22 87 25 = . . 5 = . . 38 17 = . . 7 = . .

57 33 = . . 3 = . . 73 41 = . . 1 = . . 75 54 = . . 4 = . .

36 14 = . . . = . . 48 36 = . . . = . . 59 37 = . . . = . .

27 16 = . . . = . . 94 53 = . . . = . . 86 45 = . . . = . .

99 88 = . . . = . . 78 34 = . . . = . . 62 41 = . . . = . .

55 34 = . . . = . . 88 55 = . . . = . . 86 64 = . . . = . .

38 25 = . . . = . . 92 71 = . . . = . . 66 64 = . . . = . .

85

Week 30-31; Term 3 Theme: Habits and products.

NCD The subtraction we are facing this week is actually the most difficult operation so far for the learners. It therefore needs plenty practice. Two approaches as before: On the (empty) number line. As a sum with expanded notation. The two approaches that should be

discussed/shown to learners are for 54 38 looking like: On the (empty) number line.

Or shorter: As a sum with expanded notation:

54 38 = 24 8 = 20 4 = 16

Rounding off to the nearest 5. The correct way of rounding off is: go to the nearest multiple of 5.

Examples: Round off to the nearest 5: 2325; 4240; 116115 etc. This is often used when it comes to money. N$ 49.99 is actually less than N$ 50; in reality there is no single cent pay back as change so you pay N50. If you buy 3 articles that are prized similarly, then it can be your advantage: N$ 9.99 + N$ 29.99 + N$ 49.99 = N$ 89.97 this is rounded off to N$ 89.95. When rounding off to the nearest 5 a number line with only the multiples of 5 can help. There are two versions:

Not the whole number line up to 100 is shown; if learners can pick up the correct way of rounding off up to 70; then they can be challenged with numbers between 70 and 100. The other version looks like:


Count in tens forwards and backwards

bridging hundreds in the range 1-500

starting from any number.

Count in hundreds forwards and

backwards starting from any number

in the range 1-500

Subtract a two digit number from

another two digit number, bridging the

ten.



Recite the table of 4.

Decompose numbers in hundreds; tens

and units.

Compare surface areas of various basic

shapes correctly.

Express dollars into cents and vice

versa; no decimal comma as yet.

Work out change in dollars or cents.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Important point: The 8 is split into 4 and 4 because we have 4 units available in 54. (You have done a lot of work revising the number bonds and the friends of 10. Now we are using it.)

4 4

54 44 34

4

10 0

10 10

24 20

4

16

54

4

0 24 20

4

16

30

86



Table of four.

1 × 4 = 4 . × 4 = .

.

. × 4 = . . . × 4 = .

.

. × 4 = . . . × 4 = .

. × 4 = . .

. × 4 = . . . × 4 = . .

. . × 4 = . .

100 50 . . . 150 . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

73 45 = . . 5 = . . 2 = . .

2 3

62 37 = . . 7 = . . 5 = . .

5 2

85 57 = . . 7 = . . . = . .

. .

34 28 = . . 8 = . . . = . .

. .

4 4

54 38 = 24 8 = 20 4 = 16

3 6

46 29 = 26 9 = 20 3 = 17

Subtract; first two examples. You can use the number snake.

87

Subtract on the number line. Two examples.

74 38 = 36 83 45 = 48

63 27 = . . 92 39 = . .

54 15 = . . 32 26 = .

73 44 = . . 95 48 = . .

41 23 = . . 68 29 = . .

Make the number. HHundreds; TTens and UUnits.

Remember Hundreds first then Tens; last the Units!

Place values: 2T 3U 4H 3H 6U 7T 7U 1H 5T 2T 3U 4H

Number: 423 . . . . . . . . .

Place values: 5T 2H 9U 7U 1H 7T 5T 3H 0U 1H 0T 2U

Number: . . . . . . . . . . . .

Round off to the nearest 5. Use the number line.

Example: 18 rounds off to 20, because18 is closer to 20 than to

15.

Number 43 56 27 79 34 39 72 22

Rounded off to

the nearest 5: . . . . . . . . . . . . . . . .

What about 87 ; 96 and 98? Round off to the nearest 5.

87 . . 96 . . 98 . . .

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

0

0 0

0

0

0

0

0

74 0 44 54 64 40

4 10 4

36

10 10

0 43 53 63 73 40 83

3 2

48

10 10 10 10

88



What is more? How much more? Subtract: 76 52 = 24.

52 or 76 ? 88 or 42 ? 27 or 53 ? 78 or 36 ? 39 or 76?

76 is 24 more

than 52

. . is . . more

than . .

. . is . . more

than . .

. . is . . more

than . .

. . is . . more

than . .

Time table of 4. Fill in the right number in the box.

3 × 4 = . . 2 × 4 = . 7 × 4 = . . 1 × 4 = . 5 × 4 = . .

10 × 4 = . . 6 × 4 = . . 9 × 4 = . . 4 × 4 = . . 8 × 4 = . .

100 50 . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

90 100 10 20 30 40 50 60 70 80

4 . . . . . . . . . . . . . . . . .

Subtract. You may use the number snake.

91 36 = . . 6 = . . . = . .

. .

77 28 = . . 8 = . . . = . .

. .

3 2

62 45 = 22 5 = 20 3 = 17 66 39 = . . 9 = . . . = . .

. .

54 28 = . . 8 = . . . = . .

. .

33 17 = . . 7 = . . . = . .

. .

89

In the shop. How much change do I get?

Article Name Price Paid with Change

Lemon 80 cents 100

cents 100 80 = 20 cents

. . . 40 cents 50 cents . . . . = . . cents

. . . . 14 dollar 20 dollar . . . . = . . dollar

. . . . . 8 dollar 10 dollar . . . . = . . dollar

. . . . .

2 dollar 5 dollar . . . . = . . dollar

Drawn are pieces of chocolate. What is the biggest piece?

Cut out the square below and count how many times you

need it to cover the shapes.

90

Week 32; Term 3 Theme: Life Cycle NCD As stated earlier the counting activities in class are meant to support (mental)computation skills. That is why it is important to count like: 23; 123; 223; 323; 423, as well for subtraction: 468; 368; 268; 168; 68 counting in hundreds, starting anywhere. The same applies for tens: 243; 233; 223; 213; 203; 193; 183; 173 etc. If you have practiced this type of counting then you can easily calculate:

264 142 = 164 42 = 124 2 = 122. Addition is a move to the right on the number line; subtraction to the left. This is to be repeated on a regular basis. These movements on the number line as well remind learners that if you add something to a number, the number becomes bigger. If you subtract something, the number becomes smaller.In the worksheet there will be an exercise on forming an addition and a subtraction, given 3 numbers.For instance the number 8, 4 and 12 can be used to make an addition: 4 + 8 = 12. (I see 8 + 4 = 12 as similar because in an addition you may swop the numbers without changing the answer.)

They can be used as well to make a subtraction: 12 4 = 8 as well as 12 8 = 4. Learners can be encouraged to find there own number triplets and form additions and subtractions. In the scheme of work, grouping of 2 and 5 is mentioned. This can be done in class with grouping stones or beans. Give 35 beans; learners to divide them in groups of 5. Then they count the number of groups they have made. Conclusion to be drawn by the learners: 35 beans can be divided in 7 groups of five.







in the range 1-500

Subtract a two digit number from

another two digit number, bridging the

ten.



Identify place values for any number up

to 100.

Mention the time from a clock face in

hours and half hours.

Collect, organize and display data on

the theme life cycle

Add and subtract any 2 numbers in the

range 1-100.

91



Subtract on the number line.

81 47 = 34 54 45 = . .

77 19 = . . 65 48 = . .

43 26 = . . 91 43 = . .

34 25 = . . 84 29 = . .

26 18 = . 63 47 = . .

54 26 = . . 75 36 = . .

Write down 3 sums.

100 50 . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

7

15

8

15 7 = 8

7 + 8 = 15

15 8 = 7

5

14

9

. . . = .

. + . = . .

. . . = .

3

12

9

. . . = .

. + . = . .

. . . = .

4

18

14

. . . = . .

. + . . = . .

. . . . = .

13

15

28

. . . . = . .

. . + . . = . .

. . . . = . .

13

24

11

. . . . = . .

. . + . . = . .

. . . . = . .

15

14

29

. . . . = . .

. . + . . = . .

. . . . = . .

0

0 0

0

0

0

0

0

0 81 0

10 10 10 10

41 51 61 71 40

1 6

34

0 0

92

Subtract. Draw a number line.

Expand, fill in the numbers on the dots.

No H T U No H T U No H T U

456 = 400 + 50 + 6 312 = . 00 + . 0 + . 294 = . 00 + . 0 + .

157 = . 00 + . 0 + . 244 = . 00 + . 0 + . 373 = . 00 + . 0 + .

471 = . . . + . . + . 398 = . . . + . . + . 422 = . . . + . . + .

. . . = 400 + 30 + 9 . . . = 200 + 40 + 7 . . . = 300 + 60

. . . = 100 + 70 + 4 . . . = 400 + 7 . . . = 200 + 80 + 8

266 = . . . + . . + . 402 = . . . + . 380 = . . . + . . .

. . . = 300 + 60 + 2 . . . = 200 + 9 . . . = 400 + 40 + 4

Draw the hands of the clock.

8 o’clock 11 o’clock half past 2 half past 11

84 57 = . . . = . . . = . .

. .

44 26 = . . . = . . . = . .

. .

56 38 = . . .= . . . = . .

. .

83 44 = . . . = . . . = . .

. .

62 48 = . . 8 = . . . = . .

. .

37 19 = . . 9 = . . . = . .

. .

55 36 = . . 6 = . . . = . .

. .

3 4

74 37 = 44 7 = 40 3 = 37

93

Week 33-34; Term 3 Theme: Saving water.

NCD These 2 weeks towards the end of the year are to be used for revision and consolidation. Revise basic knowledge (with basic knowledge I mean things they have to know by heart) like friends of ten; number bonds for numbers 2-9. Other things that should go rather fast are: 30 + 5 = 35; 47 = 40 + 7; addition and subtraction in the range 1-10; number image recognition; table of 2; 5 and 10. If there are gaps in this knowledge, one should first address these rather than to continue. The best approach to doubling a number in the range 1-100 is to add the number to itself: double of 34 is 34 + 34 = 68. The best approach to halving any even number in the range 1-100 is to split the number suitably: half of 76 is the same as half of (60 + 16) and half both the numbers separately: Half of 60 is 30 Half of 16 is 8 When grouping larger numbers one has to avoid counting one by one. For instance to find the number of groups of two in a group of 76 items one can approach it as follows: This approach is as well suitable to half a number. Of course 76 is not an easy number to group in groups of 2. One has to build it up slowly. When grouping in tens the place value of the tens play of course an important role. At this stage of grouping remainders are avoided.







in the range 1-500

Half any even number less than 100

Double any number up to 50.

Order any three whole numbers in the

range 1-100.

Group any even number in groups of 2

up to 100.

Group any multiple of ten up to 100 in

groups of 10.

Add & subtract any number in the range

1-100.

Compare various surface areas of 2D

shapes using improvised units.

Half of 76 is 30 + 8 = 38

76 = 70 + 6 = 60 + 10 + 6

30 + 30 5 + 5 3 + 3

30 gr of 2; 5 gr of 2; 3 gr of 2; altogether 38 groups of two.

94



Find half of.

10

0

50 . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

H

32 = . . + . .

H

. . + . = . .

So half of 32 is . .

H

78 = . . + . .

H

. . + . = . .


H

52 = . . + . .

H

. . + . = . .


H

48 = 40 + 8

H

20 + 4 = 24

So half of 48 is 24

H

62 = 60 + .

H

. . + . = . .


H

86 = . . + .

H

. . + . = . .


H

24 = . . + .

H

. . + . = . .


H

88 = . . + .

H

. . + . = . .


H

42 = . . + .

H

. . + . = . .


H

36 = 20 + 16

H

10 + 8 = 18

So half of 36 is 18

H

58 = 40 + 18

H

. . + . = . .


H

74= 60 + . .

H

. . + . = . .


H

92 = 80 + . .

H

. . + . = . .


H

54 = . . + . .

H

. . + . = . .


H

96 = . . + . .

H

. . + . = . .


95

Double the number: add it to itself. [easy]

Double the number: add it to itself. [hard]

Subtract. Draw your own number line on another paper.

32 32 + 32 = 64

Double of 32 is 64

21 21 + . . = . .

Double of 21 is . .

43 . . + . . = . .

Double of 43 is . .

14 . . + . . = . .

Double of 14 is . .

33 33 + . . = . .

Double of 33 is . .

41 . . + . . = . .

Double of 41 is . .

24 . . + . . = . .

Double of 24 is . .

42 . . + . . = . .

Double of 42 is . .

12 . . + . . = . .

Double of 12 is . .

2 6

28 + 28 = 48 + 8 = 50 + 6 = 56

Double 28:

4 .

36 + 36 = . . + 6 = . . + . = . .

Double 36:

. .

. . + . . = . . + . = . . + . = . .

Double 27:

. .

. . + . . = . . + . = . . + . = . .

Double 49:

. .

. . + . . = . . + . = . . + . = . .

Double 19:

. .

. . + . . = . . + . = . . + . = . .

Double 45:

74 38 = . . . = . . . = . .

. .

81 53 = . . . = . . . = . .

. .

47 39 = . . 9 = . . . = . .

. .

55 27 = . . 7 = . . . = . .

. .

63 36 = . . . = . . . = . .

. .

4 2

72 26 = 52 6 = 50 4 = 46

96



Take 5 more and 5 less.

Two fives make a ten. How many groups of 10 fingers can

you make?

. . groups of ten . . groups of ten . . groups of ten

100 50 . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

31 5 more 36

5 less 26 53

5 more . .

5 less . .

88 5 more

. . 5 less

. . 35 5 more

. . 5 less

. .

76 5 more

. . 5 less

. . 64 5 more

. . 5 less

. .

92 5 more

. . 5 less

. . 19 5 more

. . 5 less

. .

47 5 more

. . 5 less

. . 50 5 more

. . 5 less

. .

73 5 more

. . 5 less

. . 94 5 more

. . 5 less

. .

97

Write the numbers from small to big.

17; 14; 19 14; 17; 19 25; 39; 35 . . . . .

.

34; 57; 46 . . . . .

. 83; 61; 42 . . . . .

. 23; 9; 43 . . . . .

. 93; 87; 95 . . . . .

. 55; 64; 54 . . . . .

. 23; 32; 27 . . . . .

. 88; 18; 81 . . . . .

. 45; 54; 53 . . . . .

. 57; 37; 47 . . . . .

. 67; 62; 69 . . . . .

. 83; 93; 73 . . . . .

. 74; 71; 72 . . . . .

. 44; 22; 33 . . . . .

.

Add or subtract. Some are short.

54 27 =34 7 = 30 3 = 27

4 3

38 + 18 = 48 + 8 = 50 + 6 = 56

2 6 (a) 45 + 17 = (b) 62 34 =

(c) 39 28 = (d) 56 + 22 =

(e) 25 + 45 = (f) 71 48 =

(g) 34 + 42 = (h) 67 45 =

(i) 70 42 = (j) 66 + 28 =

(k) 34 + 34 = (l) 42 39 =

(m) 84 48 = (n) 57 52 =

(o) 47 + 37 = (p) 45 +46 =

(r) 21 + 63 = (s) 80 26 =

(t) 27 + 72 = (u) 87 78 =

(v)38 + 15 = (w)63 41 =

. . 100 10 . . . . . . . . . . . . . .

98

Week 35; Term 3 Theme: Change in the sky.

NCD A nice activity in class on orientation on the number line is as follows: A learner gets a paper hat with any number on it between 0 and 500, let say 345. The learner wearing the hat does not know the number him or herself. Another learner is asked to position the learner with the hat correctly between 0 and 500. [To make this a bit easier the space in front of the class can be sub divided into 5:

0 100 – 200 – 300 – 400 – 500. This may be done by putting papers on the wall with the multiples of 100.] The learner with the hat is now asked what number is on your hat. Estimate; check you position between 300 and 400. Depending on the answer the learner with the hat is repositioned. Either to the right if the number is too small; or to the left if the number is too big. All the time after repositioning the learner he/she has to come up with a new number until the right number which is on the hat is mentioned. If the class room is too small the paper with 300 can be moved all the way to the left (as seen as from the learners position) and 400 all the way to the right of the class room. Of course one can do this activity first with a number between 1 and 100. All kind of subdivisions are possible: 0-25-50-75-100 just to bring some structure on the number line. Make sure the spaces in between the numbers is the same! Wrong: 0 25 50 75 100 Correct: 0 25 50 75 100 Multistep problems will be done with a minibus picking up and letting out passengers on stopping places. Pictures will show the number of passengers in the bus; learners have to conclude what happened and write this down in the form of a multistep sum. This activity can be the subject of a role play with learners as passengers moving through the class. A good opportunity, to make your maths lesson more exciting.






backwards starting from any number in

the range 1-500



Decompose any number in the range 1-

500

Compare various surface areas of 2D

shapes using improvised units.

Add & subtract any number in the range 1-

100.

Round off to the nearest 5.

Recite the time table of 2; 3; 4; 5 and 10.

Solve multistep problems using addition

and subtraction.

99


Count in ones.

Table of 2. Fill in the numbers on the number line first.

3 × 2 = . . 7 × 2 = . . 1 × 2 = . . 4 × 2 = . . 8 × 2 = . .

5 × 2 = . . 2 × 2 = . . 6 × 2 = . . 9 × 2 = . . 10 × 2 = . .

Table of 3. Fill in the number line first.

6 × 3 = . . 8 × 3 = . . 10 × 3 = . . 5 × 3 = . . 7 × 3 = . .

4 × 3 = . . 2 × 3 = . 3 × 3 = . 9 × 3 = . . 1 × 3 = .

Table of 4.

3 × 4 = . . 6 × 4 = . . 10 × 4 = . . 4 × 4 = . . 9 × 4 = . .

5 × 4 = . . 7 × 4 = . . 8 × 4 = . . 2 × 4 = . . 1 × 4 = .

Table of 5.

8 × 5 = . . 6 × 5 = . . 2 × 5 = . . 4 × 5 = . . 7 × 5 = . .

5 × 5 = . . 9 × 5 = . . 3 × 5 = . . 10 × 5 = . . 1 × 5 = .

2 . . . . . . . . . . . . . 20

3 . . . . . . . . . . . . . . . .

+ 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4

0 . . . . . . . . . . . . . . . . . .

. . . 198 . . . . . . . . . . . . 301 . . . . . . . . .

. . . 279 . . . . . . . . . . . . 400

0 . . . . . . . . .

. . . 309 . . . . . . . . . . . 99 . . . . . . . .

. . . 75 . . . . . . . . . . . 189 . . . . . . . .

100

Passengers in the minibus, write down the sum.


47 29 =27 9 = 20 2 = 18

7 2

46 + 37 = 76 + 7 = 80 + 3 = 83

4 3 (a) 54 + 38 = (b) 83 55 =

(c) 47 19 = (d) 64 + 27 =

(e) 46 + 47 = (f) 82 63 =

(g) 56 + 35 = (h) 77 58 =

(i) 80 37 = (j) 37 + 21 =

(k) 36 +63 = (l) 51 15 =

(m) 41 + 39 = (n) 66 44 =

. . . . . . . . = .

6 4 + 5 = 7

. . . . . . . . = .

101

Week 36; Term 3 Theme: Uses of energy.

NCD In the last week consolidation and revision are the main issues. 80% of the time in mathematics is to be spend On Number Concept Development. This NCD is made up of orientation on numbers; counting and computations. Learners are at this stage expected to have a certain fluency in addition and subtraction in the range of 1-100. Some learners however will still take time to bridge the 10 when adding and subtracting. Fluency bridging the ten can only be expected half way grade 3. It is important that the notation used supports mental calculations later on. In the past many learners calculated 37 + 24 as follows: This of course gives a correct answer, but it has two clear disadvantages. This addition process does not mimic the mental process of addition which is much more replacing

one addition by another addition: 37 + 24 57 + 4 60 + 1 61. For the learners the 4 & 7 are dealt with in the same way as the 3 & 2. As a result learners do not make enough difference between the units and the tens. Learners can add as shown in the box after they have practiced column notation: Attention is first given to the bigger parts of the numbers: the tens. Only when that is done we look at the ‘leftovers’. Scientific research has shown this approach is better than the addition with trading the tens, which is more abstract for learners in grade 2-3. You may claim that is less efficient, which may be true, but one has to take in account that our teaching of mathematics is aimed at creating understanding rather than the speed of calculations. [Point is the column notation is still way faster than counting 37; count 24 and recount the whole group once more.]







in the range 1-500



Decompose any number in the range 1-

500

Compare lengths with improvised units.

Add & subtract any number in the range

1-100.

Round off to the nearest 5 & 10.

Group objects in 2’s; 3’s and 5’s; no

remainders.

Solve multistep problems using addition

and subtraction.

37 + 24

61

37 + 24

50 + 11

60 + 1 61

102


Count in tens

Count in hundreds.

Add and subtract.


47 29 =27 9 = 20 2 = 18

7 2

46 + 37 = 76 + 7 = 80 + 3 = 83

4 3 (a) 36 + 37 = (b) 89 35 =

(c) 27 18 = (d) 53 + 18 =

(e) 46 + 26 = (f) 91 74 =

(g) 88 + 11 = (h) 76 67 =

(i) 72 29 = (j) 33 + 57 =

(k) 43 35 = (ℓ) 22 + 39 =

16 + 12 20 = 28 20 = 8 47 12 30 = 35 30 = 5

38 14 + 10 = . . + 10 = . . 17 + 21 15 = . . 15 = . .

22 + 16 20 = . . .. . . = . . 44 23 + 26 = . . .. . . = . .

48 12 + 20 = . . .. . . = . . 23 + 23 26 = . . .. . . = . .

13 + 16 + 40 = . . .. . . = . . 47 22 23 = . . .. . . = .

+10

. . .

10 +10 +10 +10 10 10

384 . . . . . . . . . . . . . . . . . .

0 243 +100

. . . +100

. . . 100

. . . 100

. .

103

Form the number. Hu hundred; T tens and Un units.

How many fruits?

Round off to the nearest 5 and 10. First fill in the numbers.

Number Nearest 5 Nearest 10 Number Nearest 5 Nearest 10

27 25 30 56 . . . .

42 . . . . 77 . . . .

61 . . . . 89 . . . .

54 . . . . 44 . . . .

83 . . . . 55 . . . .

4 T

2 Hu

8 Un

248

3 T

1 Hu

5 Un

. . .

1 T

7 Un

4 Hu

. . .

1 Hu

3 T

5 Un

. . .

2 Un

3 Hu

8 T

. . .

0 Hu

2 T

1 Un

. .

0 T

1 Hu

4 Un

. . .

6 Un

5 Hu

4 T

. . .

4 Hu

8 Un

4T

. . .

3T

2 Hu

1 Un

. . .

4

4

4

3 × 4 = 12

oranges

.

.

.

.

.

. × . = . .

. . . . . . . .. .

.

.

.

.

. × . = . .

. . . . . . . .. .

.

. . × . = ..

. . . . . . . .. .

. . 100 10 20 . . . . . . . . . . . . 5 . . . . . . . . . . . . . . . . . .

104

8

3 5 7 11 9

105

Rules of the game 2-7 players. The first player throws the die let say 9. He/she moves his pawn (coin/piece of paper/anything that is small) to 9. All other players throw the die. If a player gets to a place already occupied the first player is moved a place back. Player 1 throws again let say 13. He/she has to calculate by heart where he/she will land [9 + 13 = 22]. If the player says the wrong answer the 13 steps are made backwards as a punishment. Winner: the first one that crosses the 100.

108

TWENTY FRAME

112

mathematics teachers’ manual mathematics teachers’ …€¦ · guide for grade 1 is...

Documents