Learning Mathematics With The Abacus(soroban) - 04-year 2 Activity Book

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Unit 1

Numbers up to 1000 1.01 Can you draw one square below? Ones

one square

Draw ten squares below. Count them as you draw.

10 ones make ten! How do you represent 10 on the abacus? Tens Ones

Move up 1 at Tens on your abacus. This is how it should look like...

1

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1.02 Look at the abacus images. Write the numbers they represent.

Look at the numbers above and count in tens. How many tens make 100? That’s right! 10 tens make 100. 2

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1.03 There are 100 coins in each box. Let’s count the coins in hundreds.

100,

,

,

400 ,

,

,

,

,

,

1000 .

Fill in the blanks. There are

coins altogether.

Each box contains

coins.

There are

boxes of coins.

So, 10 hundreds make 1000!

3

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1.04 Match the place values on the abacus correctly.

Ones

Tens

Hundreds

Thousands

Let’s try these on your abacus! 1. Move up 1 at Hundreds, move up 3 at Tens, move up 2 at Ones, clear abacus. 2. Move up 4 at Hundreds, move up 1 at Tens, move up 5 at Ones, clear abacus. 3. Move up 3 at Hundreds, move up 5 at Tens, move up 7 at Ones, clear abacus. 4. Move up 5 at Hundreds, move up 6 at Tens, move up 9 at Ones, clear abacus. 5. Move up 8 at Hundreds, move up 2 at Tens, move up 8 at Ones, clear abacus. 6. Move up 2 at Hundreds, move up 9 at Tens, move up 6 at Ones, clear abacus. 7. Move up 7 at Hundreds, move up 7 at Tens, move up 5 at Ones, clear abacus. 8. Move up 8 at Hundreds, move up 1 at Tens, move up 9 at Ones, clear abacus. 9. Move up 9 at Hundreds, move up 9 at Tens, move up 9 at Ones, clear abacus. 10. Move up 1 at Thousands. 4

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1.05 Write the correct numerals and number names. Thousands

Tens

Hundreds

Thousands Ones

Tens

Hundreds

Ones

1 0 1 one hundred and one Thousands

Tens

Hundreds

Thousands Hundreds

Thousands Ones

Tens

Hundreds

Tens

Thousands Ones

Hundreds

5

Ones

Tens Ones

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1.06 Visualise these numbers and draw the beads. Say the numbers out loud.

136

137

138

139

140

141

142

143 6

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1.07 Try these with your abacus. Write down the number names as shown on the abacus.

1. (1) (2)

Move up 6 at Tens

(3) Move up 2 at Ones Two hundred and sixty-two 2. (1)

2 1

Move up 7 at Tens

(3)

Move up 9 at Ones

Move up 5 at Tens

(3)

Move up 8 at Ones

3

2 1

3

2

Move up 4 at Hundreds

(2)

3

2

Move up 3 at Hundreds

(2)

3. (1)

2

Move up 2 at Hundreds

3

3 1

4. (1) (2) (3)

Move up 5 at Hundreds

1

3

Move up 1 at Tens 2

Move up 7 at Ones

3

7

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1.08 Let’s count in twos from 300. Visualise the numbers and draw the beads.

3

0

0

3

0

4

3

8

0

2

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1.09 Let’s count in fives from 360. Visualise the numbers and draw the beads.

3

6

0

3

7

0

3

9

6

5

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1.10 Let’s count in tens from 590. Visualise the numbers and draw the beads.

5

9

0

6

1

0

6

10

0

0

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1.11 Use your abacus to move the beads. Write down the numbers shown on your abacus. Say the numbers out loud.

1. Move up 2 at Hundreds, move up 7 at Ones.

2

2. Move up 7 at Tens, move up 3 at Ones. 3. Move up 8 at Hundreds, move up 3 at Tens, move up 5 at Ones. 4. Move up 1 at Hundreds, move up 9 at Tens, move up 6 at Ones. 5. Move up 6 at Hundreds, move up 1 at Tens. 6. Move up 5 at Hundreds, move up 4 at Tens, move up 1 at Ones. 7. Move up 9 at Hundreds, move up 8 at Ones. 8. Move up 3 at Hundreds, move up 1 at Tens, move up 2 at Ones. 9. Move up 4 at Hundreds, move up 1 at Tens, move up 9 at Ones. 10. Move up 1 at Thousands. 11

0

7

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1.12 Circle the smaller number.

Circle the larger number.

12

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1.13 Jenny is visualising some numbers. Write the numbers in ascending order.

ascending order

13

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1.14 Jenny is visualising some numbers. Write the numbers in descending order.

descending order

14

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1.15 Use your abacus to do the following. Clear the abacus before you start each exercise.

1. Move up 356.

13. Move up 825.

2. Move up 1000.

14. Move up 419.

3. Move up 113.

15. Move up 710.

4. Move up 978.

16. Move up 30.

5. Move up 183.

17. Move up 613.

6. Move up 52.

18. Move up 267.

7. Move up 906.

19. Move up 174.

8. Move up 515.

20. Move up 239.

9. Move up 777.

21. Move up 271.

10. Move up 49.

22. Move up 763.

11. Move up 521.

23. Move up 579.

12. Move up 257.

24. Move up 194.

15

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Unit 2

Addition with the highest total of 1000 2.01 Use your abacus to do the following.

1. (a) Up 111 (b) Up 121

2. (a) Up 315 (b) Up 151

3. (a) Up 500 (b) Up 413

4. (a) Up 132 (b) Up 557

5. (a) Up 222 (b) Up 706

6. (a) Up 713 (b) Up 166 16

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2.02 Practise with your abacus to do the following.

1. (a) Clear abacus (b) Up 101 (c) Up 38

2. (a) Clear abacus (b) Up 57 (c) Up 421

3. (a) Clear abacus (b) Up 210 (c) Up 168

4. (a) Clear abacus (b) Up 19 (c) Up 760

5. (a) Clear abacus (b) Up 333 (c) Up 165

6. (a) Clear abacus (b) Up 415 (c) Up 531

7. (a) Clear abacus (b) Up 601 (c) Up 277

8. (a) Clear abacus (b) Up 444 (c) Up 555

9. (a) Clear abacus (b) Up 322 (c) Up 655

10. (a) Clear abacus (b) Up 300 (c) Up 607

11. (a) Clear abacus (b) Up 900 (c) Up 27

12. (a) Clear abacus (b) Up 856 (c) Up 132

13. (a) Clear abacus (b) Up 715 (c) Up 182

14. (a) Clear abacus (b) Up 503 (c) Up 296 17

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2.03 Perform the following with your abacus.

1.

32 (Up 32)

+

10 (Up 10)

=

2.

114 (Up 114)

+

75 (Up 75)

=

3.

53 (Up 53)

+

35 (Up 35)

=

4.

212 (Up 212)

+

672 (Up 672)

=

5.

21 (Up 21)

+

857 (Up 857)

=

6.

608 (Up 608)

+

291 (Up 291)

=

7.

465 (Up 465)

+

532 (Up 532)

=

8.

740 (Up 740)

+

256 (Up 256)

=

18

42

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2.04 Use your abacus to calculate the following.

1. 42

2. 137 + 212 =

+ 106 =

3. 215 + 132 =

4. 87

5. 98

6. 408 + 90

+ 301 =

+ 201 = =

7. 331 + 152 =

8. 551 + 123 =

9. 170 + 516 =

10. 600 + 206 =

11. 713 + 285 =

12. 418 + 511 =

13. 60

14. 523 + 255 =

+ 200 =

15. 31 + 56

+ 211 =

16. 121 + 67

+ 300 =

17. 15 + 10

+ 173 =

18. 77 + 2

+ 910 =

19. 50 + 205 + 622 = 20. 3

+ 20

+ 876 = 19

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2.05 Let’s visualise and calculate.

What is 280 + 119? Visualise and draw the beads. Step 1:

280, up 280

Step 2:

plus 119, up 119

Step 3:

equals

280

+

119 20

=

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2.06 Let’s visualise and calculate.

What is 612 + 366? Visualise and draw the beads. Step 1:

612, up 612

Step 2:

plus 366, up 366

Step 3:

equals

612

+

366 21

=

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2.07 Match the answers correctly.

1. The Little Friend of 3 is…

1

2. The Big Friend of 7 is…

2

3. The Big Friend of 4 is…

3

4. The Little Friend of 2 is…

4

5. The Big Friend of 6 is…

5

6. The Big Friend of 5 is…

6

7. The Little Friend of 1 is…

7

8. The Big Friend of 2 is…

8

9. The Big Friend of 9 is…

9

10. The Little Friend of 4 is…

1

11. The Big Friend of 8 is…

2

12. The Big Friend of 3 is…

3

13. The Big Friend of 1 is…

4 22

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2.08 Practise the following with your abacus. Clear your abacus before you begin each exercise. 1.

Up 2 at Ones, Up 5 at Ones, Down 2 at Ones. What do you get?

2.

Up 4 at Ones, Up 5 at Ones, Down 4 at Ones. What do you get?

3.

Up 1 at Ones, Up 5 at Ones, Down 1 at Ones. What do you get?

4.

Up 3 at Ones, Up 5 at Ones, Down 3 at Ones. What do you get?

5.

Up 1 at Ones, Up 5 at Ones, Down 1 at Ones. What do you get?

6.

Up 2 at Ones, Up 5 at Ones, Down 1 at Ones. What do you get?

7.

Up 3 at Ones, Up 5 at Ones, Down 2 at Ones. What do you get?

8.

Up 3 at Ones, Up 5 at Ones, Down 1 at Ones. What do you get?

9.

Up 4 at Ones, Up 5 at Ones, Down 3 at Ones. What do you get?

10.

Up 4 at Ones, Up 5 at Ones, Down 2 at Ones. What do you get?

11.

Up 4 at Ones, Up 5 at Ones, Down 1 at Ones. What do you get?

12.

Up 1 at Ones, Down 1 at Ones, Carry 1 at Tens. What do you get?

13.

Up 2 at Ones, Down 2 at Ones, Carry 1 at Tens. What do you get?

14.

Up 3 at Ones, Down 3 at Ones, Carry 1 at Tens. What do you get?

15.

Up 4 at Ones, Down 4 at Ones, Carry 1 at Tens. What do you get?

16.

Up 5 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

17.

Up 6 at Ones, Down 6 at Ones, Carry 1 at Tens. What do you get?

18.

Up 7 at Ones, Down 7 at Ones, Carry 1 at Tens. What do you get?

19.

Up 8 at Ones, Down 8 at Ones, Carry 1 at Tens. What do you get?

20.

Up 9 at Ones, Down 9 at Ones, Carry 1 at Tens. What do you get?

21.

Up 2 at Ones, Down 1 at Ones, Carry 1 at Tens. What do you get?

22.

Up 3 at Ones, Down 1 at Ones, Carry 1 at Tens. What do you get?

23.

Up 3 at Ones, Down 2 at Ones, Carry 1 at Tens. What do you get? 23

5

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24.

Up 4 at Ones, Down 1 at Ones, Carry 1 at Tens. What do you get?

25.

Up 4 at Ones, Down 2 at Ones, Carry 1 at Tens. What do you get?

26.

Up 4 at Ones, Down 3 at Ones, Carry 1 at Tens. What do you get?

27.

Up 5 at Ones, Up 4 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

28.

Up 5 at Ones, Up 3 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

29.

Up 5 at Ones, Up 2 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

30.

Up 5 at Ones, Up 1 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

31.

Up 6 at Ones, Down 1 at Ones, Carry 1 at Tens. What do you get?

32.

Up 6 at Ones, Up 3 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

33.

Up 6 at Ones, Up 2 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

34.

Up 6 at Ones, Up 1 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

35.

Up 6 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

36.

Up 7 at Ones, Down 1 at Ones, Carry 1 at Tens. What do you get?

37.

Up 7 at Ones, Down 2 at Ones, Carry 1 at Tens. What do you get?

38.

Up 7 at Ones, Up 2 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

39.

Up 7 at Ones, Up 1 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

40.

Up 7 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

41.

Up 7 at Ones, Down 6 at Ones, Carry 1 at Tens. What do you get?

42.

Up 8 at Ones, Down 1 at Ones, Carry 1 at Tens. What do you get?

43.

Up 8 at Ones, Down 2 at Ones, Carry 1 at Tens. What do you get?

44.

Up 8 at Ones, Down 3 at Ones, Carry 1 at Tens. What do you get?

24

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45.

Up 8 at Ones, Up 1 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

46.

Up 8 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

47.

Up 8 at Ones, Down 6 at Ones, Carry 1 at Tens. What do you get?

48.

Up 8 at Ones, Down 7 at Ones, Carry 1 at Tens. What do you get?

49.

Up 9 at Ones, Down 1 at Ones, Carry 1 at Tens. What do you get?

50.

Up 9 at Ones, Down 2 at Ones, Carry 1 at Tens. What do you get?

51.

Up 9 at Ones, Down 3 at Ones, Carry 1 at Tens. What do you get?

52.

Up 9 at Ones, Down 4 at Ones, Carry 1 at Tens. What do you get?

53.

Up 9 at Ones, Down 5 at Ones, Carry 1 at Tens. What do you get?

54.

Up 9 at Ones, Down 6 at Ones, Carry 1 at Tens. What do you get?

55.

Up 9 at Ones, Down 7 at Ones, Carry 1 at Tens. What do you get?

56.

Up 9 at Ones, Down 8 at Ones, Carry 1 at Tens. What do you get?

57.

Up 13, Up 1 at Tens, Up 5 at Ones, Down 2 at Ones. What do you get?

58.

Up 24, Up 2 at Tens, Up 5 at Ones, Down 1 at Ones. What do you get?

59.

Up 35, Up 5 at Tens, Down 2 at Tens, Down 5 at Ones, Carry 1 at Tens. What do you get?

60.

Up 46, Up 5 at Tens, Down 1 at Tens, Carry 1 at Tens, Up 1 at Ones, Down 5 at Ones. What do you get?

61.

Up 57, Down 5 at Tens, Carry 1 at Hundreds, Carry 1 at Tens, Up 2 at Ones, Down 5 at Ones. What do you get?

62.

Up 68, Carry 1 at Hundreds, Up 1 at Tens, Down 5 at Tens, Down 2 at Ones, Carry 1 at Tens. What do you get?

63.

Up 79, Carry 1 at Hundreds, Up 2 at Tens, Down 5 at Tens, Down 1 at Ones, Up 5 at Tens, Down 4 at Tens. What do you get?

64.

Up 483, Up 5 at Hundreds, Down 1 at Hundreds, Down 2 at Tens, Carry 1 at Hundreds, Up 5 at Ones, Down 2 at Ones. What do you get?

25

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2.09 Work with your abacus to answer these questions correctly. 1.

What is 4 + 3? Step 1: Up 4 Step 2: Up 3 (but there are not enough beads at Ones to move . up 3). We use the little friend of 3, which is Using the little friend of 3, up 3 is… Up 5, Down little friend. So, up 3 becomes... Up , Down . Step 3: The answer is .

2.

What is 7 + 9? Step 1: Up 7 Step 2: Up 9 (but there are not enough beads at Ones to move up 9). We use the big friend of 9, which is . Using the big friend of 9, up 9 becomes… Down , Carry at . Step 3: The answer is .

3.

What is 25 + 6? Step 1: Up 25 Step 2: Up 6 (but there are not enough beads at Ones to move up 6). We use the big friend of 6, which is . Using the big friend of 6, up 6 becomes… Down 4, Carry at Tens (move the beads to carry at Tens first) But there are not enough beads at Ones to move down 4. We use the little friend of 4, which is . Using the little friend of 4, down 4 becomes… Up little friend, Down . Up , Down Step 3: The answer is . 26

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4.

What is 378 + 34? Step 1: Up 378 Step 2:

Up 34 (but there are not enough beads at Tens and Ones to move up 3 and 4). At Tens, to move up 3… we use the big friend of 3, which is . Using the big friend of 3, up 3 at Tens becomes… Down , Carry at . At Ones, to move up 4… we use the big friend of 4, which is . Using the big friend of 4, up 4 at Ones becomes… Down , Carry at .

Step 3:

5.

The answer is

.

What is 659 + 281? Step 1:

Up 659

Step 2:

Up 281 (move up 2 at Hundreds, but there are not enough beads at Tens and Ones to move up 8 and 1). At Tens, to move up 8… we use the big friend of 8, which is . Using the big friend of 8, up 8 at Tens becomes… Down , Carry at Hundreds (move the beads to carry at Hundreds first). But there are not enough beads at Tens to move down 2. We use little friend of 2, which is . Using the little friend of 2, down 2 becomes… Up little friend, Down . Up , Down . At Ones, to move up 1 we use the big friend of 1, which is . Using the big friend of 1, up 1 at Ones becomes… Down , Carry at .

Step 3:

The answer is

. 27

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2.10 When there are not enough beads, how do you move?

1.

There are not enough beads at Ones to move Up 1. a. If using the help of the little friend, Up 1 becomes… Up

, Down

.

b. If using the help of the big friend, Up 1 becomes… Down 2.

, Carry

at

.

There are not enough beads at Tens to move Up 2. a. If using the help of the little friend, Up 2 becomes… Up

, Down

.

b. If using the help of the big friend, Up 2 becomes… Down 3.

, Carry

at

.

There are not enough beads at Ones to move Up 3. a. If using the help of the little friend, Up 3 becomes… Up

, Down

.

b. If using the help of the big friend, Up 3 becomes… Down 4.

, Carry

at

.

There are not enough beads at Tens to move Up 4. a. If using the help of the little friend, Up 4 becomes… Up

, Down

.

b. If using the help of the big friend, Up 4 becomes… Down

, Carry

at 28

.

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5.

There are not enough beads at Ones to move Up 5. Using the help of the big friend, Up 5 becomes… Down

6.

, Carry

at

.

There are not enough beads at Tens to move Up 6. Using the help of the big friend, Up 6 becomes… Down

7.

, Carry

at

.

There are not enough beads at Ones to move Up 7. Using the help of the big friend, Up 7 becomes… Down

8.

, Carry

at

.

There are not enough beads at Tens to move Up 8. Using the help of the big friend, Up 8 becomes… Down

9.

, Carry

at

.

There are not enough beads at Ones to move Up 9. Using the help of the big friend, Up 9 becomes… Down

10.

, Carry

at

.

There are not enough beads at Hundreds to move Up 5. Using the help of the big friend, Up 5 becomes… Down

, Carry

at 29

.

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2.11 Use your abacus to answer the following questions. 1. 14 + 26 =

2. 27 + 13 =

3. 16 + 29 =

4. 8 + 33

5. 35 + 9

=

6. 22 + 19 =

7. 23 + 14 =

8. 12 + 23 =

9. 33 + 16 =

10. 42 + 6

=

=

11. 28 + 39 =

12. 29 + 37 =

13. 44 + 66 =

14. 66 + 99 =

15. 66 + 88 =

16. 77 + 99 =

17. 57 + 89 =

18. 74 + 75 =

19. 17 + 28 + 39 =

20. 18 + 29 + 30 =

21. 22 + 44 + 66 =

22. 33 + 66 + 99 =

23. 44 + 66 + 88 =

24. 55 + 77 + 99 =

25. 41 + 57 + 89 =

26. 73 + 74 + 75 =

27. 64 + 49 + 33 =

28. 57 + 58 + 59 =

29. 98 + 48 + 67 =

30. 71 + 89 + 97 = 30

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2.12 Work with your abacus to get the answers!

1. 134 + 257 =

2. 316 + 578 =

3. 611 + 169 =

4. 123 + 456 =

5. 234 + 345 =

6. 345 + 123 =

7. 789 + 111 =

8. 343 + 666 =

9. 413 + 354 =

10. 513 + 395 =

11. 223 + 229 =

12. 371 + 535 =

13. 777 + 199 =

14. 747 + 146 =

15. 936 + 28

16. 835 + 75

=

=

17. 738 + 175 =

18. 424 + 287 =

19. 362 + 249 =

20. 388 + 499 =

21. 615 + 97 + 108

22. 124 + 135 + 146 =

=

23. 288 + 472 + 111 =

24. 96 + 286 + 417

25. 333 + 333 + 279 =

26. 603 + 192 + 193 =

27. 276 + 344 + 239 =

28. 358 + 264 + 298 =

29. 316 + 495 + 169 =

30. 444 + 232 + 158 = 31

=

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2.13 Use your abacus to add these numbers.

1.

2.

+

83 228 68

5.

+

427 155 31

8.

+

294 234 264

11.

+

442 133 39

14.

+

867 99 8

4.

7.

10.

13.

31 119 + 97

3.

6.

+

201 564 49

9.

+

515 242 53

12.

+

631 210 88

15.

+

229 93 675

32

+

318 62 241

+

98 762 81

+

163 226 450

+

778 33 111

+

305 356 329

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16.

17.

+

248 197 75

20.

+

163 368 364

23.

+

393 278 197

26.

+

185 323 259

29.

+

369 246 135

19.

22.

25.

28.

18.

+

130 574 166

21.

+

245 426 99

24.

+

134 216 424

27.

+

299 399 99

30.

+

477 334 55

33

+

252 467 164

+

137 557 126

+

250 167 408

+

445 145 246

+

815 97 49

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Unit 3

Subtraction within the range of 1000 3.01 Use your abacus to do the following.

1. (a) Up 888 (b) Down 121

2. (a) Up 498 (b) Down 153

3. (a) Up 624 (b) Down 523

4. (a) Up 763 (b) Down 651

5. (a) Up 595 (b) Down 560

6. (a) Up 989 (b) Down 776 34

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3.02 Practise with your abacus to do the following.

1. (a) Clear abacus (b) Up 423 (c) Down 12

2. (a) Clear abacus (b) Up 516 (c) Down 511

3. (a) Clear abacus (b) Up 752 (c) Down 201

4. (a) Clear abacus (b) Up 679 (c) Down 163

5. (a) Clear abacus (b) Up 599 (c) Down 78

6. (a) Clear abacus (b) Up 885 (c) Down 560

7. (a) Clear abacus (b) Up 684 (c) Down 171

8. (a) Clear abacus (b) Up 666 (c) Down 515

9. (a) Clear abacus (b) Up 493 (c) Down 271

10. (a) Clear abacus (b) Up 306 (c) Down 201

11. (a) Clear abacus (b) Up 999 (c) Down 685

12. (a) Clear abacus (b) Up 756 (c) Down 651

13. (a) Clear abacus (b) Up 898 (c) Down 576

14. (a) Clear abacus (b) Up 895 (c) Down 665 35

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3.03 Perform the following with your abacus.

1.

32 (Up 32)

–

10 (Down 10)

=

2.

176 (Up 176)

–

75 (Down 75)

=

3.

453 (Up 453)

–

101 = (Down 101)

4.

862 (Up 862)

–

652 = (Down 652)

5.

971 (Up 971)

–

850 = (Down 850)

6.

447 (Up 447)

–

216 = (Down 216)

7.

296 (Up 296)

–

165 = (Down 165)

8.

754 (Up 754)

–

601 = (Down 601) 36

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3.04 Use your abacus to calculate the following.

1. 186 – 21

=

2. 427 – 212 =

3. 684 – 132 =

4. 787 – 225 =

5. 498 – 301 =

6. 698 – 90

7. 388 – 152 =

8. 764 – 213 =

9. 776 – 516 =

10. 640 – 200 =

11. 289 – 85

=

=

12. 603 – 601 =

13. 890 – 240 =

14. 576 – 565 =

15. 739 – 16 16. 992 –

– 502 =

61 – 611 =

17. 898 – 701 – 66

=

18. 988 – 777 – 211 = 19. 850 – 200 – 650 = 20. 993 –

81 – 712 = 37

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3.05 Let’s visualise and calculate.

What is 887 – 636? Visualise and draw the beads. Step 1:

887, up 887

Step 2:

minus 636, down 636

Step 3:

equals

887

–

636 38

=

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3.06 Let’s visualise and calculate.

What is 678 – 157? Visualise and draw the beads. Step 1:

678, up 678

Step 2:

minus 157, down 157

Step 3:

equals

678

–

157 39

=

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3.07 Let’s visualise and calculate.

What is 779 – 258? Visualise and draw the beads. Step 1:

779, up 779

Step 2:

minus 258, down 258

Step 3:

equals

779

–

258 40

=

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3.08 Let’s visualise and calculate.

What is 969 – 366? Visualise and draw the beads. Step 1:

969, up 969

Step 2:

minus 366, down 366

Step 3:

equals

969

–

366 41

=

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3.09 When there are not enough beads, how do you move?

1.

There are not enough beads at Tens to move Down 1. a. If using the help of the little friend, Down 1 becomes… Up 4 , Down 5 . b. If using the help of the big friend, Down 1 becomes… Tens . Remove 1 at Hundreds, Up 9 at

2.

There are not enough beads at Ones to move Down 2. a. If using the help of the little friend, Down 2 becomes… Up , Down . b. If using the help of the big friend, Down 2 becomes… Remove at , Up at .

3.

There are not enough beads at Tens to move Down 3. a. If using the help of the little friend, Down 3 becomes… Up , Down . b. If using the help of the big friend, Down 3 becomes… Remove at , Up at .

4.

There are not enough beads at Ones to move Down 4. a. If using the help of the little friend, Down 4 becomes… Up , Down . b. If using the help of the big friend, Down 4 becomes… Remove at , Up at .

42

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5.

There are not enough beads at Tens to move Down 5. Using the help of the big friend, Down 5 becomes… Remove at , Up at .

6.

There are not enough beads at Ones to move Down 6. Using the help of the big friend, Down 6 becomes… Remove at , Up at .

7.

There are not enough beads at Tens to move Down 7. Using the help of the big friend, Down 7 becomes… Remove at , Up at .

8.

There are not enough beads at Ones to move Down 8. Using the help of the big friend, Down 8 becomes… Remove at , Up at .

9.

There are not enough beads at Tens to move Down 9. Using the help of the big friend, Down 9 becomes… Remove at , Up at .

10.

There are not enough beads at Hundreds to move Down 5. Using the help of the big friend, Down 5 becomes… Remove at , Up at . 43

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3.10 Work with your abacus to answer these questions correctly. 1.

Step 1: Step 2:

Step 3: 2.

Step 1: Step 2:

Step 3: 3.

Step 1: Step 2:

Step 3:

Up 7 Down 3 (but there are not enough beads at Ones to move down 3). We use the little friend of 3, which is . Using the little friend of 3, down 3 becomes... Up , Down . The answer is . Up 18 Down 9 (but there are not enough beads at Ones to down 9). We use the big friend of 9, which is . Using the big friend of 9, down 9 becomes... Remove at , Up . The answer is . Up 22 Down 7 (but there are not enough beads at Ones to down 7). We use the big friend of 7, which is . Using the big friend of 7, down 7 becomes... Remove at , Up (remove the beads at Tens first). But there are not enough beads at Ones to move up 3. We use little friend of 3, which is . Using the little friend of 3, down 3 becomes... Up , Down little friend. Up , Down . The answer is . 44

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4.

Step 1: Up 463 Step 2: Down 85 (but there are not enough beads at Tens and Ones to move down 8 and 5). At Tens, to move down 8... we use the big friend of 8, which is . Using the big friend of 8, down 8 at Tens becomes... at , Up . Remove At Ones, to move down 5... we use the big friend of 5, which is . Using the big friend of 5, down 5 at Tens becomes... at , Up . Remove Step 3: The answer is

5.

.

Step 1: Up 846 Step 2: Down 267 (move down 2 at Hundreds, but there are not enough beads at Tens and Ones to move down 6 and 7) At Tens, to move down 6... . we use the big friend of 6, which is Using the big friend of 6, down 6 at Tens becomes... at , Up (remove the Remove beads first). But there are not enough beads at Tens to move up 4. . We use little friend of 4, which is Using the little friend of 4, up 4 becomes… , Down . Up At Ones, to move down 7... we use the big friend of 7, which is . Using the big friend of 7, down 7 at Ones becomes... at , Up . Remove Step 3: The answer is

.

45

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3.11 Use your abacus to answer the following questions. 1. 26 – 14 =

2. 27 – 13 =

3. 32 – 29 =

4. 33 – 8

5. 35 – 9

=

6. 48 – 19 =

7. 23 – 15 =

8. 44 – 26 =

9. 53 – 16 =

10. 42 – 7

=

=

11. 66 – 28 =

12. 74 – 17 =

13. 55 – 36 =

14. 84 – 65 =

15. 93 – 88 =

16. 71 – 59 =

17. 52 – 33 =

18. 77 – 48 =

19. 92 – 6 – 29 =

20. 88 – 29 – 30 =

21. 66 – 12 – 23 =

22. 76 – 69 – 3

=

23. 88 – 66 – 7 =

24. 77 – 58 – 4

=

25. 97 – 58 – 23 =

26. 76 – 32 – 12 =

27. 43 – 15 – 9 =

28. 82 – 58 – 17 =

29. 98 – 49 – 4 =

30. 80 – 48 – 24 = 46

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3.12 Work with your abacus to get the answers!

1. 257 – 134 =

2. 578 – 386 =

3. 611 – 169 =

4. 456 – 123 =

5. 345 – 284 =

6. 345 – 123 =

7. 732 – 45

=

8. 666 – 343 =

9. 413 – 354 =

10. 513 – 395 =

11. 632 – 229 =

12. 535 – 371 =

13. 777 – 199 =

14. 757 – 148 =

15. 936 – 58

16. 835 – 71

=

=

17. 738 – 175 =

18. 424 – 287 =

19. 362 – 249 =

20. 488 – 399 =

21. 615 – 97 – 108 =

22. 824 – 135 – 146 =

23. 648 – 472 – 111 =

24. 906 – 287 – 315 =

25. 733 – 345 – 79 =

26. 603 – 192 – 193 =

27. 976 – 344 – 239 =

28. 700 – 264 – 107 =

29. 900 – 26 – 738 =

30. 1000 – 17 – 346 = 47

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3.13 Use your abacus to subtract the numbers.

1.

1000 – 412

2.

1000 – 386

3.

1000 – 573

4.

1000 – 993

5.

1000 – 678

6.

1000 – 846

7.

1000 – 250

8.

1000 – 607

9.

1000 – 504

10.

1000 – 57

11.

1000 – 84

12.

1000 – 22

13.

1000 – 93

14.

1000 – 16

15.

1000 – 68

16.

1000 – 5

17.

1000 – 3

18.

1000 – 9

48

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19.

22.

25.

28.

31.

34.

–

823 415

20.

–

509 235

23.

–

460 185

26.

–

787 399

29.

–

900 488

32.

–

800 413

35.

–

786 462

21.

–

403 175

24.

–

580 492

27.

–

812 676

30.

–

800 669

33.

–

510 375

36.

49

–

661 453

–

306 168

–

600 484

–

966 679

–

700 351

–

200 117

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3.14 Answer the questions with the help of your abacus.

1. There are 329 people in the hall. 173 of them wear a black shirt. How many of them wear other than black? –

=

2. There are 683 people at school. 461 of them are girls. How many of them are boys? –

=

3. Zura has 554 beads now. She needs 1000 beads. How many more should she get? –

=

4. The farmer collected 520 eggs from his farm. He went to the market and sold 379 of them. How many eggs are left? –

=

5. 46 out of 800 students came late to school. How many came early? –

=

6. If Andi needs 135 more stamps to have a total of 870 stamps in his collection, how many stamps does he have now? –

= 50

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7. What do you get when you take away 728 from 916? –

=

8. There are 931 fish altogether in the pond. 268 are dead. How many are alive? –

=

9. If you remove 314 from 806, what do you get? –

=

10. The baker used up 624 eggs in 3 months. In the first month she used 236 eggs. In the third month, she used 200 eggs. How many eggs did she use in the second month? –

–

=

11. Zura, Devi and Jenny have 484 coins among them. If Jenny has 129 and Devi has 73, how many coins does Zura have? –

–

=

12. Andi has 707 coins. He gives 38 coins to Ah Wai and 342 coins to Devi. How many coins does he have left? –

–

51

=

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Unit 4

Combination of addition and subtraction within 1000 4.01 Practise the following with your abacus. Clear your abacus before you begin each exercise.

1. Up 317, Up 121, Down 215. 2. Up 782, Down 261, Up 368. 3. Up 135, Up 253, Down 176. 4. Up 893, Down 632, Up 717. 5. Up 224, Up 225, Down 318. 6. Up 387, Down 162, Up 663. 7. Up 510, Up 284, Down 684. 8. Up 441, Down 230, Up 182. 9. Up 902, Up 57, Down 509. 10. Up 449, Down 217, Up 651. 11. Up 676, Up 221, Down 270. 12. Up 199, Down 73, Up 622. 13. Up 488, Up 511, Down 889. 14. Up 253, Down 152, Up 897. 15. Up 745, Up 153, Down 191. 16. Up 587, Down 66, Up 456. 17. Up 837, Up 52, Down 238. 18. Up 668, Down 156, Up 277. 19. Up 256, Up 602, Down 357. 20. Up 987, Down 765, Up 675. 52

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4.02 Fill in the blanks with the correct numbers. Use your abacus to calculate.

1. Up 372, Down 222, Up 518 –

+

=

2. Up 897, Up 102, Down 665 +

–

=

3. Up 845, Down 720, Up 862 –

+

=

4. Up 113, Up 675, Down 727 +

–

=

5. Up 649, Down 34, Up 284 –

+

=

6. Up 405, Up 592, Down 386 +

–

=

53

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4.03 Complete the number sentences with correct numbers and symbols. Use your abacus to calculate.

1. Up 174, Down 63, Up 512 = 2. Up 291, Up 607, Down 818 = 3. Up 338, Up 511, Down 126 = 4. Up 425, Up 72, Down 371 = 5. Up 569, Down 54, Up 383 = 6. Up 807, Down 602, Up 634 = 54

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4.04 Use your abacus to calculate.

1.

83 215 – 67

2.

31 117 – 23

3.

318 61 – 257

4.

427 561 – 76

5.

201 566 –1 5 2

6.

97 702 – 88

7.

294 – 234 228

8.

815 – 210 82

9.

463 – 262 787

10.

692 – 131 417

11.

731 – 201 466

12.

788 – 33 111

13.

867 22 – 638

14.

599 – 93 181

15.

305 652 – 705

55

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16.

346 152 – 275

17.

839 – 514 151

18.

252 647 – 169

19.

968 – 363 374

20.

946 – 425 367

21.

137 552 – 126

22.

373 625 – 197

23.

134 365 – 424

24.

950 – 750 278

25.

185 313 – 258

26.

899 – 399 99

27.

445 551 – 246

28.

961 26 – 135

29.

477 – 325 726

30.

885 – 660 673

56

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4.05 Let’s visualise and calculate.

What is 297 + 602 – 629? Visualise and draw the beads.

Step 1:

297, up 297

Step 2:

plus 602, up 602

Step 3:

minus 629, down 629

Step 4:

equals 297

+

602

– 57

629

=

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What is 418 + 561 – 706? Visualise and draw the beads.

Step 1:

418, up 418

Step 2:

plus 561, up 561

Step 3:

minus 706, down 706

Step 4:

equals

418

+

561

– 58

706

=

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What is 556 + 233 – 518? Visualise and draw the beads.

Step 1:

556, up 556

Step 2:

plus 233, up 233

Step 3:

minus 518, down 518

Step 4:

equals

556

+

233

– 59

518

=

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What is 783 – 221 + 31? Visualise and draw the beads.

Step 1:

783, up 783

Step 2:

minus 221, down 221

Step 3:

plus 31, up 31

Step 4:

equals

783

–

221

+ 60

31

=

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What is 440 – 200 + 751? Visualise and draw the beads.

Step 1:

440, up 440

Step 2:

minus 200, down 200

Step 3:

plus 751, up 751

Step 4:

equals

440

–

200

+ 61

751

=

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What is 998 – 835 + 126? Visualise and draw the beads.

Step 1:

998, up 998

Step 2:

minus 835, down 835

Step 3:

plus 126, up 126

Step 4:

equals

998

–

835

+ 62

126

=

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4.06 Calculate with your abacus.

1.

224

–

187

+

442

=

2.

673

–

139

+

323

=

3.

118

+

455

–

326

=

4.

939

–

78

+

55

=

5.

35

+

585

–

216

=

6.

645

–

343

+

555

=

7.

678

–

284

+

299

=

8.

444

+

333

–

99

=

9.

500

–

78

+

194

=

10.

709

–

362

+

371

=

63

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11.

446

–

290

+

221

=

12.

895

–

261

+

232

=

13.

331

+

577

–

448

=

14.

700

–

7

+

277

=

15.

87

+

585

–

478

=

16.

867

–

565

+

333

=

17.

456

–

43

+

334

=

18.

734

+

171

–

289

=

19.

100

–

9

+

699

=

20.

602

–

346

+

255

=

64

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21.

902

–

78

+

91

=

22.

1000

–

65

+

55

=

23.

499

+

501

–

67

=

24.

502

+

298

–

123

=

25.

687

+

223

–

49

=

26.

1000

–

365

+

275

=

27.

1000

–

38

+

25

=

28.

578

+

129

–

309

=

29.

301

–

9

+

395

=

30.

204

–

86

+

716

=

65

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4.07 Rearrange the numbers so that the number sentences are true. Calculate with your abacus to check the answers.

362

257

–

+

251

861

736

+

–

38

–

+

66

163

=

652

772

368

=

78

=

198

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139

260

+

–

198

617

886

–

+

566

+

–

67

937

=

812

177

201

=

86

=

721

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63

79

–

+

371

=

780

551

+

–

111

=

559

57

–

+

68

387

340

346

=

848

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574

178

+

–

415

=

515

675

–

+

999

=

227

155

+

–

69

811

839

722

=

650

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Unit 5 Multiplication of basic facts within 2, 3, 4 and 5 times-tables 5.01

Fill in the blanks with the correct answers.

1. 2 + 2 + 2 + 2 =

How many 2’s are there above?

You can also write the above sentence as… x

2

=

Write and say the number sentence out loud!

times

two

70

equals

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2. 3 + 3 + 3 + 3 + 3 =

How many 3’s are there above? You can also write the above sentence as… x

3

=

times three equals

3. 4 + 4 =

How many 4’s are there above? You can also write the above sentence as… x

4

=

times four equals

71

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4. 5 + 5 + 5 + 5 =

How many 5’s are there above? You can also write the above sentence as… x

5

times

five

=

equals

5. 5 + 5 + 5 + 5 + 5 =

How many 5’s are there above? You can also write the above sentence as… x

5

times

five

72

=

equals

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6. 3 + 3 + 3 + 3 =

How many 3’s are there above? You can also write the above sentence as… x

3

=

times three equals

7. 4 + 4 + 4 =

How many 4’s are there above? You can also write the above sentence as… x

4

=

times four equals

73

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5.02 7

x

2

=

How do we do this? What is 7 x 2?

That’s easy! We write “2” seven times and then we add them all up to get the answer.

2 + 2 + 2 + 2 + 2 + 2 + 2=

That’s right! So, 7 x 2 =

Now, can you try 8 x 2?

That’s easy! We write “2” eight times and then we add them all up to get the answer.

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 8 x 2 = 74

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5.03 Let’s add the numbers to find answers to the multiplication problems. 1. What is 6 x 2? 2 + 2 + 2 + 2 + 2 + 2 = 12 2. What is 9 x 2?

3. What is 5 x 2?

4. What is 3 x 2?

5. What is 2 x 2?

6. What is 7 x 2?

7. What is 4 x 2?

8. What is 8 x 2?

75

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5.04

Let’s build the 2 times-tables.

2

x

2

=

2+2=

x

2

=

2+2+2=

x

2

=

2+2+2+2=

x

=

2+2+2+2+2=

x

=

2+2+2+2+2+2=

x

=

2+2+2+2+2+2+2=

x

=

2+2+2+2+2+2+2+2=

x

=

2+2+2+2+2+2+2+2+2=

x

=

76

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5.05 Let’s add the numbers to find answers to the multiplication problems. 1. What is 6 x 3? 3 + 3 + 3 + 3 + 3 + 3 = 2. What is 9 x 3?

3. What is 5 x 3?

4. What is 3 x 3?

5. What is 2 x 3?

6. What is 7 x 3?

7. What is 4 x 3?

8. What is 8 x 3?

77

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5.06

Let’s build the 3 times-tables.

3

x

3

=

3+3=

x

3

=

3+3+3=

x

3

=

3+3+3+3=

x

=

3+3+3+3+3=

x

=

3+3+3+3+3+3=

x

=

3+3+3+3+3+3+3=

x

=

3+3+3+3+3+3+3+3=

x

=

3+3+3+3+3+3+3+3+3=

x

=

78

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5.07

Let’s add the numbers to find answers to the multiplication problems. 1. What is 6 x 4? 4 + 4 + 4 + 4 + 4 + 4 = 2. What is 9 x 4?

3. What is 5 x 4?

4. What is 3 x 4?

5. What is 2 x 4?

6. What is 7 x 4?

7. What is 4 x 4?

8. What is 8 x 4?

79

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5.08

Let’s build the 4 times-tables.

4

x

4

=

4+4=

x

4

=

4+4+4=

x

4

=

4+4+4+4=

x

=

4+4+4+4+4=

x

=

4+4+4+4+4+4=

x

=

4+4+4+4+4+4+4=

x

=

4+4+4+4+4+4+4+4=

x

=

4+4+4+4+4+4+4+4+4=

x

=

80

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5.09

Let’s add the numbers to find answers to the multiplication problems. 1. What is 6 x 5? 5 + 5 + 5 + 5 + 5 + 5 = 2. What is 9 x 5?

3. What is 5 x 5?

4. What is 3 x 5?

5. What is 2 x 5?

6. What is 7 x 5?

7. What is 4 x 5?

8. What is 8 x 5?

81

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5.10

Let’s build the 5 times-tables.

5

x

5

=

5+5=

x

5

=

5+5+5=

x

5

=

5+5+5+5=

x

=

5+5+5+5+5=

x

=

5+5+5+5+5+5=

x

=

5+5+5+5+5+5+5=

x

=

5+5+5+5+5+5+5+5=

x

=

5+5+5+5+5+5+5+5+5=

x

=

82

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5.11

We need to learn the multiplication tables or times-tables by heart!

1

X

2

=

1

X

3

=

2

X

2

=

2

X

3

=

3

X

2

=

3

X

3

=

4

X

2

=

4

X

3

=

5

X

2

=

5

X

3

=

6

X

2

=

6

X

3

=

7

X

2

=

7

X

3

=

8

X

2

=

8

X

3

=

9

X

2

=

9

X

3

=

83

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Try to learn these tables by heart!

1

X

4

=

1

X

5

=

2

X

4

=

2

X

5

=

3

X

4

=

3

X

5

=

4

X

4

=

4

X

5

=

5

X

4

=

5

X

5

=

6

X

4

=

6

X

5

=

7

X

4

=

7

X

5

=

8

X

4

=

8

X

5

=

9

X

4

=

9

X

5

=

84

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5.12

Answer these questions without looking at the times-tables.

1. 4 x 3 =

2.

3x2=

3. 7 x 2 =

4.

8x3=

5. 7 x 3 =

6.

5x2=

7. 1 x 2 =

8. 9 x 3 =

9. 6 x 3 =

10.

4x2=

11. 8 x 2 =

12.

3x3=

13. 2 x 3 =

14.

6x2=

15. 9 x 2 =

16.

1x3=

17. 5 x 3 =

18.

2x2=

85

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5.13

Answer these questions without looking at the times-tables.

1. 4 x 5 =

2.

3x4=

3. 7 x 4 =

4.

8x5=

5. 7 x 5 =

6.

5x4=

7. 1 x 4 =

8. 9 x 5 =

9. 6 x 5 =

10.

4x4=

11. 8 x 4 =

12.

3x5=

13. 2 x 5 =

14.

6x4=

15. 9 x 4 =

16.

1x5=

17. 5 x 5 =

18.

2x4=

86

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5.14

Match the questions to the answers.

5x4

36

16

9x3

6x3

40

24

8x2

7x2

3

27

7x5

8x5

20

12

6x4

9x4

16

21

5x5

1x3

18

35

4x3

2x2

15

25

7x3

3x5

12

30

9x5

4x4

14

32

6x5

5x3

4

18

8x4

6x2

15

45

9x2

87

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5.15 Answer the questions and colour the boxes accordingly. 1. Colour the multiplicand YELLOW, the multiplier ORANGE and the product GREEN. 7

x

4

=

2. Colour the multiplicand ORANGE, the multiplier YELLOW and the product GREEN. 8

x

3

=

3. Colour the multiplicand GREEN, the multiplier YELLOW and the product ORANGE. 2

x

5

=

4. Colour the multiplicand YELLOW, the multiplier GREEN and the product ORANGE. 1

x

4

=

5. Colour the multiplicand RED, the multiplier ORANGE and the product YELLOW. 4

x

2

=

6. Colour the multiplicand ORANGE, the multiplier RED and the product YELLOW. 1

x

5

=

7. Colour the multiplicand GREEN, the multiplier ORANGE and the product RED. 5 x 2 = 88

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5.16 How do you show the products on the abacus? Draw the beads correctly.

1. 4 x 2 = Step 1: Display at 1st rod Step 2: Up at 2nd rod Step 3: So, 4 x 2 =

2. 6 x 3 = Step 1: Up at 1st rod Step 2: Up at 2nd rod Step 3: So, 6 x 3 =

3. 7 x 4 = Step 1: Up at 1st rod Step 2: Up at 2nd rod Step 3: So, 7 x 4 =

4. 9 x 5 = Step 1: Up at 1st rod Step 2: Up at 2nd rod Step 3: So, 9 x 5 =

89

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5.17 Draw the beads to show the products on the abacus. 1.

2.

4x5=

3x2=

3.

4.

7x3=

6x4=

5.

6.

3x3=

8x4= 90

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5.18 Visualise the products and draw the beads. Write down the answer.

9

x

3

=

6

x

2

=

1

x

5

=

2

x

4

=

6

x

5

=

8

x

3

=

91

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5.19 Visualise the products and draw the beads. Write down the answer.

92

x

5 3

x

2 2

x

9 4

x

7 5

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5.20

Answer the following questions.

1. If 4 x 3 = 12, what is 3 x 4?

3x4=

2. If 2 x 5 = 10, what is 5 x 2?

5x2=

3. If 4 x 5 = 20, what is 5 x 4?

5x4=

4. If 3 x 2 = 6, what is 2 x 3?

2x3=

5. If 3 x 5 = 15, what is 5 x 3?

5x3=

6. If 2 x 4 = 8, what is 4 x 2?

4x2=

7.

1

x

=

3

8.

3

x

=

9

9.

2

x

=

8

10.

6

x

=

12

5

x

=

20

=

32

=

40

11.

x

3

=

24

12.

13.

x

5

=

25

14.

=

28

16.

15.

7

x

93

x 8

x

4

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Unit 6

Division within 2, 3, 4 and 5 times-tables 6.01 Jenny has 21 oranges. She wants to give 3 oranges to each guest who comes to her house. How many guests will get the oranges from Jenny? How do we solve this?

First, let us look at all the oranges Jenny has. Let’s count them.

How many oranges are there? She wants to give each guest 3 oranges. So now, let’s make groups of three from these oranges. The first group has been done for you. Continue grouping the oranges in threes.

How many groups of three are there altogether? So, if Jenny wants to give 3 oranges to each guest, how many guests will get the oranges? 94

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We can also solve it this way!

How many oranges does Jenny have? How many oranges does she want to give to each guest? So, the number of guests who will get the oranges can be calculated as follows: ÷

3

=

21 divided by 3 equals

What if Jenny has 27 oranges to give to her guests? How many guests will get the oranges?

Let’s make groups of three from these 27 oranges.

How many groups of three can you make? So, how many guests will get the oranges? We can also calculate it this way: ÷

=

27 divided by 3 equals 95

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6.02 Divide the objects into groups of 2 and write the number sentences. 1.

4

÷

2

=

÷

2

=

2.

3.

÷

=

÷

=

÷

=

4.

5.

96

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6.03 Can you divide these apples into 2 groups equally? 1.

How many apples are there in each group? ÷

2

=

2.

How many apples are there in each group? ÷

2

=

3.

How many apples are there in each group? ÷

2 97

=

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6.04 Divide the objects into groups of 3 and write the number sentences. 1.

6

÷

3

=

÷

3

=

2.

3.

÷

=

÷

=

÷

=

4.

5.

98

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6.05 Can you divide these flowers into 3 groups equally? 1.

How many flowers are there in each group? ÷

3

=

2.

How many flowers are there in each group? ÷

3

=

3.

How many flowers are there in each group? ÷

3 99

=

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6.06 Divide the objects into groups of 4 and write the number sentences. 1.

÷

4

=

÷

4

=

2.

3.

÷

=

÷

=

÷

=

4.

5.

100

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6.07 Can you divide these triangles into 4 equal groups? 1.

How many triangles are there in each group? ÷

4

=

2.

How many triangles are there in each group? ÷

4

=

3.

How many triangles are there in each group? ÷

4 101

=

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6.08 Divide the dots into groups of 5 and write the number sentences.

1.

÷

5

=

÷

5

=

2.

3.

÷

=

÷

=

÷

=

4.

5.

102

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6.09 Can you divide these dots into 5 equal groups? 1.

How many dots are there in each group? ÷

5

=

2.

How many dots are there in each group? ÷

5

=

3.

How many dots are there in each group? ÷

5 103

=

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6.10 Answer the questions and colour the boxes accordingly.

1. Colour the quotient YELLOW, the divisor ORANGE and the dividend GREEN. 45

÷

5

=

2. Colour the quotient ORANGE, the divisor YELLOW and the dividend GREEN. 24

÷

4

=

3. Colour the quotient GREEN, the divisor YELLOW and the dividend ORANGE. 18

÷

2

=

4. Colour the quotient YELLOW, the divisor GREEN and the dividend ORANGE. 18

÷

3

=

5. Colour the quotient RED, the divisor ORANGE and the dividend YELLOW. 36

÷

4

=

6. Colour the quotient ORANGE, the divisor RED and the dividend YELLOW. 35

÷

5

=

7. Colour the quotient GREEN, the divisor ORANGE and the dividend RED. 21 ÷ 3 = 104

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6.11

Answer the following using the standard written method for division.

1. 2

14

2. 3

27

3. 2

10

4. 5

15

5. 4

32

6. 5

40

7. 3

18

8. 2

6

9. 3

9

10. 4

16

11. 5

35

12. 4

28

105

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6.12

Match A and B where the products equal the quotients.

A

B

2x4

30 ÷ 5

3x3

8÷4

1x2

24 ÷ 3

2x3

20 ÷ 4

1x5

45 ÷ 5

2x2

24 ÷ 4

1x4

8÷2

1x3

32 ÷ 4

3x2

15 ÷ 5

4x2

12 ÷ 3

106

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6.13 Label the rods if different reference points are chosen. Reference Point

1.

0 Reference Point

2.

Answer the questions and identify the m and n. m: number of digits for dividend n: number of digits for divisor

8÷2= 10 ÷ 5 = 28 ÷ 4 = 6÷3= 107

m

n

m–n–1

1

1

-1 or 1

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6.14 Label the rods and fill in the blanks correctly. Show the dividend, divisor and quotient on your abacus. Reference Point

Dividend

Divisor

Quotient

5 Up 5 at rod

÷

5 Up 5 at rod

=

1 Up 1 at rod

27 Up 2 at rod

÷

3 Up 3 at rod

=

9 Up 9 at rod

Up 7 at rod 6 Up 6 at rod

m= n= m-n-1= m= n= m-n-1=

÷

2 Up 2 at rod

=

3 Up 3 at rod

m= n= m-n-1=

32 Up 3 at rod

÷

4 Up 4 at rod

=

Up 2 at rod

8 Up 8 at rod

m= n= m-n-1=

108

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Dividend

16

Divisor ÷

4

Quotient =

Up 4 at rod

Up 1 at rod

Up rod

at

m= n= m-n-1=

Up rod

at

m= n= m-n-1=

Up rod

at

m= n= m-n-1=

Up 6 at rod

10

÷

Up 1 at rod

2

=

Up 2 at rod

Up 0 at rod

21

÷

Up 2 at rod

3

=

Up 3 at rod

Up 1 at rod

8

÷

Up 8 at rod

35 Up 3 at rod

4

=

Up 4 at rod

÷

5

Up rod

at

Up rod

at

m= n= m-n-1=

=

Up 5 at rod

Up 5 at rod

m= n= m-n-1=

Try again from the top and visualise the bead movements. 109

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6.15 Remember your times-tables? Try and do these without looking at them. Say the number sentences out loud.

1. 30 ÷ 5 =

;

x 5 = 30

2. 12 ÷ 4 =

;

x 4 = 12

3.

9÷3=

;

x3= 9

4. 18 ÷ 2 =

;

x 2 = 18

5. 40 ÷ 5 =

;

x 5 = 40

6. 36 ÷ 4 =

;

x 4 = 36

7. 21 ÷ 3 =

;

x 3 = 21

8. 12 ÷ 2 =

;

x 2 = 12

9. 25 ÷ 5 =

;

x 5 = 25

10. 20 ÷ 4 =

;

x 4 = 20

11. 18 ÷ 3 =

;

x 3 = 18

12. 14 ÷ 2 =

;

x 2 = 14 110