learning mathematics with the abacus(soroban) - 04-year 2 activity book
TRANSCRIPT
1
Unit 1Unit 1 Numbers up to 1000
Can you draw one square below?
1.011.01
onesquare
Draw ten squares below. Count them as you draw.
10 ones make ten!How do you represent 10 on the abacus?
Move up 1 at Tens on your abacus.This is how it should look like...
Ones
Tens Ones
2
1.021.02
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.
3
There are 100 coins in each box. Let’s count the coins in hundreds.
Fill in the blanks.
1.031.03
So, 10 hundreds make 1000!
There are coins altogether.
Each box contains coins.
There are boxes of coins.
100, , , , ,
, , , .
400
, 1000
4
1.041.04
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.
Match the place values on the abacus correctly.
Ones Tens Hundreds Thousands
Let’s try these on your abacus!
5
Write the correct numerals and number names.
1.051.05
Thousands
Hundreds Ones
Tens
Thousands
Hundreds Ones
Tens
Thousands
Hundreds Ones
Tens
Thousands
Hundreds Ones
Tens
Thousands
Hundreds Ones
Tens
Thousands
Hundreds Ones
Tens
one hundred and one1 0 1
6
Visualise these numbers and draw the beads. Say the numbers out loud.
1.061.06
136 137
138 139
140 141
142 143
7
Two hundred and sixty-two
1.071.07
Try these with your abacus. Write down the number names as shown on the abacus.
1. (1) Move up 2 at Hundreds
(2) Move up 6 at Tens
(3) Move up 2 at Ones
2. (1) Move up 3 at Hundreds
(2) Move up 7 at Tens
(3) Move up 9 at Ones
3. (1) Move up 4 at Hundreds
(2) Move up 5 at Tens
(3) Move up 8 at Ones
4. (1) Move up 5 at Hundreds
(2) Move up 1 at Tens
(3) Move up 7 at Ones
2
12
3
2 3
12
3
2 3
13
1 3
23
8
Let’s count in twos from 300. Visualise the numbers and draw the beads.
1.081.08
3 0 0
3 0 4
3 0 2
9
Let’s count in fives from 360. Visualise the numbers and draw the beads.
1.091.09
3 6 0
3 7 0
3 6 5
10
Let’s count in tens from 590. Visualise the numbers and draw the beads.
1.101.10
5 9 0
6 1 0
6 0 0
11
Use your abacus to move the beads. Write down the numbers shown on your abacus.Say the numbers out loud.
1.111.11
1. Move up 2 at Hundreds,move up 7 at Ones.
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.
2 0 7
12
1.121.12
Circle the smaller number.
Circle the larger number.
13
1.131.13
Jenny is visualising some numbers.Write the numbers in ascending order.
ascendingorder
14
1.141.14
Jenny is visualising some numbers.Write the numbers in descending order.
descendingorder
15
1.151.15
Use your abacus to do the following.Clear the abacus before you start each exercise.
1. Move up 356.
2. Move up 1000.
3. Move up 113.
4. Move up 978.
5. Move up 183.
6. Move up 52.
7. Move up 906.
8. Move up 515.
9. Move up 777.
10. Move up 49.
11. Move up 521.
12. Move up 257.
13. Move up 825.
14. Move up 419.
15. Move up 710.
16. Move up 30.
17. Move up 613.
18. Move up 267.
19. Move up 174.
20. Move up 239.
21. Move up 271.
22. Move up 763.
23. Move up 579.
24. Move up 194.
16
Unit 2Unit 2 Addition with the highest total of 1000
Use your abacus to do the following.
2.012.01
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
17
2.022.02
Practise with your abacus to do the following.
1. (a) Clear abacus 2. (a) Clear abacus(b) Up 101 (b) Up 57(c) Up 38 (c) Up 421
3. (a) Clear abacus 4. (a) Clear abacus(b) Up 210 (b) Up 19(c) Up 168 (c) Up 760
5. (a) Clear abacus 6. (a) Clear abacus(b) Up 333 (b) Up 415(c) Up 165 (c) Up 531
7. (a) Clear abacus 8. (a) Clear abacus(b) Up 601 (b) Up 444(c) Up 277 (c) Up 555
9. (a) Clear abacus 10. (a) Clear abacus(b) Up 322 (b) Up 300(c) Up 655 (c) Up 607
11. (a) Clear abacus 12. (a) Clear abacus(b) Up 900 (b) Up 856(c) Up 27 (c) Up 132
13. (a) Clear abacus 14. (a) Clear abacus(b) Up 715 (b) Up 503(c) Up 182 (c) Up 296
18
2.032.03
Perform the following with your abacus.
1. 32 + 10 = (Up 32) (Up 10)
2. 114 + 75 = (Up 114) (Up 75)
3. 53 + 35 = (Up 53) (Up 35)
4. 212 + 672 = (Up 212) (Up 672)
5. 21 + 857 = (Up 21) (Up 857)
6. 608 + 291 = (Up 608) (Up 291)
7. 465 + 532 = (Up 465) (Up 532)
8. 740 + 256 = (Up 740) (Up 256)
42
19
2.042.04
Use your abacus to calculate the following.
1. 42 + 106 = 2. 137 + 212 =
3. 215 + 132 = 4. 87 + 201 =
5. 98 + 301 = 6. 408 + 90 =
7. 331 + 152 = 8. 551 + 123 =
9. 170 + 516 = 10. 600 + 206 =
11. 713 + 285 = 12. 418 + 511 =
13. 60 + 200 = 14. 523 + 255 =
15. 31 + 56 + 211 =
16. 121 + 67 + 300 =
17. 15 + 10 + 173 =
18. 77 + 2 + 910 =
19. 50 + 205 + 622 =
20. 3 + 20 + 876 =
20
2.052.05
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
280
+
119
=
Step 3: equals
21
2.062.06
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
612
+
366
=
Step 3: equals
22
2.072.07
Match the answers correctly.
1. The Little Friend of 3 is…
2. The Big Friend of 7 is…
3. The Big Friend of 4 is…
4. The Little Friend of 2 is…
5. The Big Friend of 6 is…
6. The Big Friend of 5 is…
7. The Little Friend of 1 is…
8. The Big Friend of 2 is…
9. The Big Friend of 9 is…
10. The Little Friend of 4 is…
11. The Big Friend of 8 is…
12. The Big Friend of 3 is…
13. The Big Friend of 1 is…
1
2
3
4
5
6
7
8
9
1
2
3
4
23
2.082.08
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?
5
24
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?
25
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?
26
2.092.09
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 .
27
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: The answer is .
5. 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 1we 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 .
28
2.102.10
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 , Carry at .
2. 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 , Carry at .
3. 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 , Carry at .
4. 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 .
29
5. There are not enough beads at Ones to move Up 5.
Using the help of the big friend, Up 5 becomes…
Down , Carry at .
6. There are not enough beads at Tens to move Up 6.
Using the help of the big friend, Up 6 becomes…
Down , Carry at .
7. There are not enough beads at Ones to move Up 7.
Using the help of the big friend, Up 7 becomes…
Down , Carry at .
8. There are not enough beads at Tens to move Up 8.
Using the help of the big friend, Up 8 becomes…
Down , Carry at .
9. There are not enough beads at Ones to move Up 9.
Using the help of the big friend, Up 9 becomes…
Down , Carry at .
10. There are not enough beads at Hundreds to move Up 5.
Using the help of the big friend, Up 5 becomes…
Down , Carry at .
30
2.112.11
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 =
1 3. 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 =
31
2.122.12
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 =
1 3. 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 =
32
2.132.13
Use your abacus to add these numbers.
1. 8 3 2. 3 1 3. 3 1 8 2 2 8 1 1 9 6 2 + 6 8 + 9 7 + 2 4 1
4. 4 2 7 5. 2 0 1 6. 9 8 1 5 5 5 6 4 7 6 2 + 3 1 + 4 9 + 8 1
7. 2 9 4 8. 5 1 5 9. 1 6 3 2 3 4 2 4 2 2 2 6 + 2 6 4 + 5 3 + 4 5 0
10. 4 4 2 11. 6 3 1 12. 7 7 8 1 3 3 2 1 0 3 3 + 3 9 + 8 8 + 1 1 1
13. 8 6 7 14. 2 2 9 15. 3 0 5 9 9 9 3 3 5 6 + 8 + 6 7 5 + 3 2 9
33
16. 2 4 8 17. 1 3 0 18. 2 5 2 1 9 7 5 7 4 4 6 7 + 7 5 + 1 6 6 + 1 6 4
19. 1 6 3 20. 2 4 5 21. 1 3 7 3 6 8 4 2 6 5 5 7 + 3 6 4 + 9 9 + 1 2 6
22. 3 9 3 23. 1 3 4 24. 2 5 0 2 7 8 2 1 6 1 6 7 + 1 9 7 + 4 2 4 + 4 0 8
25. 1 8 5 26. 2 9 9 27. 4 4 5 3 2 3 3 9 9 1 4 5 + 2 5 9 + 9 9 + 2 4 6
28. 3 6 9 29. 4 7 7 30. 8 1 5 2 4 6 3 3 4 9 7 + 1 3 5 + 5 5 + 4 9
34
Unit 3Unit 3 Subtraction within the range of 1000
Use your abacus to do the following.
3.013.01
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
35
3.023.02
Practise with your abacus to do the following.
1. (a) Clear abacus 2. (a) Clear abacus(b) Up 423 (b) Up 516(c) Down 12 (c) Down 511
3. (a) Clear abacus 4. (a) Clear abacus(b) Up 752 (b) Up 679(c) Down 201 (c) Down 163
5. (a) Clear abacus 6. (a) Clear abacus(b) Up 599 (b) Up 885(c) Down 78 (c) Down 560
7. (a) Clear abacus 8. (a) Clear abacus(b) Up 684 (b) Up 666(c) Down 171 (c) Down 515
9. (a) Clear abacus 10. (a) Clear abacus(b) Up 493 (b) Up 306(c) Down 271 (c) Down 201
11. (a) Clear abacus 12. (a) Clear abacus(b) Up 999 (b) Up 756(c) Down 685 (c) Down 651
13. (a) Clear abacus 14. (a) Clear abacus(b) Up 898 (b) Up 895(c) Down 576 (c) Down 665
36
3.033.03
Perform the following with your abacus.
1. 32 – 10 = (Up 32) (Down 10)
2. 176 – 75 = (Up 176) (Down 75)
3. 453 – 101 = (Up 453) (Down 101)
4. 862 – 652 = (Up 862) (Down 652)
5. 971 – 850 = (Up 971) (Down 850)
6. 447 – 216 = (Up 447) (Down 216)
7. 296 – 165 = (Up 296) (Down 165)
8. 754 – 601 = (Up 754) (Down 601)
37
3.043.04
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 – 502 =
16. 992 – 61 – 611 =
17. 898 – 701 – 66 =
18. 988 – 777 – 211 =
19. 850 – 200 – 650 =
20. 993 – 81 – 712 =
38
3.053.05
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
887
–
636
=
Step 3: equals
39
3.063.06
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
678
–
157
=
Step 3: equals
40
3.073.07
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
779
–
258
=
Step 3: equals
41
3.083.08
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
969
–
366
=
Step 3: equals
42
3.093.09
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 , Down .b. If using the help of the big friend, Down 1 becomes… Remove at , Up 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 .
4 5
1 Hundreds 9 Tens
43
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 moveDown 5.
Using the help of the big friend, Down 5 becomes… Remove at , Up at .
44
3.103.10
Work with your abacus to answer these questions correctly.
2. Step 1: Up 18
Step 2: 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 .
Step 3: The answer is .
3. Step 1: Up 22
Step 2: 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 .
Step 3: The answer is .
1. Step 1: Up 7
Step 2: 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 .
Step 3: The answer is .
45
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...Remove at , Up .
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...Remove at , Up .
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...Remove at , Up (remove the 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…Up , Down .
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...Remove at , Up .
Step 3: The answer is .
46
3.113.11
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 =
47
3.123.12
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 =
48
3.133.13
Use your abacus to subtract the numbers.
1. 1 0 0 0 2. 1 0 0 0 3. 1 0 0 0 – 4 1 2 – 3 8 6 – 5 7 3
4. 1 0 0 0 5. 1 0 0 0 6. 1 0 0 0 – 9 9 3 – 6 7 8 – 8 4 6
7. 1 0 0 0 8. 1 0 0 0 9. 1 0 0 0 – 2 5 0 – 6 0 7 – 5 0 4
10. 1 0 0 0 11. 1 0 0 0 12. 1 0 0 0 – 5 7 – 8 4 – 2 2
13. 1 0 0 0 14. 1 0 0 0 15. 1 0 0 0 – 9 3 – 1 6 – 6 8
16. 1 0 0 0 17. 1 0 0 0 18. 1 0 0 0 – 5 – 3 – 9
49
19. 8 2 3 20. 7 8 6 21. 6 6 1 – 4 1 5 – 4 6 2 – 4 5 3
22. 5 0 9 23. 4 0 3 24. 3 0 6 – 2 3 5 – 1 7 5 – 1 6 8
25. 4 6 0 26. 5 8 0 27. 6 0 0 – 1 8 5 – 4 9 2 – 4 8 4
28. 7 8 7 29. 8 1 2 30. 9 6 6 – 3 9 9 – 6 7 6 – 6 7 9
31. 9 0 0 32. 8 0 0 33. 7 0 0 – 4 8 8 – 6 6 9 – 3 5 1
34. 8 0 0 35. 5 1 0 36. 2 0 0 – 4 1 3 – 3 7 5 – 1 1 7
50
3.143.14
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?
– =
51
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?
– – =
52
Unit 4Unit 4 Combination of addition and subtraction within 1000
Practise the following with your abacus.Clear your abacus before you begin each exercise.
4.014.01
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.
53
4.024.02
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
+ –
=
54
4.034.03
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
=
Complete the number sentences with correct numbers and symbols.Use your abacus to calculate.
55
4.044.04
Use your abacus to calculate.
1. 8 3 2. 3 1 3. 3 1 8 2 1 5 1 1 7 6 1 – 6 7 – 2 3 – 2 5 7
4. 4 2 7 5. 2 0 1 6. 9 7 5 6 1 5 6 6 7 0 2 – 7 6 – 1 5 2 – 8 8
7. 2 9 4 8. 8 1 5 9. 4 6 3 – 2 3 4 – 2 1 0 – 2 6 2 2 2 8 8 2 7 8 7
10. 6 9 2 11. 7 3 1 12. 7 8 8 – 1 3 1 – 2 0 1 – 3 3 4 1 7 4 6 6 1 1 1
13. 8 6 7 14. 5 9 9 15. 3 0 5 2 2 – 9 3 6 5 2 – 6 3 8 1 8 1 – 7 0 5
56
16. 3 4 6 17. 8 3 9 18. 2 5 2 1 5 2 – 5 1 4 6 4 7 – 2 7 5 1 5 1 – 1 6 9
19. 9 6 8 20. 9 4 6 21. 1 3 7 – 3 6 3 – 4 2 5 5 5 2 3 7 4 3 6 7 – 1 2 6
22. 3 7 3 23. 1 3 4 24. 9 5 0 6 2 5 3 6 5 – 7 5 0 – 1 9 7 – 4 2 4 2 7 8
25. 1 8 5 26. 8 9 9 27. 4 4 5 3 1 3 – 3 9 9 5 5 1 – 2 5 8 9 9 – 2 4 6
28. 9 6 1 29. 4 7 7 30. 8 8 5 2 6 – 3 2 5 – 6 6 0 – 1 3 5 7 2 6 6 7 3
57
4.054.05
Let’s visualise and calculate.
What is 297 + 602 – 629?Visualise and draw the beads.
297 +
602 – 629
=
Step 4: equals
Step 1: 297, up 297
Step 2: plus 602, up 602
Step 3: minus 629, down 629
58
What is 418 + 561 – 706?Visualise and draw the beads.
418 +
561 – 706
=
Step 4: equals
Step 1: 418, up 418
Step 2: plus 561, up 561
Step 3: minus 706, down 706
59
What is 556 + 233 – 518?Visualise and draw the beads.
556 +
233 – 518
=
Step 4: equals
Step 1: 556, up 556
Step 2: plus 233, up 233
Step 3: minus 518, down 518
60
What is 783 – 221 + 31?Visualise and draw the beads.
783 –
221 +
31 =
Step 4: equals
Step 1: 783, up 783
Step 2: minus 221, down 221
Step 3: plus 31, up 31
61
What is 440 – 200 + 751?Visualise and draw the beads.
440 – 200
+ 751
=
Step 4: equals
Step 1: 440, up 440
Step 2: minus 200, down 200
Step 3: plus 751, up 751
62
What is 998 – 835 + 126?Visualise and draw the beads.
998 – 835
+ 126
=
Step 4: equals
Step 1: 998, up 998
Step 2: minus 835, down 835
Step 3: plus 126, up 126
63
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
=
4.064.06
Calculate with your abacus.
64
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
=
65
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
=
66
4.074.07
Rearrange the numbers so that the number sentences are true.Calculate with your abacus to check the answers.
257 362 251
–
+
=
368
736 861 38
+
–
=
163
772 652 78
–
+
=
198
67
260 139 198
+
–
=
201
886 617 566
–
+
=
937
177 812 86
+
–
=
721
68
79 63 371
–
+
=
387
551 780 111
+
–
=
340
57 559 346
–
+
=
848
69
178 574 415
+
–
=
811
675 515 999
–
+
=
839
155 227 722
+
–
=
650
70
Unit 5Unit 5 Multiplication of basic facts within2, 3, 4 and 5 times-tables
Fill in the blanks with the correct answers.
5.015.01
Write and say the number sentence out loud!
times two equals
2 + 2 + 2 + 2 =
How many 2’s are there above?
You can also write the above sentence as…
x 2 =
1.
71
times four equals
4 + 4 =
How many 4’s are there above?
You can also write the above sentence as…
x 4 =
3.
times three equals
3 + 3 + 3 + 3 + 3 =
How many 3’s are there above?
You can also write the above sentence as…
x 3 =
2.
72
times five equals
5 + 5 + 5 + 5 + 5 =
How many 5’s are there above?
You can also write the above sentence as…
x 5 =
5.
times five equals
5 + 5 + 5 + 5 =
How many 5’s are there above?
You can also write the above sentence as…
x 5 =
4.
73
times three equals
3 + 3 + 3 + 3 =
How many 3’s are there above?
You can also write the above sentence as…
x 3 =
6.
times four equals
4 + 4 + 4 =
How many 4’s are there above?
You can also write the above sentence as…
x 4 =
7.
74
5.025.02
How do we do this?What is 7 x 2?
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 =
75
5.035.03
Let’s add the numbers to find answers to the multiplication problems.
1. What is 6 x 2?
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?
2 + 2 + 2 + 2 + 2 + 2 = 12
76
5.045.04
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 =
77
5.055.05
1. What is 6 x 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?
3 + 3 + 3 + 3 + 3 + 3 =
Let’s add the numbers to find answers to the multiplication problems.
78
5.065.06
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 =
79
5.075.07
1. What is 6 x 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?
4 + 4 + 4 + 4 + 4 + 4 =
Let’s add the numbers to find answers to the multiplication problems.
80
5.085.08
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 =
81
1. What is 6 x 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?
5 + 5 + 5 + 5 + 5 + 5 =
5.095.09
Let’s add the numbers to find answers to the multiplication problems.
82
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 =
5.105.10
Let’s build the 5 times-tables.
83
5.115.11
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 =
84
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 =
85
5.125.12
Answer these questions without looking at the times-tables.
1. 4 x 3 = 2. 3 x 2 =
3. 7 x 2 = 4. 8 x 3 =
5. 7 x 3 = 6. 5 x 2 =
7. 1 x 2 = 8. 9 x 3 =
9. 6 x 3 = 10. 4 x 2 =
11. 8 x 2 = 12. 3 x 3 =
13. 2 x 3 = 14. 6 x 2 =
15. 9 x 2 = 16. 1 x 3 =
17. 5 x 3 = 18. 2 x 2 =
86
1. 4 x 5 = 2. 3 x 4 =
3. 7 x 4 = 4. 8 x 5 =
5. 7 x 5 = 6. 5 x 4 =
7. 1 x 4 = 8. 9 x 5 =
9. 6 x 5 = 10. 4 x 4 =
11. 8 x 4 = 12. 3 x 5 =
13. 2 x 5 = 14. 6 x 4 =
15. 9 x 4 = 16. 1 x 5 =
17. 5 x 5 = 18. 2 x 4 =
5.135.13
Answer these questions without looking at the times-tables.
87
9 x 3
8 x 2
7 x 5
6 x 4
5 x 5
4 x 3
7 x 3
9 x 5
6 x 5
8 x 4
9 x 2
5.145.14
Match the questions to the answers.
5 x 4
6 x 3
7 x 2
8 x 5
9 x 4
1 x 3
2 x 2
3 x 5
4 x 4
5 x 3
6 x 2
36 16
40 24
3 27
20 12
16 21
18 35
15 25
12 30
14 32
4 18
15 45
88
5.155.15
Answer the questions and colour the boxes accordingly.
1. Colour the multiplicand YELLOW, the multiplier ORANGE and the product GREEN.
2. Colour the multiplicand ORANGE, the multiplier YELLOW and the product GREEN.
3. Colour the multiplicand GREEN, the multiplier YELLOW and the product ORANGE.
4. Colour the multiplicand YELLOW, the multiplier GREEN and the product ORANGE.
5. Colour the multiplicand RED, the multiplier ORANGE and the product YELLOW.
6. Colour the multiplicand ORANGE, the multiplier RED and the product YELLOW.
7. Colour the multiplicand GREEN, the multiplier ORANGE and the product RED.
7 x 4 =
8 x 3 =
2 x 5 =
1 x 4 =
4 x 2 =
1 x 5 =
5 x 2 =
89
How do you show the products on the abacus?Draw the beads correctly.
5.165.16
1. 4 x 2 = Step 1: Display at 1st rodStep 2: Up at 2nd rodStep 3: So, 4 x 2 =
2. 6 x 3 = Step 1: Up at 1st rodStep 2: Up at 2nd rodStep 3: So, 6 x 3 =
3. 7 x 4 = Step 1: Up at 1st rodStep 2: Up at 2nd rodStep 3: So, 7 x 4 =
4. 9 x 5 = Step 1: Up at 1st rodStep 2: Up at 2nd rodStep 3: So, 9 x 5 =
90
5.175.17
Draw the beads to show the products on the abacus.
1.
4 x 5 =
2.
3 x 2 =
3.
7 x 3 =
4.
6 x 4 =
5.
3 x 3 =
6.
8 x 4 =
91
5.185.18
Visualise the products and draw the beads.Write down the answer.
6 x 2 = 9 x 3 =
2 x 4 = 1 x 5 =
8 x 3 = 6 x 5 =
92
5.195.19
Visualise the products and draw the beads.Write down the answer.
5x 3
2x 2
9x 4
7x 5
93
5.205.20
Answer the following questions.
1. If 4 x 3 = 12, what is 3 x 4? 3 x 4 =
2. If 2 x 5 = 10, what is 5 x 2? 5 x 2 =
3. If 4 x 5 = 20, what is 5 x 4? 5 x 4 =
4. If 3 x 2 = 6, what is 2 x 3? 2 x 3 =
5. If 3 x 5 = 15, what is 5 x 3? 5 x 3 =
6. If 2 x 4 = 8, what is 4 x 2? 4 x 2 =
7. 1 x = 3 8. 3 x = 9
9. 2 x = 8 10. 6 x = 12
11. x 3 = 24 12. 5 x = 20
13. x 5 = 25 14. x 4 = 32
15. 7 x = 28 16. 8 x = 40
94
How do we solve this?
Unit 6Unit 6 Division within 2, 3, 4 and 5 times-tables
6.016.01
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?
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?
95
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
96
6.026.02
Divide the objects into groups of 2 and write the number sentences.
1.
4 ÷ 2 =
2.
÷ 2 =
3.
÷ =
4.
÷ =
5.
÷ =
97
6.036.03
Can you divide these apples into 2 groups equally?
1.
How many apples are there in each group?
2.
How many apples are there in each group?
3.
How many apples are there in each group?
÷ 2 =
÷ 2 =
÷ 2 =
98
1.
6 ÷ 3 =
Divide the objects into groups of 3 and write the number sentences.
6.046.04
2.
÷ 3 =
3.
÷ =
4.
÷ =
5.
÷ =
99
6.056.05
Can you divide these flowers into 3 groups equally?
1.
2.
How many flowers are there in each group?
3.
How many flowers are there in each group?
How many flowers are there in each group?
÷ 3 =
÷ 3 =
÷ 3 =
100
Divide the objects into groups of 4 and write the number sentences.
6.066.06
1.
2.
3.
4.
5.
÷ 4 =
÷ 4 =
÷ =
÷ =
÷ =
101
6.076.07
Can you divide these triangles into 4 equal groups?
1.
2.
3.
÷ 4 =
÷ 4 =
÷ 4 =
How many triangles are there in each group?
How many triangles are there in each group?
How many triangles are there in each group?
102
6.086.08
Divide the dots into groups of 5 and write the number sentences.
1.
÷ 5 =
2.
÷ 5 =
3.
÷ =
4.
÷ =
5.
÷ =
103
6.096.09
Can you divide these dots into 5 equal groups?
1.
How many dots are there in each group?
2.
How many dots are there in each group?
3.
How many dots are there in each group?
÷ 5 =
÷ 5 =
÷ 5 =
104
1. Colour the quotient YELLOW, the divisor ORANGE and the dividend GREEN.
2. Colour the quotient ORANGE, the divisor YELLOW and the dividend GREEN.
3. Colour the quotient GREEN, the divisor YELLOW and the dividend ORANGE.
4. Colour the quotient YELLOW, the divisor GREEN and the dividend ORANGE.
5. Colour the quotient RED, the divisor ORANGE and the dividend YELLOW.
6. Colour the quotient ORANGE, the divisor RED and the dividend YELLOW.
7. Colour the quotient GREEN, the divisor ORANGE and the dividend RED.
6.106.10
Answer the questions and colour the boxes accordingly.
45 ÷ 5 =
24 ÷ 4 =
18 ÷ 2 =
18 ÷ 3 =
36 ÷ 4 =
35 ÷ 5 =
21 ÷ 3 =
105
6.116.11
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
106
6.126.12
Match A and B where the products equal the quotients.
4 x 2
3 x 2
1 x 3
1 x 4
2 x 2
1 x 5
2 x 3
1 x 2
3 x 3
2 x 4
A B
30 ÷ 5
8 ÷ 4
24 ÷ 3
20 ÷ 4
45 ÷ 5
24 ÷ 4
8 ÷ 2
32 ÷ 4
15 ÷ 5
12 ÷ 3
107
m n m – n – 1
8 ÷ 2 = 1 1 -1 or 1
10 ÷ 5 =
28 ÷ 4 =
6 ÷ 3 =
6.136.13
Label the rods if different reference points are chosen.
1.
Reference Point
Reference Point
2.
Answer the questions and identify the m and n.
m: number of digits for dividend n: number of digits for divisor
0
108
6.146.14
Label the rods and fill in the blanks correctly.Show the dividend, divisor and quotient on your abacus.
Reference Point
Dividend Divisor Quotient
5Up 5 at rod
÷ 5Up 5 at rod
= 1Up 1 at rod
m =
n =
m-n-1=
27Up 2 at rod
Up 7 at rod
÷ 3Up 3 at rod
= 9Up 9 at rod m =
n =
m-n-1=
6Up 6 at rod
÷ 2Up 2 at rod
= 3Up 3 at rod
m =
n =
m-n-1=
32Up 3 at rod
Up 2 at rod
÷ 4Up 4 at rod
= 8Up 8 at rod m =
n =
m-n-1=
109
Dividend Divisor Quotient
16Up 1 at rod
Up 6 at rod
÷ 4Up 4 at rod
=Up at rod
m = n = m-n-1=
10Up 1 at rod
Up 0 at rod
÷ 2Up 2 at rod
=Up at rod
m = n = m-n-1=
21Up 2 at rod
Up 1 at rod
÷ 3Up 3 at rod
=Up at rod
m = n = m-n-1=
8Up 8 at rod
÷ 4Up 4 at rod
=Up at rod
m = n = m-n-1=
35Up 3 at rod
Up 5 at rod
÷ 5Up 5 at rod
=Up at rod
m = n = m-n-1=
Try again from the top and visualise the bead movements.
110
6.156.15
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 = ; x 3 = 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