Number

Efficient Strategies for +, −, × and ÷

1

Addition Fact Families (Set A)

Use fact families to fill in the missing numbers.

56
28
?
93
?
47
125
68
?
150
?
75
204
99
?
2

Addition Fact Families (Set B)

Fill in the missing numbers.

45
19
?
80
?
36
100
52
?
73
?
28
160
85
?
3

Subtraction Fact Families

Find the missing number. Total minus one part gives the other.

64
27
?
90
?
35
110
48
?
200
?
87
175
96
?
4

Quick Mental Addition (Set A)

Use known facts to work out each answer quickly. Circle the correct answer.

25 + 25 = ?

45
50
55

30 + 18 = ?

38
48
58

45 + 15 = ?

50
55
60

36 + 24 = ?

50
60
70
5

Quick Mental Addition (Set B)

Circle the correct answer.

48 + 35 = ?

73
83
93

156 + 44 = ?

190
200
210

275 + 125 = ?

390
400
410

367 + 233 = ?

590
600
610
6

Quick Mental Subtraction (Set A)

Circle the correct answer.

50 − 18 = ?

22
32
42

75 − 25 = ?

40
50
60

100 − 37 = ?

53
63
73

60 − 24 = ?

34
36
46
7

Quick Mental Subtraction (Set B)

Circle the correct answer.

83 − 27 = ?

46
56
66

200 − 65 = ?

125
135
145

500 − 175 = ?

315
325
335

1000 − 450 = ?

540
550
560
8

Match Related Facts (Addition/Subtraction)

Draw a line to match each addition to the related subtraction.

25 + 75 = 100
48 + 52 = 100
36 + 64 = 100
17 + 83 = 100
100 − 36 = 64
100 − 25 = 75
100 − 17 = 83
100 − 48 = 52
9

Match Multiplication and Division Facts

Draw a line to match each fact to a related fact.

7 × 8 = 56
9 × 6 = 54
12 × 5 = 60
8 × 4 = 32
60 ÷ 5 = 12
32 ÷ 8 = 4
56 ÷ 7 = 8
54 ÷ 9 = 6
10

Times Tables Quick Recall (× 6)

Circle the correct answer.

6 × 3 = ?

12
18
24

6 × 7 = ?

36
42
48

6 × 9 = ?

48
54
56

6 × 12 = ?

62
66
72
11

Times Tables Quick Recall (× 7)

Circle the correct answer.

7 × 4 = ?

21
28
35

7 × 6 = ?

36
42
49

7 × 8 = ?

49
54
56

7 × 9 = ?

56
63
72
12

Times Tables Quick Recall (× 8)

Circle the correct answer.

8 × 3 = ?

18
24
32

8 × 5 = ?

35
40
45

8 × 8 = ?

56
64
72

8 × 9 = ?

63
72
81
13

Times Tables Quick Recall (× 9)

Circle the correct answer.

9 × 4 = ?

27
36
45

9 × 6 = ?

48
54
63

9 × 7 = ?

56
63
72

9 × 11 = ?

90
99
108
14

Division Quick Recall (Set A)

Circle the correct answer.

24 ÷ 6 = ?

3
4
5

35 ÷ 7 = ?

4
5
6

48 ÷ 8 = ?

5
6
7

63 ÷ 9 = ?

6
7
8
15

Division Quick Recall (Set B)

Circle the correct answer.

56 ÷ 7 = ?

7
8
9

72 ÷ 8 = ?

8
9
10

81 ÷ 9 = ?

8
9
10

42 ÷ 6 = ?

6
7
8
16

Match Multiplications to Products

Draw a line from each multiplication to its product.

7 × 8
6 × 9
8 × 8
9 × 9
64
56
54
81
17

Match Divisions to Quotients

Draw a line from each division to its answer.

24 ÷ 4
45 ÷ 5
72 ÷ 9
35 ÷ 7
8
9
6
5
18

Addition Fact Families

Find the missing number.

100
37
?
200
?
85
150
67
?
500
?
235
1000
450
?
19

Multiplication Fact Families

Find the missing factor.

42
6
?
56
?
7
63
9
?
48
?
8
72
8
?
20

Sort by Operation

Sort each problem by the best operation to use.

How many groups of 5 in 35?
Total of 23 and 45?
How much more is 80 than 55?
6 rows of 8?
Addition
Subtraction
Multiplication
Division
21

Show Your Strategy

Solve each problem using an efficient strategy. Show your working.

48 + 35 = ___ (try splitting into tens and ones)

73 − 28 = ___ (try rounding and adjusting)

6 × 15 = ___ (try doubling: 6 × 15 = 3 × 30 = ?)

22

Times Tables Sequences

Continue the pattern.

7
14
21
28
?
?
?
9
18
27
36
?
?
?
8
16
24
32
?
?
?
23

Multiplication Fact Chains (× 6)

Fill in the missing products. Each step adds 6.

6
12
24
30
?
36
42
54
60
?
12
18
24
?
?
24

Multiplication Fact Chains (× 7)

Fill in the missing products. Each step adds 7.

7
14
28
35
?
42
49
56
?
?
21
28
42
49
?
25

Multiplication Fact Chains (× 8)

Fill in the missing products. Each step adds 8.

8
16
24
40
?
16
24
32
?
?
48
56
72
80
?
26

Multiplication Fact Chains (× 9)

Fill in the missing products. Each step adds 9.

9
18
36
45
?
45
54
72
81
?
18
27
36
?
?
27

Match Division Facts (Set A)

Draw a line from each division to its answer.

56 ÷ 8
24 ÷ 6
72 ÷ 9
30 ÷ 5
45 ÷ 5
9
7
8
4
6
28

Match Division Facts (Set B)

Draw a line from each division to its answer.

28 ÷ 4
81 ÷ 9
42 ÷ 7
30 ÷ 6
64 ÷ 8
9
6
8
7
5
29

Division Quick Recall (Set A)

Circle the correct answer.

35 ÷ 7 = ?

4
5
6

48 ÷ 8 = ?

5
6
7

63 ÷ 7 = ?

7
8
9

72 ÷ 9 = ?

7
8
9
30

Division Quick Recall (Set B)

Circle the correct answer.

24 ÷ 6 = ?

3
4
5

56 ÷ 7 = ?

7
8
9

81 ÷ 9 = ?

8
9
10

36 ÷ 4 = ?

8
9
10
31

Multiplication/Division Fact Bonds (Set A)

Find the missing number.

42
6
?
56
?
8
72
9
?
36
?
4
54
6
?
32

Multiplication/Division Fact Bonds (Set B)

Find the missing number.

48
?
6
63
7
?
81
?
9
32
4
?
108
?
12
33

Division Using Known Facts (Set A)

Use multiplication facts to help you divide.

If 7 × 9 = 63, then 63 ÷ 9 = ___

If 8 × 6 = 48, then 48 ÷ 8 = ___

If 12 × 4 = 48, then 48 ÷ 12 = ___

If 11 × 7 = 77, then 77 ÷ 11 = ___

34

Division Using Known Facts (Set B)

Use multiplication facts to help you divide.

If 6 × 6 = 36, then 36 ÷ 6 = ___

If 9 × 8 = 72, then 72 ÷ 9 = ___

If 5 × 12 = 60, then 60 ÷ 5 = ___

If 4 × 9 = 36, then 36 ÷ 4 = ___

35

Sort: Easy or Hard to Do Mentally?

Sort each calculation.

25 + 25
347 + 289
100 − 50
456 − 178
6 × 5
37 × 8
Easy to do mentally
Harder — may need a strategy
36

Addition Strategies

Circle the BEST strategy for each addition.

99 + 56: best strategy is:

Count on by 1s
Add 100, subtract 1
Use a calculator

48 + 52: best strategy is:

Count on by 1s
Make a friendly number (50 + 50)
Draw a picture

25 + 25 + 25: best strategy is:

Add 25 three times
Use 3 × 25
Count on by 1s
37

Multi-Step Problems (Set A)

Use efficient strategies. Show your working.

256 + 144 = ___

500 − 237 = ___

8 × 7 + 6 × 9 = ___

38

Multi-Step Problems (Set B)

Use efficient strategies. Show your working.

375 + 225 = ___

1000 − 463 = ___

72 ÷ 8 + 63 ÷ 9 = ___

39

Word Problems Using All Four Operations

Write a number sentence and solve.

There are 8 rows of 7 chairs. How many chairs in total?

A farmer has 96 eggs. He puts them equally into 8 cartons. How many in each?

A shop sells 45 apples on Monday and 38 on Tuesday. How many altogether?

Ben has 200 stickers. He gives away 75. How many are left?

40

Choose the Operation

Circle the correct operation to solve each problem.

5 bags of 12 oranges — to find the total:

5 + 12
5 × 12
12 − 5

60 lollies shared among 5 children:

60 + 5
60 − 5
60 ÷ 5

Had 85 cards, lost 23:

85 + 23
85 − 23
85 × 23

7 children each bring 9 cupcakes:

7 + 9
7 × 9
9 − 7
41

Write a Fact Family

Write all four related facts for each set of numbers.

Use the numbers 6, 8 and 48:

Use the numbers 7, 9 and 63:

42

Challenge: Missing Operations

Fill in the missing operation symbol: +, −, × or ÷.

8 ___ 7 = 56

63 ___ 9 = 7

125 ___ 75 = 200

300 ___ 150 = 150

9 ___ 9 = 81

43

Home Activity: Fact Family Practice

Practise using number facts efficiently at home!

  • 1Write a multiplication fact (e.g. 6 × 7 = 42). Now write three related facts using the same numbers.
  • 2Time yourself answering 10 multiplication facts. Try to beat your time each day!
  • 3Pick a number under 100. How many different ways can you make it using +, −, × or ÷?
  • 4Play 'I say a product, you say the factors' with a family member.
44

Bridge to 100 (Set A)

Find the missing part to make 100.

100
37
?
100
?
64
100
83
?
100
?
18
100
49
?
45

Which Strategy Is Most Efficient? (Set A)

Circle the most efficient strategy.

To calculate 48 + 35, the best strategy is:

Add tens then ones
Count on from 1
Round to nearest 100

To calculate 100 − 37, the best strategy is:

Standard algorithm
Count back from 100
Draw a diagram

To calculate 6 × 8, the best strategy is:

Recall from memory
Draw 6 groups of 8
Add 6 eight times

To calculate 63 ÷ 7, the best strategy is:

Recall 7 × 9 = 63
Draw 63 objects
Count by 7s from 0
46

Compensation Strategy: Addition

Round one number, add, then adjust.

49 + 36: round 49 to 50, so 50 + 36 = ___, then adjust: ___

98 + 47: round 98 to 100, so 100 + 47 = ___, then adjust: ___

199 + 83: round 199 to 200, so 200 + 83 = ___, then adjust: ___

47

Compensation Strategy: Subtraction

Round one number, subtract, then adjust.

76 − 29: round 29 to 30, so 76 − 30 = ___, then adjust: ___

125 − 49: round 49 to 50, so 125 − 50 = ___, then adjust: ___

203 − 98: round 98 to 100, so 203 − 100 = ___, then adjust: ___

48

Match Operation to Strategy

Match each calculation to the most efficient strategy.

72 + 28
300 − 145
7 × 8
84 ÷ 4
Halve 84 then halve again
Recall fact from memory
Bridge to 100
Count on from 145
49

Estimate the Answer (Set A)

Which is the best estimate?

285 + 319 ≈

500
600
700

712 − 289 ≈

300
400
500

8 × 43 ≈

280
320
360

369 ÷ 9 ≈

30
40
50
50

Double and Halve Strategy

Use doubling or halving to solve each problem.

15 × 4: halve 4 to get 2, then double: 15 × 2 = ___, so 15 × 4 = ___

24 ÷ 4: halve 24 = ___, halve again = ___

18 × 6: double 9 × 6 = ___, so 18 × 6 = ___

51

Sort Calculations by Strategy

Which strategy would you use? Sort each calculation.

6 × 9
47 + 99
3,456 + 2,789
8 × 7
298 − 99
4,321 − 1,876
Mental recall
Compensation
Standard algorithm
52

Division Using Known Multiplication Facts

Use your knowledge of multiplication to solve each division.

56 ÷ 8 = ___ because 8 × ___ = 56

63 ÷ 9 = ___ because 9 × ___ = 63

84 ÷ 4 = ___ because 4 × ___ = 84

96 ÷ 8 = ___ because 8 × ___ = 96

53

Multiplication and Division Fact Families

Complete each fact family.

72
8
?
63
9
?
56
7
?
48
?
6
84
4
?
54

Number Patterns: Four Operations

Fill in the missing numbers.

2
6
18
162
?
128
64
32
8
?
3
12
48
768
?
55

Multi-Step Calculations (Set A)

Circle the correct answer.

2 × 8 + 5 = ?

21
26
30

48 ÷ 6 + 13 = ?

21
22
23

(4 + 6) × 7 = ?

34
70
42

100 − 3 × 9 = ?

73
91
63
56

Order of Operations

Solve each calculation step by step.

3 + 4 × 5 = ___. Which operation do you do first? Why?

(3 + 4) × 5 = ___. How does the bracket change the answer?

24 ÷ 4 + 12 = ___

50 − 6 × 7 = ___

57

Word Problems: Four Operations (Set A)

Write a number sentence and solve each problem.

A school has 8 classes with 28 students each. How many students in total?

Sam has $150. He spends $37 on Monday and $48 on Tuesday. How much is left?

162 students are shared equally into 9 groups. How many in each group?

58

Word Problems: Four Operations (Set B)

Solve each problem.

A baker makes 9 trays of 16 biscuits. He eats 12. How many biscuits are left?

Jo runs 35 km each week. In 6 weeks, how far has she run?

240 books are packed into boxes of 8. How many boxes are needed?

59

Operations Used in Word Problems

Tally how many times each operation is needed in a set of problems.

ItemTallyTotal
Addition
Subtraction
Multiplication
Division
60

Inverse Operations Check

Use the inverse operation to check each answer.

If 36 + 47 = 83, check using subtraction: ___

If 6 × 9 = 54, check using division: ___

If 200 − 78 = 122, check using addition: ___

If 72 ÷ 8 = 9, check using multiplication: ___

61

Match Inverse Operations

Draw a line from each calculation to its inverse check.

45 + 38 = 83
9 × 7 = 63
150 − 67 = 83
48 ÷ 6 = 8
83 − 38 = 45
67 + 83 = 150
6 × 8 = 48
63 ÷ 7 = 9
62

Number Sentence: True or False?

Circle TRUE or FALSE.

6 × 9 = 54

TRUE
FALSE

48 ÷ 6 = 9

TRUE
FALSE

(5 + 3) × 4 = 32

TRUE
FALSE

100 − 4 × 8 = 768

TRUE
FALSE
63

Efficient Strategies Summary

Show your best strategies.

What is the most efficient way to work out 99 + 76? Show your working.

What is the most efficient way to work out 504 − 99? Show your working.

Which four-operations strategy do you find easiest? Why?

64

Create a Calculation Chain

Start with 100 and use all four operations.

Start: 100 → + 45 = ___ → × 2 = ___ → − 30 = ___ → ÷ 5 = ___

Start: 200 → ÷ 4 = ___ → × 3 = ___ → − 50 = ___ → + 75 = ___

Make your own chain starting at 50. Show each step.

65

Challenge: Multi-Step Word Problems

These problems need more than one step.

There are 5 rows of 8 chairs and 3 rows of 12 chairs. How many chairs altogether?

A shop has 200 apples. They sell 8 bags of 9 apples each. How many apples are left?

Make up your own two-step word problem and solve it.

66

Home Activity: Four Operations at Home

Use all four operations at home!

  • 1At dinner: if there are 4 people and 28 pieces of food, how many each? What operation did you use?
  • 2Grocery shop: add up 3 prices in your head. Then check with a calculator. Were you right?
  • 3Count something in the house (books, toys). Split into equal groups. How many groups?
  • 4Challenge: make a calculation chain (+ − × ÷) that starts with your age and ends with 1.
  • 5Play 'Beat the Clock' — can you recall all 6×, 7×, 8×, 9× tables in under 60 seconds?