Efficient Strategies for +, −, × and ÷
Addition Fact Families (Set A)
Use fact families to fill in the missing numbers.
Addition Fact Families (Set B)
Fill in the missing numbers.
Subtraction Fact Families
Find the missing number. Total minus one part gives the other.
Quick Mental Addition (Set A)
Use known facts to work out each answer quickly. Circle the correct answer.
25 + 25 = ?
30 + 18 = ?
45 + 15 = ?
36 + 24 = ?
Quick Mental Addition (Set B)
Circle the correct answer.
48 + 35 = ?
156 + 44 = ?
275 + 125 = ?
367 + 233 = ?
Quick Mental Subtraction (Set A)
Circle the correct answer.
50 − 18 = ?
75 − 25 = ?
100 − 37 = ?
60 − 24 = ?
Quick Mental Subtraction (Set B)
Circle the correct answer.
83 − 27 = ?
200 − 65 = ?
500 − 175 = ?
1000 − 450 = ?
Match Related Facts (Addition/Subtraction)
Draw a line to match each addition to the related subtraction.
Match Multiplication and Division Facts
Draw a line to match each fact to a related fact.
Times Tables Quick Recall (× 6)
Circle the correct answer.
6 × 3 = ?
6 × 7 = ?
6 × 9 = ?
6 × 12 = ?
Times Tables Quick Recall (× 7)
Circle the correct answer.
7 × 4 = ?
7 × 6 = ?
7 × 8 = ?
7 × 9 = ?
Times Tables Quick Recall (× 8)
Circle the correct answer.
8 × 3 = ?
8 × 5 = ?
8 × 8 = ?
8 × 9 = ?
Times Tables Quick Recall (× 9)
Circle the correct answer.
9 × 4 = ?
9 × 6 = ?
9 × 7 = ?
9 × 11 = ?
Division Quick Recall (Set A)
Circle the correct answer.
24 ÷ 6 = ?
35 ÷ 7 = ?
48 ÷ 8 = ?
63 ÷ 9 = ?
Division Quick Recall (Set B)
Circle the correct answer.
56 ÷ 7 = ?
72 ÷ 8 = ?
81 ÷ 9 = ?
42 ÷ 6 = ?
Match Multiplications to Products
Draw a line from each multiplication to its product.
Match Divisions to Quotients
Draw a line from each division to its answer.
Addition Fact Families
Find the missing number.
Multiplication Fact Families
Find the missing factor.
Sort by Operation
Sort each problem by the best operation to use.
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 = ?)
Times Tables Sequences
Continue the pattern.
Multiplication Fact Chains (× 6)
Fill in the missing products. Each step adds 6.
Multiplication Fact Chains (× 7)
Fill in the missing products. Each step adds 7.
Multiplication Fact Chains (× 8)
Fill in the missing products. Each step adds 8.
Multiplication Fact Chains (× 9)
Fill in the missing products. Each step adds 9.
Match Division Facts (Set A)
Draw a line from each division to its answer.
Match Division Facts (Set B)
Draw a line from each division to its answer.
Division Quick Recall (Set A)
Circle the correct answer.
35 ÷ 7 = ?
48 ÷ 8 = ?
63 ÷ 7 = ?
72 ÷ 9 = ?
Division Quick Recall (Set B)
Circle the correct answer.
24 ÷ 6 = ?
56 ÷ 7 = ?
81 ÷ 9 = ?
36 ÷ 4 = ?
Multiplication/Division Fact Bonds (Set A)
Find the missing number.
Multiplication/Division Fact Bonds (Set B)
Find the missing number.
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 = ___
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 = ___
Sort: Easy or Hard to Do Mentally?
Sort each calculation.
Addition Strategies
Circle the BEST strategy for each addition.
99 + 56: best strategy is:
48 + 52: best strategy is:
25 + 25 + 25: best strategy is:
Multi-Step Problems (Set A)
Use efficient strategies. Show your working.
256 + 144 = ___
500 − 237 = ___
8 × 7 + 6 × 9 = ___
Multi-Step Problems (Set B)
Use efficient strategies. Show your working.
375 + 225 = ___
1000 − 463 = ___
72 ÷ 8 + 63 ÷ 9 = ___
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?
Choose the Operation
Circle the correct operation to solve each problem.
5 bags of 12 oranges — to find the total:
60 lollies shared among 5 children:
Had 85 cards, lost 23:
7 children each bring 9 cupcakes:
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:
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
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.
Bridge to 100 (Set A)
Find the missing part to make 100.
Which Strategy Is Most Efficient? (Set A)
Circle the most efficient strategy.
To calculate 48 + 35, the best strategy is:
To calculate 100 − 37, the best strategy is:
To calculate 6 × 8, the best strategy is:
To calculate 63 ÷ 7, the best strategy is:
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: ___
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: ___
Match Operation to Strategy
Match each calculation to the most efficient strategy.
Estimate the Answer (Set A)
Which is the best estimate?
285 + 319 ≈
712 − 289 ≈
8 × 43 ≈
369 ÷ 9 ≈
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 = ___
Sort Calculations by Strategy
Which strategy would you use? Sort each calculation.
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
Multiplication and Division Fact Families
Complete each fact family.
Number Patterns: Four Operations
Fill in the missing numbers.
Multi-Step Calculations (Set A)
Circle the correct answer.
2 × 8 + 5 = ?
48 ÷ 6 + 13 = ?
(4 + 6) × 7 = ?
100 − 3 × 9 = ?
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 = ___
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?
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?
Operations Used in Word Problems
Tally how many times each operation is needed in a set of problems.
| Item | Tally | Total |
|---|---|---|
Addition | ||
Subtraction | ||
Multiplication | ||
Division |
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: ___
Match Inverse Operations
Draw a line from each calculation to its inverse check.
Number Sentence: True or False?
Circle TRUE or FALSE.
6 × 9 = 54
48 ÷ 6 = 9
(5 + 3) × 4 = 32
100 − 4 × 8 = 768
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?
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.
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.
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?