Step-by-step Maths Level 4: Missing numbers, division and word problems
Part of the Step-by-step Maths Level 4 times tables 6, 8 and 9 chapter. Chapter overview · whole chapter on one page
Missing numbers, division and word problems
Use the times table to find a missing number. 6 × ___ = 42 asks: what times 6 makes 42?
Division is the opposite. 48 ÷ 8 asks: how many groups of 8 make 48? Use the 8 facts to find the answer.
Key ideas
- Find the times table, then count the groups.
- Division asks how many groups of the number make the total.
- Check each answer by multiplying back.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think: how many groups of 6 make 42? Count in steps of the first number.6, 12, 18, 24, 30, 36, 42
- Count the groups. We said 7 numbers, so there are 7 groups.7 groups of 6
- Write the missing number. This is the number of groups.7
Check. Check: 6 × 7 = 42.
Watch out. The times table of 6 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 8 × ___ = 48. Division asks how many groups.8 × ___ = 48
- Count in 8s until you reach 48. Count the steps as you go.8, 16, 24, 32, 40, 48
- Write the answer. This is the number of groups.6
Check. Check: 8 × 6 = 48.
Watch out. The times table of 8 is the key. Division is the opposite of multiplication.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 45 ÷ 9. Each bag holds the same number, so count how many groups of this size there are.45 ÷ 9 = ___
- Count in 9s until you reach 45. Count one bag at a time.9, 18, 27, 36, 45
- Write the answer. This is the number of bags.5
Check. Check: 5 bags of 9 is 45.
Watch out. Count the groups, not the number in each group.
Watch out
Watch out. 48 ÷ 8 is 6, not 8. Check by multiplying back: 8 × 6 = 48.
Exam tip
Grown-up tip. Ask the child to check each division by multiplying back, with the same table.
Exercise 5E Practice: missing numbers, division and problems
Non-calculatorMethod. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 6 × ___ = 54. Division asks how many groups.6 × ___ = 54
- Count in 6s until you reach 54. Count the steps as you go.6, 12, 18, 24, 30, 36, 42, 48, 54
- Write the answer. This is the number of groups.9
Check. Check: 6 × 9 = 54.
Watch out. The times table of 6 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 8. The missing number is the number of groups of this size.8, 16, 24
- Find the number of counts. We counted 3 times to reach 24.3 counts
- Write the missing number. It goes in the gap.3
Check. Check: 8 × 3 = 24.
Watch out. The times table of 8 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think: how many groups of 8 make 16? Count in steps of the first number.8, 16
- Count the groups. We said 2 numbers, so there are 2 groups.2 groups of 8
- Write the missing number. This is the number of groups.2
Check. Check: 8 × 2 = 16.
Watch out. The times table of 8 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 9. The missing number is the number of groups of this size.9, 18, 27
- Find the number of counts. We counted 3 times to reach 27.3 counts
- Write the missing number. It goes in the gap.3
Check. Check: 9 × 3 = 27.
Watch out. The times table of 9 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 6. The missing number is the number of groups of this size.6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66
- Find the number of counts. We counted 11 times to reach 66.11 counts
- Write the missing number. It goes in the gap.11
Check. Check: 6 × 11 = 66.
Watch out. The times table of 6 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 6 × ___ = 24. Division asks how many groups.6 × ___ = 24
- Count in 6s until you reach 24. Count the steps as you go.6, 12, 18, 24
- Write the answer. This is the number of groups.4
Check. Check: 6 × 4 = 24.
Watch out. The times table of 6 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 9. The missing number is the number of groups of this size.9, 18, 27, 36, 45
- Find the number of counts. We counted 5 times to reach 45.5 counts
- Write the missing number. It goes in the gap.5
Check. Check: 9 × 5 = 45.
Watch out. The times table of 9 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think: how many groups of 8 make 24? Count in steps of the first number.8, 16, 24
- Count the groups. We said 3 numbers, so there are 3 groups.3 groups of 8
- Write the missing number. This is the number of groups.3
Check. Check: 8 × 3 = 24.
Watch out. The times table of 8 is the key. Division is the opposite of multiplication.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 40 ÷ 8. Each bag holds the same number, so count how many groups of this size there are.40 ÷ 8 = ___
- Count in 8s until you reach 40. Count one bag at a time.8, 16, 24, 32, 40
- Write the answer. This is the number of bags.5
Check. Check: 5 bags of 8 is 40.
Watch out. Count the groups, not the number in each group.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 6 × ___ = 60. Division asks how many groups.6 × ___ = 60
- Count in 6s until you reach 60. Count the steps as you go.6, 12, 18, 24, 30, 36, 42, 48, 54, 60
- Write the answer. This is the number of groups.10
Check. Check: 6 × 10 = 60.
Watch out. The times table of 6 is the key. Division is the opposite of multiplication.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think: how many groups of 6 make 60? Count in steps of the first number.6, 12, 18, 24, 30, 36, 42, 48, 54, 60
- Count the groups. We said 10 numbers, so there are 10 groups.10 groups of 6
- Write the missing number. This is the number of groups.10
Check. Check: 6 × 10 = 60.
Watch out. The times table of 6 is the key. Division is the opposite of multiplication.
Method. Multiply the number of groups by the number in each group.
- Write 11 groups of 8 as a multiplication. Each bag holds the same number.11 × 8
- Count in 8s, 11 times. Each count is one bag.8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88
- Write the answer. This is the total altogether.88
Check. Check: 8 × 11 = 88, and 11 × 8 is the same.
Watch out. The number of bags is the number of groups. The number in each bag is the group size.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 80 ÷ 8. Each bag holds the same number, so count how many groups of this size there are.80 ÷ 8 = ___
- Count in 8s until you reach 80. Count one bag at a time.8, 16, 24, 32, 40, 48, 56, 64, 72, 80
- Write the answer. This is the number of bags.10
Check. Check: 10 bags of 8 is 80.
Watch out. Count the groups, not the number in each group.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 32 ÷ 8. Each bag holds the same number, so count how many groups of this size there are.32 ÷ 8 = ___
- Count in 8s until you reach 32. Count one bag at a time.8, 16, 24, 32
- Write the answer. This is the number of bags.4
Check. Check: 4 bags of 8 is 32.
Watch out. Count the groups, not the number in each group.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the times table of 6. The missing number is the number of groups of this size.6, 12
- Find the number of counts. We counted 2 times to reach 12.2 counts
- Write the missing number. It goes in the gap.2
Check. Check: 6 × 2 = 12.
Watch out. The times table of 6 is the key. Division is the opposite of multiplication.
Method. Division can find how many equal groups fit. Count the groups in steps of the group size.
- Think of the division: 90 ÷ 9. Each bag holds the same number, so count how many groups of this size there are.90 ÷ 9 = ___
- Count in 9s until you reach 90. Count one bag at a time.9, 18, 27, 36, 45, 54, 63, 72, 81, 90
- Write the answer. This is the number of bags.10
Check. Check: 10 bags of 9 is 90.
Watch out. Count the groups, not the number in each group.