Times tables 6, 8 and 9
By the end of this chapter you will be able to
- Know the 6 times table facts in any order
- Know the 8 times table facts in any order
- Know the 9 times table facts, and use the 9 pattern
- Use place value to multiply by 9
- Divide and find missing numbers with the 6, 8 and 9 facts
You should already know
- Times tables 3 and 4 (chapter 4)
- Counting in twos, fives and tens (Level 3, chapter 7)
Where this leads
- Division as sharing and grouping (chapter 6)
Step-by-step practice: maths (Level 4). Small steps, repeated until fluent. Content: Recall and use the multiplication facts for the 8 times table (MD1), Recall and use the 6 and 9 times table facts (Year 4 paraphrase), Use the 9 pattern and place value to multiply by 9, for example 9 × 7 = 10 × 7 - 7 (Year 4 paraphrase), Write and calculate multiplication and division statements using the tables known (MD2).
Exercise P Do you remember?
Non-calculatorMethod. Count in fours six times.
- Count in fours. Each count is one group of 4.4, 8, 12, 16, 20, 24
- The last number we said is the answer. We counted six groups of 4.4 × 6 = 24
- Write the answer. This is the total.24
Check. Check: 6 × 4 = 24.
Watch out. Doubling twice also works: 6, 12, 24.
Method. Count in threes nine times.
- Count in threes. Each count adds 3.3, 6, 9, 12, 15, 18, 21, 24, 27
- The last number we said is the answer. We counted nine groups of 3.3 × 9 = 27
- Write the answer. This is the total.27
Check. Check: 9 × 3 = 27.
Watch out. Count the threes carefully.
Method. Count in fives seven times.
- Count in fives. Each count adds 5.5, 10, 15, 20, 25, 30, 35
- The last number we said is the answer. We counted seven groups of 5.5 × 7 = 35
- Write the answer. This is the total.35
Check. Check: 35 ÷ 5 = 7.
Watch out. The answer to a 5 fact ends in 0 or 5.
Method. Double 8.
- Double the number. Doubling is the same as 2 groups of 8.8 + 8
- Add the two groups. Two groups of 8 make 16.8 + 8 = 16
- Write the answer. This is the total.16
Check. Check: 16 ÷ 2 = 8.
Watch out. Doubling is quick. Double 8 is 16.
Method. Add a zero to the end of the number.
- Write the number 6. Multiplying by 10 makes each group ten times bigger.6
- Add a zero to the end. A zero at the end makes the number ten times as big.6 with a zero = 60
- Write the answer. This is the total.60
Check. Check: 60 ÷ 10 = 6.
Watch out. Only the zero is added.
The 6 times table
The 6 times table counts in sixes: 6, 12, 18, 24, 30 and so on. Each answer is one more group of 6.
Learn the facts in order, then say them in any order. Doubling the 3 times table gives the 6 times table.
Key ideas
- Count in sixes for the 6 times table.
- Doubling a 3 times table fact gives the 6 times table fact.
- The order does not matter.
Method. Count in 6s to find 6 groups of 7. The order of the two numbers does not matter.
- Count in 6s, 7 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42
- The last number we said is the answer. We counted in equal groups.6 × 7 = 42
- Write the answer. The order of the numbers does not change the answer.42
Check. Check: 7 × 6 is also 42.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 9. The order of the two numbers does not matter.
- Count in 6s, 9 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42, 48, 54
- The last number we said is the answer. We counted in equal groups.6 × 9 = 54
- Write the answer. The order of the numbers does not change the answer.54
Check. Check: 9 × 6 is also 54.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 12. The order of the two numbers does not matter.
- Count in 6s, 12 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
- The last number we said is the answer. We counted in equal groups.6 × 12 = 72
- Write the answer. The order of the numbers does not change the answer.72
Check. Check: 12 × 6 is also 72.
Watch out. Say the 6 times table in order until you reach the fact you need.
Watch out
Watch out. 6 × 8 is 48, not 46. Count in sixes and check the number of counts.
Exam tip
Grown-up tip. Ask: “What is 3 times the number, doubled?” to check a 6 fact.
Exercise 5A Practice: the 6 times table
Non-calculatorMethod. Count in 6s to find 6 groups of 2. The order of the two numbers does not matter.
- Count in 6s, 2 times. Each count adds one more group of 6.6, 12
- The last number we said is the answer. We counted in equal groups.6 × 2 = 12
- Write the answer. The order of the numbers does not change the answer.12
Check. Check: 2 × 6 is also 12.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 10. The order of the two numbers does not matter.
- Count in 6s, 10 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42, 48, 54, 60
- The last number we said is the answer. We counted in equal groups.6 × 10 = 60
- Write the answer. The order of the numbers does not change the answer.60
Check. Check: 10 × 6 is also 60.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 4. The order of the two numbers does not matter.
- Count in 6s, 4 times. Each count adds one more group of 6.6, 12, 18, 24
- The last number we said is the answer. We counted in equal groups.6 × 4 = 24
- Write the answer. The order of the numbers does not change the answer.24
Check. Check: 4 × 6 is also 24.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 8. The order of the two numbers does not matter.
- Count in 6s, 8 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42, 48
- The last number we said is the answer. We counted in equal groups.6 × 8 = 48
- Write the answer. The order of the numbers does not change the answer.48
Check. Check: 8 × 6 is also 48.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 5. The order of the two numbers does not matter.
- Count in 6s, 5 times. Each count adds one more group of 6.6, 12, 18, 24, 30
- The last number we said is the answer. We counted in equal groups.6 × 5 = 30
- Write the answer. The order of the numbers does not change the answer.30
Check. Check: 5 × 6 is also 30.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 6. The order of the two numbers does not matter.
- Count in 6s, 6 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36
- The last number we said is the answer. We counted in equal groups.6 × 6 = 36
- Write the answer. The order of the numbers does not change the answer.36
Check. Check: 6 × 6 is also 36.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 7. The order of the two numbers does not matter.
- Count in 6s, 7 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42
- The last number we said is the answer. We counted in equal groups.6 × 7 = 42
- Write the answer. The order of the numbers does not change the answer.42
Check. Check: 7 × 6 is also 42.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 5. The order of the two numbers does not matter.
- Count in 6s, 5 times. Each count adds one more group of 6.6, 12, 18, 24, 30
- The last number we said is the answer. We counted in equal groups.6 × 5 = 30
- Write the answer. The order of the numbers does not change the answer.30
Check. Check: 5 × 6 is also 30.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 1. The order of the two numbers does not matter.
- Count in 6s, 1 times. Each count adds one more group of 6.6
- The last number we said is the answer. We counted in equal groups.6 × 1 = 6
- Write the answer. The order of the numbers does not change the answer.6
Check. Check: 1 × 6 is also 6.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 4. The order of the two numbers does not matter.
- Count in 6s, 4 times. Each count adds one more group of 6.6, 12, 18, 24
- The last number we said is the answer. We counted in equal groups.6 × 4 = 24
- Write the answer. The order of the numbers does not change the answer.24
Check. Check: 4 × 6 is also 24.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 7. The order of the two numbers does not matter.
- Count in 6s, 7 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42
- The last number we said is the answer. We counted in equal groups.6 × 7 = 42
- Write the answer. The order of the numbers does not change the answer.42
Check. Check: 7 × 6 is also 42.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 9. The order of the two numbers does not matter.
- Count in 6s, 9 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42, 48, 54
- The last number we said is the answer. We counted in equal groups.6 × 9 = 54
- Write the answer. The order of the numbers does not change the answer.54
Check. Check: 9 × 6 is also 54.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 1. The order of the two numbers does not matter.
- Count in 6s, 1 times. Each count adds one more group of 6.6
- The last number we said is the answer. We counted in equal groups.6 × 1 = 6
- Write the answer. The order of the numbers does not change the answer.6
Check. Check: 1 × 6 is also 6.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 12. The order of the two numbers does not matter.
- Count in 6s, 12 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
- The last number we said is the answer. We counted in equal groups.6 × 12 = 72
- Write the answer. The order of the numbers does not change the answer.72
Check. Check: 12 × 6 is also 72.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 2. The order of the two numbers does not matter.
- Count in 6s, 2 times. Each count adds one more group of 6.6, 12
- The last number we said is the answer. We counted in equal groups.6 × 2 = 12
- Write the answer. The order of the numbers does not change the answer.12
Check. Check: 2 × 6 is also 12.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 11. The order of the two numbers does not matter.
- Count in 6s, 11 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66
- The last number we said is the answer. We counted in equal groups.6 × 11 = 66
- Write the answer. The order of the numbers does not change the answer.66
Check. Check: 11 × 6 is also 66.
Watch out. Say the 6 times table in order until you reach the fact you need.
The 8 times table
The 8 times table counts in eights: 8, 16, 24, 32, 40 and so on. Each answer is one more group of 8.
Doubling three times gives the 8 times table: 8 × 5 is 5 doubled three times, which is 40.
Key ideas
- Count in eights for the 8 times table.
- Doubling three times gives the 8 facts.
- The order does not matter.
Method. Count in 8s to find 8 groups of 6. The order of the two numbers does not matter.
- Count in 8s, 6 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48
- The last number we said is the answer. We counted in equal groups.8 × 6 = 48
- Write the answer. The order of the numbers does not change the answer.48
Check. Check: 6 × 8 is also 48.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 9. The order of the two numbers does not matter.
- Count in 8s, 9 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72
- The last number we said is the answer. We counted in equal groups.8 × 9 = 72
- Write the answer. The order of the numbers does not change the answer.72
Check. Check: 9 × 8 is also 72.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 11. The order of the two numbers does not matter.
- Count in 8s, 11 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88
- The last number we said is the answer. We counted in equal groups.8 × 11 = 88
- Write the answer. The order of the numbers does not change the answer.88
Check. Check: 11 × 8 is also 88.
Watch out. Say the 8 times table in order until you reach the fact you need.
Watch out
Watch out. 8 × 6 is 48, not 42. Count in eights carefully, and count the number of steps.
Exam tip
Grown-up tip. Ask the child to double three times: double 5 is 10, double 10 is 20, double 20 is 40.
Exercise 5B Practice: the 8 times table
Non-calculatorMethod. Count in 8s to find 8 groups of 7. The order of the two numbers does not matter.
- Count in 8s, 7 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56
- The last number we said is the answer. We counted in equal groups.8 × 7 = 56
- Write the answer. The order of the numbers does not change the answer.56
Check. Check: 7 × 8 is also 56.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 2. The order of the two numbers does not matter.
- Count in 8s, 2 times. Each count adds one more group of 8.8, 16
- The last number we said is the answer. We counted in equal groups.8 × 2 = 16
- Write the answer. The order of the numbers does not change the answer.16
Check. Check: 2 × 8 is also 16.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 9. The order of the two numbers does not matter.
- Count in 8s, 9 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72
- The last number we said is the answer. We counted in equal groups.8 × 9 = 72
- Write the answer. The order of the numbers does not change the answer.72
Check. Check: 9 × 8 is also 72.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 5. The order of the two numbers does not matter.
- Count in 8s, 5 times. Each count adds one more group of 8.8, 16, 24, 32, 40
- The last number we said is the answer. We counted in equal groups.8 × 5 = 40
- Write the answer. The order of the numbers does not change the answer.40
Check. Check: 5 × 8 is also 40.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 1. The order of the two numbers does not matter.
- Count in 8s, 1 times. Each count adds one more group of 8.8
- The last number we said is the answer. We counted in equal groups.8 × 1 = 8
- Write the answer. The order of the numbers does not change the answer.8
Check. Check: 1 × 8 is also 8.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 8. The order of the two numbers does not matter.
- Count in 8s, 8 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64
- The last number we said is the answer. We counted in equal groups.8 × 8 = 64
- Write the answer. The order of the numbers does not change the answer.64
Check. Check: 8 × 8 is also 64.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 6. The order of the two numbers does not matter.
- Count in 8s, 6 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48
- The last number we said is the answer. We counted in equal groups.8 × 6 = 48
- Write the answer. The order of the numbers does not change the answer.48
Check. Check: 6 × 8 is also 48.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 10. The order of the two numbers does not matter.
- Count in 8s, 10 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72, 80
- The last number we said is the answer. We counted in equal groups.8 × 10 = 80
- Write the answer. The order of the numbers does not change the answer.80
Check. Check: 10 × 8 is also 80.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 12. The order of the two numbers does not matter.
- Count in 8s, 12 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
- The last number we said is the answer. We counted in equal groups.8 × 12 = 96
- Write the answer. The order of the numbers does not change the answer.96
Check. Check: 12 × 8 is also 96.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 9. The order of the two numbers does not matter.
- Count in 8s, 9 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72
- The last number we said is the answer. We counted in equal groups.8 × 9 = 72
- Write the answer. The order of the numbers does not change the answer.72
Check. Check: 9 × 8 is also 72.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 3. The order of the two numbers does not matter.
- Count in 8s, 3 times. Each count adds one more group of 8.8, 16, 24
- The last number we said is the answer. We counted in equal groups.8 × 3 = 24
- Write the answer. The order of the numbers does not change the answer.24
Check. Check: 3 × 8 is also 24.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 10. The order of the two numbers does not matter.
- Count in 8s, 10 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72, 80
- The last number we said is the answer. We counted in equal groups.8 × 10 = 80
- Write the answer. The order of the numbers does not change the answer.80
Check. Check: 10 × 8 is also 80.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 12. The order of the two numbers does not matter.
- Count in 8s, 12 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
- The last number we said is the answer. We counted in equal groups.8 × 12 = 96
- Write the answer. The order of the numbers does not change the answer.96
Check. Check: 12 × 8 is also 96.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 2. The order of the two numbers does not matter.
- Count in 8s, 2 times. Each count adds one more group of 8.8, 16
- The last number we said is the answer. We counted in equal groups.8 × 2 = 16
- Write the answer. The order of the numbers does not change the answer.16
Check. Check: 2 × 8 is also 16.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 11. The order of the two numbers does not matter.
- Count in 8s, 11 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88
- The last number we said is the answer. We counted in equal groups.8 × 11 = 88
- Write the answer. The order of the numbers does not change the answer.88
Check. Check: 11 × 8 is also 88.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 4. The order of the two numbers does not matter.
- Count in 8s, 4 times. Each count adds one more group of 8.8, 16, 24, 32
- The last number we said is the answer. We counted in equal groups.8 × 4 = 32
- Write the answer. The order of the numbers does not change the answer.32
Check. Check: 4 × 8 is also 32.
Watch out. Say the 8 times table in order until you reach the fact you need.
The 9 times table
The 9 times table counts in nines: 9, 18, 27, 36, 45 and so on. Each answer is one more group of 9.
A useful way to learn the 9 facts is to use the 9 pattern (in section 5.4).
Key ideas
- Count in nines for the 9 times table.
- Each answer is one more group of 9.
- The order does not matter.
Method. Count in 9s to find 9 groups of 4. The order of the two numbers does not matter.
- Count in 9s, 4 times. Each count adds one more group of 9.9, 18, 27, 36
- The last number we said is the answer. We counted in equal groups.9 × 4 = 36
- Write the answer. The order of the numbers does not change the answer.36
Check. Check: 4 × 9 is also 36.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 7. The order of the two numbers does not matter.
- Count in 9s, 7 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54, 63
- The last number we said is the answer. We counted in equal groups.9 × 7 = 63
- Write the answer. The order of the numbers does not change the answer.63
Check. Check: 7 × 9 is also 63.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 11. The order of the two numbers does not matter.
- Count in 9s, 11 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
- The last number we said is the answer. We counted in equal groups.9 × 11 = 99
- Write the answer. The order of the numbers does not change the answer.99
Check. Check: 11 × 9 is also 99.
Watch out. Say the 9 times table in order until you reach the fact you need.
Watch out
Watch out. 9 × 7 is 63, not 56. Count in nines carefully.
Exam tip
Grown-up tip. Ask: “Which 9 fact is quickest for you? Say it, then check it with the 9 pattern.”
Exercise 5C Practice: the 9 times table
Non-calculatorMethod. Count in 9s to find 9 groups of 6. The order of the two numbers does not matter.
- Count in 9s, 6 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54
- The last number we said is the answer. We counted in equal groups.9 × 6 = 54
- Write the answer. The order of the numbers does not change the answer.54
Check. Check: 6 × 9 is also 54.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 4. The order of the two numbers does not matter.
- Count in 9s, 4 times. Each count adds one more group of 9.9, 18, 27, 36
- The last number we said is the answer. We counted in equal groups.9 × 4 = 36
- Write the answer. The order of the numbers does not change the answer.36
Check. Check: 4 × 9 is also 36.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 9. The order of the two numbers does not matter.
- Count in 9s, 9 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54, 63, 72, 81
- The last number we said is the answer. We counted in equal groups.9 × 9 = 81
- Write the answer. The order of the numbers does not change the answer.81
Check. Check: 9 × 9 is also 81.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 11. The order of the two numbers does not matter.
- Count in 9s, 11 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
- The last number we said is the answer. We counted in equal groups.9 × 11 = 99
- Write the answer. The order of the numbers does not change the answer.99
Check. Check: 11 × 9 is also 99.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 7. The order of the two numbers does not matter.
- Count in 9s, 7 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54, 63
- The last number we said is the answer. We counted in equal groups.9 × 7 = 63
- Write the answer. The order of the numbers does not change the answer.63
Check. Check: 7 × 9 is also 63.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 10. The order of the two numbers does not matter.
- Count in 9s, 10 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54, 63, 72, 81, 90
- The last number we said is the answer. We counted in equal groups.9 × 10 = 90
- Write the answer. The order of the numbers does not change the answer.90
Check. Check: 10 × 9 is also 90.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 2. The order of the two numbers does not matter.
- Count in 9s, 2 times. Each count adds one more group of 9.9, 18
- The last number we said is the answer. We counted in equal groups.9 × 2 = 18
- Write the answer. The order of the numbers does not change the answer.18
Check. Check: 2 × 9 is also 18.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 1. The order of the two numbers does not matter.
- Count in 9s, 1 times. Each count adds one more group of 9.9
- The last number we said is the answer. We counted in equal groups.9 × 1 = 9
- Write the answer. The order of the numbers does not change the answer.9
Check. Check: 1 × 9 is also 9.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 3. The order of the two numbers does not matter.
- Count in 9s, 3 times. Each count adds one more group of 9.9, 18, 27
- The last number we said is the answer. We counted in equal groups.9 × 3 = 27
- Write the answer. The order of the numbers does not change the answer.27
Check. Check: 3 × 9 is also 27.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 10. The order of the two numbers does not matter.
- Count in 9s, 10 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54, 63, 72, 81, 90
- The last number we said is the answer. We counted in equal groups.9 × 10 = 90
- Write the answer. The order of the numbers does not change the answer.90
Check. Check: 10 × 9 is also 90.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 8. The order of the two numbers does not matter.
- Count in 9s, 8 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54, 63, 72
- The last number we said is the answer. We counted in equal groups.9 × 8 = 72
- Write the answer. The order of the numbers does not change the answer.72
Check. Check: 8 × 9 is also 72.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 8. The order of the two numbers does not matter.
- Count in 9s, 8 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54, 63, 72
- The last number we said is the answer. We counted in equal groups.9 × 8 = 72
- Write the answer. The order of the numbers does not change the answer.72
Check. Check: 8 × 9 is also 72.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 12. The order of the two numbers does not matter.
- Count in 9s, 12 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108
- The last number we said is the answer. We counted in equal groups.9 × 12 = 108
- Write the answer. The order of the numbers does not change the answer.108
Check. Check: 12 × 9 is also 108.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 6. The order of the two numbers does not matter.
- Count in 9s, 6 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54
- The last number we said is the answer. We counted in equal groups.9 × 6 = 54
- Write the answer. The order of the numbers does not change the answer.54
Check. Check: 6 × 9 is also 54.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 1. The order of the two numbers does not matter.
- Count in 9s, 1 times. Each count adds one more group of 9.9
- The last number we said is the answer. We counted in equal groups.9 × 1 = 9
- Write the answer. The order of the numbers does not change the answer.9
Check. Check: 1 × 9 is also 9.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 4. The order of the two numbers does not matter.
- Count in 9s, 4 times. Each count adds one more group of 9.9, 18, 27, 36
- The last number we said is the answer. We counted in equal groups.9 × 4 = 36
- Write the answer. The order of the numbers does not change the answer.36
Check. Check: 4 × 9 is also 36.
Watch out. Say the 9 times table in order until you reach the fact you need.
The 9 pattern and multiplying by 9
In the 9 times table, the digits of each answer add to 9. For 9 × 4 = 36, the digits 3 and 6 add to 9.
Another way: 9 is 10 take away 1. So 9 × 7 is 10 × 7 take away one 7: 70 - 7 = 63.
Key ideas
- The digits of each 9 answer add to 9.
- 9 × a number = 10 × the number take away the number.
- Use either method to check the other.
Method. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.4 - 1 = 3
- Find the ones digit. The two digits must add to 9.9 - 3 = 6
- Write the answer. Put the tens digit and the ones digit together.36
Check. Check: 3 + 6 = 9, and 36 is 9 × 4.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 7. Multiplying by 10 adds a zero to the end.10 × 7 = 70
- Take away one 7. There is one group of 9 less than ten groups.70 - 7 = 63
- Write the answer. This is 9 groups of the number.63
Check. Check: 9 × 7 = 63, so 63 + 7 = 70.
Watch out. This method works for any number, not only the 9 facts.
Method. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.6 - 1 = 5
- Find the ones digit. The two digits must add to 9.9 - 5 = 4
- Write the answer. Put the tens digit and the ones digit together.54
Check. Check: 5 + 4 = 9, and 54 is 9 × 6.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Watch out
Watch out. 9 × 5 is 45, not 40. Take one 5 away from 10 × 5 = 50: 50 - 5 = 45.
Exam tip
Grown-up tip. Ask: “Do the digits add to 9? Does 10 times the number take away one number give the answer?”
Exercise 5D Practice: the 9 pattern and place value
Non-calculatorMethod. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.3 - 1 = 2
- Find the ones digit. The two digits must add to 9.9 - 2 = 7
- Write the answer. Put the tens digit and the ones digit together.27
Check. Check: 2 + 7 = 9, and 27 is 9 × 3.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 11. Multiplying by 10 adds a zero to the end.10 × 11 = 110
- Take away one 11. There is one group of 9 less than ten groups.110 - 11 = 99
- Write the answer. This is 9 groups of the number.99
Check. Check: 9 × 11 = 99, so 99 + 11 = 110.
Watch out. This method works for any number, not only the 9 facts.
Method. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.4 - 1 = 3
- Find the ones digit. The two digits must add to 9.9 - 3 = 6
- Write the answer. Put the tens digit and the ones digit together.36
Check. Check: 3 + 6 = 9, and 36 is 9 × 4.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 10. Multiplying by 10 adds a zero to the end.10 × 10 = 100
- Take away one 10. There is one group of 9 less than ten groups.100 - 10 = 90
- Write the answer. This is 9 groups of the number.90
Check. Check: 9 × 10 = 90, so 90 + 10 = 100.
Watch out. This method works for any number, not only the 9 facts.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 12. Multiplying by 10 adds a zero to the end.10 × 12 = 120
- Take away one 12. There is one group of 9 less than ten groups.120 - 12 = 108
- Write the answer. This is 9 groups of the number.108
Check. Check: 9 × 12 = 108, so 108 + 12 = 120.
Watch out. This method works for any number, not only the 9 facts.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 7. Multiplying by 10 adds a zero to the end.10 × 7 = 70
- Take away one 7. There is one group of 9 less than ten groups.70 - 7 = 63
- Write the answer. This is 9 groups of the number.63
Check. Check: 9 × 7 = 63, so 63 + 7 = 70.
Watch out. This method works for any number, not only the 9 facts.
Method. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.12 - 1 = 11
- Find the ones digit. The two digits must add to 9.9 - 11 = -2
- Write the answer. Put the tens digit and the ones digit together.108
Check. Check: 11 + -2 = 9, and 108 is 9 × 12.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 3. Multiplying by 10 adds a zero to the end.10 × 3 = 30
- Take away one 3. There is one group of 9 less than ten groups.30 - 3 = 27
- Write the answer. This is 9 groups of the number.27
Check. Check: 9 × 3 = 27, so 27 + 3 = 30.
Watch out. This method works for any number, not only the 9 facts.
Method. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.8 - 1 = 7
- Find the ones digit. The two digits must add to 9.9 - 7 = 2
- Write the answer. Put the tens digit and the ones digit together.72
Check. Check: 7 + 2 = 9, and 72 is 9 × 8.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 4. Multiplying by 10 adds a zero to the end.10 × 4 = 40
- Take away one 4. There is one group of 9 less than ten groups.40 - 4 = 36
- Write the answer. This is 9 groups of the number.36
Check. Check: 9 × 4 = 36, so 36 + 4 = 40.
Watch out. This method works for any number, not only the 9 facts.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 5. Multiplying by 10 adds a zero to the end.10 × 5 = 50
- Take away one 5. There is one group of 9 less than ten groups.50 - 5 = 45
- Write the answer. This is 9 groups of the number.45
Check. Check: 9 × 5 = 45, so 45 + 5 = 50.
Watch out. This method works for any number, not only the 9 facts.
Method. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.2 - 1 = 1
- Find the ones digit. The two digits must add to 9.9 - 1 = 8
- Write the answer. Put the tens digit and the ones digit together.18
Check. Check: 1 + 8 = 9, and 18 is 9 × 2.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.6 - 1 = 5
- Find the ones digit. The two digits must add to 9.9 - 5 = 4
- Write the answer. Put the tens digit and the ones digit together.54
Check. Check: 5 + 4 = 9, and 54 is 9 × 6.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.9 - 1 = 8
- Find the ones digit. The two digits must add to 9.9 - 8 = 1
- Write the answer. Put the tens digit and the ones digit together.81
Check. Check: 8 + 1 = 9, and 81 is 9 × 9.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 2. Multiplying by 10 adds a zero to the end.10 × 2 = 20
- Take away one 2. There is one group of 9 less than ten groups.20 - 2 = 18
- Write the answer. This is 9 groups of the number.18
Check. Check: 9 × 2 = 18, so 18 + 2 = 20.
Watch out. This method works for any number, not only the 9 facts.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 6. Multiplying by 10 adds a zero to the end.10 × 6 = 60
- Take away one 6. There is one group of 9 less than ten groups.60 - 6 = 54
- Write the answer. This is 9 groups of the number.54
Check. Check: 9 × 6 = 54, so 54 + 6 = 60.
Watch out. This method works for any number, not only the 9 facts.
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.
Chapter summary
| Skill | Method |
|---|---|
| The 6 times table | Count in sixes; doubling a 3 fact gives a 6 fact |
| The 8 times table | Count in eights; doubling three times gives an 8 fact |
| The 9 times table | Count in nines; each answer is one more group of 9 |
| The 9 pattern | The digits of each answer add to 9; or 10 times the number take away the number |
| Missing numbers and division | Use the table; check by multiplying back |
Can you…?
- I can recall the 6 times table facts, in any order
- I can recall the 8 times table facts, in any order
- I can recall the 9 times table facts, and check them with the 9 pattern
- I can multiply by 9 using 10 times the number take away the number
- I can find a missing number and divide with the 6, 8 and 9 facts
Key terms
- pattern
- a rule that repeats, such as the digits of the 9 times table adding to 9
- product
- the answer to a multiplication
- inverse
- the operation that undoes another; division undoes multiplication
- multiple
- a number in the times table of another, such as 48 is a multiple of 8
Exercise 5Z Check-up
Non-calculatorMethod. Count in 8s to find 8 groups of 5. The order of the two numbers does not matter.
- Count in 8s, 5 times. Each count adds one more group of 8.8, 16, 24, 32, 40
- The last number we said is the answer. We counted in equal groups.8 × 5 = 40
- Write the answer. The order of the numbers does not change the answer.40
Check. Check: 5 × 8 is also 40.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 12. The order of the two numbers does not matter.
- Count in 8s, 12 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
- The last number we said is the answer. We counted in equal groups.8 × 12 = 96
- Write the answer. The order of the numbers does not change the answer.96
Check. Check: 12 × 8 is also 96.
Watch out. Say the 8 times table in order until you reach the fact you need.
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, 32, 40, 48, 56, 64, 72, 80, 88, 96
- Find the number of counts. We counted 12 times to reach 96.12 counts
- Write the missing number. It goes in the gap.12
Check. Check: 8 × 12 = 96.
Watch out. The times table of 8 is the key. Division is the opposite of multiplication.
Method. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.3 - 1 = 2
- Find the ones digit. The two digits must add to 9.9 - 2 = 7
- Write the answer. Put the tens digit and the ones digit together.27
Check. Check: 2 + 7 = 9, and 27 is 9 × 3.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Count in 8s to find 8 groups of 11. The order of the two numbers does not matter.
- Count in 8s, 11 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88
- The last number we said is the answer. We counted in equal groups.8 × 11 = 88
- Write the answer. The order of the numbers does not change the answer.88
Check. Check: 11 × 8 is also 88.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 8 × ___ = 64. Division asks how many groups.8 × ___ = 64
- Count in 8s until you reach 64. Count the steps as you go.8, 16, 24, 32, 40, 48, 56, 64
- Write the answer. This is the number of groups.8
Check. Check: 8 × 8 = 64.
Watch out. The times table of 8 is the key. Division is the opposite of multiplication.
Method. Count in 6s to find 6 groups of 12. The order of the two numbers does not matter.
- Count in 6s, 12 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
- The last number we said is the answer. We counted in equal groups.6 × 12 = 72
- Write the answer. The order of the numbers does not change the answer.72
Check. Check: 12 × 6 is also 72.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 5. The order of the two numbers does not matter.
- Count in 6s, 5 times. Each count adds one more group of 6.6, 12, 18, 24, 30
- The last number we said is the answer. We counted in equal groups.6 × 5 = 30
- Write the answer. The order of the numbers does not change the answer.30
Check. Check: 5 × 6 is also 30.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 8s to find 8 groups of 8. The order of the two numbers does not matter.
- Count in 8s, 8 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48, 56, 64
- The last number we said is the answer. We counted in equal groups.8 × 8 = 64
- Write the answer. The order of the numbers does not change the answer.64
Check. Check: 8 × 8 is also 64.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 4. Multiplying by 10 adds a zero to the end.10 × 4 = 40
- Take away one 4. There is one group of 9 less than ten groups.40 - 4 = 36
- Write the answer. This is 9 groups of the number.36
Check. Check: 9 × 4 = 36, so 36 + 4 = 40.
Watch out. This method works for any number, not only the 9 facts.
Total 19 marks. Allow about 19 minutes.
Exercise 5X Practice test questions
Non-calculatorMethod. Count in 8s to find 8 groups of 3. The order of the two numbers does not matter.
- Count in 8s, 3 times. Each count adds one more group of 8.8, 16, 24
- The last number we said is the answer. We counted in equal groups.8 × 3 = 24
- Write the answer. The order of the numbers does not change the answer.24
Check. Check: 3 × 8 is also 24.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 12. The order of the two numbers does not matter.
- Count in 6s, 12 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
- The last number we said is the answer. We counted in equal groups.6 × 12 = 72
- Write the answer. The order of the numbers does not change the answer.72
Check. Check: 12 × 6 is also 72.
Watch out. Say the 6 times table in order until you reach the fact you need.
Method. Count in 9s to find 9 groups of 6. The order of the two numbers does not matter.
- Count in 9s, 6 times. Each count adds one more group of 9.9, 18, 27, 36, 45, 54
- The last number we said is the answer. We counted in equal groups.9 × 6 = 54
- Write the answer. The order of the numbers does not change the answer.54
Check. Check: 6 × 9 is also 54.
Watch out. Say the 9 times table in order until you reach the fact you need.
Method. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.6 - 1 = 5
- Find the ones digit. The two digits must add to 9.9 - 5 = 4
- Write the answer. Put the tens digit and the ones digit together.54
Check. Check: 5 + 4 = 9, and 54 is 9 × 6.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Count in 8s to find 8 groups of 4. The order of the two numbers does not matter.
- Count in 8s, 4 times. Each count adds one more group of 8.8, 16, 24, 32
- The last number we said is the answer. We counted in equal groups.8 × 4 = 32
- Write the answer. The order of the numbers does not change the answer.32
Check. Check: 4 × 8 is also 32.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Use the 3 or 4 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 8 × ___ = 24. Division asks how many groups.8 × ___ = 24
- Count in 8s until you reach 24. Count the steps as you go.8, 16, 24
- Write the answer. 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. Use the 9 pattern. The digits of each answer add to 9.
- Find the tens digit. Take 1 from the number you multiply by 9.2 - 1 = 1
- Find the ones digit. The two digits must add to 9.9 - 1 = 8
- Write the answer. Put the tens digit and the ones digit together.18
Check. Check: 1 + 8 = 9, and 18 is 9 × 2.
Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.
Method. Use place value: 9 is 10 take away 1, so 9 times a number is 10 times it take away the number.
- Work out 10 × 11. Multiplying by 10 adds a zero to the end.10 × 11 = 110
- Take away one 11. There is one group of 9 less than ten groups.110 - 11 = 99
- Write the answer. This is 9 groups of the number.99
Check. Check: 9 × 11 = 99, so 99 + 11 = 110.
Watch out. This method works for any number, not only the 9 facts.
Method. Count in 8s to find 8 groups of 6. The order of the two numbers does not matter.
- Count in 8s, 6 times. Each count adds one more group of 8.8, 16, 24, 32, 40, 48
- The last number we said is the answer. We counted in equal groups.8 × 6 = 48
- Write the answer. The order of the numbers does not change the answer.48
Check. Check: 6 × 8 is also 48.
Watch out. Say the 8 times table in order until you reach the fact you need.
Method. Count in 6s to find 6 groups of 6. The order of the two numbers does not matter.
- Count in 6s, 6 times. Each count adds one more group of 6.6, 12, 18, 24, 30, 36
- The last number we said is the answer. We counted in equal groups.6 × 6 = 36
- Write the answer. The order of the numbers does not change the answer.36
Check. Check: 6 × 6 is also 36.
Watch out. Say the 6 times table in order until you reach the fact you need.