Times tables 6 to 12
By the end of this chapter you will be able to
- Know the 7 times table facts in any order
- Use the 11 pattern
- Use 10 and 2 to multiply by 12
- Know the 6, 8 and 9 facts, and use the commutative law
- Use the tables to solve equal-group problems
You should already know
- Times tables 3, 4, 6, 8 and 9 (Level 4, chapters 4 and 5)
- Multiplying by 10 (Level 4, chapter 4)
Where this leads
- Long multiplication of two-digit numbers by one-digit numbers (chapter 4)
- Short division (chapter 5)
Step-by-step practice: maths (Level 5). Small steps, repeated until fluent. Content: Recall multiplication and division facts for the 6, 7, 8, 9, 11 and 12 times tables (Y4 paraphrase), Recognise products of two numbers as multiples, and use the commutative law (Y4 paraphrase), Use place value and known facts to multiply mentally, for example 12 × 7 = 10 × 7 + 2 × 7 (Y4 paraphrase), Solve one-step problems with equal groups using the times tables (Y4 paraphrase).
Exercise P Do you remember?
Non-calculatorMethod. Count in 4s to find 6 groups of 4. The order of the numbers does not matter.
- Count in 4s, 6 times. Each count adds one more group of 4.4, 8, 12, 16, 20, 24
- The last number we said is the answer. We counted 6 groups of 4.4 × 6 = 24
- Write the answer. The order of the two numbers does not change the answer.24
Check. Check: 6 × 4 is also 24.
Watch out. Learn the 4 times table in order, then say it in any order.
Method. Count in 3s to find 9 groups of 3. The order of the numbers does not matter.
- Count in 3s, 9 times. Each count adds one more group of 3.3, 6, 9, 12, 15, 18, 21, 24, 27
- The last number we said is the answer. We counted 9 groups of 3.3 × 9 = 27
- Write the answer. The order of the two numbers does not change the answer.27
Check. Check: 9 × 3 is also 27.
Watch out. Learn the 3 times table in order, then say it in any order.
Method. Count in 5s to find 7 groups of 5. The order of the numbers does not matter.
- Count in 5s, 7 times. Each count adds one more group of 5.5, 10, 15, 20, 25, 30, 35
- The last number we said is the answer. We counted 7 groups of 5.5 × 7 = 35
- Write the answer. The order of the two numbers does not change the answer.35
Check. Check: 7 × 5 is also 35.
Watch out. Learn the 5 times table in order, then say it in any order.
Method. Count in 8s to find 4 groups of 8. The order of the 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 4 groups of 8.8 × 4 = 32
- Write the answer. The order of the two numbers does not change the answer.32
Check. Check: 4 × 8 is also 32.
Watch out. Learn the 8 times table in order, then say it in any order.
Method. Count in 9s to find 5 groups of 9. The order of the numbers does not matter.
- Count in 9s, 5 times. Each count adds one more group of 9.9, 18, 27, 36, 45
- The last number we said is the answer. We counted 5 groups of 9.9 × 5 = 45
- Write the answer. The order of the two numbers does not change the answer.45
Check. Check: 5 × 9 is also 45.
Watch out. Learn the 9 times table in order, then say it in any order.
The 7 times table
The 7 times table counts in sevens: 7, 14, 21, 28, 35 and so on. Each answer is one more group of 7.
Some facts are easy to check: 7 × 2 is 14, so 7 × 4 is 14 + 14 = 28.
Key ideas
- Count in sevens for the 7 times table.
- Doubling a 7 fact gives a fact for twice as many groups.
- The order of the two numbers does not matter.
Method. Count in 7s to find 8 groups of 7. The order of the numbers does not matter.
- Count in 7s, 8 times. Each count adds one more group of 7.7, 14, 21, 28, 35, 42, 49, 56
- The last number we said is the answer. We counted 8 groups of 7.7 × 8 = 56
- Write the answer. The order of the two numbers does not change the answer.56
Check. Check: 8 × 7 is also 56.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 9 groups of 7. The order of the numbers does not matter.
- Count in 7s, 9 times. Each count adds one more group of 7.7, 14, 21, 28, 35, 42, 49, 56, 63
- The last number we said is the answer. We counted 9 groups of 7.7 × 9 = 63
- Write the answer. The order of the two numbers does not change the answer.63
Check. Check: 9 × 7 is also 63.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 7 make 42? Count in steps of the number we know.7, 14, 21, 28, 35, 42
- Count the groups. We said 6 numbers, so there are 6 groups.6 groups of 7
- Write the missing number. This is the number of groups.6
Check. Check: 6 × 7 = 42.
Watch out. Count the groups carefully. Stop when you reach the total.
Watch out
Watch out. 7 × 8 is 56, not 54. Count in sevens and check the number of counts.
Exam tip
Grown-up tip. Ask: “What is 7 × 4? Now double it. What is 7 × 8?”
Exercise 3A Practice: the 7 times table
Non-calculatorMethod. Count in 7s to find 5 groups of 7. The order of the numbers does not matter.
- Count in 7s, 5 times. Each count adds one more group of 7.7, 14, 21, 28, 35
- The last number we said is the answer. We counted 5 groups of 7.7 × 5 = 35
- Write the answer. The order of the two numbers does not change the answer.35
Check. Check: 5 × 7 is also 35.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 12 groups of 7. The order of the numbers does not matter.
- Count in 7s, 12 times. Each count adds one more group of 7.7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84
- The last number we said is the answer. We counted 12 groups of 7.7 × 12 = 84
- Write the answer. The order of the two numbers does not change the answer.84
Check. Check: 12 × 7 is also 84.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 7 make 42? Count in steps of the number we know.7, 14, 21, 28, 35, 42
- Count the groups. We said 6 numbers, so there are 6 groups.6 groups of 7
- Write the missing number. This is the number of groups.6
Check. Check: 6 × 7 = 42.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 7 make 56? Count in steps of the number we know.7, 14, 21, 28, 35, 42, 49, 56
- Count the groups. We said 8 numbers, so there are 8 groups.8 groups of 7
- Write the missing number. This is the number of groups.8
Check. Check: 8 × 7 = 56.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 7 make 63? Count in steps of the number we know.7, 14, 21, 28, 35, 42, 49, 56, 63
- Count the groups. We said 9 numbers, so there are 9 groups.9 groups of 7
- Write the missing number. This is the number of groups.9
Check. Check: 9 × 7 = 63.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in 7s to find 1 groups of 7. The order of the numbers does not matter.
- Count in 7s, 1 times. Each count adds one more group of 7.7
- The last number we said is the answer. We counted 1 groups of 7.7 × 1 = 7
- Write the answer. The order of the two numbers does not change the answer.7
Check. Check: 1 × 7 is also 7.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 10 groups of 7. The order of the numbers does not matter.
- Count in 7s, 10 times. Each count adds one more group of 7.7, 14, 21, 28, 35, 42, 49, 56, 63, 70
- The last number we said is the answer. We counted 10 groups of 7.7 × 10 = 70
- Write the answer. The order of the two numbers does not change the answer.70
Check. Check: 10 × 7 is also 70.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 3 groups of 7. The order of the numbers does not matter.
- Count in 7s, 3 times. Each count adds one more group of 7.7, 14, 21
- The last number we said is the answer. We counted 3 groups of 7.7 × 3 = 21
- Write the answer. The order of the two numbers does not change the answer.21
Check. Check: 3 × 7 is also 21.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 5 groups of 7. The order of the numbers does not matter.
- Count in 7s, 5 times. Each count adds one more group of 7.7, 14, 21, 28, 35
- The last number we said is the answer. We counted 5 groups of 7.7 × 5 = 35
- Write the answer. The order of the two numbers does not change the answer.35
Check. Check: 5 × 7 is also 35.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 10 groups of 7. The order of the numbers does not matter.
- Count in 7s, 10 times. Each count adds one more group of 7.7, 14, 21, 28, 35, 42, 49, 56, 63, 70
- The last number we said is the answer. We counted 10 groups of 7.7 × 10 = 70
- Write the answer. The order of the two numbers does not change the answer.70
Check. Check: 10 × 7 is also 70.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 6 groups of 7. The order of the numbers does not matter.
- Count in 7s, 6 times. Each count adds one more group of 7.7, 14, 21, 28, 35, 42
- The last number we said is the answer. We counted 6 groups of 7.7 × 6 = 42
- Write the answer. The order of the two numbers does not change the answer.42
Check. Check: 6 × 7 is also 42.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 2 groups of 7. The order of the numbers does not matter.
- Count in 7s, 2 times. Each count adds one more group of 7.7, 14
- The last number we said is the answer. We counted 2 groups of 7.7 × 2 = 14
- Write the answer. The order of the two numbers does not change the answer.14
Check. Check: 2 × 7 is also 14.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 4 groups of 7. The order of the numbers does not matter.
- Count in 7s, 4 times. Each count adds one more group of 7.7, 14, 21, 28
- The last number we said is the answer. We counted 4 groups of 7.7 × 4 = 28
- Write the answer. The order of the two numbers does not change the answer.28
Check. Check: 4 × 7 is also 28.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 7 groups of 7. The order of the numbers does not matter.
- Count in 7s, 7 times. Each count adds one more group of 7.7, 14, 21, 28, 35, 42, 49
- The last number we said is the answer. We counted 7 groups of 7.7 × 7 = 49
- Write the answer. The order of the two numbers does not change the answer.49
Check. Check: 7 × 7 is also 49.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 3 groups of 7. The order of the numbers does not matter.
- Count in 7s, 3 times. Each count adds one more group of 7.7, 14, 21
- The last number we said is the answer. We counted 3 groups of 7.7 × 3 = 21
- Write the answer. The order of the two numbers does not change the answer.21
Check. Check: 3 × 7 is also 21.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 7s to find 2 groups of 7. The order of the numbers does not matter.
- Count in 7s, 2 times. Each count adds one more group of 7.7, 14
- The last number we said is the answer. We counted 2 groups of 7.7 × 2 = 14
- Write the answer. The order of the two numbers does not change the answer.14
Check. Check: 2 × 7 is also 14.
Watch out. Learn the 7 times table in order, then say it in any order.
The 11 times table
For 11 × 1 to 11 × 9, the answer has the same digit twice: 11 × 7 = 77.
For 11 × 10, 11 × 11 and 11 × 12, use 10 times the number plus the number once more: 11 × 12 = 120 + 12 = 132.
Key ideas
- The digit is written twice for 11 × 1 to 11 × 9.
- For 10, 11 and 12, add the number to 10 times the number.
- Check with the division: total ÷ 11.
Method. Write the digit twice. This works for 11 times 1 to 11 times 9.
- Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.7 and 7
- Read the two digits as one number. Put them side by side.77 = 77
- Write the answer. This is 11 groups of the number.77
Check. Check: 77 ÷ 11 = 7.
Watch out. The pattern works for 1 to 9. For 10 to 12, use 10 times the number plus the number.
Method. Use 10 times the number, then add the number once more.
- Work out 10 × 12. Multiplying by 10 adds a zero.10 × 12 = 120
- Add one more 12. There is one group of 11 for each 10 and 1.120 + 12 = 132
- Write the answer. This is the total.132
Check. Check: 132 ÷ 11 = 12.
Watch out. Do not write the digit twice for 10, 11 and 12; the pattern is different.
Method. Count in 11s to find 4 groups of 11. The order of the numbers does not matter.
- Count in 11s, 4 times. Each count adds one more group of 11.11, 22, 33, 44
- The last number we said is the answer. We counted 4 groups of 11.11 × 4 = 44
- Write the answer. The order of the two numbers does not change the answer.44
Check. Check: 4 × 11 is also 44.
Watch out. Learn the 11 times table in order, then say it in any order.
Watch out
Watch out. The pattern stops at 9. 11 × 10 is 110, not 1010 and not 100.
Exam tip
Grown-up tip. Ask the child to say the pattern for 11 × 3, then for 11 × 12, and to notice the difference.
Exercise 3B Practice: the 11 times table
Non-calculatorMethod. Count in 11s to find 12 groups of 11. The order of the numbers does not matter.
- Count in 11s, 12 times. Each count adds one more group of 11.11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132
- The last number we said is the answer. We counted 12 groups of 11.11 × 12 = 132
- Write the answer. The order of the two numbers does not change the answer.132
Check. Check: 12 × 11 is also 132.
Watch out. Learn the 11 times table in order, then say it in any order.
Method. Use 10 times the number, then add the number once more.
- Work out 10 × 11. Multiplying by 10 adds a zero.10 × 11 = 110
- Add one more 11. There is one group of 11 for each 10 and 1.110 + 11 = 121
- Write the answer. This is the total.121
Check. Check: 121 ÷ 11 = 11.
Watch out. Do not write the digit twice for 10, 11 and 12; the pattern is different.
Method. Write the digit twice. This works for 11 times 1 to 11 times 9.
- Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.4 and 4
- Read the two digits as one number. Put them side by side.44 = 44
- Write the answer. This is 11 groups of the number.44
Check. Check: 44 ÷ 11 = 4.
Watch out. The pattern works for 1 to 9. For 10 to 12, use 10 times the number plus the number.
Method. Write the digit twice. This works for 11 times 1 to 11 times 9.
- Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.5 and 5
- Read the two digits as one number. Put them side by side.55 = 55
- Write the answer. This is 11 groups of the number.55
Check. Check: 55 ÷ 11 = 5.
Watch out. The pattern works for 1 to 9. For 10 to 12, use 10 times the number plus the number.
Method. Count in 11s to find 8 groups of 11. The order of the numbers does not matter.
- Count in 11s, 8 times. Each count adds one more group of 11.11, 22, 33, 44, 55, 66, 77, 88
- The last number we said is the answer. We counted 8 groups of 11.11 × 8 = 88
- Write the answer. The order of the two numbers does not change the answer.88
Check. Check: 8 × 11 is also 88.
Watch out. Learn the 11 times table in order, then say it in any order.
Method. Write the digit twice. This works for 11 times 1 to 11 times 9.
- Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.3 and 3
- Read the two digits as one number. Put them side by side.33 = 33
- Write the answer. This is 11 groups of the number.33
Check. Check: 33 ÷ 11 = 3.
Watch out. The pattern works for 1 to 9. For 10 to 12, use 10 times the number plus the number.
Method. Use 10 times the number, then add the number once more.
- Work out 10 × 10. Multiplying by 10 adds a zero.10 × 10 = 100
- Add one more 10. There is one group of 11 for each 10 and 1.100 + 10 = 110
- Write the answer. This is the total.110
Check. Check: 110 ÷ 11 = 10.
Watch out. Do not write the digit twice for 10, 11 and 12; the pattern is different.
Method. Count in 11s to find 5 groups of 11. The order of the numbers does not matter.
- Count in 11s, 5 times. Each count adds one more group of 11.11, 22, 33, 44, 55
- The last number we said is the answer. We counted 5 groups of 11.11 × 5 = 55
- Write the answer. The order of the two numbers does not change the answer.55
Check. Check: 5 × 11 is also 55.
Watch out. Learn the 11 times table in order, then say it in any order.
Method. Count in 11s to find 12 groups of 11. The order of the numbers does not matter.
- Count in 11s, 12 times. Each count adds one more group of 11.11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132
- The last number we said is the answer. We counted 12 groups of 11.11 × 12 = 132
- Write the answer. The order of the two numbers does not change the answer.132
Check. Check: 12 × 11 is also 132.
Watch out. Learn the 11 times table in order, then say it in any order.
Method. Count in 11s to find 2 groups of 11. The order of the numbers does not matter.
- Count in 11s, 2 times. Each count adds one more group of 11.11, 22
- The last number we said is the answer. We counted 2 groups of 11.11 × 2 = 22
- Write the answer. The order of the two numbers does not change the answer.22
Check. Check: 2 × 11 is also 22.
Watch out. Learn the 11 times table in order, then say it in any order.
Method. Count in 11s to find 7 groups of 11. The order of the numbers does not matter.
- Count in 11s, 7 times. Each count adds one more group of 11.11, 22, 33, 44, 55, 66, 77
- The last number we said is the answer. We counted 7 groups of 11.11 × 7 = 77
- Write the answer. The order of the two numbers does not change the answer.77
Check. Check: 7 × 11 is also 77.
Watch out. Learn the 11 times table in order, then say it in any order.
Method. Write the digit twice. This works for 11 times 1 to 11 times 9.
- Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.6 and 6
- Read the two digits as one number. Put them side by side.66 = 66
- Write the answer. This is 11 groups of the number.66
Check. Check: 66 ÷ 11 = 6.
Watch out. The pattern works for 1 to 9. For 10 to 12, use 10 times the number plus the number.
Method. Write the digit twice. This works for 11 times 1 to 11 times 9.
- Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.1 and 1
- Read the two digits as one number. Put them side by side.11 = 11
- Write the answer. This is 11 groups of the number.11
Check. Check: 11 ÷ 11 = 1.
Watch out. The pattern works for 1 to 9. For 10 to 12, use 10 times the number plus the number.
Method. Write the digit twice. This works for 11 times 1 to 11 times 9.
- Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.9 and 9
- Read the two digits as one number. Put them side by side.99 = 99
- Write the answer. This is 11 groups of the number.99
Check. Check: 99 ÷ 11 = 9.
Watch out. The pattern works for 1 to 9. For 10 to 12, use 10 times the number plus the number.
Method. Count in 11s to find 1 groups of 11. The order of the numbers does not matter.
- Count in 11s, 1 times. Each count adds one more group of 11.11
- The last number we said is the answer. We counted 1 groups of 11.11 × 1 = 11
- Write the answer. The order of the two numbers does not change the answer.11
Check. Check: 1 × 11 is also 11.
Watch out. Learn the 11 times table in order, then say it in any order.
Method. Count in 11s to find 4 groups of 11. The order of the numbers does not matter.
- Count in 11s, 4 times. Each count adds one more group of 11.11, 22, 33, 44
- The last number we said is the answer. We counted 4 groups of 11.11 × 4 = 44
- Write the answer. The order of the two numbers does not change the answer.44
Check. Check: 4 × 11 is also 44.
Watch out. Learn the 11 times table in order, then say it in any order.
The 12 times table
12 is 10 and 2. To multiply by 12, work out 10 times the number and 2 times the number, then add.
For example, 12 × 7 = 70 + 14 = 84.
Key ideas
- 12 is 10 + 2.
- Work out 10 times and 2 times, then add.
- The answer to a 12 fact is always even.
Method. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 7 = 10 × 7 + 2 × 7
- Work out each part. Both parts are facts we know.10 × 7 = 70, and 2 × 7 = 14
- Add the two parts. The total is the answer.70 + 14 = 84
- Write the answer. This is the answer to 12 times the number.84
Check. Check: 84 ÷ 12 = 7.
Watch out. Do not add 12 to the number only once. Work out both parts.
Method. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 12 = 10 × 12 + 2 × 12
- Work out each part. Both parts are facts we know.10 × 12 = 120, and 2 × 12 = 24
- Add the two parts. The total is the answer.120 + 24 = 144
- Write the answer. This is the answer to 12 times the number.144
Check. Check: 144 ÷ 12 = 12.
Watch out. Do not add 12 to the number only once. Work out both parts.
Method. Count in 12s to find 6 groups of 12. The order of the numbers does not matter.
- Count in 12s, 6 times. Each count adds one more group of 12.12, 24, 36, 48, 60, 72
- The last number we said is the answer. We counted 6 groups of 12.12 × 6 = 72
- Write the answer. The order of the two numbers does not change the answer.72
Check. Check: 6 × 12 is also 72.
Watch out. Learn the 12 times table in order, then say it in any order.
Watch out
Watch out. Do not write 12 × 7 as 10 + 2 + 7. Multiply both parts by 7 and add.
Exam tip
Grown-up tip. Ask the child to split 12 into 10 and 2 every time, until they can see the answer.
Exercise 3C Practice: the 12 times table
Non-calculatorMethod. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 10 = 10 × 10 + 2 × 10
- Work out each part. Both parts are facts we know.10 × 10 = 100, and 2 × 10 = 20
- Add the two parts. The total is the answer.100 + 20 = 120
- Write the answer. This is the answer to 12 times the number.120
Check. Check: 120 ÷ 12 = 10.
Watch out. Do not add 12 to the number only once. Work out both parts.
Method. Count in 12s to find 7 groups of 12. The order of the numbers does not matter.
- Count in 12s, 7 times. Each count adds one more group of 12.12, 24, 36, 48, 60, 72, 84
- The last number we said is the answer. We counted 7 groups of 12.12 × 7 = 84
- Write the answer. The order of the two numbers does not change the answer.84
Check. Check: 7 × 12 is also 84.
Watch out. Learn the 12 times table in order, then say it in any order.
Method. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 4 = 10 × 4 + 2 × 4
- Work out each part. Both parts are facts we know.10 × 4 = 40, and 2 × 4 = 8
- Add the two parts. The total is the answer.40 + 8 = 48
- Write the answer. This is the answer to 12 times the number.48
Check. Check: 48 ÷ 12 = 4.
Watch out. Do not add 12 to the number only once. Work out both parts.
Method. Count in 12s to find 3 groups of 12. The order of the numbers does not matter.
- Count in 12s, 3 times. Each count adds one more group of 12.12, 24, 36
- The last number we said is the answer. We counted 3 groups of 12.12 × 3 = 36
- Write the answer. The order of the two numbers does not change the answer.36
Check. Check: 3 × 12 is also 36.
Watch out. Learn the 12 times table in order, then say it in any order.
Method. Count in 12s to find 2 groups of 12. The order of the numbers does not matter.
- Count in 12s, 2 times. Each count adds one more group of 12.12, 24
- The last number we said is the answer. We counted 2 groups of 12.12 × 2 = 24
- Write the answer. The order of the two numbers does not change the answer.24
Check. Check: 2 × 12 is also 24.
Watch out. Learn the 12 times table in order, then say it in any order.
Method. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 5 = 10 × 5 + 2 × 5
- Work out each part. Both parts are facts we know.10 × 5 = 50, and 2 × 5 = 10
- Add the two parts. The total is the answer.50 + 10 = 60
- Write the answer. This is the answer to 12 times the number.60
Check. Check: 60 ÷ 12 = 5.
Watch out. Do not add 12 to the number only once. Work out both parts.
Method. Count in 12s to find 6 groups of 12. The order of the numbers does not matter.
- Count in 12s, 6 times. Each count adds one more group of 12.12, 24, 36, 48, 60, 72
- The last number we said is the answer. We counted 6 groups of 12.12 × 6 = 72
- Write the answer. The order of the two numbers does not change the answer.72
Check. Check: 6 × 12 is also 72.
Watch out. Learn the 12 times table in order, then say it in any order.
Method. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 11 = 10 × 11 + 2 × 11
- Work out each part. Both parts are facts we know.10 × 11 = 110, and 2 × 11 = 22
- Add the two parts. The total is the answer.110 + 22 = 132
- Write the answer. This is the answer to 12 times the number.132
Check. Check: 132 ÷ 12 = 11.
Watch out. Do not add 12 to the number only once. Work out both parts.
Method. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 1 = 10 × 1 + 2 × 1
- Work out each part. Both parts are facts we know.10 × 1 = 10, and 2 × 1 = 2
- Add the two parts. The total is the answer.10 + 2 = 12
- Write the answer. This is the answer to 12 times the number.12
Check. Check: 12 ÷ 12 = 1.
Watch out. Do not add 12 to the number only once. Work out both parts.
Method. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 2 = 10 × 2 + 2 × 2
- Work out each part. Both parts are facts we know.10 × 2 = 20, and 2 × 2 = 4
- Add the two parts. The total is the answer.20 + 4 = 24
- Write the answer. This is the answer to 12 times the number.24
Check. Check: 24 ÷ 12 = 2.
Watch out. Do not add 12 to the number only once. Work out both parts.
Method. Count in 12s to find 4 groups of 12. The order of the numbers does not matter.
- Count in 12s, 4 times. Each count adds one more group of 12.12, 24, 36, 48
- The last number we said is the answer. We counted 4 groups of 12.12 × 4 = 48
- Write the answer. The order of the two numbers does not change the answer.48
Check. Check: 4 × 12 is also 48.
Watch out. Learn the 12 times table in order, then say it in any order.
Method. Count in 12s to find 5 groups of 12. The order of the numbers does not matter.
- Count in 12s, 5 times. Each count adds one more group of 12.12, 24, 36, 48, 60
- The last number we said is the answer. We counted 5 groups of 12.12 × 5 = 60
- Write the answer. The order of the two numbers does not change the answer.60
Check. Check: 5 × 12 is also 60.
Watch out. Learn the 12 times table in order, then say it in any order.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 12 make 96? Count in steps of the number we know.12, 24, 36, 48, 60, 72, 84, 96
- Count the groups. We said 8 numbers, so there are 8 groups.8 groups of 12
- Write the missing number. This is the number of groups.8
Check. Check: 8 × 12 = 96.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 12 make 120? Count in steps of the number we know.12, 24, 36, 48, 60, 72, 84, 96, 108, 120
- Count the groups. We said 10 numbers, so there are 10 groups.10 groups of 12
- Write the missing number. This is the number of groups.10
Check. Check: 10 × 12 = 120.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 7 = 10 × 7 + 2 × 7
- Work out each part. Both parts are facts we know.10 × 7 = 70, and 2 × 7 = 14
- Add the two parts. The total is the answer.70 + 14 = 84
- Write the answer. This is the answer to 12 times the number.84
Check. Check: 84 ÷ 12 = 7.
Watch out. Do not add 12 to the number only once. Work out both parts.
Method. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 6 = 10 × 6 + 2 × 6
- Work out each part. Both parts are facts we know.10 × 6 = 60, and 2 × 6 = 12
- Add the two parts. The total is the answer.60 + 12 = 72
- Write the answer. This is the answer to 12 times the number.72
Check. Check: 72 ÷ 12 = 6.
Watch out. Do not add 12 to the number only once. Work out both parts.
The 6, 8 and 9 facts, and the commutative law
The 6, 8 and 9 times tables are the same in any order: 9 × 6 is the same as 6 × 9, both 54.
This is the commutative law. You can use it to swap two numbers and find a missing one.
Key ideas
- The order of the numbers does not change the product.
- Use the commutative law to swap the factors.
- Missing numbers can be found by counting the groups.
Method. Count in 9s to find 6 groups of 9. The order of the 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 6 groups of 9.9 × 6 = 54
- Write the answer. The order of the two numbers does not change the answer.54
Check. Check: 6 × 9 is also 54.
Watch out. Learn the 9 times table in order, then say it in any order.
Method. Multiplication can be done in either order. Swap the numbers to find the missing one.
- Look at the left side. The two numbers are the same as on the right, in the other order.8 × 5 = 40
- Swap the two numbers. Multiplication can be done in either order, and the answer is the same.5 × 8 = 40
- Write the missing number. This is the number that goes in the box.8
Check. Check: 5 × 8 = 40, the same as 8 × 5.
Watch out. This is the commutative law. The order of the numbers does not change the product.
Method. Count in 8s to find 7 groups of 8. The order of the 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 7 groups of 8.8 × 7 = 56
- Write the answer. The order of the two numbers does not change the answer.56
Check. Check: 7 × 8 is also 56.
Watch out. Learn the 8 times table in order, then say it in any order.
Watch out
Watch out. The commutative law works for multiplication, not for division or subtraction. 12 ÷ 3 is not the same as 3 ÷ 12.
Exam tip
Grown-up tip. Ask: “Is 8 × 6 the same as 6 × 8? How do you know?”
Exercise 3D Practice: the 6, 8 and 9 facts, and swapping factors
Non-calculatorMethod. Multiplication can be done in either order. Swap the numbers to find the missing one.
- Look at the left side. The two numbers are the same as on the right, in the other order.11 × 3 = 33
- Swap the two numbers. Multiplication can be done in either order, and the answer is the same.3 × 11 = 33
- Write the missing number. This is the number that goes in the box.11
Check. Check: 3 × 11 = 33, the same as 11 × 3.
Watch out. This is the commutative law. The order of the numbers does not change the product.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 11 make 132? Count in steps of the number we know.11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132
- Count the groups. We said 12 numbers, so there are 12 groups.12 groups of 11
- Write the missing number. This is the number of groups.12
Check. Check: 12 × 11 = 132.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in 12s to find 7 groups of 12. The order of the numbers does not matter.
- Count in 12s, 7 times. Each count adds one more group of 12.12, 24, 36, 48, 60, 72, 84
- The last number we said is the answer. We counted 7 groups of 12.12 × 7 = 84
- Write the answer. The order of the two numbers does not change the answer.84
Check. Check: 7 × 12 is also 84.
Watch out. Learn the 12 times table in order, then say it in any order.
Method. Count in 7s to find 1 groups of 7. The order of the numbers does not matter.
- Count in 7s, 1 times. Each count adds one more group of 7.7
- The last number we said is the answer. We counted 1 groups of 7.7 × 1 = 7
- Write the answer. The order of the two numbers does not change the answer.7
Check. Check: 1 × 7 is also 7.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 8 make 40? Count in steps of the number we know.8, 16, 24, 32, 40
- Count the groups. We said 5 numbers, so there are 5 groups.5 groups of 8
- Write the missing number. This is the number of groups.5
Check. Check: 5 × 8 = 40.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Multiplication can be done in either order. Swap the numbers to find the missing one.
- Look at the left side. The two numbers are the same as on the right, in the other order.7 × 8 = 56
- Swap the two numbers. Multiplication can be done in either order, and the answer is the same.8 × 7 = 56
- Write the missing number. This is the number that goes in the box.7
Check. Check: 8 × 7 = 56, the same as 7 × 8.
Watch out. This is the commutative law. The order of the numbers does not change the product.
Method. Multiplication can be done in either order. Swap the numbers to find the missing one.
- Look at the left side. The two numbers are the same as on the right, in the other order.8 × 8 = 64
- Swap the two numbers. Multiplication can be done in either order, and the answer is the same.8 × 8 = 64
- Write the missing number. This is the number that goes in the box.8
Check. Check: 8 × 8 = 64, the same as 8 × 8.
Watch out. This is the commutative law. The order of the numbers does not change the product.
Method. Count in 12s to find 11 groups of 12. The order of the numbers does not matter.
- Count in 12s, 11 times. Each count adds one more group of 12.12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132
- The last number we said is the answer. We counted 11 groups of 12.12 × 11 = 132
- Write the answer. The order of the two numbers does not change the answer.132
Check. Check: 11 × 12 is also 132.
Watch out. Learn the 12 times table in order, then say it in any order.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 9 make 9? Count in steps of the number we know.9
- Count the groups. We said 1 numbers, so there are 1 groups.1 groups of 9
- Write the missing number. This is the number of groups.1
Check. Check: 1 × 9 = 9.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in 7s to find 6 groups of 7. The order of the numbers does not matter.
- Count in 7s, 6 times. Each count adds one more group of 7.7, 14, 21, 28, 35, 42
- The last number we said is the answer. We counted 6 groups of 7.7 × 6 = 42
- Write the answer. The order of the two numbers does not change the answer.42
Check. Check: 6 × 7 is also 42.
Watch out. Learn the 7 times table in order, then say it in any order.
Method. Count in 6s to find 11 groups of 6. The order of the 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 11 groups of 6.6 × 11 = 66
- Write the answer. The order of the two numbers does not change the answer.66
Check. Check: 11 × 6 is also 66.
Watch out. Learn the 6 times table in order, then say it in any order.
Method. Count in 12s to find 1 groups of 12. The order of the numbers does not matter.
- Count in 12s, 1 times. Each count adds one more group of 12.12
- The last number we said is the answer. We counted 1 groups of 12.12 × 1 = 12
- Write the answer. The order of the two numbers does not change the answer.12
Check. Check: 1 × 12 is also 12.
Watch out. Learn the 12 times table in order, then say it in any order.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 7 make 49? Count in steps of the number we know.7, 14, 21, 28, 35, 42, 49
- Count the groups. We said 7 numbers, so there are 7 groups.7 groups of 7
- Write the missing number. This is the number of groups.7
Check. Check: 7 × 7 = 49.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 11 make 22? Count in steps of the number we know.11, 22
- Count the groups. We said 2 numbers, so there are 2 groups.2 groups of 11
- Write the missing number. This is the number of groups.2
Check. Check: 2 × 11 = 22.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in 9s to find 7 groups of 9. The order of the 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 7 groups of 9.9 × 7 = 63
- Write the answer. The order of the two numbers does not change the answer.63
Check. Check: 7 × 9 is also 63.
Watch out. Learn the 9 times table in order, then say it in any order.
Method. Count in 7s to find 2 groups of 7. The order of the numbers does not matter.
- Count in 7s, 2 times. Each count adds one more group of 7.7, 14
- The last number we said is the answer. We counted 2 groups of 7.7 × 2 = 14
- Write the answer. The order of the two numbers does not change the answer.14
Check. Check: 2 × 7 is also 14.
Watch out. Learn the 7 times table in order, then say it in any order.
Equal groups and division with the tables
When things are put into equal groups, multiply the number of groups by the number in each group. To find how many groups, divide.
A division is worked out with the matching times table fact. 54 ÷ 6 asks: 6 times what makes 54?
Key ideas
- Multiply the number of groups by the number in each group.
- Division asks how many groups of a number make a total.
- Check each division by multiplying back.
Method. Use the multiplication fact to find the division.
- Think of the multiplication: 9 × ___ = 72. Division asks how many groups of the number make the total.9 × ___ = 72
- Count in 9s until you reach 72. Count the steps as you go.9, 18, 27, 36, 45, 54, 63, 72
- Write the answer. This is the number of groups.8
Check. Check: 8 × 9 = 72.
Watch out. Use the times table fact that matches. Division is the opposite of multiplication.
Method. Division with equal groups: the number of boxes is the total divided by the box size.
- Find the total and the size of each box. The total is how many; the box holds a certain number.54 cups in boxes of 6
- Think: how many groups of the box size make the total? This is a division, which we can check with the table.6 × ___ = 54
- Count the boxes. Count in the box size until you reach the total.6, 12, 18, 24, 30, 36, 42, 48, 54
- Write the answer. This is the number of boxes.9
Check. Check: 9 boxes of 6 hold 9 × 6 = 54 cups.
Watch out. Check the answer makes sense: each box holds the same number.
Method. Multiply the number of groups by the number in each group.
- Find the number of bags and the number in each. Multiply the number of equal groups by the size of each group.6 bags of 8
- Work out the multiplication. Use the times table for this number.6 × 8 = 48
- Write the answer. This is the total number of sweets.48
Check. Check: 48 ÷ 6 = 8, so each bag has 8.
Watch out. If you are not sure of the fact, count in the times table, one group at a time.
Watch out
Watch out. Check which operation the problem needs: sharing into groups is division; the total of equal groups is multiplication.
Exam tip
Grown-up tip. Ask the child to say “groups of” in each problem before they choose multiply or divide.
Exercise 3E Practice: equal groups and missing numbers in division
Non-calculatorMethod. Division with equal groups: the number of boxes is the total divided by the box size.
- Find the total and the size of each box. The total is how many; the box holds a certain number.110 muffins in boxes of 11
- Think: how many groups of the box size make the total? This is a division, which we can check with the table.11 × ___ = 110
- Count the boxes. Count in the box size until you reach the total.11, 22, 33, 44, 55, 66, 77, 88, 99, 110
- Write the answer. This is the number of boxes.10
Check. Check: 10 boxes of 11 hold 10 × 11 = 110 muffins.
Watch out. Check the answer makes sense: each box holds the same number.
Method. Multiply the number of groups by the number in each group.
- Find the number of bags and the number in each. Multiply the number of equal groups by the size of each group.5 bags of 12
- Work out the multiplication. Use the times table for this number.5 × 12 = 60
- Write the answer. This is the total number of sweets.60
Check. Check: 60 ÷ 5 = 12, so each bag has 12.
Watch out. If you are not sure of the fact, count in the times table, one group at a time.
Method. Multiply the number of groups by the number in each group.
- Find the number of bags and the number in each. Multiply the number of equal groups by the size of each group.2 bags of 8
- Work out the multiplication. Use the times table for this number.2 × 8 = 16
- Write the answer. This is the total number of sweets.16
Check. Check: 16 ÷ 2 = 8, so each bag has 8.
Watch out. If you are not sure of the fact, count in the times table, one group at a time.
Method. Division with equal groups: the number of boxes is the total divided by the box size.
- Find the total and the size of each box. The total is how many; the box holds a certain number.36 cups in boxes of 9
- Think: how many groups of the box size make the total? This is a division, which we can check with the table.9 × ___ = 36
- Count the boxes. Count in the box size until you reach the total.9, 18, 27, 36
- Write the answer. This is the number of boxes.4
Check. Check: 4 boxes of 9 hold 4 × 9 = 36 cups.
Watch out. Check the answer makes sense: each box holds the same number.
Method. Division with equal groups: the number of boxes is the total divided by the box size.
- Find the total and the size of each box. The total is how many; the box holds a certain number.121 pencils in boxes of 11
- Think: how many groups of the box size make the total? This is a division, which we can check with the table.11 × ___ = 121
- Count the boxes. Count in the box size until you reach the total.11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121
- Write the answer. This is the number of boxes.11
Check. Check: 11 boxes of 11 hold 11 × 11 = 121 pencils.
Watch out. Check the answer makes sense: each box holds the same number.
Method. Multiply the number of groups by the number in each group.
- Find the number of bags and the number in each. Multiply the number of equal groups by the size of each group.9 bags of 12
- Work out the multiplication. Use the times table for this number.9 × 12 = 108
- Write the answer. This is the total number of sweets.108
Check. Check: 108 ÷ 9 = 12, so each bag has 12.
Watch out. If you are not sure of the fact, count in the times table, one group at a time.
Method. Use the multiplication fact to find the division.
- Think of the multiplication: 11 × ___ = 99. Division asks how many groups of the number make the total.11 × ___ = 99
- Count in 11s until you reach 99. Count the steps as you go.11, 22, 33, 44, 55, 66, 77, 88, 99
- Write the answer. This is the number of groups.9
Check. Check: 9 × 11 = 99.
Watch out. Use the times table fact that matches. Division is the opposite of multiplication.
Method. Multiply the number of groups by the number in each group.
- Find the number of bags and the number in each. Multiply the number of equal groups by the size of each group.8 bags of 6
- Work out the multiplication. Use the times table for this number.8 × 6 = 48
- Write the answer. This is the total number of sweets.48
Check. Check: 48 ÷ 8 = 6, so each bag has 6.
Watch out. If you are not sure of the fact, count in the times table, one group at a time.
Method. Division with equal groups: the number of boxes is the total divided by the box size.
- Find the total and the size of each box. The total is how many; the box holds a certain number.18 stickers in boxes of 9
- Think: how many groups of the box size make the total? This is a division, which we can check with the table.9 × ___ = 18
- Count the boxes. Count in the box size until you reach the total.9, 18
- Write the answer. This is the number of boxes.2
Check. Check: 2 boxes of 9 hold 2 × 9 = 18 stickers.
Watch out. Check the answer makes sense: each box holds the same number.
Method. Multiply the number of groups by the number in each group.
- Find the number of bags and the number in each. Multiply the number of equal groups by the size of each group.3 bags of 11
- Work out the multiplication. Use the times table for this number.3 × 11 = 33
- Write the answer. This is the total number of sweets.33
Check. Check: 33 ÷ 3 = 11, so each bag has 11.
Watch out. If you are not sure of the fact, count in the times table, one group at a time.
Method. Division with equal groups: the number of boxes is the total divided by the box size.
- Find the total and the size of each box. The total is how many; the box holds a certain number.132 stickers in boxes of 11
- Think: how many groups of the box size make the total? This is a division, which we can check with the table.11 × ___ = 132
- Count the boxes. Count in the box size until you reach the total.11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132
- Write the answer. This is the number of boxes.12
Check. Check: 12 boxes of 11 hold 12 × 11 = 132 stickers.
Watch out. Check the answer makes sense: each box holds the same number.
Method. Use the multiplication fact to find the division.
- Think of the multiplication: 9 × ___ = 81. Division asks how many groups of the number make the total.9 × ___ = 81
- Count in 9s until you reach 81. Count the steps as you go.9, 18, 27, 36, 45, 54, 63, 72, 81
- Write the answer. This is the number of groups.9
Check. Check: 9 × 9 = 81.
Watch out. Use the times table fact that matches. Division is the opposite of multiplication.
Method. Division with equal groups: the number of boxes is the total divided by the box size.
- Find the total and the size of each box. The total is how many; the box holds a certain number.48 pencils in boxes of 8
- Think: how many groups of the box size make the total? This is a division, which we can check with the table.8 × ___ = 48
- Count the boxes. Count in the box size until you reach the total.8, 16, 24, 32, 40, 48
- Write the answer. This is the number of boxes.6
Check. Check: 6 boxes of 8 hold 6 × 8 = 48 pencils.
Watch out. Check the answer makes sense: each box holds the same number.
Method. Multiply the number of groups by the number in each group.
- Find the number of bags and the number in each. Multiply the number of equal groups by the size of each group.3 bags of 6
- Work out the multiplication. Use the times table for this number.3 × 6 = 18
- Write the answer. This is the total number of sweets.18
Check. Check: 18 ÷ 3 = 6, so each bag has 6.
Watch out. If you are not sure of the fact, count in the times table, one group at a time.
Method. Division with equal groups: the number of boxes is the total divided by the box size.
- Find the total and the size of each box. The total is how many; the box holds a certain number.90 muffins in boxes of 9
- Think: how many groups of the box size make the total? This is a division, which we can check with the table.9 × ___ = 90
- Count the boxes. Count in the box size until you reach the total.9, 18, 27, 36, 45, 54, 63, 72, 81, 90
- Write the answer. This is the number of boxes.10
Check. Check: 10 boxes of 9 hold 10 × 9 = 90 muffins.
Watch out. Check the answer makes sense: each box holds the same number.
Method. Use the multiplication fact to find the division.
- Think of the multiplication: 7 × ___ = 84. Division asks how many groups of the number make the total.7 × ___ = 84
- Count in 7s until you reach 84. Count the steps as you go.7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84
- Write the answer. This is the number of groups.12
Check. Check: 12 × 7 = 84.
Watch out. Use the times table fact that matches. Division is the opposite of multiplication.
Chapter summary
| Skill | Method |
|---|---|
| The 7 times table | Count in sevens; double a fact to extend it |
| The 11 times table | For 1 to 9 write the digit twice; for 10 to 12 use 10 times plus the number |
| The 12 times table | Split 12 into 10 and 2; multiply each part; add |
| 6, 8 and 9 facts | Recall in any order; the commutative law swaps the factors |
| Equal groups | Groups × size = total; total ÷ size = groups |
Can you…?
- I can recall the 7 times table facts, in any order
- I can use the 11 pattern to multiply by 11
- I can use 10 and 2 to multiply by 12
- I can recall the 6, 8 and 9 times table facts in any order
- I can use the commutative law to swap two factors
- I can use the tables to solve equal-group problems and find missing numbers
Key terms
- factor
- a number that is multiplied by another
- product
- the answer to a multiplication
- commutative
- the order of the numbers does not change the answer (for multiplication)
- equal groups
- groups that each have the same number of things
Exercise 3Z Check-up
Non-calculatorMethod. Division with equal groups: the number of boxes is the total divided by the box size.
- Find the total and the size of each box. The total is how many; the box holds a certain number.63 cups in boxes of 7
- Think: how many groups of the box size make the total? This is a division, which we can check with the table.7 × ___ = 63
- Count the boxes. Count in the box size until you reach the total.7, 14, 21, 28, 35, 42, 49, 56, 63
- Write the answer. This is the number of boxes.9
Check. Check: 9 boxes of 7 hold 9 × 7 = 63 cups.
Watch out. Check the answer makes sense: each box holds the same number.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 6 make 60? Count in steps of the number we know.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: 10 × 6 = 60.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in 11s to find 8 groups of 11. The order of the numbers does not matter.
- Count in 11s, 8 times. Each count adds one more group of 11.11, 22, 33, 44, 55, 66, 77, 88
- The last number we said is the answer. We counted 8 groups of 11.11 × 8 = 88
- Write the answer. The order of the two numbers does not change the answer.88
Check. Check: 8 × 11 is also 88.
Watch out. Learn the 11 times table in order, then say it in any order.
Method. Use the multiplication fact to find the division.
- Think of the multiplication: 6 × ___ = 24. Division asks how many groups of the number make the total.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: 4 × 6 = 24.
Watch out. Use the times table fact that matches. Division is the opposite of multiplication.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 7 make 84? Count in steps of the number we know.7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84
- Count the groups. We said 12 numbers, so there are 12 groups.12 groups of 7
- Write the missing number. This is the number of groups.12
Check. Check: 12 × 7 = 84.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Multiply the number of groups by the number in each group.
- Find the number of bags and the number in each. Multiply the number of equal groups by the size of each group.6 bags of 8
- Work out the multiplication. Use the times table for this number.6 × 8 = 48
- Write the answer. This is the total number of sweets.48
Check. Check: 48 ÷ 6 = 8, so each bag has 8.
Watch out. If you are not sure of the fact, count in the times table, one group at a time.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 7 make 42? Count in steps of the number we know.7, 14, 21, 28, 35, 42
- Count the groups. We said 6 numbers, so there are 6 groups.6 groups of 7
- Write the missing number. This is the number of groups.6
Check. Check: 6 × 7 = 42.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in 12s to find 7 groups of 12. The order of the numbers does not matter.
- Count in 12s, 7 times. Each count adds one more group of 12.12, 24, 36, 48, 60, 72, 84
- The last number we said is the answer. We counted 7 groups of 12.12 × 7 = 84
- Write the answer. The order of the two numbers does not change the answer.84
Check. Check: 7 × 12 is also 84.
Watch out. Learn the 12 times table in order, then say it in any order.
Method. Write the digit twice. This works for 11 times 1 to 11 times 9.
- Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.7 and 7
- Read the two digits as one number. Put them side by side.77 = 77
- Write the answer. This is 11 groups of the number.77
Check. Check: 77 ÷ 11 = 7.
Watch out. The pattern works for 1 to 9. For 10 to 12, use 10 times the number plus the number.
Method. Count in 7s to find 7 groups of 7. The order of the numbers does not matter.
- Count in 7s, 7 times. Each count adds one more group of 7.7, 14, 21, 28, 35, 42, 49
- The last number we said is the answer. We counted 7 groups of 7.7 × 7 = 49
- Write the answer. The order of the two numbers does not change the answer.49
Check. Check: 7 × 7 is also 49.
Watch out. Learn the 7 times table in order, then say it in any order.
Total 19 marks. Allow about 19 minutes.
Exercise 3X Practice test questions
Non-calculatorMethod. Count in steps of the known number until you reach the total.
- Think: how many groups of 12 make 84? Count in steps of the number we know.12, 24, 36, 48, 60, 72, 84
- Count the groups. We said 7 numbers, so there are 7 groups.7 groups of 12
- Write the missing number. This is the number of groups.7
Check. Check: 7 × 12 = 84.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 7 make 56? Count in steps of the number we know.7, 14, 21, 28, 35, 42, 49, 56
- Count the groups. We said 8 numbers, so there are 8 groups.8 groups of 7
- Write the missing number. This is the number of groups.8
Check. Check: 8 × 7 = 56.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Count in 9s to find 9 groups of 9. The order of the 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 9 groups of 9.9 × 9 = 81
- Write the answer. The order of the two numbers does not change the answer.81
Check. Check: 9 × 9 is also 81.
Watch out. Learn the 9 times table in order, then say it in any order.
Method. Use the multiplication fact to find the division.
- Think of the multiplication: 12 × ___ = 108. Division asks how many groups of the number make the total.12 × ___ = 108
- Count in 12s until you reach 108. Count the steps as you go.12, 24, 36, 48, 60, 72, 84, 96, 108
- Write the answer. This is the number of groups.9
Check. Check: 9 × 12 = 108.
Watch out. Use the times table fact that matches. Division is the opposite of multiplication.
Method. Count in 6s to find 12 groups of 6. The order of the 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 12 groups of 6.6 × 12 = 72
- Write the answer. The order of the two numbers does not change the answer.72
Check. Check: 12 × 6 is also 72.
Watch out. Learn the 6 times table in order, then say it in any order.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 7 make 77? Count in steps of the number we know.7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77
- Count the groups. We said 11 numbers, so there are 11 groups.11 groups of 7
- Write the missing number. This is the number of groups.11
Check. Check: 11 × 7 = 77.
Watch out. Count the groups carefully. Stop when you reach the total.
Method. Write the digit twice. This works for 11 times 1 to 11 times 9.
- Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.5 and 5
- Read the two digits as one number. Put them side by side.55 = 55
- Write the answer. This is 11 groups of the number.55
Check. Check: 55 ÷ 11 = 5.
Watch out. The pattern works for 1 to 9. For 10 to 12, use 10 times the number plus the number.
Method. Split 12 into 10 and 2, then add the two results.
- Split 12 into 10 and 2. Multiply each part by the number.12 × 6 = 10 × 6 + 2 × 6
- Work out each part. Both parts are facts we know.10 × 6 = 60, and 2 × 6 = 12
- Add the two parts. The total is the answer.60 + 12 = 72
- Write the answer. This is the answer to 12 times the number.72
Check. Check: 72 ÷ 12 = 6.
Watch out. Do not add 12 to the number only once. Work out both parts.
Method. Write the digit twice. This works for 11 times 1 to 11 times 9.
- Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.9 and 9
- Read the two digits as one number. Put them side by side.99 = 99
- Write the answer. This is 11 groups of the number.99
Check. Check: 99 ÷ 11 = 9.
Watch out. The pattern works for 1 to 9. For 10 to 12, use 10 times the number plus the number.
Method. Count in steps of the known number until you reach the total.
- Think: how many groups of 12 make 48? Count in steps of the number we know.12, 24, 36, 48
- Count the groups. We said 4 numbers, so there are 4 groups.4 groups of 12
- Write the missing number. This is the number of groups.4
Check. Check: 4 × 12 = 48.
Watch out. Count the groups carefully. Stop when you reach the total.