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Step-by-step practice: Maths · Level 5Chapter 3 · Times tables 6 to 12
Level 5 · Chapter 3

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-calculator
1
FWhat is 4 × 6?
2
FWhat is 9 × 3?
3
FWhat is 5 × 7?
4
FWhat is 8 × 4?
5
FWhat is 9 × 5?
3.1

The 7 times table

Level 5
Recall the 7 times table facts, in any order
Video lesson: The 7 times tableComing soon

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.
Worked example 3.1.1
What is 7 × 8?

Method. Count in 7s to find 8 groups of 7. The order of the numbers does not matter.

  1. Count in 7s, 8 times. Each count adds one more group of 7.
    7, 14, 21, 28, 35, 42, 49, 56
  2. The last number we said is the answer. We counted 8 groups of 7.
    7 × 8 = 56
  3. 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.

Worked example 3.1.2
What is 9 × 7?

Method. Count in 7s to find 9 groups of 7. The order of the numbers does not matter.

  1. Count in 7s, 9 times. Each count adds one more group of 7.
    7, 14, 21, 28, 35, 42, 49, 56, 63
  2. The last number we said is the answer. We counted 9 groups of 7.
    7 × 9 = 63
  3. 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.

Worked example 3.1.3
___ × 7 = 42. What is the missing number?

Method. Count in steps of the known number until you reach the total.

  1. Think: how many groups of 7 make 42? Count in steps of the number we know.
    7, 14, 21, 28, 35, 42
  2. Count the groups. We said 6 numbers, so there are 6 groups.
    6 groups of 7
  3. 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-calculator
1
FWhat is 7 × 5?
2
FWhat is 7 × 12?
3
F___ × 7 = 42. What is the missing number?
4
F___ × 7 = 56. What is the missing number?
5
F___ × 7 = 63. What is the missing number?
6
FWhat is 7 × 1?
7
FWhat is 7 × 10?
8
FWhat is 7 × 3?
9
FWhat is 5 × 7?
10
FWhat is 10 × 7?
11
FWhat is 6 × 7?
12
FWhat is 2 × 7?
13
FWhat is 7 × 4?
14
FWhat is 7 × 7?
15
FWhat is 3 × 7?
16
FWhat is 7 × 2?
3.2

The 11 times table

Level 5
Use the 11 pattern: write the digit twice, Multiply by 11 up to 12 times 11
Video lesson: The 11 times tableComing soon

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.
Worked example 3.2.1
What is 11 × 7?

Method. Write the digit twice. This works for 11 times 1 to 11 times 9.

  1. Write the number twice. In the 11 times table, a one-digit answer has the same digit twice.
    7 and 7
  2. Read the two digits as one number. Put them side by side.
    77 = 77
  3. 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.

Worked example 3.2.2
What is 11 × 12?

Method. Use 10 times the number, then add the number once more.

  1. Work out 10 × 12. Multiplying by 10 adds a zero.
    10 × 12 = 120
  2. Add one more 12. There is one group of 11 for each 10 and 1.
    120 + 12 = 132
  3. 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.

Worked example 3.2.3
What is 11 × 4?

Method. Count in 11s to find 4 groups of 11. The order of the numbers does not matter.

  1. Count in 11s, 4 times. Each count adds one more group of 11.
    11, 22, 33, 44
  2. The last number we said is the answer. We counted 4 groups of 11.
    11 × 4 = 44
  3. 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-calculator
1
FWhat is 11 × 12?
2
FWhat is 11 × 11?
3
FWhat is 11 × 4?
4
FWhat is 11 × 5?
5
FWhat is 11 × 8?
6
FWhat is 11 × 3?
7
FWhat is 11 × 10?
8
FWhat is 5 × 11?
9
FWhat is 12 × 11?
10
FWhat is 11 × 2?
11
FWhat is 11 × 7?
12
FWhat is 11 × 6?
13
FWhat is 11 × 1?
14
FWhat is 11 × 9?
15
FWhat is 1 × 11?
16
FWhat is 4 × 11?
3.3

The 12 times table

Level 5
Use 10 times and 2 times to multiply by 12, Recall the 12 times table facts
Video lesson: The 12 times tableComing soon

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.
Worked example 3.3.1
Use 10 and 2 to work out 12 × 7.

Method. Split 12 into 10 and 2, then add the two results.

  1. Split 12 into 10 and 2. Multiply each part by the number.
    12 × 7 = 10 × 7 + 2 × 7
  2. Work out each part. Both parts are facts we know.
    10 × 7 = 70, and 2 × 7 = 14
  3. Add the two parts. The total is the answer.
    70 + 14 = 84
  4. 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.

Worked example 3.3.2
Use 10 and 2 to work out 12 × 12.

Method. Split 12 into 10 and 2, then add the two results.

  1. Split 12 into 10 and 2. Multiply each part by the number.
    12 × 12 = 10 × 12 + 2 × 12
  2. Work out each part. Both parts are facts we know.
    10 × 12 = 120, and 2 × 12 = 24
  3. Add the two parts. The total is the answer.
    120 + 24 = 144
  4. 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.

Worked example 3.3.3
What is 12 × 6?

Method. Count in 12s to find 6 groups of 12. The order of the numbers does not matter.

  1. Count in 12s, 6 times. Each count adds one more group of 12.
    12, 24, 36, 48, 60, 72
  2. The last number we said is the answer. We counted 6 groups of 12.
    12 × 6 = 72
  3. 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-calculator
1
FUse 10 and 2 to work out 12 × 10.
2
FWhat is 12 × 7?
3
FUse 10 and 2 to work out 12 × 4.
4
FWhat is 12 × 3?
5
FWhat is 2 × 12?
6
FUse 10 and 2 to work out 12 × 5.
7
FWhat is 12 × 6?
8
FUse 10 and 2 to work out 12 × 11.
9
FUse 10 and 2 to work out 12 × 1.
10
FUse 10 and 2 to work out 12 × 2.
11
FWhat is 12 × 4?
12
FWhat is 12 × 5?
13
F___ × 12 = 96. What is the missing number?
14
F___ × 12 = 120. What is the missing number?
15
FUse 10 and 2 to work out 12 × 7.
16
FUse 10 and 2 to work out 12 × 6.
3.4

The 6, 8 and 9 facts, and the commutative law

Level 5
Recall the 6, 8 and 9 times table facts in any order, Use the commutative law: the order of two factors does not change the product
Video lesson: The 6, 8 and 9 facts, and the commutative lawComing soon

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.
Worked example 3.4.1
What is 9 × 6?

Method. Count in 9s to find 6 groups of 9. The order of the numbers does not matter.

  1. Count in 9s, 6 times. Each count adds one more group of 9.
    9, 18, 27, 36, 45, 54
  2. The last number we said is the answer. We counted 6 groups of 9.
    9 × 6 = 54
  3. 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.

Worked example 3.4.2
8 × 5 = 5 × ___. What is the missing number?

Method. Multiplication can be done in either order. Swap the numbers to find the missing one.

  1. Look at the left side. The two numbers are the same as on the right, in the other order.
    8 × 5 = 40
  2. Swap the two numbers. Multiplication can be done in either order, and the answer is the same.
    5 × 8 = 40
  3. 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.

Worked example 3.4.3
What is 7 × 8?

Method. Count in 8s to find 7 groups of 8. The order of the numbers does not matter.

  1. Count in 8s, 7 times. Each count adds one more group of 8.
    8, 16, 24, 32, 40, 48, 56
  2. The last number we said is the answer. We counted 7 groups of 8.
    8 × 7 = 56
  3. 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-calculator
1
R11 × 3 = 3 × ___. What is the missing number?
2
F___ × 11 = 132. What is the missing number?
3
FWhat is 7 × 12?
4
FWhat is 7 × 1?
5
F___ × 8 = 40. What is the missing number?
6
R7 × 8 = 8 × ___. What is the missing number?
7
R8 × 8 = 8 × ___. What is the missing number?
8
FWhat is 11 × 12?
9
F___ × 9 = 9. What is the missing number?
10
FWhat is 7 × 6?
11
FWhat is 6 × 11?
12
FWhat is 12 × 1?
13
F___ × 7 = 49. What is the missing number?
14
F___ × 11 = 22. What is the missing number?
15
FWhat is 9 × 7?
16
FWhat is 7 × 2?
3.5

Equal groups and division with the tables

Level 5
Use the tables to solve one-step problems with equal groups, Find a missing number in a division with the tables
Video lesson: Equal groups and division with the tablesComing soon

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.
Worked example 3.5.1
72 ÷ 9 = ___

Method. Use the multiplication fact to find the division.

  1. Think of the multiplication: 9 × ___ = 72. Division asks how many groups of the number make the total.
    9 × ___ = 72
  2. Count in 9s until you reach 72. Count the steps as you go.
    9, 18, 27, 36, 45, 54, 63, 72
  3. 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.

Worked example 3.5.2
A shop has 54 cups. They are packed into boxes of 6. How many boxes are there?

Method. Division with equal groups: the number of boxes is the total divided by the box size.

  1. 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
  2. Think: how many groups of the box size make the total? This is a division, which we can check with the table.
    6 × ___ = 54
  3. Count the boxes. Count in the box size until you reach the total.
    6, 12, 18, 24, 30, 36, 42, 48, 54
  4. 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.

Worked example 3.5.3
There are 6 bags. Each bag has 8 sweets. How many sweets are there altogether?

Method. Multiply the number of groups by the number in each group.

  1. 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
  2. Work out the multiplication. Use the times table for this number.
    6 × 8 = 48
  3. 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-calculator
1
PSA shop has 110 muffins. They are packed into boxes of 11. How many boxes are there?
2
PSThere are 5 bags. Each bag has 12 sweets. How many sweets are there altogether?
3
PSThere are 2 bags. Each bag has 8 sweets. How many sweets are there altogether?
4
PSA shop has 36 cups. They are packed into boxes of 9. How many boxes are there?
5
PSA shop has 121 pencils. They are packed into boxes of 11. How many boxes are there?
6
PSThere are 9 bags. Each bag has 12 sweets. How many sweets are there altogether?
7
F99 ÷ 11 = ___
8
PSThere are 8 bags. Each bag has 6 sweets. How many sweets are there altogether?
9
PSA shop has 18 stickers. They are packed into boxes of 9. How many boxes are there?
10
PSThere are 3 bags. Each bag has 11 sweets. How many sweets are there altogether?
11
PSA shop has 132 stickers. They are packed into boxes of 11. How many boxes are there?
12
F81 ÷ 9 = ___
13
PSA shop has 48 pencils. They are packed into boxes of 8. How many boxes are there?
14
PSThere are 3 bags. Each bag has 6 sweets. How many sweets are there altogether?
15
PSA shop has 90 muffins. They are packed into boxes of 9. How many boxes are there?
16
F84 ÷ 7 = ___

Chapter summary

SkillMethod
The 7 times tableCount in sevens; double a fact to extend it
The 11 times tableFor 1 to 9 write the digit twice; for 10 to 12 use 10 times plus the number
The 12 times tableSplit 12 into 10 and 2; multiply each part; add
6, 8 and 9 factsRecall in any order; the commutative law swaps the factors
Equal groupsGroups × 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-calculator
1
A shop has 63 cups. They are packed into boxes of 7. How many boxes are there?
2
___ × 6 = 60. What is the missing number?
3
What is 11 × 8?
4
24 ÷ 6 = ___
5
___ × 7 = 84. What is the missing number?
6
There are 6 bags. Each bag has 8 sweets. How many sweets are there altogether?
7
___ × 7 = 42. What is the missing number?
8
What is 7 × 12?
9
What is 11 × 7?
10
What is 7 × 7?

Total 19 marks. Allow about 19 minutes.

Exercise 3X  Practice test questions

Non-calculator
1
F___ × 12 = 84. What is the missing number?[1 mark]
2
F___ × 7 = 56. What is the missing number?[1 mark]
3
FWhat is 9 × 9?[1 mark]
4
F108 ÷ 12 = ___[1 mark]
5
FWhat is 12 × 6?[2 marks]
6
F___ × 7 = 77. What is the missing number?[2 marks]
7
FWhat is 11 × 5?[2 marks]
8
FUse 10 and 2 to work out 12 × 6.[3 marks]
9
FWhat is 11 × 9?[3 marks]
10
F___ × 12 = 48. What is the missing number?[3 marks]

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