Step-by-step Maths Level 5: The 6, 8 and 9 facts, and the commutative law

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.
   11 × 3 = 33
2. Swap the two numbers. Multiplication can be done in either order, and the answer is the same.
   3 × 11 = 33
3. 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.

1. 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
2. Count the groups. We said 12 numbers, so there are 12 groups.
   12 groups of 11
3. 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.

1. Count in 12s, 7 times. Each count adds one more group of 12.
   12, 24, 36, 48, 60, 72, 84
2. The last number we said is the answer. We counted 7 groups of 12.
   12 × 7 = 84
3. 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.

1. Count in 7s, 1 times. Each count adds one more group of 7.
   7
2. The last number we said is the answer. We counted 1 groups of 7.
   7 × 1 = 7
3. 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.

1. Think: how many groups of 8 make 40? Count in steps of the number we know.
   8, 16, 24, 32, 40
2. Count the groups. We said 5 numbers, so there are 5 groups.
   5 groups of 8
3. 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.

1. Look at the left side. The two numbers are the same as on the right, in the other order.
   7 × 8 = 56
2. Swap the two numbers. Multiplication can be done in either order, and the answer is the same.
   8 × 7 = 56
3. 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.

1. Look at the left side. The two numbers are the same as on the right, in the other order.
   8 × 8 = 64
2. Swap the two numbers. Multiplication can be done in either order, and the answer is the same.
   8 × 8 = 64
3. 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.

1. Count in 12s, 11 times. Each count adds one more group of 12.
   12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132
2. The last number we said is the answer. We counted 11 groups of 12.
   12 × 11 = 132
3. 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.

1. Think: how many groups of 9 make 9? Count in steps of the number we know.
   9
2. Count the groups. We said 1 numbers, so there are 1 groups.
   1 groups of 9
3. 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.

1. Count in 7s, 6 times. Each count adds one more group of 7.
   7, 14, 21, 28, 35, 42
2. The last number we said is the answer. We counted 6 groups of 7.
   7 × 6 = 42
3. 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.

1. Count in 6s, 11 times. Each count adds one more group of 6.
   6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66
2. The last number we said is the answer. We counted 11 groups of 6.
   6 × 11 = 66
3. 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.

1. Count in 12s, 1 times. Each count adds one more group of 12.
   12
2. The last number we said is the answer. We counted 1 groups of 12.
   12 × 1 = 12
3. 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.

1. Think: how many groups of 7 make 49? Count in steps of the number we know.
   7, 14, 21, 28, 35, 42, 49
2. Count the groups. We said 7 numbers, so there are 7 groups.
   7 groups of 7
3. 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.

1. Think: how many groups of 11 make 22? Count in steps of the number we know.
   11, 22
2. Count the groups. We said 2 numbers, so there are 2 groups.
   2 groups of 11
3. 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.

1. Count in 9s, 7 times. Each count adds one more group of 9.
   9, 18, 27, 36, 45, 54, 63
2. The last number we said is the answer. We counted 7 groups of 9.
   9 × 7 = 63
3. 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.

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