Explain which is the most efficient factor to partition to solve a multiplication problem | Maths

Starter quiz

What is the missing number in the equation below? 8 × ______ = 24

'3' ✓
What is the missing number in the equation below? 7 × ______ = 56

'8' ✓
What is the missing number in the equation below? ______ × 12 = 72

'6' ✓
Tick the two equations that show that multiplication is commutative.

9 × 11 = 99 ✓

999 = 99 × 11

99 = 9 × 11 ✓
There are 500 potatoes shared amongst 24 crates. Match the objects with group size or number of groups.

24 crates

⇔

number of groups of potatoes ✓

500 potatoes

⇔

group size ✓
Tick all the equations, showing the distributive law, that are represented by this stacked number line.

5 × 6 + 1 × 6 = 6 × 6 ✓

6 × 6 = 24 + 12

6 × 6 − 1 × 6 = 5 × 6 ✓

Exit quiz

Which of these equations represents this image?

3 × 4 + 3 × 4 = 24 ✓

2 × 12 + 2 × 12 = 24
Which of these equations represents this image?

1 × 4 + 5 × 4 = 24

1 × 6 + 3 × 6 = 24 ✓
Which number would fill all the gaps in this equation? (It is the same number for each gap.) ______ × 6 + 4 × 6 = 7 × ___ + 7 × ___ = 42

'3' ✓
Tick the expressions that have a value of 45

2 × 9 + 3 × 9 ✓

5 × 3 + 5 × 6 ✓

5 × 9 + 2 × 9
Tick the expressions that have a value of 54

4 × 6 + 5 × 6 ✓

5 × 6 + 2 × 6

10 × 6 − 1 × 6 ✓
There are 6 squads of 16 players in a rounders competition. How many players are there in total? Use the distributive rule to calculate your answer.

'96' ✓

Worksheet

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Lesson Details

Key learning points

Multiplying a number by a group of numbers added together is the same as doing each multiplication separately.
This means a factor can be partitioned to solve multiplication problems more efficiently.
It is important to consider which factor to partition so that it enables you to solve a problem more efficiently.
The factor being partitioned can represent the group size or the number of groups.

Common misconception

Children may inaccurately describe which factor has been partitioned to solve a multiplication problem.

Present children with lots of opportunities to create arrays, split them using a partitioning line and describe what they see before going on to use this to calculate.

Keywords

Multiples - A multiple is the product of a number and an integer.
Partition - Partitioning is the act of splitting an object or value down into smaller parts.
Distributive law - The distributive law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.