Year 4

Autumn Transition Therapy

Can multiply two-digit by one-digit numbers using partitioning and known facts

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Vocabulary activity

Introduction

Being able to answer this question needs the skill of multiplying a 2-digit number by a 1-digit number. In this therapy, we will focus on how to use partitioning

and known facts to multiply numbers.

Jermain donated £26 to charity. If Kyle donated four times as much, how much did Kyle donate?

Revisiting partitioning

Partitioning is a strategy that splits (partitions) numbers into smaller amounts. For example, the number 46 can be

partitioned into:4 tens and 6 ones

40 + 6

Revisiting partitioning

Diagrams can also show partitioning.

6

0446

40

6

46

Your turn

Choose two numbers to partition using a method of your choice.

57

124

7992

326

Revisiting known facts

To be successful, it is important that you can recall key number facts and use these to find other facts.

If we know

3 x 8 = 24,

what else do we know?

Talk to your partnerWhat other

number facts could you derive (find) from this

statement?

Revisiting known facts

3 x 8 = 24

8 x 3 = 24

30 x 8 = 240

24 ÷ 8 = 3

24 ÷ 3 = 8

80 x 3 = 240

of 24 = 8

How many did you find?

Using partitioning and known facts

Let’s use partitioning and known facts to find the product

of 24 and 5.

How could we partition 24?

20 x 5Using known facts helps here.

If we know 2 x 5 = 10,then we know

20 x 5 = 100

24 x 5

24 = 20 + 4

Step one

4 x 5 = 20Step two

Step three

Add them together

100 + 20 = 120

So, 24 x 5 = 120

42 x 442 = 40 + 2

Tens Ones Tens Ones10

10

10

1

1

To help us partitionthe 2-digit number,

we can use resources like base ten

apparatus and counters.

For example, we can partition 42 like this:

10

Using partitioning and known facts

Once you have partitioned the 2-digit number, multiply each

part by the 1-digit number.

42 x 4

40 x 4 = 1602 x 4 = 8If we know 4 x 4 = 16, then we

know 40 x 4 = 160 because 40 is ten times greater than 4. This means the product will also be ten times greater.

Using partitioning and known facts

Finally, add up both numbers to get the

product.40 x 4 = 160

2 x 4 = 8

160 + 8 = 168 42 x 4 = 168

Using partitioning and known facts

Choose 2 calculations then use the steps to find the product.

Your turn

Remember the steps:

1. Partition the number.2. Multiply each number by the 1-digit number, using known facts. 3. Add both numbers together to find the product.

34 x 4

46 x 523 x 8

84 x 2

27 x 3

This could be recorded more efficiently using a grid.

Tens Ones

Grid method

x 40 2

4 160 8

42 x 4

= 168

Use the grid method to solve one of these calculations.

Your turn

x 40 2

4 160 8

56 x 342 x 4

= 168126 x 2

46 x 428 x 5

Use the grid method to solve this problem.

Your turn

x 40 2

4 160 8

42 x 4

= 168

Each week, Luke saves £5. How much would he have

saved after a year?

Or we could use the expanded method.

Expanded method

42 x 4

40 + 2

x 4

2 x 4 8

40 x 4 1 6 0

total 1 6 8

Use the expanded method to solve one of these problems.

Your turn

42 x 4 42 x 5

355 x 3

24 x 865 x 3

40 + 2

x 4

2 x 4 8

40 x 4 1 6 0

total 1 6 8

Use the grid method to solve this problem.

Your turn

Laptops are packed in boxes of 8. How many laptops would there be altogether

in 25 boxes?

42 x 4

40 + 2

x 4

2 x 4 8

40 x 4 1 6 0

total 1 6 8

Let’s return to the problem from the beginning of the session.

x times as much/many

Jermain donated £26 to charity. If Kyle donated four times as much, how much did Kyle donate?

The key phrase in this question is ‘four times as much’. This phrase suggests that the problem involves multiplication. To understand

how to solve problems like this, a bar model can be helpful.

x times as much/many

Jermain donated £26 to charity. If Kyle donated four times as much, how much did Kyle donate?

From this we can see that Kyle donated 4 lots of 26 or 26 x 4. This can be solved using any of our methods.

x times as much/many

26 x 4

So, Kyle raised £104.

How much money did they raise altogether?

26 = 20 + 6

x 4

6 x 4 2 4

20 x 4 8 0

total 1 0 4

Your turn

Draw a bar model to represent this problem

then solve it using a method of your choice.

Recipe for oat biscuits

85g wholemeal flour85g of porridge oats

50g butter1 tablespoon of syrup2 tablespoons of milk

A chef is making oat biscuits. He wants to make 3 times as many as this recipe makes. How

many grams of porridge oats will be needed?

Remember

When multiplying 2-digit by 1-digit numbers, try to:

✓ partition numbers to make them easier to work with;✓ look for known multiplication facts that you can use to

help you to calculate;✓ identify key words or phrases, such as ‘times as

many/much’ to signpost a multiplication calculation;✓ draw a bar model to help you to ‘see’ the mathematics.