New
New
Year 5

# Explain that different lengths can be composed additively and multiplicatively

I can explain that different lengths can be represented as addition and multiplication.

New
New
Year 5

# Explain that different lengths can be composed additively and multiplicatively

I can explain that different lengths can be represented as addition and multiplication.

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## Slide deck

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## Lesson details

### Key learning points

1. Partitioning 100 in different ways can be used to compose lengths.
2. There are four 25s in 100 so there are four 25cm lengths in 1m.
3. 1m divided into four equal parts is 25cm or 0.25m.
4. 1m divided into five equal parts is 20cm or 0.2m.

### Common misconception

Pupils think that when a whole is divided into x parts, they need to have x interval markers.

Encourage pupils to make connections between the bar model and the number line, drawing attention to where each whole has been divided.

### Keywords

• Common - Something is common when it is frequently used or it occurs regularly.

• Compose - Larger numbers can be composed of smaller numbers.

• Partition - The act of splitting an object or value down into smaller parts.

Be sure to give time to pupils linking the numbers within an equation to the corresponding image that it represents. Asking 'what does each number represent?' can be a helpful way to assess understanding of how the image and equation connect.
Teacher tip

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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## Worksheet

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## Starter quiz

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### 6 Questions

Q1.
Convert 2.5 metres into centimetres. cm
Correct Answer: 250, 250 cm
Q2.
Match the descriptions.
Correct Answer:100 divided into 2 equal parts,each part has a value of 50

each part has a value of 50

Correct Answer:100 divided into 4 equal parts,each part has a value of 25

each part has a value of 25

Correct Answer:100 divided into 5 equal parts,each part has a value of 20.

each part has a value of 20.

Q3.
What is the missing number on the number line?
Correct Answer: 75
Q4.
Complete: 0.1 is __________ of 10
one tenth the size
Correct answer: one hundredth the size
one hundred times the size
ten times the size
Q5.
Which equations represent this bar model?
Correct answer: 20 × 5 = 100
Correct answer: 100 ÷ 20 = 5
20 + 20 + 20 + 20 = 100
Correct answer: 2 × 20 + 3 × 20 = 100
Q6.
What is the missing number in this equation? 25 × = 175
Correct Answer: 7, seven

## Exit quiz

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### 6 Questions

Q1.
Match the descriptions.
Correct Answer:1 m divided into 2 equal parts,each part has a value of 0.5 m.

each part has a value of 0.5 m.

Correct Answer:1 m divided into 4 equal parts,each part has a value of 0.25 m.

each part has a value of 0.25 m.

Correct Answer:1 m divided into 5 equal parts,each part has a value of 0.2 m.

each part has a value of 0.2 m.

Q2.
Look at the number line. Which letter is pointing to 75 cm?
a
b
Correct answer: c
d
Q3.
In metres, what is the value of each of the partitioned parts? m
Correct Answer: 0.5, 0.50, half
Q4.
Tick the equations that could represent this number line.
Correct answer: 0.25 m × 4 = 1 m
1 m ÷ 4 = 25 m
0.25 m + 0.25 m + 0.25 m = 1 m
Correct answer: 1 m = 0.25 m + 0.25 m + 0.25 m + 0.25 m
Q5.
Tick the image that represents the equation: 0.2 m × 5 = 1 m
Correct Answer: An image in a quiz
Q6.
1.4 m is composed of:
Correct answer: 5 lots of 0.2 m add 2 lots of 0.2 m
Correct answer: 7 lots of 0.2 m
Correct answer: 10 lots of 0.2 m minus 3 lots of 0.2 m
4 lots of 0.2 m plus 4 lots of 0.2 m