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Use knowledge of multiplication and division to solve comparison and change problems

I can use knowledge of multiplication and division to solve comparison and change problems.

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Lesson 9 of 10

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Year 5

Use knowledge of multiplication and division to solve comparison and change problems

I can use knowledge of multiplication and division to solve comparison and change problems.

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Lesson details

Key learning points

Change can be described using multiplication or division. Division can be represented as multiplication by a fraction.
The sentence 'The __________ is ___ times the size of the __________' supports us to describe a comparison or change.
If units are different, we should convert so that they are the same - this supports us to calculate.
To find a missing factor, we can divide the product by the known factor.

Keywords

Comparison - When a comparison is made, we are determining how different two objects are. In this case, how many times longer, taller or deeper an object is than another.
Change - A comparison can also be made between an object before, and then after, a change. Examples of a change include a change in height of a flower due to growth.

Common misconception

Manipulating equations can result in errors.

To find a missing factor, we can use known facts where applicable, or we can divide the product by the known factor. Always encourage children to describe each part of the equation and what it represents.

It is important that children are fluent with their times table facts so they can focus on the scaling structure without overload. Always offer practical examples where possible.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
One fifth times the value of £450 is

Correct Answer: £90, 90, 90 pounds, £90.00

Q2.
A tree is six times the height it was when it was planted. It was 1 m 20 cm when it was planted. How tall is it now in metres and centimetres?

6 m 60 cm

Correct answer: 6 m 120 cm

Correct answer: 7 m and 20 cm

1 m 26 cm

Q3.
Sam has saved £10.50 Jacob has one tenth times the money that Sam has. How much money does Jacob have?

£1.00

£1.50

Correct answer: £1.05

15 p

Q4.
Dividing 770 ml by 7 is the same as mulitplying by which fraction?

$${1}\over{6}$$

Correct answer: $${1}\over{7}$$

$${1}\over{5}$$

$${7}\over{1}$$

Q5.
Alex can run 100 m in 30 seconds. A cheetah can run this far in one fifth of the time it takes Alex. The cheetah takes seconds to run 100 m.

20 m

Correct answer: 6 seconds

20 seconds

5 seconds

Q6.
The dolls house door is $${1}\over{10}$$ the height of a real door. The height of a real door is 2 m. What is the height of the dolls house door in cm?

0.2 m

Correct answer: 20 cm

2 cm

200 cm

Assessment exit quiz

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6 Questions

Q1.
Jacob has a netball that has a mass of 500 g and a tennis ball that is one quarter of the mass of the netball. Does this bar model represent this?

Yes

Correct answer: No

Q2.
Jacob has a netball that has a mass of 500 g and a tennis ball that is one quarter of the mass of the netball. The mass of the tennis ball is g

Correct Answer: 125, 125g, one hundred and twenty-five

Q3.
The jug contains a 1 l 500 ml volume of water. This is 3 times the 500 ml volume of water in the glass. Which equations represent this?

1 l 500 ml × 3 = 500 ml

500 ml × $${1}\over{3}$$ = 1 l 500 ml

Correct answer: 500 ml × 3 = 1 l 500 ml

Correct answer: 1 l 500 ml × $${1}\over{3}$$ = 500 ml

Q4.
A flight to America takes 12 hours. A flight to Spain takes 3 hours. How many times as long is a flight to America than a flight to Spain?

$${1}\over{4}$$ times as long

3 times as long

Correct answer: 4 times as long

$${1}\over{3}$$ times as long

Q5.
Lucas is saving to buy a new games console. He needs £240. He currently has £30. He needs times his current amount to buy the new console.

Correct Answer: 8, eight

Q6.
Lucas is saving to buy a new games console. He needs £240. He currently has £30. How much more money does he need to save? Does this bar model represent this problem?

Correct answer: Yes

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UnitMaths / Compare and describe measurements using knowledge of multiplication and division

Maths

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Use knowledge of multiplication and division to solve comparison and change problems

Use knowledge of multiplication and division to solve comparison and change problems

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.One fifth times the value of £450 is

Q2.A tree is six times the height it was when it was planted. It was 1 m 20 cm when it was planted. How tall is it now in metres and centimetres?

Q3.Sam has saved £10.50 Jacob has one tenth times the money that Sam has. How much money does Jacob have?

Q4.Dividing 770 ml by 7 is the same as mulitplying by which fraction?

Q5.Alex can run 100 m in 30 seconds. A cheetah can run this far in one fifth of the time it takes Alex. The cheetah takes seconds to run 100 m.

Q6.The dolls house door is $${1}\over{10}$$ the height of a real door. The height of a real door is 2 m. What is the height of the dolls house door in cm?

Assessment exit quiz

6 Questions

Q1.Jacob has a netball that has a mass of 500 g and a tennis ball that is one quarter of the mass of the netball. Does this bar model represent this?

Q2.Jacob has a netball that has a mass of 500 g and a tennis ball that is one quarter of the mass of the netball. The mass of the tennis ball is g

Q3.The jug contains a 1 l 500 ml volume of water. This is 3 times the 500 ml volume of water in the glass. Which equations represent this?

Q4.A flight to America takes 12 hours. A flight to Spain takes 3 hours. How many times as long is a flight to America than a flight to Spain?

Q5.Lucas is saving to buy a new games console. He needs £240. He currently has £30. He needs times his current amount to buy the new console.

Q6.Lucas is saving to buy a new games console. He needs £240. He currently has £30. How much more money does he need to save? Does this bar model represent this problem?

Lesson appears in

UnitMaths / Compare and describe measurements using knowledge of multiplication and division

Maths

Q1.
One fifth times the value of £450 is

Q2.
A tree is six times the height it was when it was planted. It was 1 m 20 cm when it was planted. How tall is it now in metres and centimetres?

Q3.
Sam has saved £10.50 Jacob has one tenth times the money that Sam has. How much money does Jacob have?

Q4.
Dividing 770 ml by 7 is the same as mulitplying by which fraction?

Q5.
Alex can run 100 m in 30 seconds. A cheetah can run this far in one fifth of the time it takes Alex. The cheetah takes seconds to run 100 m.

Q6.
The dolls house door is $${1}\over{10}$$ the height of a real door. The height of a real door is 2 m. What is the height of the dolls house door in cm?

Q1.
Jacob has a netball that has a mass of 500 g and a tennis ball that is one quarter of the mass of the netball. Does this bar model represent this?

Q2.
Jacob has a netball that has a mass of 500 g and a tennis ball that is one quarter of the mass of the netball. The mass of the tennis ball is g

Q3.
The jug contains a 1 l 500 ml volume of water. This is 3 times the 500 ml volume of water in the glass. Which equations represent this?

Q4.
A flight to America takes 12 hours. A flight to Spain takes 3 hours. How many times as long is a flight to America than a flight to Spain?

Q5.
Lucas is saving to buy a new games console. He needs £240. He currently has £30. He needs times his current amount to buy the new console.

Q6.
Lucas is saving to buy a new games console. He needs £240. He currently has £30. How much more money does he need to save? Does this bar model represent this problem?