Solve problems involving comparison and change
I can solve problems involving comparison and change deciding when to use multiplication or division.
Solve problems involving comparison and change
I can solve problems involving comparison and change deciding when to use multiplication or division.
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Lesson details
Key learning points
- A change in length can be described using multiplication or division.
- Comparison and change problems can be represented visually to support understanding.
- To find ___ times a length, we know we will be multiplying the length by ___.
- To find a unit fraction times a length, divide the length into the number of equal parts represented by the denominator.
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.
Unit fraction - A unit fraction is a fraction where the numerator is one.
Common misconception
Children may say 'ten times shorter' which is imprecise. Children are more familiar with multiplication resulting in an increase, and need to appreciate that it can also result in a decrease.
We say, 'ten times the original height' because this is more precise especially when the scale factor is fractional. When we multiply by a unit fraction, it is the same as dividing the whole by the denominator. This results in a decrease in length.
To help you plan your year 5 maths lesson on: Solve problems involving comparison and change, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 5 maths lesson on: Solve problems involving comparison and change, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 2 maths lessons from the Compare and describe measurements using knowledge of multiplication and division unit, dive into the full primary maths curriculum, or learn more about lesson planning.
Licence
Prior knowledge starter quiz
6 Questions
Q1.A pencil was 20 cm long. It is now one quarter of its original length. Which expression represents its new length?
Q2.Which sentence matches this bar model?

Q3.Compare the heights of the tree and the car. The tree is times the height of the car.

Q4.A pencil was 20 cm long. It is now $${1}\over{4}$$ of its original length. How long is the pencil now?
Q5.The white bar is 360 cm long. How long is the blue bar? The blue bar is cm long.

Q6.Match the possible heights of the tree to the heights of the car. The car is one fifth times the height of the tree.

The tree is 50 m tall -
The car is 10 m tall
The tree is 5 m tall -
The car is 1 m tall
The tree is 500 cm -
The car is 100 cm tall
The tree is 50 cm tall -
The car is 10 cm tall
Assessment exit quiz
6 Questions
Q1.Jacob runs 300 m in 1 minute. Izzy walks one third times the distance. How far does Izzy walk?
Q2.Jacob runs 300 m in 1 minute. Izzy walks one third times the distance. How much further does Jacob run than Izzy walks?
Q3.True or false? 160 x $${1}\over{4}$$ = 160 ÷ 4
Q4.Which two equations can you write from this bar model to calculate the length of the blue bar?

Q5.The bus ride to school is 7 km. The bus broke down one half times the distance from school. The bus still had km left to travel.
Q6.Match a multiplication expression to a division equivalent.
400 m x $${1}\over{4}$$ -
0.4 km ÷ 4
4 km x $${1}\over{4}$$ -
4,000 m ÷ 4
400 cm x $${1}\over{4}$$ -
4 m ÷ 4
4 m x $${1}\over{4}$$ -
400 cm ÷ 4