Maths · KS3 and GCSE · Interactive lesson
Rearranging formulae step by step
Start with distance, speed and time. Use opposite operations to find an unknown quantity, then build towards rearranging formulae with letters.
Choose your view
Explore an interactive example, then try the questions at your own pace.
KS3 / GCSE · start with the idea
By the end of this lesson: Find an unknown by undoing multiplication or division.
The interactive diagram and controls are in Stage 2, “Explore one example”. Read the idea here, then try it next.
- Distance = speed × time.
- To find time, divide the distance by the speed.
- Imagine covering 20 metres each second. How many seconds would 120 metres take?
Useful starting points
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What do the words mean?
- Subject
- The quantity on its own on one side of a formula.
- Inverse operation
- An operation that undoes another: division undoes multiplication.
- Symbols
- d: distance; v: speed in this example; t: time. F: resultant force; m: mass; a: acceleration. V: voltage; I: current; R: resistance.
Change the example
This is the lesson example. Your practice question uses its own numbers.
Something to try
Keep the distance the same. Reduce the speed. Should the journey take more or less time?
Notice what changes
How particle motion works +
Starts paused. Press Play, then add energy to see the warmer particles move faster.
Particles keep the same size. Liquid particles move around; solid particles vibrate around fixed positions. This is a simplified model, with the change in motion exaggerated to make it easier to see.
About the playback +
About this model
Distance in metres; average speed in metres per second; time in seconds.
More about this diagram
Still picture. Play particle motion in Stage 2.
Time = 6 seconds
Still picture of the example from Stage 2. Use the back arrow to change it.
Work through it
Starting example: read the steps below
- We know the distance: 120 metres.
- The average speed is 20 m/s: 20 metres per second on average.
- Time = distance ÷ speed = 120 ÷ 20.
- Time = 6 seconds.
Try on your own
Your turn. No rush.
Question 1
A journey is 120 m. The average speed is 20 m/s. How many seconds does it take?
About these questions
Questions appear in a mixed order. Work at your own pace and stop whenever you like.
These questions use their own numbers, separate from the lesson example. You can stop whenever you like. Answers last for this visit to the page.
A good place to pause
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Can you name the quantity you want and choose an operation that leaves it on its own?
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Notes for parents and tutors
These lessons cover selected KS3 and GCSE ideas for England; they are not a complete course. The level notes explain where GCSE methods or optional extensions begin. Maurice can help you choose material for your course and exam board.
The content draws on the DfE Maths curriculum, DfE Science curriculum and AQA GCSE Physics specification. Level labels are guidance, not exam-board endorsements. For AQA Radioactivity, calculating net decline as a ratio is Higher-tier work. Net means the overall change; ask Maurice whether this extension is relevant to your course. Explanations and practice were reviewed during development on 21 October 2026; Maurice should check their fit before assigning work.
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