The resource journal · Free sample

The pattern behind the formula

Before you memorise a rule, look for the relationship it describes.

GCSE · Foundational thinking5–10 minute exploration

01 / Start with a question.

A bicycle hire company charges a fixed £5 fee plus £3 per hour. A two-hour ride costs £11. What does a five-hour ride cost?

02 / Explain the why.

The fixed fee happens once. The hourly cost changes with the length of the ride. The relationship is C = 5 + 3h. Can you explain why doubling the ride time doesn’t double the total cost?

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03 / Keep asking.

What assumption did you make? How could you test it? Can you describe your reasoning to someone who has never seen this question?

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