Reach for the Star | GCSE Mathematics

L065: Direct and inverse proportion

Objective

Solve direct and inverse proportion problems and represent relationships.

Calculator: Non-calculator core; calculator optional only for checking where labelled.

Visual model for Direct and inverse proportion
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for direct and inverse proportion.

Core practice

y is inversely proportional to x². If y=12 at x=2, find y at x=4.

Reasoning

A graph through the origin appears curved upward. Can y be directly proportional to x? Explain.

Exam-style

Solve an exam-style problem involving direct and inverse proportion. Show working, include a check and interpret your answer.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L065: Direct and inverse proportion

Objective: Solve direct and inverse proportion problems and represent relationships.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I identified the correct reference quantity, ratio, rate or multiplier and kept the units and proportional relationship clear.

Even Better If (EBI)

I will state the whole or reference quantity, show the multiplier or unit-rate step and check whether the result is sensible in context.

Stretch and deep challenge

Stretch: y is inversely proportional to x². If y=12 at x=2, find y at x=4.

Deep challenge: A graph through the origin appears curved upward. Can y be directly proportional to x? Explain.