Reach for the Star

Direct and inverse proportion · Optional extension

L065 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

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

Reveal a worked check after attempting

y=k/x², k=48; y=3.

Deep challenge

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

Reveal a worked check after attempting

Direct proportion y=kx is a straight line through the origin; a curved graph does not fit.

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.