Reach for the Star

Circle equations pathway · Optional extension

L090 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

A circle has equation x²+y²=49. Find y-values when x=0 and when x=5.

Reveal a worked check after attempting

x=0 gives y=±7; x=5 gives y=±√24=±2√6.

Deep challenge

Can (7,7) lie on the circle x²+y²=49? Justify by substitution.

Reveal a worked check after attempting

No, 7²+7²=98, not 49.

Recall & Review: feedback and extension integration

Lesson L090: Circle equations pathway

Objective: Connect circle and coordinate geometry at the appropriate tier.

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 selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.

Even Better If (EBI)

I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.

Stretch and deep challenge

Stretch: A circle has equation x²+y²=49. Find y-values when x=0 and when x=5.

Deep challenge: Can (7,7) lie on the circle x²+y²=49? Justify by substitution.