Reach for the Star

Cubic reciprocal and other graphs · Optional extension

L063 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

For y=12/x, find points when x=−3 and x=4, and identify the missing x-value.

Reveal a worked check after attempting

(−3,−4) and (4,3); x=0 excluded.

Deep challenge

Compare y=x³ and y=−x³ at x=−2 and x=2. What symmetry relates them?

Reveal a worked check after attempting

Values are (−8,8) and (8,−8); reflection in the x-axis maps one graph to the other.

Recall & Review: feedback and extension integration

Lesson L063: Cubic reciprocal and other graphs

Objective: Recognise graph families and estimate solutions graphically.

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 represented the algebraic structure accurately, kept each transformation valid and checked the result by substitution, graph or equivalent reasoning.

Even Better If (EBI)

I will show the missing inverse operation or algebraic step, keep signs and brackets accurate and test the result in the original relationship.

Stretch and deep challenge

Stretch: For y=12/x, find points when x=−3 and x=4, and identify the missing x-value.

Deep challenge: Compare y=x³ and y=−x³ at x=−2 and x=2. What symmetry relates them?