Reach for the Star

Functions pathway · Optional extension

L085 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

If f(x)=x²+2x, find f(−3) and solve f(x)=0.

Reveal a worked check after attempting

f(−3)=9−6=3; x(x+2)=0 gives x=0 or −2.

Deep challenge

Let f(x)=2x+1 and g(x)=x². Compare f(g(3)) and g(f(3)).

Reveal a worked check after attempting

f(9)=19; g(7)=49; composition order matters.

Recall & Review: feedback and extension integration

Lesson L085: Functions pathway

Objective: Interpret functions 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 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: If f(x)=x²+2x, find f(−3) and solve f(x)=0.

Deep challenge: Let f(x)=2x+1 and g(x)=x². Compare f(g(3)) and g(f(3)).