Reach for the Star

Vector reasoning pathway · Optional extension

L083 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

If a=(4,−1) and b=(−2,5), find 3a+2b.

Reveal a worked check after attempting

(12,−3)+(−4,10)=(8,7).

Deep challenge

Prove vector AB+BC=AC for A=(1,1),B=(4,3),C=(7,−2).

Reveal a worked check after attempting

AB=(3,2),BC=(3,−5); sum=(6,−3)=AC.

Recall & Review: feedback and extension integration

Lesson L083: Vector reasoning pathway

Objective: Reason with vectors 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: If a=(4,−1) and b=(−2,5), find 3a+2b.

Deep challenge: Prove vector AB+BC=AC for A=(1,1),B=(4,3),C=(7,−2).