Reach for the Star | GCSE Mathematics

L083: Vector reasoning pathway

Objective

Reason with vectors at the appropriate tier.

Calculator: Non-calculator core; calculator optional only for checking where labelled.

Visual model for Vector reasoning pathway
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for vector reasoning pathway.

Core practice

If a=(4,−1) and b=(−2,5), find 3a+2b.

Reasoning

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

Exam-style

Solve an exam-style problem involving vector reasoning pathway. Show working, include a check and interpret your answer.

WWW / EBI

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).