Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Use the magnitude of a vector in context
Geometry
CCSS HSN.VM.A.1CCSS HSN.VM.A.3England: GCSE Higher Geometry
Objective and success criteria
Students will: Use the magnitude of a vector in context.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Vectors
Leads to: the next skill in this area.
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Vectors). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- a = (5, 4) and b = (1, −4). Find 3a − 2b. Type it like (2, −1). → (13, 20)Prompt: Multiply each component by the scalar.
- Find the magnitude of the vector (−8, 15). → 17Prompt: Magnitude = √(x² + y²).
- a = (−5, 0) and b = (−1, 6). Find a − b. Type it like (2, −1). → (−4, −6)Prompt: Multiply each component by the scalar.
Hook · 5 min
- Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
- Share the objective: Use the magnitude of a vector in context. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Find the magnitude of (7, 6) to 1 decimal place.
- Step 1: √(49 + 36) = √85
- Step 2: ≈ 9.2
- Answer: 9.2
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Find the magnitude of (−6, 8) to 1 decimal place. → 10Prompt: |v| = √(x² + y²).
- A drone's velocity is (16, −30) metres per second (east, north). What is its speed in m/s? → 34Prompt: Speed is the magnitude of the velocity vector.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- The vector (k, 8) has magnitude 10, and k is positive. Find k. → 6Prompt: k² + (second component)² = magnitude².
- A drone's velocity is (14, −48) metres per second (east, north). What is its speed in m/s? → 50Prompt: Speed is the magnitude of the velocity vector.
Watch out for
- Thinking a square turned on its corner is no longer a square.
- Reading the wrong scale on a protractor.
Support and stretch
Support
- Review first: Vectors.
- Use concrete materials: rulers and protractors.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-10.
Free lesson plan from eurekami.com/lesson-plan-builder