Math lesson plan · 10th grade (Year 11 in England) · 60 minutes
Find exact distances between points and test for right angles
Geometry
CCSS HSG.GPE.B.4CCSS HSG.GPE.B.7England: GCSE Higher Geometry
Objective and success criteria
Students will: Find exact distances between points and test for right angles.
- 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: Distance and midpoint between points; Simplify surds (radicals)
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 · 6 min
- Quick retrieval from earlier learning (Distance and midpoint between points; Simplify surds (radicals)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify √112. It can be written as k√7. What is k? → 4Prompt: Look for the largest square number that divides it.
- Find the midpoint of (2, −6) and (2, −2). Type it like (2, −1). → (2, −4)Prompt: The midpoint is the average of the coordinates.
- Simplify √80. It can be written as k√5. What is k? → 4Prompt: Look for the largest square number that divides it.
Hook · 6 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: Find exact distances between points and test for right angles. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Find the exact distance between (5, 3) and (6, −4). Simplify the surd.
- Step 1: d = √(1² + 7²) = √50
- Step 2: = 5√2
- Answer: 5√2
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 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 exact distance between (0, 2) and (5, 8). Simplify the surd. → √61Prompt: d = √((x₂ − x₁)² + (y₂ − y₁)²).
- Is the triangle with vertices A(3, 4), B(2, 7) and C(0, 2) right-angled? (Yes / No) → NoPrompt: Work out the squared length of each side (no need to square-root).
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Find the exact distance between (3, 5) and (−2, −1). Simplify the surd. → √61Prompt: d = √((x₂ − x₁)² + (y₂ − y₁)²).
- Is the triangle with vertices A(−1, −4), B(0, −1) and C(−7, −2) right-angled? (Yes / No) → YesPrompt: Work out the squared length of each side (no need to square-root).
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: Distance and midpoint between points.
- 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