Math lesson plan · 9th grade (Year 10 in England) · 60 minutes
Find a missing endpoint from a midpoint
Geometry
CCSS HSG.GPE.B.6England: GCSE Higher Geometry
Objective and success criteria
Students will: Find a missing endpoint from a midpoint.
- 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
Leads to: Find the point that divides a segment in a given ratio
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). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the midpoint of (0, 9) and (6, 5). Type it like (2, −1). → (3, 7)Prompt: The midpoint is the average of the coordinates.
- Find the midpoint of (2, 5) and (6, 11). Type it like (2, −1). → (4, 8)Prompt: The midpoint is the average of the coordinates.
- Find the midpoint of (6, −9) and (4, −13). Type it like (2, −1). → (5, −11)Prompt: The midpoint is the average of the coordinates.
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 a missing endpoint from a midpoint. 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: The midpoint of P(−9, 9) and Q(a, b) is (0, 4). Find b.
- Step 1: (9 + b)/2 = 4 → b = −1
- Answer: -1
- 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.
- The midpoint of P(−2, −5) and Q(a, b) is (0, −6). Find b. → -7Prompt: Midpoint coordinate = (first + second) ÷ 2.
- The midpoint of P(−1, 9) and Q(a, b) is (4, 7). Find b. → 5Prompt: Midpoint coordinate = (first + second) ÷ 2.
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.
- The midpoint of P(4, −4) and Q(a, b) is (0, −4). Find b. → -4Prompt: Midpoint coordinate = (first + second) ÷ 2.
- The midpoint of P(−4, 0) and Q(a, b) is (−1, 0). Find a. → 2Prompt: Midpoint coordinate = (first + second) ÷ 2.
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
- Move on to: Find the point that divides a segment in a given ratio.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder