Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Distance and midpoint between points
Geometry
CCSS 8.G.B.8CCSS HSG.GPE.B.7England: GCSE Foundation GeometryEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Distance and midpoint between points.
- 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: Pythagoras' theorem; Coordinates in all four quadrants
Leads to: Equation of a circle; Find a missing endpoint from a midpoint; Find exact distances between points and test for right angles
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 (Pythagoras' theorem; Coordinates in all four quadrants). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
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: Distance and midpoint between points. 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 midpoint of (3, −5) and (3, −3). Type it like (2, −1).
- Step 1: x = (3 + 3) ÷ 2 = 3
- Step 2: y = (−5 + (−3)) ÷ 2 = −4
- Step 3: (3, −4)
- Answer: (3, −4)
- 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 midpoint of (2, 2) and (−8, −2). Type it like (2, −1). → (−3, 0)Prompt: The midpoint is the average of the coordinates.
- Find the midpoint of (4, 5) and (−2, −5). Type it like (2, −1). → (1, 0)Prompt: The midpoint is the average of the coordinates.
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 midpoint of (4, 7) and (0, 15). Type it like (2, −1). → (2, 11)Prompt: The midpoint is the average of the coordinates.
- Find the midpoint of (5, −6) and (15, 0). Type it like (2, −1). → (10, −3)Prompt: The midpoint is the average of the coordinates.
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: Pythagoras' theorem.
- 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: Equation of a circle; Find a missing endpoint from a midpoint; Find exact distances between points and test for right angles.
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder