Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
Find the point that divides a segment in a given ratio
Geometry
CCSS HSG.GPE.B.6England: GCSE Higher Geometry
Objective and success criteria
Students will: Find the point that divides a segment in a given ratio.
- 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: Find a missing endpoint from a midpoint
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 · 4 min
- Quick retrieval from earlier learning (Find a missing endpoint from a midpoint). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- The midpoint of P(−2, 7) and Q(a, b) is (2, 5). Find a. → 6Prompt: Midpoint coordinate = (first + second) ÷ 2.
- The midpoint of P(−4, 6) and Q(a, b) is (−2, −1). Find b. → -8Prompt: Midpoint coordinate = (first + second) ÷ 2.
- The midpoint of P(−7, 5) and Q(a, b) is (0, 2). Find b. → -1Prompt: Midpoint coordinate = (first + second) ÷ 2.
Hook · 3 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 the point that divides a segment in a given ratio. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: P divides AB so that AP : PB = 2 : 1. A is (−5, 1) and P is (1, 7). Find B. Type it like (2, −1).
- Step 1: one part = (3, 3)
- Step 2: (4, 10)
- Answer: (4, 10)
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- P divides AB so that AP : PB = 3 : 2. A is (2, −5) and P is (−7, 1). Find B. Type it like (2, −1). → (−13, 5)Prompt: AP is 3 parts; the whole of AB is 5 parts.
- P divides AB so that AP : PB = 3 : 2. A is (−2, −4) and P is (−5, −1). Find B. Type it like (2, −1). → (−7, 1)Prompt: AP is 3 parts; the whole of AB is 5 parts.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- P divides AB so that AP : PB = 1 : 3. A is (−2, −5) and P is (−3, −4). Find B. Type it like (2, −1). → (−6, −1)Prompt: AP is 1 part; the whole of AB is 4 parts.
- P divides AB so that AP : PB = 3 : 2. A is (0, 4) and P is (6, −5). Find B. Type it like (2, −1). → (10, −11)Prompt: AP is 3 parts; the whole of AB is 5 parts.
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: Find a missing endpoint from a midpoint.
- 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