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Math lesson plan · 10th grade (Year 11 in England) · 60 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 · 6 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.
  1. The midpoint of P(−5, −7) and Q(a, b) is (−3, −1). Find b. → 5Prompt: Midpoint coordinate = (first + second) ÷ 2.
  2. The midpoint of P(−7, 1) and Q(a, b) is (1, 5). Find a. → 9Prompt: Midpoint coordinate = (first + second) ÷ 2.
  3. The midpoint of P(−9, 5) and Q(a, b) is (−1, 4). Find a. → 7Prompt: Midpoint coordinate = (first + second) ÷ 2.

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 the point that divides a segment in a given ratio. 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: 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 · 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.
  1. P divides AB so that AP : PB = 3 : 2. A is (1, −1) and P is (10, 8). Find B. Type it like (2, −1). → (16, 14)Prompt: AP is 3 parts; the whole of AB is 5 parts.
  2. P divides AB so that AP : PB = 1 : 2. A is (−2, 3) and P is (−5, 2). Find B. Type it like (2, −1). → (−11, 0)Prompt: AP is 1 part; the whole of AB is 3 parts.

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.
  1. P divides AB so that AP : PB = 3 : 2. A is (−3, 3) and P is (−12, 0). Find B. Type it like (2, −1). → (−18, −2)Prompt: AP is 3 parts; the whole of AB is 5 parts.
  2. P divides AB so that AP : PB = 1 : 3. A is (0, 1) and P is (−2, 3). Find B. Type it like (2, −1). → (−8, 9)Prompt: AP is 1 part; the whole of AB is 4 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

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Find the point that divides a segment in a given ratio

Name

Date

Score/ 8

  1. Question 1

    P lies on AB with AP : PB = 2 : 3. A is (−1, 1) and B is (14, 6). Find P. Type it like (2, −1).

    xy−20−16−12−8−448121620−20−16−12−8−4481216200AB

    Answer

  2. Question 2

    P divides AB so that AP : PB = 3 : 2. A is (4, 3) and P is (−5, −3). Find B. Type it like (2, −1).

    Answer

  3. Question 3

    P lies on AB with AP : PB = 1 : 4. A is (−2, −5) and B is (13, 10). Find P. Type it like (2, −1).

    xy−20−16−12−8−448121620−20−16−12−8−4481216200AB

    Answer

  4. Question 4

    P divides AB so that AP : PB = 3 : 2. A is (5, −5) and P is (8, −14). Find B. Type it like (2, −1).

    Answer

  5. Question 5

    P lies on AB with AP : PB = 1 : 2. A is (−4, −6) and B is (2, −3). Find P. Type it like (2, −1).

    xy−20−16−12−8−448121620−20−16−12−8−4481216200AB

    Answer

  6. Question 6

    P divides AB so that AP : PB = 1 : 2. A is (4, 5) and P is (7, 2). Find B. Type it like (2, −1).

    Answer

  7. Question 7

    P lies on AB with AP : PB = 2 : 3. A is (−4, −1) and B is (1, 4). Find P. Type it like (2, −1).

    xy−20−16−12−8−448121620−20−16−12−8−4481216200AB

    Answer

  8. Question 8

    P divides AB so that AP : PB = 2 : 1. A is (−3, −2) and P is (−9, 4). Find B. Type it like (2, −1).

    Answer

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Answer key: Find the point that divides a segment in a given ratio

  1. 1. (5, 3)

  2. 2. (−11, −7)

  3. 3. (1, −2)

  4. 4. (10, −20)

  5. 5. (−2, −5)

  6. 6. (13, −4)

  7. 7. (−2, 1)

  8. 8. (−12, 7)