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Math lesson plan · 10th grade (Year 11 in England) · 60 minutes

Write the vector between two points

Geometry

CCSS HSN.VM.A.2England: GCSE Higher Geometry

Objective and success criteria

Students will: Write the vector between two 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: Vectors

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 (Vectors). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. a = (−2, −2) and b = (5, −3). Find a + b. Type it like (2, −1). → (3, −5)Prompt: Multiply each component by the scalar.
  2. Find the magnitude of the vector (5, −12). → 13Prompt: Magnitude = √(x² + y²).
  3. a = (3, −4) and b = (1, 6). Find 3a + 3b. Type it like (2, −1). → (12, 6)Prompt: Multiply each component by the scalar.

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: Write the vector between two 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: P is (5, −2) and the vector PQ is (−1, 5). Find the coordinates of Q. Type them like (2, −1).
  • Step 1: (4, 3)
  • Answer: (4, 3)
  • 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 is (−3, 5) and the vector PQ is (−1, −3). Find the coordinates of Q. Type them like (2, −1). → (−4, 2)Prompt: Start at P and move by the vector.
  2. P is (1, 5) and the vector PQ is (−2, 5). Find the coordinates of Q. Type them like (2, −1). → (−1, 10)Prompt: Start at P and move by the vector.

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 is (−5, 4) and the vector PQ is (−4, −2). Find the coordinates of Q. Type them like (2, −1). → (−9, 2)Prompt: Start at P and move by the vector.
  2. P is (1, −2) and the vector PQ is (4, 1). Find the coordinates of Q. Type them like (2, −1). → (5, −1)Prompt: Start at P and move by the vector.

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: Vectors.
  • 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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Write the vector between two points

Name

Date

Score/ 8

  1. Question 1

    P is (−2, 6) and the vector PQ is (3, −6). Find the coordinates of Q. Type them like (2, −1).

    Answer

  2. Question 2

    A is (−2, 3) and B is (0, −5). Write the vector AB as a column vector, typed like (2, −1).

    xy−8−6−4−22468−8−6−4−224680AB

    Answer

  3. Question 3

    P is (4, 6) and the vector PQ is (1, −2). Find the coordinates of Q. Type them like (2, −1).

    Answer

  4. Question 4

    A is (−7, 7) and B is (5, −7). Write the vector AB as a column vector, typed like (2, −1).

    xy−8−6−4−22468−8−6−4−224680AB

    Answer

  5. Question 5

    P is (2, 0) and the vector PQ is (−3, −5). Find the coordinates of Q. Type them like (2, −1).

    Answer

  6. Question 6

    A is (−3, −5) and B is (3, −5). Write the vector AB as a column vector, typed like (2, −1).

    xy−8−6−4−22468−8−6−4−224680AB

    Answer

  7. Question 7

    P is (0, −1) and the vector PQ is (−4, 6). Find the coordinates of Q. Type them like (2, −1).

    Answer

  8. Question 8

    A is (−1, −7) and B is (−7, 1). Write the vector AB as a column vector, typed like (2, −1).

    xy−8−6−4−22468−8−6−4−224680AB

    Answer

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Answer key: Write the vector between two points

  1. 1. (1, 0)

  2. 2. (2, −8)

  3. 3. (5, 4)

  4. 4. (12, −14)

  5. 5. (−1, −5)

  6. 6. (6, 0)

  7. 7. (−4, 5)

  8. 8. (−6, 8)