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Math lesson plan · 7th grade (Year 8 in England) · 60 minutes

Find the constant of proportionality from a graph

Ratio and proportion

CCSS 7.RP.A.2.BCCSS 7.RP.A.2.DEngland: KS3 Ratio, proportion and rates of change

Objective and success criteria

Students will: Find the constant of proportionality from a graph.

  • 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 the constant of proportionality from a table; Coordinates in the first quadrant

Leads to: Decide if a graph shows a proportional relationship

Materials: Bar models, Double number lines, Ratio tables, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 6 min

  • Quick retrieval from earlier learning (Find the constant of proportionality from a table; Coordinates in the first quadrant). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Number of tickets (x): 4, 7, 9. Cost (y): 20, 35, 45. What is the constant of proportionality k (y = kx)? → 5Prompt: k = y ÷ x.
  2. x: 2, 4, 8. y: 5, 10, 20. Find k in y = kx. Give a fraction or decimal. → 5/2 (2 1/2)Prompt: Divide any y by its x.
  3. Number of tickets (x): 1, 5, 8. Cost (y): 3, 15, 24. What is the constant of proportionality k (y = kx)? → 3Prompt: k = y ÷ x.

Hook · 6 min

  • Share a recipe for 4 people and ask how much is needed for 6.
  • Share the objective: Find the constant of proportionality from a graph. 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.
  • Model one question from the student sheet, thinking aloud.
  • 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.

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.

Watch out for

  • Adding the same amount to both parts instead of multiplying.
  • Mixing up part-to-part and part-to-whole ratios.

Support and stretch

Support

  • Review first: Find the constant of proportionality from a table.
  • Use concrete materials: bar models.
  • 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: Decide if a graph shows a proportional relationship.
  • 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-7.

Free lesson plan from eurekami.com/lesson-plan-builder

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Find the constant of proportionality from a graph

Name

Date

Score/ 8

  1. Question 1

    A proportional graph passes through (2, 1). What is k? Give a fraction in simplest form.

    xy12345678123456780y = 0.5x(2, 1)

    Answer(as a fraction)

  2. Question 2

    The line passes through (0, 0) and (1, 4). What is the constant of proportionality?

    xy12345624681012141618200y = 4x(1, 4)

    Answer

  3. Question 3

    On a proportional graph of cost (y) against kilograms (x), the point (1, 3) is marked. What does this point tell you?

    xy1234561530450y = 3x(1, 3)
    • A. 3 kg cost 1
    • B. 1 kg costs 3
    • C. Every kg costs 1 more than the last
    • D. The graph starts at 3

  4. Question 4

    The line passes through (0, 0) and (1, 5). What is the constant of proportionality?

    xy12345624681012141618200y = 5x(1, 5)

    Answer

  5. Question 5

    On a proportional graph of cost (y) against kilograms (x), the point (1, 7) is marked. What does this point tell you?

    xy1234561530450y = 7x(1, 7)
    • A. The graph starts at 7
    • B. 1 kg costs 7
    • C. 7 kg cost 1
    • D. Every kg costs 1 more than the last

  6. Question 6

    A proportional graph passes through (3, 2). What is k? Give a fraction in simplest form.

    xy12345678123456780y = 0.666666667x(3, 2)

    Answer(as a fraction)

  7. Question 7

    The line passes through (0, 0) and (3, 18). What is the constant of proportionality?

    xy12345624681012141618200y = 6x(3, 18)

    Answer

  8. Question 8

    On a proportional graph of cost (y) against kilograms (x), the point (1, 5) is marked. What does this point tell you?

    xy1234561530450y = 5x(1, 5)
    • A. 1 kg costs 5
    • B. The graph starts at 5
    • C. Every kg costs 1 more than the last
    • D. 5 kg cost 1

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Answer key: Find the constant of proportionality from a graph

  1. 1. 1/2

  2. 2. 4

  3. 3. B. 1 kg costs 3

  4. 4. 5

  5. 5. B. 1 kg costs 7

  6. 6. 2/3

  7. 7. 6

  8. 8. A. 1 kg costs 5