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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): 7, 8, 9. Cost (y): 105, 120, 135. What is the constant of proportionality k (y = kx)? → 15Prompt: 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): 4, 5, 8. Cost (y): 56, 70, 112. What is the constant of proportionality k (y = kx)? → 14Prompt: 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

    On a proportional graph of cost (y) against kilograms (x), the point (1, 6) is marked. What does this point tell you?

    xy1234561530450y = 6x(1, 6)
    • A. The graph starts at 6
    • B. 1 kg costs 6
    • C. 6 kg cost 1
    • D. Every kg costs 1 more than the last

  2. Question 2

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

    xy12345624681012141618200y = 5x(1, 5)

    Answer

  3. Question 3

    A proportional graph passes through (3, 4). What is k? Give a fraction in simplest form.

    xy12345678123456780y = 1.333333333x(3, 4)

    Answer(as a fraction)

  4. Question 4

    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. 5 kg cost 1
    • B. The graph starts at 5
    • C. 1 kg costs 5
    • D. Every kg costs 1 more than the last

  5. Question 5

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

    xy12345624681012141618200y = 4x(1, 4)

    Answer

  6. Question 6

    A proportional graph passes through (4, 3). What is k? Give a fraction in simplest form.

    xy12345678123456780y = 0.75x(4, 3)

    Answer(as a fraction)

  7. Question 7

    On a proportional graph of cost (y) against kilograms (x), the point (1, 8) is marked. What does this point tell you?

    xy1234561530450y = 8x(1, 8)
    • A. Every kg costs 1 more than the last
    • B. 8 kg cost 1
    • C. 1 kg costs 8
    • D. The graph starts at 8

  8. Question 8

    The line passes through (0, 0) and (2, 10). What is the constant of proportionality?

    xy12345624681012141618200y = 5x(2, 10)

    Answer

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Answer key: Find the constant of proportionality from a graph

  1. 1. B. 1 kg costs 6

  2. 2. 5

  3. 3. 4/3

  4. 4. C. 1 kg costs 5

  5. 5. 4

  6. 6. 3/4

  7. 7. C. 1 kg costs 8

  8. 8. 5