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Proportional or not?: 7th grade math

Unit rates with fractions; recognise proportional relationships (tables, graphs, y = kx). A free 7th grade lesson plan, a question set with answers and a printable sheet with its key. Copy it and make it yours.

Lesson plan

Goal

  • Students can do this: unit rates with fractions; recognise proportional relationships (tables, graphs, y = kx).

Teach (10 min)

  • In a proportional relationship, y ÷ x is always the same number k. It is the constant of proportionality, and y = kx.
  • If y = 10 when x = 4, then k = 10 ÷ 4 = 2.5. For y = 3x, x = 7 gives y = 21, and y = 21 gives x = 21 ÷ 3 = 7.
  • Work one example on the board while students say each step aloud, then do one together.

Practise (15 min)

  • Students work the printable sheet in pairs, then alone.
  • Or practise it as a game with no sign-up: https://peabody.kids/math/ratio.constant?lesson=7-ratio-const-1&at=7

Exit ticket (5 min)

  • Three questions on a slip:
  • 1. A proportional relationship is y = 2x. What is the constant of proportionality?
  • 2. A proportional relationship is y = 2x. What is the constant of proportionality?
  • 3. In a proportional relationship, y = 4 when x = 2. The relationship is y = kx. What is k, the constant of proportionality?

Question set

10 questions that read in words, easiest first. Questions that need a picture are on the printable sheet below.

  1. A proportional relationship is y = 2x. What is the constant of proportionality?
  2. A proportional relationship is y = 2x. What is the constant of proportionality?
  3. In a proportional relationship, y = 4 when x = 2. The relationship is y = kx. What is k, the constant of proportionality?
  4. This table shows a proportional relationship. x: 1, 3, 5, 6 y: 8, 24, 40, 48 What is the constant of proportionality?
  5. A proportional relationship is y = 2x. What is the constant of proportionality?
  6. In a proportional relationship, y = 15 when x = 3. The relationship is y = kx. What is k, the constant of proportionality?
  7. This table shows a proportional relationship. x: 6, 12, 18, 24 y: 30, 60, 90, 120 What is the constant of proportionality?
  8. This table shows a proportional relationship. x: 3, 6, 9, 12 y: 12, 24, 36, 48 What is the constant of proportionality?
  9. In a proportional relationship, y = 32 when x = 4. The relationship is y = kx. What is k, the constant of proportionality?
  10. In a proportional relationship, y = 27 when x = 3. The relationship is y = kx. What is k, the constant of proportionality?
Answers
  1. 2
  2. 2
  3. 2
  4. 8
  5. 2
  6. 5
  7. 5
  8. 4
  9. 8
  10. 9

Printable sheet

Name: ____________________   Date: ____________

Proportional or not? (7th grade)

  1. This table shows a proportional relationship.
    x: 6, 12, 18, 24
    y: 36, 72, 108, 144
    What is the constant of proportionality?
  2. This table shows a proportional relationship.
    x: 2, 4, 6, 8
    y: 10, 20, 30, 40
    What is the constant of proportionality?
  3. This table shows a proportional relationship.
    x: 2, 3, 5, 8
    y: 14, 21, 35, 56
    What is the constant of proportionality?
  4. This table shows a proportional relationship.
    x: 3, 4, 6, 10
    y: 6, 8, 12, 20
    What is the constant of proportionality?
  5. In a proportional relationship, y = 5 when x = 1. The relationship is y = kx. What is k, the constant of proportionality?
  6. This table shows a proportional relationship.
    x: 1, 3, 4, 5
    y: 5, 15, 20, 25
    What is the constant of proportionality?
  7. The cost c (in dollars) of p pounds of apples is c = 17.5p. How many pounds of apples can you buy for $105?
  8. The cost c (in dollars) of p pounds of apples is c = 9p. How much do 8 pounds of apples cost?
  9. The distance d (in miles) a car travels in t hours is d = 12.5t. How many hours does the car need to travel 37.5 miles?
  10. This table shows a proportional relationship.
    x: 1, 3, 4, 8
    y: 22, 66, 88, 176
    What is the constant of proportionality?
  11. The distance d (in miles) a car travels in t hours is d = 11t. How many hours does the car need to travel 121 miles?
  12. The number of words w a student types in n minutes is w = 4n. How many minutes does the student need to type 32 words?
Key
  1. 6
  2. 5
  3. 7
  4. 2
  5. 5
  6. 5
  7. 6 pounds
  8. $72.00
  9. 3 hours
  10. 22
  11. 11 hours
  12. 8 minutes

Written by Peabody from its own skill pages. Free, no ads, no sign-in. Children can practise this on Peabody. More from teachers: teacher-shared resources.