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Math lesson plan · 8th grade (Year 9 in England) · 45 minutes

Make predictions with a line of best fit

Statistics and probability

CCSS 8.SP.A.2CCSS 8.SP.A.3England: KS3 StatisticsEngland: GCSE Foundation Statistics

Objective and success criteria

Students will: Make predictions with a line of best fit.

  • 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: Describe association in scatter plots; Graphs of linear equations y = mx + b

Leads to: Interpret the slope and intercept of a line of best fit

Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 5 min

  • Quick retrieval from earlier learning (Describe association in scatter plots; Graphs of linear equations y = mx + b). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. What association would you expect between: Age of a car and its resale value? (Positive / Negative / None) → NegativePrompt: Imagine one quantity increasing. What tends to happen to the other?
  2. What association would you expect between: Outside temperature and heating bill? (Positive / Negative / None) → NegativePrompt: Imagine one quantity increasing. What tends to happen to the other?
  3. What association would you expect between: Height of a tree and the length of its shadow at noon? (Positive / Negative / None) → PositivePrompt: Imagine one quantity increasing. What tends to happen to the other?

Hook · 5 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Make predictions with a line of best fit. Read the success criteria together.

I do: model it · 10 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: The line of best fit for test score (y) against hours of practice (x) is y = 5x + 23. Predict the score after 6 hours.
  • Step 1: 5 × 6 + 23 = 53
  • Answer: 53
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 10 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. The line of best fit for test score (y) against hours of practice (x) is y = 7x + 25. Predict the score after 5 hours. → 60Prompt: Substitute the x-value into the equation.
  2. A line of best fit is y = 1x + 4. For which x does it predict y = 14? → 10Prompt: Set the equation equal to the y-value.

You do: independent practice · 10 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 · 5 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. A line of best fit is y = 1.5x + 6. For which x does it predict y = 18? → 8Prompt: Set the equation equal to the y-value.
  2. The line of best fit for test score (y) against hours of practice (x) is y = 5x + 37. Predict the score after 6 hours. → 67Prompt: Substitute the x-value into the equation.

Watch out for

  • Forgetting to put data in order before finding the median.
  • Reading a bar's height wrongly when the scale goes up in 2s or 5s.

Support and stretch

Support

  • Review first: Describe association in scatter plots.
  • Use concrete materials: squared paper for charts.
  • 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: Interpret the slope and intercept of a line of best fit.
  • 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-8.

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

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Make predictions with a line of best fit

Name

Date

Score/ 8

  1. Question 1

    Data was collected for x from 1 to 8, and the line of best fit is y = 4x + 16. Luis uses it to predict y when x = 47. Why should Luis be careful?

    xy1234567891028560y = 4x + 16(1, 22)(2, 25)(3, 26)(4, 33)(5, 36)(6, 42)(7, 46)(8, 49)
    • A. The line has a positive slope
    • B. The answer will be a decimal
    • C. x is far outside the data range, so the trend may not continue
    • D. Lines of best fit can never be used

  2. Question 2

    The line of best fit for test score (y) against hours of practice (x) is y = 8x + 42. Predict the score after 6 hours.

    Answer

  3. Question 3

    A line of best fit is y = 1.5x + 10. For which x does it predict y = 20.5?

    Answer

  4. Question 4

    Data was collected for x from 1 to 8, and the line of best fit is y = 2x + 6. Zoe uses it to predict y when x = 58. Why should Zoe be careful?

    xy123456789104812162024280y = 2x + 6(1, 8)(2, 10)(3, 13)(4, 15)(5, 14)(6, 18)(7, 20)(8, 20)
    • A. The answer will be a decimal
    • B. Lines of best fit can never be used
    • C. x is far outside the data range, so the trend may not continue
    • D. The line has a positive slope

  5. Question 5

    The line of best fit for test score (y) against hours of practice (x) is y = 8x + 45. Predict the score after 2 hours.

    Answer

  6. Question 6

    A line of best fit is y = 1.5x + 8. For which x does it predict y = 17?

    Answer

  7. Question 7

    Data was collected for x from 1 to 8, and the line of best fit is y = 4x + 14. Isla uses it to predict y when x = 33. Why should Isla be careful?

    xy12345678910612182430364248540y = 4x + 14(1, 17)(2, 21)(3, 25)(4, 32)(5, 35)(6, 36)(7, 41)(8, 47)
    • A. The line has a positive slope
    • B. The answer will be a decimal
    • C. x is far outside the data range, so the trend may not continue
    • D. Lines of best fit can never be used

  8. Question 8

    The line of best fit for test score (y) against hours of practice (x) is y = 4x + 27. Predict the score after 6 hours.

    Answer

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Answer key: Make predictions with a line of best fit

  1. 1. C. x is far outside the data range, so the trend may not continue

  2. 2. 90

  3. 3. 7

  4. 4. C. x is far outside the data range, so the trend may not continue

  5. 5. 61

  6. 6. 6

  7. 7. C. x is far outside the data range, so the trend may not continue

  8. 8. 51