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Math lesson plan · 8th grade (Year 9 in England) · 30 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 · 4 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: Daily screen time and hours of sleep? (Positive / Negative / None) → NegativePrompt: Imagine one quantity increasing. What tends to happen to the other?
  2. What association would you expect between: Hours spent revising and test score? (Positive / Negative / None) → PositivePrompt: 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 · 3 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 · 7 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 · 6 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 = 8x + 35. Predict the score after 4 hours. → 67Prompt: Substitute the x-value into the equation.
  2. A line of best fit is y = 1.5x + 6. For which x does it predict y = 13.5? → 5Prompt: Set the equation equal to the y-value.

You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. The line of best fit for test score (y) against hours of practice (x) is y = 4x + 21. Predict the score after 9 hours. → 57Prompt: Substitute the x-value into the equation.
  2. A line of best fit is y = 2.5x + 1. For which x does it predict y = 13.5? → 5Prompt: Set the equation equal to the y-value.

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/ 6

  1. Question 1

    A line of best fit is y = 2.5x + 1. For which x does it predict y = 18.5?

    Answer

  2. Question 2

    The line of best fit for test score (y) against hours of practice (x) is y = 8x + 41. Predict the score after 4 hours.

    Answer

  3. Question 3

    Data was collected for x from 1 to 8, and the line of best fit is y = 4x + 7. Felix uses it to predict y when x = 55. Why should Felix be careful?

    xy123456789106121824303642480y = 4x + 7(1, 10)(2, 15)(3, 20)(4, 23)(5, 25)(6, 32)(7, 34)(8, 38)
    • A. The line has a positive slope
    • B. x is far outside the data range, so the trend may not continue
    • C. Lines of best fit can never be used
    • D. The answer will be a decimal

  4. Question 4

    A line of best fit is y = 1x + 4. For which x does it predict y = 12?

    Answer

  5. Question 5

    The line of best fit for test score (y) against hours of practice (x) is y = 8x + 38. Predict the score after 9 hours.

    Answer

  6. Question 6

    Data was collected for x from 1 to 8, and the line of best fit is y = 2x + 8. Chloe uses it to predict y when x = 34. Why should Chloe be careful?

    xy12345678910481216202428320y = 2x + 8(1, 9)(2, 13)(3, 14)(4, 18)(5, 17)(6, 22)(7, 23)(8, 24)
    • A. The line has a positive slope
    • B. x is far outside the data range, so the trend may not continue
    • C. The answer will be a decimal
    • D. Lines of best fit can never be used

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Answer key: Make predictions with a line of best fit

  1. 1. 7

  2. 2. 73

  3. 3. B. x is far outside the data range, so the trend may not continue

  4. 4. 8

  5. 5. 110

  6. 6. B. x is far outside the data range, so the trend may not continue