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Math lesson plan · 12th grade (Year 13 in England) · 45 minutes

Interpret correlation coefficients and avoid the causation trap

Statistics and probability

CCSS HSS.ID.C.8CCSS HSS.ID.C.9England: GCSE Higher StatisticsEngland: A-level Statistics

Objective and success criteria

Students will: Interpret correlation coefficients and avoid the causation trap.

  • 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: Scatter graphs and correlation

Leads to: the next skill in this area.

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 (Scatter graphs and correlation). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.

Hook · 5 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Interpret correlation coefficients and avoid the causation trap. 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: A data set has correlation coefficient r = −0.95. How would you describe the correlation?
  • Step 1: Strong negative
  • Answer: Strong negative
  • 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. A data set has correlation coefficient r = 0.05. How would you describe the correlation? (Strong positive / Moderate positive / Little or no linear correlation) → Little or no linear correlationPrompt: The sign gives the direction; the size gives the strength.
  2. Homes with more smart speakers use more electricity. Does this show that one causes the other? (Yes: strong correlation proves causation / Yes, but only if r is above 0.9 / No: the correlation must be a calculation error / Not necessarily: a third factor, household size and number of devices, could explain both) → Not necessarily: a third factor, household size and number of devices, could explain bothPrompt: Correlation describes how two variables move together.

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. Homes with more smart speakers use more electricity. Does this show that one causes the other? (Yes, but only if r is above 0.9 / Not necessarily: a third factor, household size and number of devices, could explain both / Yes: strong correlation proves causation / No: the correlation must be a calculation error) → Not necessarily: a third factor, household size and number of devices, could explain bothPrompt: Correlation describes how two variables move together.
  2. A data set has correlation coefficient r = 0.93. How would you describe the correlation? (Strong positive / Moderate positive / Little or no linear correlation) → Strong positivePrompt: The sign gives the direction; the size gives the strength.

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: Scatter graphs and correlation.
  • 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

  • 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-12.

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

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Interpret correlation coefficients and avoid the causation trap

Name

Date

Score/ 8

  1. Question 1

    Towns with more libraries have more crime. Does this show that one causes the other?

    • A. Not necessarily: a third factor, population size, could explain both
    • B. No: the correlation must be a calculation error
    • C. Yes: strong correlation proves causation
    • D. Yes, but only if r is above 0.9

  2. Question 2

    A data set has correlation coefficient r = 0.05. How would you describe the correlation?

    • A. Strong positive
    • B. Moderate positive
    • C. Little or no linear correlation

  3. Question 3

    Homes with more smart speakers use more electricity. Does this show that one causes the other?

    • A. No: the correlation must be a calculation error
    • B. Not necessarily: a third factor, household size and number of devices, could explain both
    • C. Yes: strong correlation proves causation
    • D. Yes, but only if r is above 0.9

  4. Question 4

    A data set has correlation coefficient r = 0.38. How would you describe the correlation?

    • A. Strong positive
    • B. Moderate positive
    • C. Little or no linear correlation

  5. Question 5

    Ice-cream sales and sunburn cases are strongly correlated. Does this show that one causes the other?

    • A. Yes, but only if r is above 0.9
    • B. Not necessarily: a third factor, hot, sunny weather, could explain both
    • C. Yes: strong correlation proves causation
    • D. No: the correlation must be a calculation error

  6. Question 6

    A data set has correlation coefficient r = −0.1. How would you describe the correlation?

    • A. Strong negative
    • B. Moderate negative
    • C. Little or no linear correlation

  7. Question 7

    A data set has correlation coefficient r = −0.95. How would you describe the correlation?

    • A. Strong negative
    • B. Moderate negative
    • C. Little or no linear correlation

  8. Question 8

    Children with bigger shoe sizes have better reading scores. Does this show that one causes the other?

    • A. Yes: strong correlation proves causation
    • B. No: the correlation must be a calculation error
    • C. Yes, but only if r is above 0.9
    • D. Not necessarily: a third factor, age, could explain both

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Answer key: Interpret correlation coefficients and avoid the causation trap

  1. 1. A. Not necessarily: a third factor, population size, could explain both

  2. 2. C. Little or no linear correlation

  3. 3. B. Not necessarily: a third factor, household size and number of devices, could explain both

  4. 4. B. Moderate positive

  5. 5. B. Not necessarily: a third factor, hot, sunny weather, could explain both

  6. 6. C. Little or no linear correlation

  7. 7. A. Strong negative

  8. 8. D. Not necessarily: a third factor, age, could explain both