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Math lesson plan · 12th grade (Year 13 in England) · 60 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 · 6 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 · 6 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 · 12 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 · 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.
  1. A data set has correlation coefficient r = 0.38. How would you describe the correlation? (Strong positive / Moderate positive / Little or no linear correlation) → Moderate positivePrompt: The sign gives the direction; the size gives the strength.
  2. Ice-cream sales and sunburn cases are strongly correlated. Does this show that one causes the other? (No: the correlation must be a calculation error / Not necessarily: a third factor, hot, sunny weather, could explain both / Yes: strong correlation proves causation / Yes, but only if r is above 0.9) → Not necessarily: a third factor, hot, sunny weather, could explain bothPrompt: Correlation describes how two variables move together.

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.
  1. A data set has correlation coefficient r = −0.82. How would you describe the correlation? (Strong negative / Moderate negative / Little or no linear correlation) → Strong negativePrompt: The sign gives the direction; the size gives the strength.
  2. Children with bigger shoe sizes have better reading scores. Does this show that one causes the other? (Not necessarily: a third factor, age, could explain both / 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, age, could explain bothPrompt: Correlation describes how two variables move together.

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, but only if r is above 0.9
    • D. Yes: strong correlation proves causation

  2. Question 2

    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

  3. Question 3

    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. No: the correlation must be a calculation error
    • C. Not necessarily: a third factor, hot, sunny weather, could explain both
    • D. Yes: strong correlation proves causation

  4. Question 4

    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

  5. Question 5

    A data set has correlation coefficient r = −0.45. How would you describe the correlation?

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

  6. Question 6

    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

  7. Question 7

    A data set has correlation coefficient r = 0.93. How would you describe the correlation?

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

  8. Question 8

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

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

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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. A. Strong negative

  3. 3. C. Not necessarily: a third factor, hot, sunny weather, could explain both

  4. 4. C. Little or no linear correlation

  5. 5. B. Moderate negative

  6. 6. B. Moderate positive

  7. 7. A. Strong positive

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