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Math lesson plan · 11th grade (Year 12 in England) · 45 minutes

Test for independence using a two-way table

Statistics and probability

CCSS HSS.CP.A.4CCSS HSS.CP.A.5England: A-level Statistics

Objective and success criteria

Students will: Test for independence using a two-way table.

  • 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: Conditional probability and independence; Joint and conditional relative frequencies in two-way tables

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 (Conditional probability and independence; Joint and conditional relative frequencies in two-way tables). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Survey: Likes science & is in Club — 16; Likes science & not in Club — 20; Doesn't like science & in Club — 8; neither — 7. Given a student is in the Club, what is the probability they like science? Simplest form. → 2/3Prompt: 'Given' means only look at the Club members.
  2. How students travel to school: Year 9: cycle 24, walk 39 Year 10: cycle 28, walk 19 What proportion of all students are "Year 10 and walks"? Give a decimal to 2 decimal places. → 0.17Prompt: A joint relative frequency = cell count ÷ grand total.
  3. P(A) = 0.6, P(B) = 0.2 and P(A and B) = 0.22. Are A and B independent? (Yes / No) → NoPrompt: A and B are independent if P(A and B) = P(A) × P(B).

Hook · 5 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Test for independence using a two-way table. 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: Club survey: Plays chess: likes puzzles 18, doesn't 12 No chess: likes puzzles 36, doesn't 24 Are "plays chess" and "likes puzzles" independent?
  • Step 1: 18/30 = 36/60
  • Step 2: Yes
  • Answer: Yes
  • 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. Club survey: Plays chess: likes puzzles 48, doesn't 24 No chess: likes puzzles 80, doesn't 40 Are "plays chess" and "likes puzzles" independent? (Yes / No) → YesPrompt: Compare P(likes puzzles | chess) with P(likes puzzles | no chess).
  2. Club survey: Plays chess: likes puzzles 30, doesn't 24 No chess: likes puzzles 90, doesn't 72 Are "plays chess" and "likes puzzles" independent? (Yes / No) → YesPrompt: Compare P(likes puzzles | chess) with P(likes puzzles | no chess).

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. Club survey: Plays chess: likes puzzles 124, doesn't 60 No chess: likes puzzles 72, doesn't 40 Are "plays chess" and "likes puzzles" independent? (Yes / No) → NoPrompt: Compare P(likes puzzles | chess) with P(likes puzzles | no chess).
  2. Club survey: Plays chess: likes puzzles 144, doesn't 96 No chess: likes puzzles 48, doesn't 32 Are "plays chess" and "likes puzzles" independent? (Yes / No) → YesPrompt: Compare P(likes puzzles | chess) with P(likes puzzles | no chess).

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: Conditional probability and independence.
  • 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-11.

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

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Test for independence using a two-way table

Name

Date

Score/ 8

  1. Question 1

    Club survey: Plays chess: likes puzzles 36, doesn't 60 No chess: likes puzzles 60, doesn't 100 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  2. Question 2

    Club survey: Plays chess: likes puzzles 24, doesn't 12 No chess: likes puzzles 72, doesn't 36 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  3. Question 3

    Club survey: Plays chess: likes puzzles 96, doesn't 96 No chess: likes puzzles 80, doesn't 80 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  4. Question 4

    Club survey: Plays chess: likes puzzles 100, doesn't 60 No chess: likes puzzles 60, doesn't 36 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  5. Question 5

    Club survey: Plays chess: likes puzzles 41, doesn't 30 No chess: likes puzzles 24, doesn't 25 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  6. Question 6

    Club survey: Plays chess: likes puzzles 64, doesn't 60 No chess: likes puzzles 60, doesn't 64 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  7. Question 7

    Club survey: Plays chess: likes puzzles 76, doesn't 48 No chess: likes puzzles 36, doesn't 28 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  8. Question 8

    Club survey: Plays chess: likes puzzles 48, doesn't 36 No chess: likes puzzles 32, doesn't 24 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

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Answer key: Test for independence using a two-way table

  1. 1. A. Yes

  2. 2. A. Yes

  3. 3. A. Yes

  4. 4. A. Yes

  5. 5. B. No

  6. 6. B. No

  7. 7. B. No

  8. 8. A. Yes