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Math lesson plan · 11th grade (Year 12 in England) · 30 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 · 4 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 — 7; Likes science & not in Club — 5; Doesn't like science & in Club — 7; neither — 8. Given a student is in the Club, what is the probability they like science? Simplest form. → 1/2Prompt: 'Given' means only look at the Club members.
  2. How students travel to school: Year 9: cycle 28, walk 35 Year 10: cycle 27, walk 26 What proportion of all students are "Year 9 and cycles"? Give a decimal to 2 decimal places. → 0.24Prompt: A joint relative frequency = cell count ÷ grand total.
  3. P(A) = 0.3, P(B) = 0.4 and P(A and B) = 0.08. Are A and B independent? (Yes / No) → NoPrompt: A and B are independent if P(A and B) = P(A) × P(B).

Hook · 3 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 · 7 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 · 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. Club survey: Plays chess: likes puzzles 96, doesn't 64 No chess: likes puzzles 144, doesn't 96 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 32, doesn't 40 No chess: likes puzzles 48, doesn't 60 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 · 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. Club survey: Plays chess: likes puzzles 20, doesn't 24 No chess: likes puzzles 32, doesn't 52 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 34, doesn't 36 No chess: likes puzzles 90, doesn't 112 Are "plays chess" and "likes puzzles" independent? (Yes / No) → NoPrompt: 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/ 6

  1. Question 1

    Club survey: Plays chess: likes puzzles 48, doesn't 24 No chess: likes puzzles 24, doesn't 12 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  2. Question 2

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

    • A. Yes
    • B. No

  3. Question 3

    Club survey: Plays chess: likes puzzles 45, doesn't 60 No chess: likes puzzles 54, doesn't 72 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  4. Question 4

    Club survey: Plays chess: likes puzzles 76, doesn't 96 No chess: likes puzzles 60, doesn't 84 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  5. Question 5

    Club survey: Plays chess: likes puzzles 80, doesn't 40 No chess: likes puzzles 48, doesn't 24 Are "plays chess" and "likes puzzles" independent?

    • A. Yes
    • B. No

  6. Question 6

    Club survey: Plays chess: likes puzzles 16, doesn't 8 No chess: likes puzzles 32, doesn't 16 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. B. No

  5. 5. A. Yes

  6. 6. A. Yes