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Math lesson plan · 8th grade (Year 9 in England) · 30 minutes

Relative frequencies in two-way tables

Statistics and probability

CCSS 8.SP.A.4England: KS3 StatisticsEngland: GCSE Foundation Statistics

Objective and success criteria

Students will: Relative frequencies in two-way tables.

  • 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: 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 (Two-way tables). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A two-way table: Year 7 — cats 7, dogs 8; Year 8 — cats 18, dogs 18. How many Year 8 students are there? → 36Prompt: Find the row or column you need.
  2. Year 7 — cats 20, dogs 13; Year 8 — cats 20, dogs 7. A Year 7 student is picked at random. What is the probability they prefer cats? Give a fraction in simplest form. → 20/33Prompt: Only look at the Year 7 row.
  3. A two-way table: Year 7 — cats 9, dogs 12; Year 8 — cats 6, dogs 12. How many students prefer dogs? → 24Prompt: Find the row or column you need.

Hook · 3 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Relative frequencies in two-way tables. 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: Year 9 survey. Have a pet: 23 with a phone, 11 without. No pet: 16 with a phone, 20 without. Of the students WITH a phone, what fraction have a pet? Give a fraction in simplest form.
  • Step 1: 23 + 16 = 39
  • Step 2: 23/39
  • Answer: 23/39
  • 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. Year 9 survey. Have a pet: 9 with a phone, 10 without. No pet: 11 with a phone, 24 without. Of the students WITH a phone, what fraction have a pet? Give a fraction in simplest form. → 9/20Prompt: Only look at the students with a phone.
  2. 30 students in Club A and 20 students in Club B were asked if they recycle at home. 12 in Club A and 8 in Club B said yes. What percentage of Club A recycle at home? → 40Prompt: Relative frequency = count ÷ group total.

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. 80 students in Club A and 40 students in Club B were asked if they recycle at home. 56 in Club A and 32 in Club B said yes. What percentage of Club A recycle at home? → 70Prompt: Relative frequency = count ÷ group total.
  2. In Class X, 10 of 50 students bike to school. In Class Y, 12 of 40 students bike to school. Which class has the higher proportion of cyclists? (X / Y / The same) → YPrompt: Compare proportions, not raw counts.

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: Two-way tables.
  • 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-8.

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

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Relative frequencies in two-way tables

Name

Date

Score/ 6

  1. Question 1

    Year 9 survey. Have a pet: 29 with a phone, 27 without. No pet: 28 with a phone, 24 without. Of the students WITH a phone, what fraction have a pet? Give a fraction in simplest form.

    Answer(as a fraction)

  2. Question 2

    In Class X, 12 of 40 students bike to school. In Class Y, 18 of 60 students bike to school. Which class has the higher proportion of cyclists?

    • A. X
    • B. Y
    • C. The same

  3. Question 3

    20 students in Club A and 20 students in Club B were asked if they recycle at home. 8 in Club A and 4 in Club B said yes. What percentage of Club A recycle at home?

    Answer

  4. Question 4

    Year 9 survey. Have a pet: 21 with a phone, 12 without. No pet: 14 with a phone, 30 without. Of the students WITH a phone, what fraction have a pet? Give a fraction in simplest form.

    Answer(as a fraction)

  5. Question 5

    In Class X, 14 of 20 students bike to school. In Class Y, 16 of 20 students bike to school. Which class has the higher proportion of cyclists?

    • A. X
    • B. Y
    • C. The same

  6. Question 6

    40 students in Club A and 40 students in Club B were asked if they recycle at home. 28 in Club A and 32 in Club B said yes. What percentage of Club B recycle at home?

    Answer

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Answer key: Relative frequencies in two-way tables

  1. 1. 29/57

  2. 2. C. The same

  3. 3. 40

  4. 4. 3/5

  5. 5. B. Y

  6. 6. 80