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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 17, dogs 12; Year 8 — cats 18, dogs 16. How many Year 8 students are there? → 34Prompt: Find the row or column you need.
  2. Year 7 — cats 13, dogs 10; Year 8 — cats 20, dogs 8. A Year 7 student is picked at random. What is the probability they prefer cats? Give a fraction in simplest form. → 13/23Prompt: Only look at the Year 7 row.
  3. A two-way table: Year 7 — cats 11, dogs 13; Year 8 — cats 6, dogs 5. How many students are in the table altogether? → 35Prompt: 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: 11 with a phone, 27 without. No pet: 21 with a phone, 16 without. Of the students WITH a phone, what fraction have a pet? Give a fraction in simplest form. → 11/32Prompt: Only look at the students with a phone.
  2. 50 students in Club A and 30 students in Club B were asked if they recycle at home. 20 in Club A and 24 in Club B said yes. What percentage of Club B recycle at home? → 80Prompt: 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. Year 9 survey. Have a pet: 10 with a phone, 11 without. No pet: 12 with a phone, 7 without. Of the students WITH a phone, what fraction have a pet? Give a fraction in simplest form. → 5/11Prompt: Only look at the students with a phone.
  2. 60 students in Club A and 40 students in Club B were asked if they recycle at home. 12 in Club A and 16 in Club B said yes. What percentage of Club B recycle at home? → 40Prompt: Relative frequency = count ÷ group total.

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

    In Class X, 16 of 20 students bike to school. In Class Y, 24 of 60 students bike to school. Which class has the higher proportion of cyclists?

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

  2. Question 2

    70 students in Club A and 70 students in Club B were asked if they recycle at home. 56 in Club A and 14 in Club B said yes. What percentage of Club B recycle at home?

    Answer

  3. Question 3

    Year 9 survey. Have a pet: 29 with a phone, 24 without. No pet: 11 with a phone, 16 without. Of the students WITH a phone, what fraction have a pet? Give a fraction in simplest form.

    Answer(as a fraction)

  4. Question 4

    In Class X, 40 of 50 students bike to school. In Class Y, 48 of 60 students bike to school. Which class has the higher proportion of cyclists?

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

  5. Question 5

    20 students in Club A and 60 students in Club B were asked if they recycle at home. 14 in Club A and 36 in Club B said yes. What percentage of Club B recycle at home?

    Answer

  6. Question 6

    Year 9 survey. Have a pet: 29 with a phone, 28 without. No pet: 27 with a phone, 25 without. Of the students WITH a phone, what fraction have a pet? Give a fraction in simplest form.

    Answer(as a fraction)

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Answer key: Relative frequencies in two-way tables

  1. 1. A. X

  2. 2. 20

  3. 3. 29/40

  4. 4. C. The same

  5. 5. 60

  6. 6. 29/56