Math lesson plan · 8th grade (Year 9 in England) · 60 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 · 6 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.
- 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.
- 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.
- 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 · 6 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 · 12 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 · 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.
- 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.
- 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 · 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.
- 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.
- 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