Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Joint and conditional relative frequencies in two-way tables
Statistics and probability
CCSS HSS.ID.B.5CCSS 8.SP.A.4England: GCSE Foundation Statistics
Objective and success criteria
Students will: Joint and conditional 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; Percentages, fractions and decimals
Leads to: Test for independence using a two-way table
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 (Two-way tables; Percentages, fractions and decimals). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A two-way table: Year 7 — cats 9, dogs 11; Year 8 — cats 7, dogs 17. How many students are in the table altogether? → 44Prompt: Find the row or column you need.
- Write 60% as a fraction in simplest form. → 3/5Prompt: Per cent means out of 100.
- Year 7 — cats 20, dogs 13; Year 8 — cats 11, dogs 13. 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.
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Joint and conditional relative frequencies in two-way tables. 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: How students travel to school: Year 9: cycle 8, walk 30 Year 10: cycle 23, walk 40 What proportion of all students are "Year 10 and cycles"? Give a decimal to 2 decimal places.
- Step 1: Total = 101
- Step 2: 23 ÷ 101 ≈ 0.23
- Answer: 0.23
- 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.
- How students travel to school: Year 9: cycle 19, walk 15 Year 10: cycle 13, walk 27 What proportion of all students are "Year 9 and cycles"? Give a decimal to 2 decimal places. → 0.26Prompt: A joint relative frequency = cell count ÷ grand total.
- Survey of streaming habits: Under 16: watch daily 18, not daily 25 16 and over: watch daily 5, not daily 26 What percentage of the under-16s watch daily? Round to the nearest whole percent. → 42Prompt: Conditional relative frequency: use only that row's total.
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.
- Survey of streaming habits: Under 16: watch daily 32, not daily 17 16 and over: watch daily 35, not daily 27 What percentage of the under-16s watch daily? Round to the nearest whole percent. → 65Prompt: Conditional relative frequency: use only that row's total.
- How students travel to school: Year 9: cycle 21, walk 24 Year 10: cycle 36, walk 40 What proportion of all students are "Year 9 and cycles"? Give a decimal to 2 decimal places. → 0.17Prompt: A joint relative frequency = cell count ÷ grand 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
- Move on to: Test for independence using a two-way table.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder