• 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.

1. A two-way table: Year 7 — cats 9, dogs 15; Year 8 — cats 16, dogs 5. How many students prefer dogs? → 20Prompt: Find the row or column you need.
2. Write 40% as a decimal. → 0.4Prompt: Per cent means out of 100.
3. Year 7 — cats 13, dogs 19; Year 8 — cats 19, dogs 7. A Year 7 student is picked at random. What is the probability they prefer cats? Give a fraction in simplest form. → 13/32Prompt: Only look at the Year 7 row.

• 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.

• 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.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. How students travel to school: Year 9: cycle 20, walk 36 Year 10: cycle 6, walk 21 What proportion of all students are "Year 10 and walks"? Give a decimal to 2 decimal places. → 0.25Prompt: A joint relative frequency = cell count ÷ grand total.
2. Survey of streaming habits: Under 16: watch daily 39, not daily 26 16 and over: watch daily 17, not daily 32 What percentage of the 16-and-overs watch daily? Round to the nearest whole percent. → 35Prompt: Conditional relative frequency: use only that row's total.

• 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.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. Survey of streaming habits: Under 16: watch daily 12, not daily 28 16 and over: watch daily 20, not daily 15 What percentage of the under-16s watch daily? Round to the nearest whole percent. → 30Prompt: Conditional relative frequency: use only that row's total.
2. How students travel to school: Year 9: cycle 5, walk 35 Year 10: cycle 31, walk 28 What proportion of all students are "Year 9 and walks"? Give a decimal to 2 decimal places. → 0.35Prompt: A joint relative frequency = cell count ÷ grand total.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-9.