• Quick retrieval from earlier learning (Tree diagrams and Venn diagrams). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. A bag has 7 red and 6 blue counters. Two are taken with replacement. What is the probability both are red? Give a fraction in simplest form. → 49/169Prompt: Multiply along the branches of the tree diagram.
2. In a class of 26, 13 play guitar, 19 play piano and 10 play both. One student is chosen at random. What is the probability they play guitar or piano (or both)? Simplest form. → 11/13Prompt: Draw a Venn diagram. Put the 'both' number in the overlap first.
3. A bag has 5 red and 6 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form. → 2/11Prompt: Multiply along the branches of the tree diagram.

• Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
• Share the objective: Complete and use a two-set Venn diagram. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: In a club of 32 students, 19 play chess, 13 play the guitar and 5 do neither. How many do both?
• Step 1: 32 − 5 = 27
• Step 2: 19 + 13 − 27 = 5
• Answer: 5
• 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. In a club of 30 students, 11 play chess, 17 play the guitar and 5 do neither. How many do both? → 3Prompt: How many do at least one activity?
2. Venn diagram of 39 people: apples only 15, bananas only 6, both 10, neither 8. A person is chosen at random. Find the probability they like both apples and bananas. Give a fraction in its simplest form. → 10/39Prompt: Decide which regions of the diagram you need.

• 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. In a club of 37 students, 21 play chess, 11 play the guitar and 11 do neither. How many do both? → 6Prompt: How many do at least one activity?
2. Venn diagram of 40 people: apples only 10, bananas only 10, both 10, neither 10. A person is chosen at random. Find the probability they like apples or bananas (or both). Give a fraction in its simplest form. → 3/4Prompt: Decide which regions of the diagram you need.

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