• 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 5 red and 7 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form. → 5/33Prompt: Multiply along the branches of the tree diagram.
2. In a class of 39, 18 play guitar, 17 play piano and 6 play both. One student is chosen at random. What is the probability they play both? Simplest form. → 2/13Prompt: Draw a Venn diagram. Put the 'both' number in the overlap first.
3. A bag has 7 red and 3 blue counters. Two are taken with replacement. What is the probability both are red? Give a fraction in simplest form. → 49/100Prompt: 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, 23 play chess, 15 play the guitar and 4 do neither. How many do both? → 12Prompt: How many do at least one activity?
2. Venn diagram of 28 people: apples only 4, bananas only 6, both 8, neither 10. A person is chosen at random. Find the probability they like apples but not bananas. Give a fraction in its simplest form. → 1/7Prompt: 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. Venn diagram of 46 people: apples only 17, bananas only 9, both 10, neither 10. A person is chosen at random. Find the probability they like both apples and bananas. Give a fraction in its simplest form. → 5/23Prompt: Decide which regions of the diagram you need.
2. In a club of 41 students, 29 play chess, 17 play the guitar and 4 do neither. How many do both? → 9Prompt: How many do at least one activity?

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