• 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 2 red and 2 blue counters. Two are taken with replacement. What is the probability both are red? Give a fraction in simplest form. → 1/4Prompt: Multiply along the branches of the tree diagram.
2. In a class of 31, 7 play guitar, 16 play piano and 2 play both. One student is chosen at random. What is the probability they play both? Simplest form. → 2/31Prompt: Draw a Venn diagram. Put the 'both' number in the overlap first.
3. A bag has 2 red and 6 blue counters. Two are taken with replacement. What is the probability both are red? Give a fraction in simplest form. → 1/16Prompt: 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: Use tree diagrams for picks without replacement. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: A bag has 8 red and 7 blue counters. Two are taken out without replacement. Find P(both red) as a fraction in simplest form.
• Step 1: 8/15 × 7/14 = 56/210
• Step 2: = 4/15
• Answer: 4/15
• 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. A bag has 7 red and 6 blue counters. Two are taken out without replacement. Find P(both red) as a fraction in simplest form. → 7/26Prompt: After the first red is taken, there is one fewer red and one fewer counter.
2. A playlist has 3 pop songs and 2 rock songs. Two different songs are picked at random. Find P(one of each type) as a fraction in simplest form. → 3/5Prompt: There are two routes: pop then rock, or rock then pop.

• 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. A box has 2 vanilla and 4 chocolate biscuits. Two are eaten at random. Find P(at least one chocolate) as a fraction in simplest form. → 14/15Prompt: 'At least one' = 1 − P(none).
2. A playlist has 5 pop songs and 7 rock songs. Two different songs are picked at random. Find P(one of each type) as a fraction in simplest form. → 35/66Prompt: There are two routes: pop then rock, or rock then pop.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-10.