• 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 7 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form. → 1/36Prompt: Multiply along the branches of the tree diagram.
2. In a class of 27, 21 play guitar, 13 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. → 8/9Prompt: Draw a Venn diagram. Put the 'both' number in the overlap first.
3. A bag has 7 red and 5 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form. → 7/22Prompt: 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 2 red and 4 blue counters. Two are taken out without replacement. Find P(both red) as a fraction in simplest form. → 1/15Prompt: After the first red is taken, there is one fewer red and one fewer counter.
2. A playlist has 2 pop songs and 3 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 6 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 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.
2. A bag has 7 red and 8 blue counters. Two are taken out without replacement. Find P(both red) as a fraction in simplest form. → 1/5Prompt: After the first red is taken, there is one fewer red and one fewer counter.

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