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Math lesson plan · 9th grade (Year 10 in England) · 30 minutes

Tree diagrams and Venn diagrams

Statistics and probability

CCSS HSS.CP.A.2CCSS HSS.CP.B.7England: GCSE Foundation ProbabilityEngland: GCSE Higher Probability

Objective and success criteria

Students will: Tree diagrams and Venn diagrams.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Compound events and sample spaces

Leads to: Conditional probability and independence; Binomial probability; Complete and use a two-set Venn diagram

Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 4 min

  • Quick retrieval from earlier learning (Compound events and sample spaces). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Two fair dice are rolled and the scores added. What is the probability the total is 9? Give a fraction in simplest form. → 1/9Prompt: There are 6 × 6 = 36 equally likely outcomes.
  2. A coin is flipped 3 times. How many outcomes are in the sample space? → 8Prompt: Each flip has 2 outcomes.
  3. Zara has 5 T-shirts, 3 pairs of trousers and 2 pairs of trainers. How many different outfits (one of each) can Zara make? → 30Prompt: Use the counting principle: multiply the number of choices.

Hook · 3 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Tree diagrams and Venn diagrams. Read the success criteria together.

I do: model it · 7 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: A bag has 3 red and 6 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form.
  • Step 1: 3/9 × 2/8 = 6/72
  • Step 2: = 1/12
  • Answer: 1/12
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 6 min

  • 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 4 red and 5 blue counters. Two are taken with replacement. What is the probability both are red? Give a fraction in simplest form. → 16/81Prompt: Multiply along the branches of the tree diagram.
  2. In a class of 30, 20 play guitar, 13 play piano and 6 play both. One student is chosen at random. What is the probability they play both? Simplest form. → 1/5Prompt: Draw a Venn diagram. Put the 'both' number in the overlap first.

You do: independent practice · 7 min

  • 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.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. In a class of 18, 6 play guitar, 13 play piano and 4 play both. One student is chosen at random. What is the probability they play guitar or piano (or both)? Simplest form. → 5/6Prompt: Draw a Venn diagram. Put the 'both' number in the overlap first.
  2. A bag has 5 red and 2 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form. → 10/21Prompt: Multiply along the branches of the tree diagram.

Watch out for

  • Forgetting to put data in order before finding the median.
  • Reading a bar's height wrongly when the scale goes up in 2s or 5s.

Support and stretch

Support

  • Review first: Compound events and sample spaces.
  • Use concrete materials: squared paper for charts.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Move on to: Conditional probability and independence; Binomial probability; Complete and use a two-set Venn diagram.
  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

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

Free lesson plan from eurekami.com/lesson-plan-builder

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Tree diagrams and Venn diagrams

Name

Date

Score/ 6

  1. Question 1

    A bag has 6 red and 2 blue counters. Two are taken with replacement. What is the probability both are red? Give a fraction in simplest form.

    Answer(as a fraction)

  2. Question 2

    In a class of 21, 13 play guitar, 10 play piano and 8 play both. One student is chosen at random. What is the probability they play both? Simplest form.

    Answer(as a fraction)

  3. Question 3

    A bag has 4 red and 3 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form.

    Answer(as a fraction)

  4. Question 4

    In a class of 29, 18 play guitar, 14 play piano and 8 play both. One student is chosen at random. What is the probability they play guitar or piano (or both)? Simplest form.

    Answer(as a fraction)

  5. Question 5

    A bag has 6 red and 7 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form.

    Answer(as a fraction)

  6. Question 6

    In a class of 27, 9 play guitar, 15 play piano and 4 play both. One student is chosen at random. What is the probability they play guitar or piano (or both)? Simplest form.

    Answer(as a fraction)

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Answer key: Tree diagrams and Venn diagrams

  1. 1. 9/16

  2. 2. 8/21

  3. 3. 2/7

  4. 4. 24/29

  5. 5. 5/26

  6. 6. 20/27