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

Complete and use a two-set Venn diagram

Statistics and probability

CCSS HSS.CP.A.1England: GCSE Foundation ProbabilityEngland: GCSE Higher Probability

Objective and success criteria

Students will: Complete and use a two-set Venn diagram.

  • 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: Tree diagrams and Venn diagrams

Leads to: Use the addition rule P(A or B)

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 (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 3 red and 3 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 30, 16 play guitar, 10 play piano and 5 play both. One student is chosen at random. What is the probability they play both? Simplest form. → 1/6Prompt: Draw a Venn diagram. Put the 'both' number in the overlap first.
  3. A bag has 7 red and 2 blue counters. Two are taken with replacement. What is the probability both are red? Give a fraction in simplest form. → 49/81Prompt: Multiply along the branches of the tree diagram.

Hook · 3 min

  • 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.

I do: model it · 7 min

  • 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.

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. In a club of 44 students, 22 play chess, 23 play the guitar and 7 do neither. How many do both? → 8Prompt: How many do at least one activity?
  2. Venn diagram of 54 people: apples only 18, bananas only 15, both 13, neither 8. A person is chosen at random. Find the probability they like apples but not bananas. Give a fraction in its simplest form. → 1/3Prompt: Decide which regions of the diagram you need.

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. Venn diagram of 29 people: apples only 12, bananas only 5, both 9, neither 3. A person is chosen at random. Find the probability they like apples or bananas (or both). Give a fraction in its simplest form. → 26/29Prompt: Decide which regions of the diagram you need.
  2. In a club of 52 students, 28 play chess, 26 play the guitar and 7 do neither. How many do both? → 9Prompt: How many do at least one activity?

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: Tree diagrams and Venn diagrams.
  • 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: Use the addition rule P(A or B).
  • 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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Complete and use a two-set Venn diagram

Name

Date

Score/ 6

  1. Question 1

    In a club of 43 students, 25 play chess, 21 play the guitar and 2 do neither. How many do both?

    Answer

  2. Question 2

    Venn diagram of 32 people: apples only 5, bananas only 17, both 9, neither 1. A person is chosen at random. Find the probability they like apples but not bananas. Give a fraction in its simplest form.

    Answer(as a fraction)

  3. Question 3

    In a club of 36 students, 28 play chess, 21 play the guitar and 2 do neither. How many do both?

    Answer

  4. Question 4

    Venn diagram of 46 people: apples only 17, bananas only 10, both 11, neither 8. A person is chosen at random. Find the probability they like both apples and bananas. Give a fraction in its simplest form.

    Answer(as a fraction)

  5. Question 5

    In a club of 42 students, 20 play chess, 28 play the guitar and 9 do neither. How many do both?

    Answer

  6. Question 6

    Venn diagram of 32 people: apples only 12, bananas only 5, both 13, neither 2. A person is chosen at random. Find the probability they like apples but not bananas. Give a fraction in its simplest form.

    Answer(as a fraction)

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Answer key: Complete and use a two-set Venn diagram

  1. 1. 5

  2. 2. 5/32

  3. 3. 15

  4. 4. 11/46

  5. 5. 15

  6. 6. 3/8