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Math lesson plan · 7th grade (Year 8 in England) · 30 minutes

Compare experimental and theoretical probability

Statistics and probability

CCSS 7.SP.C.6CCSS 7.SP.C.7.BEngland: KS3 ProbabilityEngland: GCSE Foundation Probability

Objective and success criteria

Students will: Compare experimental and theoretical probability.

  • 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: Experimental probability and expected results

Leads to: the next skill in this area.

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 (Experimental probability and expected results). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Diego flips a drawing pin 80 times. It lands point up 50 times. What is the relative frequency of landing point up? Give a fraction in simplest form. → 5/8Prompt: Relative frequency = number of times it happened ÷ number of trials.
  2. The probability of an event is 1/2. The experiment is done 50 times. How many times would you expect the event to happen? → 25Prompt: Expected number = probability × number of trials.
  3. Diego flips a drawing pin 40 times. It lands point up 37 times. What is the relative frequency of landing point up? Give a fraction in simplest form. → 37/40Prompt: Relative frequency = number of times it happened ÷ number of trials.

Hook · 3 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Compare experimental and theoretical probability. 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 drawing pin is dropped 40 times. It lands point up 31 times. What is the experimental probability of landing point up? Give a fraction in simplest form.
  • Step 1: 31/40
  • Answer: 31/40
  • 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 drawing pin is dropped 25 times. It lands point up 5 times. What is the experimental probability of landing point up? Give a fraction in simplest form. → 1/5Prompt: Experimental probability = times it happened ÷ number of trials.
  2. A die is rolled 120 times and lands on 4 exactly 19 times. How many 4s would you expect from a fair die? How many more or fewer did you get? Give (actual − expected). → -1Prompt: Expected = number of rolls × 1/6.

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. A die is rolled 120 times and lands on 4 exactly 18 times. How many 4s would you expect from a fair die? How many more or fewer did you get? Give (actual − expected). → -2Prompt: Expected = number of rolls × 1/6.
  2. Kofi flips a coin 20 times and Mei flips it 2000 times. Whose proportion of heads is likely to be closer to 0.5? (Mei / Both will be exactly 0.5 / Kofi) → MeiPrompt: More trials usually give results closer to the theoretical probability.

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: Experimental probability and expected results.
  • 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

  • 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-7.

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

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Compare experimental and theoretical probability

Name

Date

Score/ 6

  1. Question 1

    A drawing pin is dropped 80 times. It lands point up 49 times. What is the experimental probability of landing point up? Give a fraction in simplest form.

    Answer(as a fraction)

  2. Question 2

    Luis flips a coin 20 times and Aisha flips it 500 times. Whose proportion of heads is likely to be closer to 0.5?

    • A. Both will be exactly 0.5
    • B. Aisha
    • C. Luis

  3. Question 3

    A die is rolled 600 times and lands on 4 exactly 114 times. How many 4s would you expect from a fair die? How many more or fewer did you get? Give (actual − expected).

    Answer

  4. Question 4

    A drawing pin is dropped 25 times. It lands point up 8 times. What is the experimental probability of landing point up? Give a fraction in simplest form.

    Answer(as a fraction)

  5. Question 5

    Liam flips a coin 20 times and Ines flips it 1000 times. Whose proportion of heads is likely to be closer to 0.5?

    • A. Liam
    • B. Both will be exactly 0.5
    • C. Ines

  6. Question 6

    A die is rolled 300 times and lands on 4 exactly 60 times. How many 4s would you expect from a fair die? How many more or fewer did you get? Give (actual − expected).

    Answer

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Answer key: Compare experimental and theoretical probability

  1. 1. 49/80

  2. 2. B. Aisha

  3. 3. 14

  4. 4. 8/25

  5. 5. C. Ines

  6. 6. 10