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

Experimental probability and expected results

Statistics and probability

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

Objective and success criteria

Students will: Experimental probability and expected results.

  • 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: Probability of simple events

Leads to: Expected value; Compare experimental and theoretical probability

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 (Probability of simple events). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. What is the probability of rolling an even number on a fair six-sided dice? Give a fraction in simplest form. → 1/2Prompt: List all the equally likely outcomes.
  2. The probability a spinner lands on blue is 0.8. What is the probability it does NOT land on blue? Give a decimal. → 0.2Prompt: An event either happens or it does not: the two probabilities add up to 1 (or 100%).
  3. What is the probability of rolling a number greater than 4 on a fair six-sided dice? Give a fraction in simplest form. → 1/3Prompt: List all the equally likely outcomes.

Hook · 3 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Experimental probability and expected results. 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: Jamal flips a drawing pin 50 times. It lands point up 10 times. What is the relative frequency of landing point up? Give a fraction in simplest form.
  • Step 1: 10/50
  • Step 2: = 1/5
  • Answer: 1/5
  • 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. Maya flips a drawing pin 20 times. It lands point up 17 times. What is the relative frequency of landing point up? Give a fraction in simplest form. → 17/20Prompt: Relative frequency = number of times it happened ÷ number of trials.
  2. The probability of an event is 3/10. The experiment is done 300 times. How many times would you expect the event to happen? → 90Prompt: Expected number = probability × number of trials.

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. The probability of an event is 2/5. The experiment is done 130 times. How many times would you expect the event to happen? → 52Prompt: Expected number = probability × number of trials.
  2. Priya flips a drawing pin 50 times. It lands point up 38 times. What is the relative frequency of landing point up? Give a fraction in simplest form. → 19/25Prompt: Relative frequency = number of times it happened ÷ number of trials.

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: Probability of simple events.
  • 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: Expected value; Compare experimental and theoretical probability.
  • 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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Experimental probability and expected results

Name

Date

Score/ 6

  1. Question 1

    Daniel flips a drawing pin 60 times. It lands point up 55 times. What is the relative frequency of landing point up? Give a fraction in simplest form.

    Answer(as a fraction)

  2. Question 2

    The probability of an event is 1/6. The experiment is done 180 times. How many times would you expect the event to happen?

    Answer

  3. Question 3

    Lucia flips a drawing pin 100 times. It lands point up 53 times. What is the relative frequency of landing point up? Give a fraction in simplest form.

    Answer(as a fraction)

  4. Question 4

    The probability of an event is 3/10. The experiment is done 220 times. How many times would you expect the event to happen?

    Answer

  5. Question 5

    Kofi flips a drawing pin 100 times. It lands point up 23 times. What is the relative frequency of landing point up? Give a fraction in simplest form.

    Answer(as a fraction)

  6. Question 6

    The probability of an event is 1/3. The experiment is done 66 times. How many times would you expect the event to happen?

    Answer

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Answer key: Experimental probability and expected results

  1. 1. 11/12

  2. 2. 30

  3. 3. 53/100

  4. 4. 66

  5. 5. 23/100

  6. 6. 22