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

Spot biased and fair samples

Statistics and probability

CCSS 7.SP.A.1England: KS3 Statistics

Objective and success criteria

Students will: Spot biased and fair samples.

  • 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: Samples and populations

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 (Samples and populations). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. In a random sample of 25 students, 13 said they walk to school. There are 775 students in the school. Estimate how many walk to school. → 403Prompt: Assume the sample represents the whole school.
  2. A survey is planned by asking only the members of the football team about favourite sports. Is this likely to give a fair (unbiased) sample? (Yes / No, it is biased) → No, it is biasedPrompt: Does every member of the population have the same chance of being chosen?
  3. In a random sample of 20 students, 8 said they walk to school. There are 580 students in the school. Estimate how many walk to school. → 232Prompt: Assume the sample represents the whole school.

Hook · 3 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Spot biased and fair samples. 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: You want to find out which school lunch is most popular. Which sampling method is the fairest (least biased)?
  • Step 1: Ask every 10th student on the register, across all years: everyone has an equal chance.
  • Answer: Ask every 10th student on the register, across all years
  • 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. You want to find out which school lunch is most popular. Which sampling method is the fairest (least biased)? (Ask the first 10 students in the vegetarian queue / Ask every 10th student on the register, across all years / Ask only Year 7 / Ask the kitchen staff) → Ask every 10th student on the register, across all yearsPrompt: A fair sample gives everyone the same chance of being chosen.
  2. To check a factory's light bulbs, an inspector tests every 50th bulb made during the day. Is this sample likely to be biased? (Yes, biased / No, fair) → No, fairPrompt: Does everyone in the population have a fair chance of being chosen?

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. You want to find out which school lunch is most popular. Which sampling method is the fairest (least biased)? (Ask the first 10 students in the vegetarian queue / Ask every 10th student on the register, across all years / Ask only Year 7 / Ask the kitchen staff) → Ask every 10th student on the register, across all yearsPrompt: A fair sample gives everyone the same chance of being chosen.
  2. To check a factory's light bulbs, an inspector tests every 50th bulb made during the day. Is this sample likely to be biased? (Yes, biased / No, fair) → No, fairPrompt: Does everyone in the population have a fair chance of being chosen?

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: Samples and populations.
  • 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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Spot biased and fair samples

Name

Date

Score/ 6

  1. Question 1

    You want to find out how many hours of sleep teenagers get. Which sampling method is the fairest (least biased)?

    • A. Ask students in the library at 8 am
    • B. Use a random number generator to pick students from every year group
    • C. Post a poll that only night-owl gamers see
    • D. Ask your own class only

  2. Question 2

    To find students' favourite subject, a student council picks 40 names at random from the full school list. Is this sample likely to be biased?

    • A. Yes, biased
    • B. No, fair

  3. Question 3

    You want to find out how much time students spend on sport. Which sampling method is the fairest (least biased)?

    • A. Ask the football team
    • B. Ask people leaving the gym
    • C. Ask only your friends
    • D. Pick 50 names at random from the whole school list

  4. Question 4

    You want to find out how people in a town travel to work. Which sampling method is the fairest (least biased)?

    • A. Choose 100 households at random from the town's address list
    • B. Ask cyclists in a bike shop
    • C. Ask drivers at a petrol station
    • D. Ask people waiting at a bus stop

  5. Question 5

    To find how much students read, a teacher asks only the book club. Is this sample likely to be biased?

    • A. Yes, biased
    • B. No, fair

  6. Question 6

    To check a factory's light bulbs, an inspector tests every 50th bulb made during the day. Is this sample likely to be biased?

    • A. Yes, biased
    • B. No, fair

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Answer key: Spot biased and fair samples

  1. 1. B. Use a random number generator to pick students from every year group

  2. 2. B. No, fair

  3. 3. D. Pick 50 names at random from the whole school list

  4. 4. A. Choose 100 households at random from the town's address list

  5. 5. A. Yes, biased

  6. 6. B. No, fair