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

Samples and populations

Statistics and probability

CCSS 7.SP.A.1CCSS 7.SP.A.2England: KS3 StatisticsEngland: GCSE Foundation Statistics

Objective and success criteria

Students will: Samples and populations.

  • 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: Proportional relationships

Leads to: Use a random sample to make predictions; Spot biased and fair samples

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 (Proportional relationships). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Is this relationship proportional? x: 1, 3, 5 → y: 8, 24, 40 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
  2. Priya can type 21 words in 3 minutes. At the same rate, how many words in 8 minutes? → 56Prompt: Find the words per minute first.
  3. Is this relationship proportional? x: 3, 4, 10 → y: 27, 37, 90 (Yes, proportional / No, not proportional) → No, not proportionalPrompt: Find y ÷ x for each pair.

Hook · 3 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Samples and populations. 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 random sample of 50 students, 3 said they walk to school. There are 1850 students in the school. Estimate how many walk to school.
  • Step 1: 3/50 × 1850 = 111
  • Answer: 111
  • 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 random sample of 25 students, 21 said they walk to school. There are 400 students in the school. Estimate how many walk to school. → 336Prompt: Assume the sample represents the whole school.
  2. A survey is planned by asking people leaving a gym how often they exercise. 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?

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 survey is planned by asking people leaving a gym how often they exercise. 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?
  2. In a random sample of 20 students, 12 said they walk to school. There are 620 students in the school. Estimate how many walk to school. → 372Prompt: Assume the sample represents the whole school.

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: Proportional relationships.
  • 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 a random sample to make predictions; Spot biased and fair samples.
  • 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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Samples and populations

Name

Date

Score/ 6

  1. Question 1

    A survey is planned by picking names out of a hat containing every student's name. Is this likely to give a fair (unbiased) sample?

    • A. Yes
    • B. No, it is biased

  2. Question 2

    In a random sample of 20 students, 7 said they walk to school. There are 440 students in the school. Estimate how many walk to school.

    Answer

  3. Question 3

    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?

    • A. Yes
    • B. No, it is biased

  4. Question 4

    In a random sample of 40 students, 3 said they walk to school. There are 880 students in the school. Estimate how many walk to school.

    Answer

  5. Question 5

    A survey is planned by asking every 10th person on the school register. Is this likely to give a fair (unbiased) sample?

    • A. Yes
    • B. No, it is biased

  6. Question 6

    In a random sample of 40 students, 15 said they walk to school. There are 720 students in the school. Estimate how many walk to school.

    Answer

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Answer key: Samples and populations

  1. 1. A. Yes

  2. 2. 154

  3. 3. B. No, it is biased

  4. 4. 66

  5. 5. A. Yes

  6. 6. 270