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

Use a random sample to make predictions

Statistics and probability

CCSS 7.SP.A.2England: KS3 Statistics

Objective and success criteria

Students will: Use a random sample to make predictions.

  • 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, 22 said they walk to school. There are 875 students in the school. Estimate how many walk to school. → 770Prompt: Assume the sample represents the whole school.
  2. 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? (Yes / No, it is biased) → YesPrompt: Does every member of the population have the same chance of being chosen?
  3. In a random sample of 25 students, 5 said they walk to school. There are 325 students in the school. Estimate how many walk to school. → 65Prompt: 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: Use a random sample to make predictions. 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 20 students, 10 walk or cycle to school. Predict how many of the school's 460 students walk or cycle to school.
  • Step 1: 10/20 × 460 = 230
  • Answer: 230
  • 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 50 students, 33 want a longer lunch break. Predict how many of the school's 500 students want a longer lunch break. → 330Prompt: Find the fraction of the sample first.
  2. Scientists tag 34 fish in a lake and release them. Later they catch 50 fish and 6 are tagged. Estimate the number of fish in the lake (nearest whole number). → 283Prompt: The fraction tagged in the sample should match the fraction tagged in the lake.

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. In a random sample of 20 students, 18 want a longer lunch break. Predict how many of the school's 200 students want a longer lunch break. → 180Prompt: Find the fraction of the sample first.
  2. Scientists tag 54 fish in a lake and release them. Later they catch 60 fish and 8 are tagged. Estimate the number of fish in the lake (nearest whole number). → 405Prompt: The fraction tagged in the sample should match the fraction tagged in the lake.

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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Use a random sample to make predictions

Name

Date

Score/ 6

  1. Question 1

    Scientists tag 22 fish in a lake and release them. Later they catch 50 fish and 4 are tagged. Estimate the number of fish in the lake (nearest whole number).

    Answer

  2. Question 2

    In a random sample of 40 students, 28 walk or cycle to school. Predict how many of the school's 960 students walk or cycle to school.

    Answer

  3. Question 3

    Scientists tag 20 fish in a lake and release them. Later they catch 40 fish and 7 are tagged. Estimate the number of fish in the lake (nearest whole number).

    Answer

  4. Question 4

    In a random sample of 20 students, 18 walk or cycle to school. Predict how many of the school's 460 students walk or cycle to school.

    Answer

  5. Question 5

    Scientists tag 31 fish in a lake and release them. Later they catch 40 fish and 4 are tagged. Estimate the number of fish in the lake (nearest whole number).

    Answer

  6. Question 6

    In a random sample of 50 students, 26 walk or cycle to school. Predict how many of the school's 1300 students walk or cycle to school.

    Answer

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Answer key: Use a random sample to make predictions

  1. 1. 275

  2. 2. 672

  3. 3. 114

  4. 4. 414

  5. 5. 310

  6. 6. 676