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Math lesson plan · 7th grade (Year 8 in England) · 60 minutes

Compare two groups using centre and spread

Statistics and probability

CCSS 7.SP.B.3CCSS 7.SP.B.4England: KS3 StatisticsEngland: GCSE Foundation Statistics

Objective and success criteria

Students will: Compare two groups using centre and spread.

  • 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: Mean absolute deviation (MAD); Find quartiles and the interquartile range

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 · 6 min

  • Quick retrieval from earlier learning (Mean absolute deviation (MAD); Find quartiles and the interquartile range). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. The mean of 14, 13, 11, −2 is 9. Find the mean absolute deviation. → 5.5Prompt: Find how far each value is from the mean (ignore signs).
  2. Find the lower quartile (Q1) of: 36, 35, 20, 27, 32, 42, 30, 6, 27, 41, 45 → 27Prompt: Order the data and find the median.
  3. Lucia's scores: 12, 15, 18, 15. Elena's scores: 8, 22, 15, 15. Both have mean 15. Whose scores are more consistent (smaller MAD)? (Lucia / Elena) → LuciaPrompt: MAD measures how spread out the data is around the mean.

Hook · 6 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Compare two groups using centre and spread. Read the success criteria together.

I do: model it · 12 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Class A's mean height is 145 cm and Class B's is 157 cm. Both have a mean absolute deviation of 3 cm. The difference in means is how many MADs?
  • Step 1: 157 − 145 = 12
  • Step 2: 12 ÷ 3 = 4
  • Answer: 4
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 12 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. Class A's mean height is 160 cm and Class B's is 164 cm. Both have a mean absolute deviation of 2 cm. The difference in means is how many MADs? → 2Prompt: Find the difference between the means.
  2. Minutes of daily reading. Omar's group: 12, 12, 19, 20, 29, 24, 13. Ines's group: 14, 16, 21, 23, 32, 29, 19. Using medians, which group typically reads for longer? (Omar's group / Ines's group / They are the same) → Ines's groupPrompt: Order each list and find the middle value.

You do: independent practice · 17 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 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 7 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Minutes of daily reading. Ana's group: 13, 11, 27, 30, 19, 25, 11. Kwame's group: 18, 13, 31, 35, 20, 27, 12. Using medians, which group typically reads for longer? (Ana's group / Kwame's group / They are the same) → Kwame's groupPrompt: Order each list and find the middle value.
  2. Class A's mean height is 142 cm and Class B's is 150 cm. Both have a mean absolute deviation of 4 cm. The difference in means is how many MADs? → 2Prompt: Find the difference between the means.

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: Mean absolute deviation (MAD).
  • 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 two groups using centre and spread

Name

Date

Score/ 8

  1. Question 1

    Two basketball players' points per game: Kwame has median 18 and IQR 5; Hiro has median 18 and IQR 2. Who is more consistent?

    • A. Kwame
    • B. Hiro

  2. Question 2

    Class A's mean height is 160 cm and Class B's is 166 cm. Both have a mean absolute deviation of 3 cm. The difference in means is how many MADs?

    Answer

  3. Question 3

    Minutes of daily reading. Daniel's group: 11, 11, 19, 17, 30, 28, 16. Felix's group: 13, 14, 21, 22, 31, 32, 20. Using medians, which group typically reads for longer?

    • A. Daniel's group
    • B. Felix's group
    • C. They are the same

  4. Question 4

    Two basketball players' points per game: Isla has median 18 and IQR 9; Diego has median 18 and IQR 6. Who is more consistent?

    • A. Isla
    • B. Diego

  5. Question 5

    Class A's mean height is 141 cm and Class B's is 153 cm. Both have a mean absolute deviation of 3 cm. The difference in means is how many MADs?

    Answer

  6. Question 6

    Minutes of daily reading. Diego's group: 13, 28, 23, 29, 16, 13, 12. Ben's group: 18, 33, 26, 34, 22, 18, 17. Using medians, which group typically reads for longer?

    • A. Diego's group
    • B. Ben's group
    • C. They are the same

  7. Question 7

    Two basketball players' points per game: Sofia has median 18 and IQR 12; Ana has median 18 and IQR 9. Who is more consistent?

    • A. Sofia
    • B. Ana

  8. Question 8

    Class A's mean height is 145 cm and Class B's is 157 cm. Both have a mean absolute deviation of 4 cm. The difference in means is how many MADs?

    Answer

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Answer key: Compare two groups using centre and spread

  1. 1. B. Hiro

  2. 2. 2

  3. 3. B. Felix's group

  4. 4. B. Diego

  5. 5. 4

  6. 6. B. Ben's group

  7. 7. B. Ana

  8. 8. 3