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Math lesson plan · 7th grade (Year 8 in England) · 30 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 · 4 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, 16, 11, 15 is 14. Find the mean absolute deviation. → 1.5Prompt: Find how far each value is from the mean (ignore signs).
  2. Find the upper quartile (Q3) of: 39, 20, 33, 4, 6, 45, 7, 12, 8, 31, 32 → 33Prompt: Order the data and find the median.
  3. Maya's scores: 14, 16, 18, 16. Noah's scores: 10, 22, 16, 16. Both have mean 16. Whose scores are more consistent (smaller MAD)? (Maya / Noah) → MayaPrompt: MAD measures how spread out the data is around the mean.

Hook · 3 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 · 7 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 · 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. Class A's mean height is 151 cm and Class B's is 167 cm. Both have a mean absolute deviation of 4 cm. The difference in means is how many MADs? → 4Prompt: Find the difference between the means.
  2. Minutes of daily reading. Elena's group: 27, 29, 15, 22, 19, 24, 25. Hiro's group: 35, 37, 26, 33, 29, 33, 34. Using medians, which group typically reads for longer? (Elena's group / Hiro's group / They are the same) → Hiro's groupPrompt: Order each list and find the middle value.

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. Minutes of daily reading. Yuki's group: 10, 19, 24, 11, 29, 15, 27. Felix's group: 16, 24, 28, 17, 33, 20, 30. Using medians, which group typically reads for longer? (Yuki's group / Felix's group / They are the same) → Felix's groupPrompt: Order each list and find the middle value.
  2. Two basketball players' points per game: Liam has median 18 and IQR 5; Hana has median 18 and IQR 10. Who is more consistent? (Liam / Hana) → LiamPrompt: Consistency is about spread, not the average.

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/ 6

  1. Question 1

    Class A's mean height is 144 cm and Class B's is 156 cm. Both have a mean absolute deviation of 3 cm. The difference in means is how many MADs?

    Answer

  2. Question 2

    Minutes of daily reading. Ben's group: 27, 21, 13, 23, 26, 24, 26. Priya's group: 30, 26, 17, 28, 28, 27, 32. Using medians, which group typically reads for longer?

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

  3. Question 3

    Two basketball players' points per game: Jamal has median 18 and IQR 8; Arjun has median 18 and IQR 10. Who is more consistent?

    • A. Jamal
    • B. Arjun

  4. Question 4

    Class A's mean height is 146 cm and Class B's is 150 cm. Both have a mean absolute deviation of 2 cm. The difference in means is how many MADs?

    Answer

  5. Question 5

    Minutes of daily reading. Arjun's group: 10, 13, 14, 12, 12, 22, 15. Ines's group: 17, 17, 21, 17, 17, 26, 21. Using medians, which group typically reads for longer?

    • A. Arjun's group
    • B. Ines's group
    • C. They are the same

  6. Question 6

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

    • A. Ethan
    • B. Ravi

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Answer key: Compare two groups using centre and spread

  1. 1. 4

  2. 2. B. Priya's group

  3. 3. A. Jamal

  4. 4. 2

  5. 5. B. Ines's group

  6. 6. B. Ravi