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Math lesson plan · 7th grade (Year 8 in England) · 45 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 · 5 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 11, 14, 15, 12, −2 is 10. Find the mean absolute deviation. → 4.8Prompt: Find how far each value is from the mean (ignore signs).
  2. Find the upper quartile (Q3) of: 20, 25, 21, 10, 16, 32, 28 → 28Prompt: Order the data and find the median.
  3. Aisha's scores: 9, 11, 13, 11. Kofi's scores: 4, 18, 11, 11. Both have mean 11. Whose scores are more consistent (smaller MAD)? (Aisha / Kofi) → AishaPrompt: MAD measures how spread out the data is around the mean.

Hook · 5 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 · 10 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 · 10 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 146 cm and Class B's is 156 cm. Both have a mean absolute deviation of 5 cm. The difference in means is how many MADs? → 2Prompt: Find the difference between the means.
  2. Minutes of daily reading. Sofia's group: 14, 23, 26, 21, 11, 27, 11. Elena's group: 22, 31, 33, 26, 15, 35, 18. Using medians, which group typically reads for longer? (Sofia's group / Elena's group / They are the same) → Elena's groupPrompt: Order each list and find the middle value.

You do: independent practice · 10 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 · 5 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Minutes of daily reading. Ravi's group: 26, 20, 17, 27, 29, 28, 15. Arjun's group: 35, 29, 26, 38, 41, 39, 27. Using medians, which group typically reads for longer? (Ravi's group / Arjun's group / They are the same) → Arjun's groupPrompt: Order each list and find the middle value.
  2. Two basketball players' points per game: Omar has median 18 and IQR 4; Mei has median 18 and IQR 6. Who is more consistent? (Omar / Mei) → OmarPrompt: 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/ 8

  1. Question 1

    Two basketball players' points per game: Chloe has median 18 and IQR 4; Noah has median 18 and IQR 6. Who is more consistent?

    • A. Chloe
    • B. Noah

  2. Question 2

    Minutes of daily reading. Liam's group: 29, 22, 17, 25, 10, 23, 13. Zara's group: 34, 29, 24, 32, 14, 31, 17. Using medians, which group typically reads for longer?

    • A. Liam's group
    • B. Zara's group
    • C. They are the same

  3. Question 3

    Class A's mean height is 143 cm and Class B's is 153 cm. Both have a mean absolute deviation of 5 cm. The difference in means is how many MADs?

    Answer

  4. Question 4

    Two basketball players' points per game: Ravi has median 18 and IQR 7; Tariq has median 18 and IQR 4. Who is more consistent?

    • A. Ravi
    • B. Tariq

  5. Question 5

    Minutes of daily reading. Sofia's group: 23, 13, 18, 20, 30, 13, 15. Luis's group: 29, 22, 25, 28, 39, 20, 21. Using medians, which group typically reads for longer?

    • A. Sofia's group
    • B. Luis's group
    • C. They are the same

  6. Question 6

    Class A's mean height is 141 cm and Class B's is 145 cm. Both have a mean absolute deviation of 2 cm. The difference in means is how many MADs?

    Answer

  7. Question 7

    Two basketball players' points per game: Hana has median 18 and IQR 4; Lucia has median 18 and IQR 7. Who is more consistent?

    • A. Hana
    • B. Lucia

  8. Question 8

    Minutes of daily reading. Chloe's group: 21, 29, 16, 15, 30, 25, 11. Fatima's group: 30, 35, 22, 21, 37, 34, 18. Using medians, which group typically reads for longer?

    • A. Chloe's group
    • B. Fatima's group
    • C. They are the same

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Answer key: Compare two groups using centre and spread

  1. 1. A. Chloe

  2. 2. B. Zara's group

  3. 3. 2

  4. 4. B. Tariq

  5. 5. B. Luis's group

  6. 6. 2

  7. 7. A. Hana

  8. 8. B. Fatima's group