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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 6, 7, 5, 13, 19 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: 39, 48, 14, 36, 8, 15, 42, 42, 4, 33, 18 → 42Prompt: Order the data and find the median.
  3. Aisha's scores: 19, 22, 25, 22. Ana's scores: 16, 28, 22, 22. Both have mean 22. Whose scores are more consistent (smaller MAD)? (Aisha / Ana) → 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 148 cm and Class B's is 164 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. Hiro's group: 11, 27, 22, 25, 15, 27, 26. Amara's group: 16, 28, 23, 28, 17, 30, 27. Using medians, which group typically reads for longer? (Hiro's group / Amara's group / They are the same) → Amara'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. Class A's mean height is 140 cm and Class B's is 156 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. Two basketball players' points per game: Kai has median 18 and IQR 8; Leo has median 18 and IQR 5. Who is more consistent? (Kai / Leo) → LeoPrompt: 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

    Class A's mean height is 155 cm and Class B's is 163 cm. Both have a mean absolute deviation of 4 cm. The difference in means is how many MADs?

    Answer

  2. Question 2

    Two basketball players' points per game: Hiro has median 18 and IQR 8; Ravi has median 18 and IQR 13. Who is more consistent?

    • A. Hiro
    • B. Ravi

  3. Question 3

    Minutes of daily reading. Aisha's group: 11, 11, 22, 17, 17, 19, 16. Ava's group: 13, 16, 25, 22, 18, 23, 17. Using medians, which group typically reads for longer?

    • A. Aisha's group
    • B. Ava's group
    • C. They are the same

  4. Question 4

    Class A's mean height is 157 cm and Class B's is 161 cm. Both have a mean absolute deviation of 2 cm. The difference in means is how many MADs?

    Answer

  5. Question 5

    Two basketball players' points per game: Chloe has median 18 and IQR 9; Grace has median 18 and IQR 11. Who is more consistent?

    • A. Chloe
    • B. Grace

  6. Question 6

    Minutes of daily reading. Liam's group: 18, 11, 21, 26, 28, 22, 13. Ravi's group: 23, 16, 26, 30, 31, 25, 18. Using medians, which group typically reads for longer?

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

  7. Question 7

    Class A's mean height is 148 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?

    Answer

  8. Question 8

    Two basketball players' points per game: Daniel has median 18 and IQR 12; Felix has median 18 and IQR 10. Who is more consistent?

    • A. Daniel
    • B. Felix

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Answer key: Compare two groups using centre and spread

  1. 1. 2

  2. 2. A. Hiro

  3. 3. B. Ava's group

  4. 4. 2

  5. 5. A. Chloe

  6. 6. B. Ravi's group

  7. 7. 3

  8. 8. B. Felix