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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 20, 14, 14, 14, 18 is 16. Find the mean absolute deviation. → 2.4Prompt: Find how far each value is from the mean (ignore signs).
  2. Find the lower quartile (Q1) of: 40, 29, 33, 27, 1, 2, 37, 33, 43, 32, 41 → 27Prompt: Order the data and find the median.
  3. Nia's scores: 25, 26, 27, 26. Tariq's scores: 22, 30, 26, 26. Both have mean 26. Whose scores are more consistent (smaller MAD)? (Nia / Tariq) → NiaPrompt: 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 141 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? → 3Prompt: Find the difference between the means.
  2. Minutes of daily reading. Sam's group: 28, 24, 12, 11, 16, 20, 20. Diego's group: 35, 32, 19, 19, 22, 25, 26. Using medians, which group typically reads for longer? (Sam's group / Diego's group / They are the same) → Diego'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. Zoe's group: 18, 30, 29, 30, 28, 28, 19. Felix's group: 27, 38, 37, 36, 36, 37, 25. Using medians, which group typically reads for longer? (Zoe's group / Felix's group / They are the same) → Felix's groupPrompt: Order each list and find the middle value.
  2. Class A's mean height is 159 cm and Class B's is 171 cm. Both have a mean absolute deviation of 3 cm. The difference in means is how many MADs? → 4Prompt: 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: Ava has median 18 and IQR 7; Sofia has median 18 and IQR 5. Who is more consistent?

    • A. Ava
    • B. Sofia

  2. Question 2

    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

  3. Question 3

    Minutes of daily reading. Diego's group: 28, 21, 30, 10, 10, 10, 26. Ines's group: 37, 29, 35, 15, 18, 18, 35. Using medians, which group typically reads for longer?

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

  4. Question 4

    Two basketball players' points per game: Mei has median 18 and IQR 5; Sofia has median 18 and IQR 3. Who is more consistent?

    • A. Mei
    • B. Sofia

  5. Question 5

    Class A's mean height is 152 cm and Class B's is 167 cm. Both have a mean absolute deviation of 5 cm. The difference in means is how many MADs?

    Answer

  6. Question 6

    Minutes of daily reading. Sam's group: 13, 26, 12, 17, 18, 20, 23. Kofi's group: 16, 28, 17, 21, 24, 25, 27. Using medians, which group typically reads for longer?

    • A. Sam's group
    • B. Kofi's group
    • C. They are the same

  7. Question 7

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

    • A. Arjun
    • B. Zara

  8. Question 8

    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

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Answer key: Compare two groups using centre and spread

  1. 1. B. Sofia

  2. 2. 2

  3. 3. B. Ines's group

  4. 4. B. Sofia

  5. 5. 3

  6. 6. B. Kofi's group

  7. 7. B. Zara

  8. 8. 4