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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 16, 13, 22, 14, 20 is 17. Find the mean absolute deviation. → 3.2Prompt: Find how far each value is from the mean (ignore signs).
  2. Find the upper quartile (Q3) of: 24, 1, 50, 9, 30, 16, 28 → 30Prompt: Order the data and find the median.
  3. Sofia's scores: 25, 26, 27, 26. Amara's scores: 22, 30, 26, 26. Both have mean 26. Whose scores are more consistent (smaller MAD)? (Sofia / Amara) → SofiaPrompt: 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 148 cm and Class B's is 160 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.
  2. Minutes of daily reading. Isla's group: 18, 27, 10, 27, 13, 19, 27. Hiro's group: 27, 36, 21, 36, 20, 30, 35. Using medians, which group typically reads for longer? (Isla'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. Two basketball players' points per game: Sofia has median 18 and IQR 8; Amara has median 18 and IQR 11. Who is more consistent? (Sofia / Amara) → SofiaPrompt: Consistency is about spread, not the average.
  2. Class A's mean height is 158 cm and Class B's is 166 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/ 6

  1. Question 1

    Two basketball players' points per game: Arjun has median 18 and IQR 11; Luis has median 18 and IQR 16. Who is more consistent?

    • A. Arjun
    • B. Luis

  2. Question 2

    Minutes of daily reading. Lucia's group: 14, 23, 25, 23, 26, 10, 15. Arjun's group: 23, 33, 35, 34, 35, 17, 26. Using medians, which group typically reads for longer?

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

  3. Question 3

    Class A's mean height is 153 cm and Class B's is 165 cm. Both have a mean absolute deviation of 4 cm. The difference in means is how many MADs?

    Answer

  4. Question 4

    Two basketball players' points per game: Kofi has median 18 and IQR 12; Jamal has median 18 and IQR 17. Who is more consistent?

    • A. Kofi
    • B. Jamal

  5. Question 5

    Minutes of daily reading. Isla's group: 14, 15, 17, 19, 24, 20, 29. Sam's group: 18, 22, 21, 23, 29, 28, 37. Using medians, which group typically reads for longer?

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

  6. Question 6

    Class A's mean height is 142 cm and Class B's is 154 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. A. Arjun

  2. 2. B. Arjun's group

  3. 3. 3

  4. 4. A. Kofi

  5. 5. B. Sam's group

  6. 6. 4