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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, 18, 24, 15, 22 is 19. Find the mean absolute deviation. → 3.2Prompt: Find how far each value is from the mean (ignore signs).
  2. Find the lower quartile (Q1) of: 6, 2, 50, 32, 14, 26, 39, 8, 37, 3, 19 → 6Prompt: Order the data and find the median.
  3. Grace's scores: 25, 27, 29, 27. Leo's scores: 22, 32, 27, 27. Both have mean 27. Whose scores are more consistent (smaller MAD)? (Grace / Leo) → GracePrompt: 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 160 cm and Class B's is 172 cm. Both have a mean absolute deviation of 4 cm. The difference in means is how many MADs? → 3Prompt: Find the difference between the means.
  2. Minutes of daily reading. Diego's group: 23, 11, 20, 21, 17, 13, 22. Hiro's group: 32, 21, 30, 31, 27, 23, 32. Using medians, which group typically reads for longer? (Diego'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: 21, 30, 14, 17, 18, 26, 19. Noah's group: 29, 38, 19, 24, 24, 35, 25. Using medians, which group typically reads for longer? (Yuki's group / Noah's group / They are the same) → Noah's groupPrompt: Order each list and find the middle value.
  2. Two basketball players' points per game: Ines has median 18 and IQR 4; Zoe has median 18 and IQR 2. Who is more consistent? (Ines / Zoe) → ZoePrompt: 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

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

    • A. Kai
    • B. Luis

  2. Question 2

    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

  3. Question 3

    Minutes of daily reading. Kai's group: 11, 22, 30, 13, 24, 23, 27. Chloe's group: 17, 32, 36, 23, 34, 31, 36. Using medians, which group typically reads for longer?

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

  4. Question 4

    Two basketball players' points per game: Omar has median 18 and IQR 7; Ines has median 18 and IQR 12. Who is more consistent?

    • A. Omar
    • B. Ines

  5. Question 5

    Class A's mean height is 150 cm and Class B's is 158 cm. Both have a mean absolute deviation of 4 cm. The difference in means is how many MADs?

    Answer

  6. Question 6

    Minutes of daily reading. Isla's group: 19, 13, 21, 21, 26, 16, 27. Fatima's group: 28, 22, 28, 26, 31, 25, 34. Using medians, which group typically reads for longer?

    • A. Isla'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. Kai

  2. 2. 4

  3. 3. B. Chloe's group

  4. 4. A. Omar

  5. 5. 2

  6. 6. B. Fatima's group