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Math lesson plan · 7th grade (Year 8 in England) · 60 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 · 6 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 10, 14, 16, 20 is 15. Find the mean absolute deviation. → 3Prompt: Find how far each value is from the mean (ignore signs).
  2. Find the lower quartile (Q1) of: 31, 4, 45, 3, 6, 29, 35 → 4Prompt: Order the data and find the median.
  3. Kofi's scores: 14, 17, 20, 17. Ana's scores: 9, 25, 17, 17. Both have mean 17. Whose scores are more consistent (smaller MAD)? (Kofi / Ana) → KofiPrompt: MAD measures how spread out the data is around the mean.

Hook · 6 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 · 12 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 · 12 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 164 cm. Both have a mean absolute deviation of 2 cm. The difference in means is how many MADs? → 2Prompt: Find the difference between the means.
  2. Minutes of daily reading. Nia's group: 10, 26, 25, 28, 23, 12, 11. Noah's group: 12, 29, 29, 30, 28, 16, 16. Using medians, which group typically reads for longer? (Nia's group / Noah's group / They are the same) → Noah's groupPrompt: Order each list and find the middle value.

You do: independent practice · 17 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 · 7 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: Kai has median 18 and IQR 12; Daniel has median 18 and IQR 15. Who is more consistent? (Kai / Daniel) → KaiPrompt: Consistency is about spread, not the average.
  2. Class A's mean height is 144 cm and Class B's is 152 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/ 8

  1. Question 1

    Two basketball players' points per game: Ava has median 18 and IQR 6; Felix has median 18 and IQR 8. Who is more consistent?

    • A. Ava
    • B. Felix

  2. Question 2

    Class A's mean height is 151 cm and Class B's is 171 cm. Both have a mean absolute deviation of 5 cm. The difference in means is how many MADs?

    Answer

  3. Question 3

    Minutes of daily reading. Lucia's group: 30, 10, 22, 19, 16, 30, 25. Ava's group: 38, 16, 31, 26, 24, 39, 33. Using medians, which group typically reads for longer?

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

  4. Question 4

    Two basketball players' points per game: Sofia has median 18 and IQR 6; Hiro has median 18 and IQR 8. Who is more consistent?

    • A. Sofia
    • B. Hiro

  5. Question 5

    Class A's mean height is 156 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?

    Answer

  6. Question 6

    Minutes of daily reading. Ben's group: 21, 25, 29, 10, 28, 15, 12. Jamal's group: 29, 29, 35, 14, 35, 23, 18. Using medians, which group typically reads for longer?

    • A. Ben's group
    • B. Jamal's group
    • C. They are the same

  7. Question 7

    Two basketball players' points per game: Nia has median 18 and IQR 7; Ana has median 18 and IQR 5. Who is more consistent?

    • A. Nia
    • B. Ana

  8. Question 8

    Class A's mean height is 155 cm and Class B's is 161 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. Ava

  2. 2. 4

  3. 3. B. Ava's group

  4. 4. A. Sofia

  5. 5. 4

  6. 6. B. Jamal's group

  7. 7. B. Ana

  8. 8. 2