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Math lesson plan · 10th grade (Year 11 in England) · 30 minutes

Reason about standard deviation without calculating

Statistics and probability

CCSS HSS.ID.A.2CCSS HSS.ID.A.3England: GCSE Higher Statistics

Objective and success criteria

Students will: Reason about standard deviation without calculating.

  • 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: Spread: standard deviation

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 (Spread: standard deviation). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Find the population standard deviation of: 5, 9 → 2Prompt: Find the mean, then each value's distance from it.
  2. Set A: 24, 25, 25, 26, 25. Set B: 17, 22, 25, 28, 33. Which set has the larger standard deviation? (A / B / They are equal) → BPrompt: Standard deviation measures how spread out the data are from the mean.
  3. Set A: 21, 26, 29, 32, 37. Set B: 28, 29, 29, 30, 29. Which set has the larger standard deviation? (A / B / They are equal) → APrompt: Standard deviation measures how spread out the data are from 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: Reason about standard deviation without calculating. 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: Set X: 34, 36, 38, 40, 42 Set Y: 22, 30, 38, 46, 54 Both have mean 38. Which set has the larger standard deviation?
  • Step 1: Y
  • Answer: Y
  • 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. Set X: 49, 51, 53, 55, 57 Set Y: 35, 44, 53, 62, 71 Both have mean 53. Which set has the larger standard deviation? (X / Y / They are equal) → YPrompt: Standard deviation measures how far values are from the mean.
  2. A set of test scores has standard deviation 3. The teacher adds 15 bonus points to every score. What is the new standard deviation? → 3Prompt: Adding the same amount shifts all values but keeps the gaps.

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. A set of test scores has standard deviation 14. The teacher adds 8 bonus points to every score. What is the new standard deviation? → 14Prompt: Adding the same amount shifts all values but keeps the gaps.
  2. Set X: 31, 40, 49, 58, 67 Set Y: 47, 48, 49, 50, 51 Both have mean 49. Which set has the larger standard deviation? (X / Y / They are equal) → XPrompt: Standard deviation measures how far values are from the mean.

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: Spread: standard deviation.
  • 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-10.

Free lesson plan from eurekami.com/lesson-plan-builder

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Reason about standard deviation without calculating

Name

Date

Score/ 6

  1. Question 1

    A set of test scores has standard deviation 3. The teacher adds 5 bonus points to every score. What is the new standard deviation?

    Answer

  2. Question 2

    Set X: 35, 40, 45, 50, 55 Set Y: 41, 43, 45, 47, 49 Both have mean 45. Which set has the larger standard deviation?

    • A. X
    • B. Y
    • C. They are equal

  3. Question 3

    Some lengths have standard deviation 6 cm. Every length is multiplied by 4. What is the new standard deviation, in cm?

    Answer

  4. Question 4

    Set X: 21, 23, 25, 27, 29 Set Y: 5, 15, 25, 35, 45 Both have mean 25. Which set has the larger standard deviation?

    • A. X
    • B. Y
    • C. They are equal

  5. Question 5

    Some lengths have standard deviation 4 cm. Every length is multiplied by 3. What is the new standard deviation, in cm?

    Answer

  6. Question 6

    Set X: 21, 28, 35, 42, 49 Set Y: 31, 33, 35, 37, 39 Both have mean 35. Which set has the larger standard deviation?

    • A. X
    • B. Y
    • C. They are equal

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Answer key: Reason about standard deviation without calculating

  1. 1. 3

  2. 2. A. X

  3. 3. 24

  4. 4. B. Y

  5. 5. 12

  6. 6. A. X