Back to the lesson plan builder
Lesson length30 min45 min60 min
Questions🔀 New questions

Print the plan for yourself; the student sheet prints on its own page after it.

Math lesson plan · 11th grade (Year 12 in England) · 30 minutes

Combine regions of a normal curve with the 68–95–99.7 rule

Statistics and probability

CCSS HSS.ID.A.4England: A-level Statistics

Objective and success criteria

Students will: Combine regions of a normal curve with the 68–95–99.7 rule.

  • 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: The normal distribution (68–95–99.7 rule); Calculate and use z-scores

Leads to: Find normal probabilities with z-scores and technology

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 (The normal distribution (68–95–99.7 rule); Calculate and use z-scores). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A variable is normally distributed with mean 72 and standard deviation 10. About what percentage of values lie between 52 and 92? → 95Prompt: How many standard deviations from the mean are these limits?
  2. A test has mean 75 and standard deviation 7. Find the z-score of a mark of 68. → -1Prompt: z = (x − mean) ÷ standard deviation.
  3. Scores have mean 86 and standard deviation 6. What is the z-score of 89? → 0.5Prompt: z = (x − mean) ÷ standard deviation.

Hook · 3 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Combine regions of a normal curve with the 68–95–99.7 rule. 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: A quantity is normally distributed with mean 21 and standard deviation 9. What percentage of values lie between 3 and 30?
  • Step 1: z from −2 to 1
  • Step 2: 81.5%
  • Answer: 81.5
  • 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. A quantity is normally distributed with mean 71 and standard deviation 6. What percentage of values lie between 65 and 71? → 34Prompt: Convert each end to 'number of standard deviations from the mean'.
  2. A factory fills 400 bottles. Volumes are normally distributed with mean 454 ml and standard deviation 24 ml. About how many bottles hold more than 502 ml? → 10Prompt: That value is 2 standard deviations from the mean.

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 quantity is normally distributed with mean 63 and standard deviation 5. What percentage of values lie between 63 and 78? → 49.85Prompt: Convert each end to 'number of standard deviations from the mean'.
  2. A factory fills 1000 bottles. Volumes are normally distributed with mean 373 ml and standard deviation 32 ml. About how many bottles hold less than 309 ml? → 25Prompt: That value is 2 standard deviations 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: The normal distribution (68–95–99.7 rule).
  • 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

  • Move on to: Find normal probabilities with z-scores and technology.
  • 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-11.

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

eurekami

Combine regions of a normal curve with the 68–95–99.7 rule

Name

Date

Score/ 6

  1. Question 1

    A quantity is normally distributed with mean 23 and standard deviation 5. What percentage of values lie between 13 and 23?

    Answer

  2. Question 2

    A factory fills 600 bottles. Volumes are normally distributed with mean 403 ml and standard deviation 31 ml. About how many bottles hold less than 372 ml?

    Answer

  3. Question 3

    A quantity is normally distributed with mean 58 and standard deviation 6. What percentage of values lie between 58 and 76?

    Answer

  4. Question 4

    A factory fills 200 bottles. Volumes are normally distributed with mean 239 ml and standard deviation 10 ml. About how many bottles hold more than 249 ml?

    Answer

  5. Question 5

    A quantity is normally distributed with mean 42 and standard deviation 6. What percentage of values lie between 30 and 48?

    Answer

  6. Question 6

    A factory fills 200 bottles. Volumes are normally distributed with mean 472 ml and standard deviation 47 ml. About how many bottles hold more than 519 ml?

    Answer

Free from eurekami.com

for the adult only

Answer key: Combine regions of a normal curve with the 68–95–99.7 rule

  1. 1. 47.5

  2. 2. 96

  3. 3. 49.85

  4. 4. 32

  5. 5. 81.5

  6. 6. 32