Math lesson plan · 11th grade (Year 12 in England) · 45 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 · 5 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.
- A variable is normally distributed with mean 138 and standard deviation 10. About what percentage of values lie between 108 and 168? → 99.7Prompt: How many standard deviations from the mean are these limits?
- A test has mean 57 and standard deviation 3. Find the z-score of a mark of 54. → -1Prompt: z = (x − mean) ÷ standard deviation.
- Scores have mean 83 and standard deviation 4. What is the z-score of 77? → -1.5Prompt: z = (x − mean) ÷ standard deviation.
Hook · 5 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 · 10 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 · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- A quantity is normally distributed with mean 76 and standard deviation 3. What percentage of values lie between 70 and 76? → 47.5Prompt: Convert each end to 'number of standard deviations from the mean'.
- A factory fills 400 bottles. Volumes are normally distributed with mean 250 ml and standard deviation 27 ml. About how many bottles hold less than 196 ml? → 10Prompt: That value is 2 standard deviations from the mean.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A factory fills 1000 bottles. Volumes are normally distributed with mean 500 ml and standard deviation 43 ml. About how many bottles hold less than 457 ml? → 160Prompt: That value is 1 standard deviation from the mean.
- A quantity is normally distributed with mean 63 and standard deviation 10. What percentage of values lie between 63 and 93? → 49.85Prompt: Convert each end to 'number of 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