Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
The normal distribution (68–95–99.7 rule)
Statistics and probability
CCSS HSS.ID.A.4
Objective and success criteria
Students will: The normal distribution (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: Spread: standard deviation
Leads to: Combine regions of a normal curve with the 68–95–99.7 rule
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.
- Find the population standard deviation of: 2, 10 → 4Prompt: Find the mean, then each value's distance from it.
- Set A: 13, 18, 21, 24, 29. Set B: 20, 21, 21, 22, 21. 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.
- Find the population standard deviation of: 1, 9 → 4Prompt: Find the mean, then each value's distance from it.
Hook · 3 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: The normal distribution (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 variable is normally distributed with mean 103 and standard deviation 5. About what percentage of values lie between 98 and 108?
- Step 1: They are 1 standard deviation either side of the mean.
- Step 2: ≈ 68%
- Answer: 68
- 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.
- A variable is normally distributed with mean 166 and standard deviation 6. About what percentage of values lie between 160 and 172? → 68Prompt: How many standard deviations from the mean are these limits?
- Scores have mean 84 and standard deviation 12. What is the z-score of 60? → -2Prompt: z = (x − mean) ÷ standard deviation.
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.
- Scores have mean 113 and standard deviation 3. What is the z-score of 114.5? → 0.5Prompt: z = (x − mean) ÷ standard deviation.
- A variable is normally distributed with mean 119 and standard deviation 11. About what percentage of values lie between 97 and 141? → 95Prompt: How many standard deviations from the mean are these limits?
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
- Move on to: Combine regions of a normal curve with the 68–95–99.7 rule.
- 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