Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Spread: standard deviation
Statistics and probability
CCSS HSS.ID.A.2CCSS HSS.ID.A.3
Objective and success criteria
Students will: Spread: standard deviation.
- 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, median, mode and range; Square roots and cube roots
Leads to: The normal distribution (68–95–99.7 rule); Reason about standard deviation without calculating; Calculate variance and standard deviation
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 (Mean, median, mode and range; Square roots and cube roots). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the mean of: 14, 23, 14, 17, 15, 21, 22 → 18Prompt: Add all the numbers.
- What is √4? → 2Prompt: Which number multiplied by itself gives this?
- Find the median of: 3, 13, 25, 28, 27, 19 → 22Prompt: Put the numbers in order first.
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Spread: standard deviation. 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: Find the population standard deviation of: 8, 16
- Step 1: Mean = 12
- Step 2: Squared distances: 16, 16
- Step 3: σ = √(32 ÷ 2) = 4
- Answer: 4
- 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.
- Find the population standard deviation of: 5, 7, 5, 7 → 1Prompt: Find the mean, then each value's distance from it.
- Set A: 7, 12, 15, 18, 23. Set B: 14, 15, 15, 16, 15. 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.
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.
- Set A: 17, 22, 25, 28, 33. Set B: 24, 25, 25, 26, 25. 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: 10, 12, 10, 12 → 1Prompt: Find the mean, then each value's distance from it.
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, median, mode and range.
- 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: The normal distribution (68–95–99.7 rule); Reason about standard deviation without calculating; Calculate variance and standard deviation.
- 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