Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Calculate variance and standard deviation
Statistics and probability
CCSS HSS.ID.A.2England: A-level Statistics
Objective and success criteria
Students will: Calculate variance and 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: 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 · 5 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: 8, 10, 8, 10 → 1Prompt: Find the mean, then each value's distance from it.
- Set A: 20, 21, 21, 22, 21. Set B: 13, 18, 21, 24, 29. 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.
- Find the population standard deviation of: 3, 7, 3, 7 → 2Prompt: Find the mean, then each value's distance from it.
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Calculate variance and 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 variance of 27, 30, 31, 29, 28 (treat them as the whole population).
- Step 1: mean = 29
- Step 2: ((−2)² + (−1)² + 0² + 1² + 2²) ÷ 5 = 2
- Answer: 2
- 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 variance of 14, 11, 12, 15, 13 (treat them as the whole population). → 2Prompt: Find the mean first.
- Find the population standard deviation of 14, 14, 5, 13, 10, 4. Give 2 decimal places. → 4.12Prompt: σ = √( Σ(x − mean)² ÷ n ).
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.
- Find the population standard deviation of 10, 19, 13, 8, 10, 13. Give 2 decimal places. → 3.53Prompt: σ = √( Σ(x − mean)² ÷ n ).
- Find the variance of 4, 6, 5, 4, 6 (treat them as the whole population). → 0.8Prompt: Find the mean first.
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-11.
Free lesson plan from eurekami.com/lesson-plan-builder