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: 6, 11, 6, 13 → 9Prompt: Add all the numbers.
What is √9? → 3Prompt: Which number multiplied by itself gives this?
Find the median of: 1, 12, 17, 10, 11, 15 → 11.5Prompt: 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: 7, 13 → 3Prompt: Find the mean, then each value's distance from it.
Set A: 9, 14, 17, 20, 25. Set B: 16, 17, 17, 18, 17. 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: 5, 10, 13, 16, 21. Set B: 12, 13, 13, 14, 13. 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: 7, 9, 7, 9 → 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