Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Test for independence using a two-way table
Statistics and probability
CCSS HSS.CP.A.4CCSS HSS.CP.A.5England: A-level Statistics
Objective and success criteria
Students will: Test for independence using a two-way table.
- 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: Conditional probability and independence; Joint and conditional relative frequencies in two-way tables
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 (Conditional probability and independence; Joint and conditional relative frequencies in two-way tables). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Survey: Likes science & is in Club — 18; Likes science & not in Club — 11; Doesn't like science & in Club — 6; neither — 18. Given a student is in the Club, what is the probability they like science? Simplest form. → 3/4Prompt: 'Given' means only look at the Club members.
- How students travel to school: Year 9: cycle 25, walk 17 Year 10: cycle 25, walk 26 What proportion of all students are "Year 10 and cycles"? Give a decimal to 2 decimal places. → 0.27Prompt: A joint relative frequency = cell count ÷ grand total.
- P(A) = 0.3, P(B) = 0.5 and P(A and B) = 0.25. Are A and B independent? (Yes / No) → NoPrompt: A and B are independent if P(A and B) = P(A) × P(B).
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Test for independence using a two-way table. 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: Club survey: Plays chess: likes puzzles 18, doesn't 12 No chess: likes puzzles 36, doesn't 24 Are "plays chess" and "likes puzzles" independent?
- Step 1: 18/30 = 36/60
- Step 2: Yes
- Answer: Yes
- 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.
- Club survey: Plays chess: likes puzzles 36, doesn't 18 No chess: likes puzzles 36, doesn't 18 Are "plays chess" and "likes puzzles" independent? (Yes / No) → YesPrompt: Compare P(likes puzzles | chess) with P(likes puzzles | no chess).
- Club survey: Plays chess: likes puzzles 22, doesn't 24 No chess: likes puzzles 30, doesn't 44 Are "plays chess" and "likes puzzles" independent? (Yes / No) → NoPrompt: Compare P(likes puzzles | chess) with P(likes puzzles | no chess).
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.
- Club survey: Plays chess: likes puzzles 43, doesn't 32 No chess: likes puzzles 60, doesn't 51 Are "plays chess" and "likes puzzles" independent? (Yes / No) → NoPrompt: Compare P(likes puzzles | chess) with P(likes puzzles | no chess).
- Club survey: Plays chess: likes puzzles 43, doesn't 24 No chess: likes puzzles 40, doesn't 27 Are "plays chess" and "likes puzzles" independent? (Yes / No) → NoPrompt: Compare P(likes puzzles | chess) with P(likes puzzles | no chess).
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: Conditional probability and independence.
- 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