Math lesson plan · 10th grade (Year 11 in England) · 60 minutes
Conditional probability and independence
Statistics and probability
CCSS HSS.CP.A.3CCSS HSS.CP.A.4CCSS HSS.CP.B.6England: GCSE Higher Probability
Objective and success criteria
Students will: Conditional probability and independence.
- 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: Tree diagrams and Venn diagrams; Two-way tables
Leads to: Use P(A | B) = P(A and B) ÷ P(B); Test for independence using a two-way table
Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Tree diagrams and Venn diagrams; Two-way tables). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A bag has 6 red and 4 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form. → 1/3Prompt: Multiply along the branches of the tree diagram.
- A two-way table: Year 7 — cats 12, dogs 19; Year 8 — cats 10, dogs 8. How many students are in the table altogether? → 49Prompt: Find the row or column you need.
- In a class of 28, 17 play guitar, 11 play piano and 3 play both. One student is chosen at random. What is the probability they play guitar or piano (or both)? Simplest form. → 25/28Prompt: Draw a Venn diagram. Put the 'both' number in the overlap first.
Hook · 6 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Conditional probability and independence. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Survey: Likes science & is in Club — 19; Likes science & not in Club — 11; Doesn't like science & in Club — 5; neither — 12. Given a student is in the Club, what is the probability they like science? Simplest form.
- Step 1: Club members: 19 + 5 = 24
- Step 2: P = 19/24
- Answer: 19/24
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Survey: Likes science & is in Club — 19; Likes science & not in Club — 24; Doesn't like science & in Club — 25; neither — 15. Given a student is in the Club, what is the probability they like science? Simplest form. → 19/44Prompt: 'Given' means only look at the Club members.
- P(A) = 0.5, P(B) = 0.5 and P(A and B) = 0.25. Are A and B independent? (Yes / No) → YesPrompt: A and B are independent if P(A and B) = P(A) × P(B).
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Survey: Likes science & is in Club — 24; Likes science & not in Club — 9; Doesn't like science & in Club — 10; neither — 11. Given a student is in the Club, what is the probability they like science? Simplest form. → 12/17Prompt: 'Given' means only look at the Club members.
- P(A) = 0.5, P(B) = 0.2 and P(A and B) = 0.1. Are A and B independent? (Yes / No) → YesPrompt: A and B are independent if P(A and B) = P(A) × P(B).
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: Tree diagrams and Venn diagrams.
- 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: Use P(A | B) = P(A and B) ÷ P(B); Test for independence using a two-way table.
- 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