Math lesson plan · 9th grade (Year 10 in England) · 60 minutes
Tree diagrams and Venn diagrams
Statistics and probability
CCSS HSS.CP.A.2CCSS HSS.CP.B.7England: GCSE Foundation ProbabilityEngland: GCSE Higher Probability
Objective and success criteria
Students will: Tree diagrams and Venn diagrams.
- 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: Compound events and sample spaces
Leads to: Conditional probability and independence; Binomial probability; Complete and use a two-set Venn diagram
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 (Compound events and sample spaces). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Two fair dice are rolled and the scores added. What is the probability the total is 3? Give a fraction in simplest form. → 1/18Prompt: There are 6 × 6 = 36 equally likely outcomes.
- A coin is flipped 3 times. How many outcomes are in the sample space? → 8Prompt: Each flip has 2 outcomes.
- Liam has 2 T-shirts, 4 pairs of trousers and 2 pairs of trainers. How many different outfits (one of each) can Liam make? → 16Prompt: Use the counting principle: multiply the number of choices.
Hook · 6 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Tree diagrams and Venn diagrams. 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: A bag has 3 red and 6 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form.
- Step 1: 3/9 × 2/8 = 6/72
- Step 2: = 1/12
- Answer: 1/12
- 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.
- A bag has 7 red and 4 blue counters. Two are taken without replacement. What is the probability both are red? Give a fraction in simplest form. → 21/55Prompt: Multiply along the branches of the tree diagram.
- In a class of 33, 19 play guitar, 12 play piano and 4 play both. One student is chosen at random. What is the probability they play both? Simplest form. → 4/33Prompt: Draw a Venn diagram. Put the 'both' number in the overlap first.
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.
- A bag has 2 red and 6 blue counters. Two are taken with replacement. What is the probability both are red? Give a fraction in simplest form. → 1/16Prompt: Multiply along the branches of the tree diagram.
- In a class of 18, 10 play guitar, 7 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. → 7/9Prompt: Draw a Venn diagram. Put the 'both' number in the overlap 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: Compound events and sample spaces.
- 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: Conditional probability and independence; Binomial probability; Complete and use a two-set Venn diagram.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder