Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Permutations and combinations
Statistics and probability
CCSS HSS.CP.B.9
Objective and success criteria
Students will: Permutations and combinations.
- 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: Expected value; Binomial probability; Find a coefficient in a binomial expansion
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 (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 10? Give a fraction in simplest form. → 1/12Prompt: 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.
- Kwame has 2 T-shirts, 4 pairs of trousers and 2 pairs of trainers. How many different outfits (one of each) can Kwame make? → 16Prompt: Use the counting principle: multiply the number of choices.
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Permutations and combinations. 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: In how many ways can 1st, 2nd, 3rd and 4th place be awarded among 7 runners?
- Step 1: 7 × 6 × 5 × 4 = 840
- Answer: 840
- 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.
- In how many ways can a team of 4 be chosen from 5 players (order does not matter)? → 5Prompt: Order does not matter: use combinations nCr.
- Mei has 6 different books to put on a shelf. In how many different orders can they be arranged? → 720Prompt: How many choices for the first spot, then the second…?
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.
- Aisha has 7 different books to put on a shelf. In how many different orders can they be arranged? → 5040Prompt: How many choices for the first spot, then the second…?
- In how many ways can 1st, 2nd, 3rd and 4th place be awarded among 9 runners? → 3024Prompt: Order matters: use permutations nPr.
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: Expected value; Binomial probability; Find a coefficient in a binomial expansion.
- 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