Math lesson plan · 12th grade (Year 13 in England) · 45 minutes
Find probabilities using combinations
Statistics and probability
CCSS HSS.CP.B.9England: A-level Statistics
Objective and success criteria
Students will: Find probabilities using 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: Permutations and combinations
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 (Permutations and combinations). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- In how many ways can 1st, 2nd, 3rd place be awarded among 8 runners? → 336Prompt: Order matters: use permutations nPr.
- Jamal 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 a team of 2 be chosen from 7 players (order does not matter)? → 21Prompt: Order does not matter: use combinations nCr.
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Find probabilities using 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: A team of 4 is chosen at random from 7 girls and 5 boys. Find the probability that the team is all girls, as a fraction in simplest form.
- Step 1: 7C4 / 12C4 = 35/495
- Step 2: = 7/99
- Answer: 7/99
- 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.
- A team of 3 is chosen at random from 8 girls and 6 boys. Find the probability that the team is all girls, as a fraction in simplest form. → 2/13Prompt: Favourable outcomes: choose all the team from the girls.
- In a game you choose 3 different numbers from 1 to 30. Then 3 winning numbers are drawn. What is the probability that you match all 3? Give a fraction. → 1/4060Prompt: Order doesn't matter: count combinations.
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.
- In a game you choose 4 different numbers from 1 to 27. Then 4 winning numbers are drawn. What is the probability that you match all 4? Give a fraction. → 1/17550Prompt: Order doesn't matter: count combinations.
- A team of 3 is chosen at random from 8 girls and 3 boys. Find the probability that the team is all girls, as a fraction in simplest form. → 56/165Prompt: Favourable outcomes: choose all the team from the girls.
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: Permutations and combinations.
- 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-12.
Free lesson plan from eurekami.com/lesson-plan-builder