Math lesson plan · 12th grade (Year 13 in England) · 45 minutes
Find a coefficient in a binomial expansion
Algebra
CCSS HSA.APR.C.5England: A-level Pure Mathematics
Objective and success criteria
Students will: Find a coefficient in a binomial expansion.
- 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; Expand three binomials
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Permutations and combinations; Expand three binomials). 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 7 runners? → 210Prompt: Order matters: use permutations nPr.
- Expand and simplify: (x − 4)(x + 2)(x − 1) → x^3-3x^2-6x+8Prompt: Expand two of the brackets first.
- Lucia 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…?
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Find a coefficient in a binomial expansion. 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: Find the coefficient of x in the expansion of (1 + x)⁴.
- Step 1: 4C1 = 4
- Answer: 4
- 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.
- Find the coefficient of x in the expansion of (1 + x)⁶. → 6Prompt: The coefficients are a row of Pascal's triangle.
- Find the coefficient of x² in (1 + 3x)⁶. → 135Prompt: The term is nCk × a^(n−k) × (bx)^k.
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.
- Find the coefficient of x⁷ in the expansion of (1 + x)⁸. → 8Prompt: The coefficients are a row of Pascal's triangle.
- Find the term independent of x in (x + 1/x)⁸. → 70Prompt: A general term is nCk xⁿ⁻ᵏ (1/x)ᵏ = nCk xⁿ⁻²ᵏ.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Permutations and combinations.
- Use concrete materials: balance scales or a balance drawing.
- 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