Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Generate and model with recursive sequences
Algebra
CCSS HSF.IF.A.3CCSS HSF.BF.A.2England: A-level Pure Mathematics
Objective and success criteria
Students will: Generate and model with recursive sequences.
- 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: Use aₙ = a₁ + (n − 1)d for arithmetic sequences; Find the ratio and terms of a geometric sequence
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 (Use aₙ = a₁ + (n − 1)d for arithmetic sequences; Find the ratio and terms of a geometric sequence). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- An arithmetic sequence starts −1, 3, 7, … Find the 56th term. → 219Prompt: Find the common difference d.
- What is the common ratio of the geometric sequence 96, 48, 24, 12, …? → 0.5Prompt: Divide a term by the term before it.
- In an arithmetic sequence, a₂ = −13 and a₁₂ = −33. Find the common difference d. → -2Prompt: From term 2 to term 12 there are 10 steps of d.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Generate and model with recursive sequences. 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: u₁ = −3 and uₙ₊₁ = −uₙ + 0. Find u₄.
- Step 1: u₂ = 3, u₃ = −3
- Step 2: u₄ = 3
- Answer: 3
- 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.
- u₁ = 0 and uₙ₊₁ = 3uₙ + 0. Find u₄. → 0Prompt: Use each term to make the next one.
- A loan of $1400 grows by 1% interest each month, then a payment of $100 is made. So Bₙ₊₁ = 1.01Bₙ − 100. What is the balance after 3 months? Round to 2 decimal places. → 1139.41Prompt: B₀ is the starting balance. Apply the rule three times.
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.
- Which rule generates 3, 11, 35, 107, …? (uₙ₊₁ = 3uₙ − 2 / uₙ₊₁ = 3uₙ + 2 / uₙ₊₁ = uₙ + 3 / uₙ₊₁ = 4uₙ − 1) → uₙ₊₁ = 3uₙ + 2Prompt: Test each rule on the first term, then the second.
- u₁ = 3 and uₙ₊₁ = −2uₙ + 0. Find u₄. → -24Prompt: Use each term to make the next one.
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: Use aₙ = a₁ + (n − 1)d for arithmetic sequences.
- 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-11.
Free lesson plan from eurekami.com/lesson-plan-builder