Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Use aₙ = a₁ + (n − 1)d for arithmetic sequences
Algebra
CCSS HSF.BF.A.2CCSS HSF.LE.A.2England: GCSE Foundation Algebra
Objective and success criteria
Students will: Use aₙ = a₁ + (n − 1)d for arithmetic 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: Linear sequences: the nth term
Leads to: Decide if a sequence is arithmetic, geometric or neither; Sum an arithmetic series and find its length; Generate and model with recursive sequences
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 (Linear sequences: the nth term). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the nth term of the sequence 5, 6, 7, 8, … → n+4Prompt: The common difference tells you the number in front of n.
- The nth term of a sequence is 9n − 5. What is the 12th term? → 103Prompt: Substitute n = 12.
- Is 134 a term in the sequence with nth term 4n − 4? (Yes / No) → NoPrompt: Solve 4n − 4 = 134.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Use aₙ = a₁ + (n − 1)d for arithmetic 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: An arithmetic sequence starts 11, 17, 23, … Find the 75th term.
- Step 1: d = 6
- Step 2: a₇₅ = 11 + 74 × 6 = 455
- Answer: 455
- 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.
- An arithmetic sequence starts 15, 13, 11, … Find the 29th term. → -41Prompt: Find the common difference d.
- In an arithmetic sequence, a₃ = −3 and a₁₀ = −24. Find the first term a₁. → 3Prompt: From term 3 to term 10 there are 7 steps of d.
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.
- An arithmetic sequence starts 10, 6, 2, … Find the 99th term. → -382Prompt: Find the common difference d.
- In an arithmetic sequence, a₂ = −5 and a₈ = −11. Find the first term a₁. → -4Prompt: From term 2 to term 8 there are 6 steps of d.
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: Linear sequences: the nth term.
- 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
- Move on to: Decide if a sequence is arithmetic, geometric or neither; Sum an arithmetic series and find its length; Generate and model with recursive sequences.
- 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