Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Decide if a sequence is arithmetic, geometric or neither
Algebra
CCSS HSF.LE.A.1CCSS HSF.BF.A.2England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Decide if a sequence is arithmetic, geometric or neither.
- 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 20, 25, 30, … Find the 50th term. → 265Prompt: Find the common difference d.
- What is the common ratio of the geometric sequence −2, −6, −18, −54, …? → 3Prompt: Divide a term by the term before it.
- In an arithmetic sequence, a₂ = −16 and a₅ = −34. Find the first term a₁. → -10Prompt: From term 2 to term 5 there are 3 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: Decide if a sequence is arithmetic, geometric or neither. 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: Is 2, 6, 18, 54, 162, … arithmetic, geometric or neither?
- Step 1: Geometric
- Answer: Geometric
- 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.
- Is 1, 4, 9, 16, 25, … arithmetic, geometric or neither? (Arithmetic / Geometric / Neither) → NeitherPrompt: Arithmetic: you add the same amount each time.
- What type of sequence does aₙ = 3 × 3ⁿ produce? (Arithmetic / Geometric / Neither) → GeometricPrompt: Write out the first three or four terms.
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.
- Is 5, 10, 20, 40, 80, … arithmetic, geometric or neither? (Arithmetic / Geometric / Neither) → GeometricPrompt: Arithmetic: you add the same amount each time.
- What type of sequence does aₙ = 7 × 3ⁿ produce? (Arithmetic / Geometric / Neither) → GeometricPrompt: Write out the first three or four terms.
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-9.
Free lesson plan from eurekami.com/lesson-plan-builder