Math lesson plan · 9th grade (Year 10 in England) · 30 minutes
Find the ratio and terms of a geometric sequence
Algebra
CCSS HSF.BF.A.2CCSS HSF.LE.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Find the ratio and terms of a geometric sequence.
- 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; Laws of exponents (indices)
Leads to: Decide if a sequence is arithmetic, geometric or neither; Sum a finite geometric series; 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 · 4 min
- Quick retrieval from earlier learning (Linear sequences: the nth term; Laws of exponents (indices)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the nth term of the sequence 9, 4, −1, −6, … → -5n+14Prompt: The common difference tells you the number in front of n.
- Simplify y¹² ÷ y⁷ and write it as y to a single power. What is the power? → 5Prompt: Dividing powers of the same base: subtract the exponents.
- The nth term of a sequence is 4n + 5. What is the 100th term? → 405Prompt: Substitute n = 100.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Find the ratio and terms of a geometric sequence. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: What is the common ratio of the geometric sequence 1, 4, 16, 64, …?
- Step 1: 4 ÷ 1 = 4
- Answer: 4
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- What is the common ratio of the geometric sequence 1, 4, 16, 64, …? → 4Prompt: Divide a term by the term before it.
- Find the 7th term of the geometric sequence 3, 6, 12, … → 192Prompt: aₙ = a₁ × rⁿ⁻¹.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- What is the common ratio of the geometric sequence 2, 10, 50, 250, …? → 5Prompt: Divide a term by the term before it.
- Find the 5th term of the geometric sequence 1, 5, 25, … → 625Prompt: aₙ = a₁ × rⁿ⁻¹.
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 a finite geometric series; 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