Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Exponential growth and decay
Algebra
CCSS HSF.LE.A.1CCSS HSF.LE.A.2CCSS HSF.IF.C.8.BEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Exponential growth and decay.
- 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: Laws of exponents (indices); Compound interest and depreciation
Leads to: Exponential models; Logarithms; Arithmetic and geometric sequences and series
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 (Laws of exponents (indices); Compound interest and depreciation). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify y¹³ ÷ y⁵ and write it as y to a single power. What is the power? → 8Prompt: Dividing powers of the same base: subtract the exponents.
- $1300 is saved at 10% compound interest per year. How much is in the account after 4 years? Round to 2 decimal places (type the number only). → 1903.33Prompt: Each year the amount is multiplied by 1.1.
- Evaluate 4⁻² as a fraction. → 1/16Prompt: A negative exponent means 'one over' the positive power.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Exponential growth and decay. 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: y = 17 × 1.1ˣ. Find y when x = 4. Round to 2 decimal places if needed.
- Step 1: 1.1⁴ = 1.4641
- Step 2: 17 × 1.4641 = 24.8897
- Answer: 24.89
- 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.
- y = 6 × 1.5ˣ. Find y when x = 3. Round to 2 decimal places if needed. → 20.25Prompt: Work out the power first.
- Does y = 30(3)ˣ show exponential growth or decay? (Growth / Decay) → GrowthPrompt: Look at the base b being raised to the power x.
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.
- Kai's bacteria culture starts with 280 cells and doubles every 5 hours. How many cells after 10 hours? → 1120Prompt: How many doubling periods fit into 10 hours?
- Does y = 81(1.05)ˣ show exponential growth or decay? (Growth / Decay) → GrowthPrompt: Look at the base b being raised to the power x.
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: Laws of exponents (indices).
- 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: Exponential models; Logarithms; Arithmetic and geometric sequences and series.
- 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