Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Read the growth or decay rate from y = a(1 ± r)ᵗ
Algebra
CCSS HSF.LE.B.5CCSS HSF.IF.C.8.BEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Read the growth or decay rate from y = a(1 ± r)ᵗ.
- 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: Exponential growth and decay; Percentage increase and decrease
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 (Exponential growth and decay; Percentage increase and decrease). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- y = 4 × 3ˣ. Find y when x = 2. Round to 2 decimal places if needed. → 36Prompt: Work out the power first.
- A bike costs $120. In a sale it is 25% off. What is the sale price? (Type the number only.) → 90Prompt: Find 25% of 120 first.
- Does y = 55(3)ˣ show exponential growth or decay? (Growth / Decay) → GrowthPrompt: Look at the base b being raised to the power x.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Read the growth or decay rate from y = a(1 ± r)ᵗ. 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 = 350(0.92)áµ—. Which describes the change each time period?
- Step 1: 0.92 = 1 − 0.08
- Step 2: decay of 8%
- Answer: decay of 8%
- 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 = 550(0.8)ᵗ. Which describes the change each time period? (growth of 20% / decay of 20% / decay of 80% / growth of 80%) → decay of 20%Prompt: Compare the base with 1.
- A medicine dose of 2050 mg in the body falls by 5% each hour. Which model gives the amount after t hours? (y = 2050(0.05)ᵗ / y = 2050(1.05)ᵗ / y = 2050 − 5t / y = 2050(0.95)ᵗ) → y = 2050(0.95)ᵗPrompt: Each period you multiply by the same factor.
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.
- Zara's laptop battery loses 5% of its remaining charge every hour. What number is the charge multiplied by each hour? Give a decimal. → 0.95Prompt: After losing a percentage, what percentage is left?
- Leo's video channel has 900 subscribers and grows by 3% each month. Which model gives the subscribers after t months? (y = 900(0.03)ᵗ / y = 900(1.03)ᵗ / y = 900(0.97)ᵗ / y = 900 + 3t) → y = 900(1.03)ᵗPrompt: Each period you multiply by the same factor.
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: Exponential growth and decay.
- 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