Math lesson plan · 11th grade (Year 12 in England) · 60 minutes
Exponential models
Algebra
CCSS HSF.LE.A.2CCSS HSF.LE.B.5CCSS HSF.IF.C.8.B
Objective and success criteria
Students will: Exponential models.
- 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
Leads to: Continuous growth and the number e
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Exponential growth and decay). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- y = 27 × 1.5ˣ. Find y when x = 2. Round to 2 decimal places if needed. → 60.75Prompt: Work out the power first.
- Does y = 82(2)ˣ show exponential growth or decay? (Growth / Decay) → GrowthPrompt: Look at the base b being raised to the power x.
- Ravi's bacteria culture starts with 400 cells and doubles every 4 hours. How many cells after 16 hours? → 6400Prompt: How many doubling periods fit into 16 hours?
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Exponential models. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A population of 1000 grows by 5% each year. Write the model P(t) = 1000(b)áµ— and find P(5), to the nearest whole number.
- Step 1: P(t) = 1000(1.05)áµ—
- Step 2: P(5) ≈ 1276.28
- Step 3: ≈ 1276
- Answer: 1276
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- A population of 2000 shrinks by 2% each year. Write the model P(t) = 2000(b)ᵗ and find P(6), to the nearest whole number. → 1772Prompt: The growth factor b is 1 − r = 0.98.
- An exponential function y = abˣ passes through (1, 4) and (2, 8). What is b? → 2Prompt: Divide the two y-values: the a cancels.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A population of 2000 shrinks by 6% each year. Write the model P(t) = 2000(b)ᵗ and find P(7), to the nearest whole number. → 1297Prompt: The growth factor b is 1 − r = 0.94.
- An exponential function y = abˣ passes through (1, 12) and (2, 48). What is b? → 4Prompt: Divide the two y-values: the a cancels.
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
- Move on to: Continuous growth and the number e.
- 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-11.
Free lesson plan from eurekami.com/lesson-plan-builder