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Math lesson plan · 9th grade (Year 10 in England) · 60 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 · 6 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.
  1. y = 2 × 0.5ˣ. Find y when x = 2. Round to 2 decimal places if needed. → 0.5Prompt: Work out the power first.
  2. A bike costs $360. In a sale it is 10% off. What is the sale price? (Type the number only.) → 324Prompt: Find 10% of 360 first.
  3. Does y = 81(1.2)ˣ show exponential growth or decay? (Growth / Decay) → GrowthPrompt: Look at the base b being raised to the power x.

Hook · 6 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)áµ—. 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: 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 · 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.
  1. y = 270(0.92)ᵗ. Which describes the change each time period? (decay of 92% / growth of 92% / decay of 8% / growth of 8%) → decay of 8%Prompt: Compare the base with 1.
  2. A medicine dose of 1700 mg in the body falls by 20% each hour. Which model gives the amount after t hours? (y = 1700(1.2)ᵗ / y = 1700 − 20t / y = 1700(0.2)ᵗ / y = 1700(0.8)ᵗ) → y = 1700(0.8)ᵗPrompt: Each period you multiply by the same factor.

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.
  1. A medicine dose of 1200 mg in the body falls by 20% each hour. Which model gives the amount after t hours? (y = 1200(0.2)ᵗ / y = 1200 − 20t / y = 1200(0.8)ᵗ / y = 1200(1.2)ᵗ) → y = 1200(0.8)ᵗPrompt: Each period you multiply by the same factor.
  2. y = 60(1.2)ᵗ. Which describes the change each time period? (decay of 20% / growth of 20% / growth of 120%) → growth of 20%Prompt: Compare the base with 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: 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

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Read the growth or decay rate from y = a(1 ± r)ᵗ

Name

Date

Score/ 8

  1. Question 1

    y = 20(0.98)áµ—. Which describes the change each time period?

    • A. decay of 98%
    • B. growth of 2%
    • C. growth of 98%
    • D. decay of 2%

  2. Question 2

    Tariq's laptop battery loses 2% of its remaining charge every hour. What number is the charge multiplied by each hour? Give a decimal.

    Answer

  3. Question 3

    Daniel's video channel has 1200 subscribers and grows by 25% each month. Which model gives the subscribers after t months?

    • A. y = 1200(1.25)áµ—
    • B. y = 1200(0.25)áµ—
    • C. y = 1200(0.75)áµ—
    • D. y = 1200 + 25t

  4. Question 4

    y = 700(0.96)áµ—. Which describes the change each time period?

    • A. growth of 4%
    • B. decay of 4%
    • C. decay of 96%
    • D. growth of 96%

  5. Question 5

    Leo's laptop battery loses 10% of its remaining charge every hour. What number is the charge multiplied by each hour? Give a decimal.

    Answer

  6. Question 6

    A medicine dose of 100 mg in the body falls by 2% each hour. Which model gives the amount after t hours?

    • A. y = 100(0.98)áµ—
    • B. y = 100 − 2t
    • C. y = 100(0.02)áµ—
    • D. y = 100(1.02)áµ—

  7. Question 7

    y = 170(0.92)áµ—. Which describes the change each time period?

    • A. growth of 8%
    • B. growth of 92%
    • C. decay of 92%
    • D. decay of 8%

  8. Question 8

    Isla's laptop battery loses 15% of its remaining charge every hour. What number is the charge multiplied by each hour? Give a decimal.

    Answer

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Answer key: Read the growth or decay rate from y = a(1 ± r)ᵗ

  1. 1. D. decay of 2%

  2. 2. 0.98

  3. 3. A. y = 1200(1.25)áµ—

  4. 4. B. decay of 4%

  5. 5. 0.9

  6. 6. A. y = 100(0.98)áµ—

  7. 7. D. decay of 8%

  8. 8. 0.85