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Math lesson plan · 9th grade (Year 10 in England) · 30 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 · 4 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 = 48 × 0.5ˣ. Find y when x = 2. Round to 2 decimal places if needed. → 12Prompt: Work out the power first.
  2. A bike costs $250. In a sale it is 25% off. What is the sale price? (Type the number only.) → 187.5Prompt: Find 25% of 250 first.
  3. Does y = 23(0.95)ˣ show exponential growth or decay? (Growth / Decay) → DecayPrompt: Look at the base b being raised to the power x.

Hook · 3 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 · 7 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 · 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.
  1. y = 630(0.97)ᵗ. Which describes the change each time period? (decay of 3% / decay of 97% / growth of 97% / growth of 3%) → decay of 3%Prompt: Compare the base with 1.
  2. A medicine dose of 2900 mg in the body falls by 5% each hour. Which model gives the amount after t hours? (y = 2900(0.05)ᵗ / y = 2900(0.95)ᵗ / y = 2900 − 5t / y = 2900(1.05)ᵗ) → y = 2900(0.95)ᵗPrompt: Each period you multiply by the same factor.

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.
  1. A medicine dose of 100 mg in the body falls by 10% each hour. Which model gives the amount after t hours? (y = 100(0.9)ᵗ / y = 100 − 10t / y = 100(0.1)ᵗ / y = 100(1.1)ᵗ) → y = 100(0.9)ᵗPrompt: Each period you multiply by the same factor.
  2. y = 880(0.98)ᵗ. Which describes the change each time period? (decay of 2% / growth of 2% / decay of 98% / growth of 98%) → decay of 2%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/ 6

  1. Question 1

    Kai's video channel has 250 subscribers and grows by 12% each month. Which model gives the subscribers after t months?

    • A. y = 250 + 12t
    • B. y = 250(0.88)áµ—
    • C. y = 250(1.12)áµ—
    • D. y = 250(0.12)áµ—

  2. Question 2

    y = 380(1.03)áµ—. Which describes the change each time period?

    • A. growth of 3%
    • B. growth of 103%
    • C. decay of 3%

  3. Question 3

    Nia's laptop battery loses 20% of its remaining charge every hour. What number is the charge multiplied by each hour? Give a decimal.

    Answer

  4. Question 4

    A medicine dose of 650 mg in the body falls by 20% each hour. Which model gives the amount after t hours?

    • A. y = 650(1.2)áµ—
    • B. y = 650 − 20t
    • C. y = 650(0.8)áµ—
    • D. y = 650(0.2)áµ—

  5. Question 5

    y = 140(0.88)áµ—. Which describes the change each time period?

    • A. growth of 12%
    • B. decay of 12%
    • C. growth of 88%
    • D. decay of 88%

  6. Question 6

    Elena's laptop battery loses 25% 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. C. y = 250(1.12)áµ—

  2. 2. A. growth of 3%

  3. 3. 0.8

  4. 4. C. y = 650(0.8)áµ—

  5. 5. B. decay of 12%

  6. 6. 0.75