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Math lesson plan · 9th grade (Year 10 in England) · 45 minutes

Compound interest and depreciation

Decimals and percentages

CCSS HSF.LE.A.1.CCCSS HSA.SSE.B.3.CEngland: GCSE Foundation RatioEngland: GCSE Higher Ratio

Objective and success criteria

Students will: Compound interest and depreciation.

  • 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: Percentage increase and decrease; Whole-number exponents

Leads to: Exponential growth and decay; Compare compounding periods and continuous interest

Materials: Place value chart with tenths and hundredths, Hundred squares, Number lines, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 5 min

  • Quick retrieval from earlier learning (Percentage increase and decrease; Whole-number exponents). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A bike costs $110. In a sale it is 25% off. What is the sale price? (Type the number only.) → 82.5Prompt: Find 25% of 110 first.
  2. Evaluate 4⁴. → 256Prompt: Write it out: 4 × 4 × 4 × 4
  3. Increase 800 by 15%. → 920Prompt: Find 15% of 800 and add it on.

Hook · 5 min

  • Show two prices or race times with decimals and ask which is bigger, then why.
  • Share the objective: Compound interest and depreciation. 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: $4800 is saved at 4% compound interest per year. How much is in the account after 3 years? Round to 2 decimal places (type the number only).
  • Step 1: 4800 × 1.04³ = 5399.3472
  • Step 2: ≈ 5399.35
  • Answer: 5399.35
  • 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.
  1. $4100 is saved at 5% compound interest per year. How much is in the account after 4 years? Round to 2 decimal places (type the number only). → 4983.58Prompt: Each year the amount is multiplied by 1.05.
  2. A car worth $11000 loses 15% of its value each year. What is it worth after 3 years? Round to the nearest whole number (type the number only). → 6755Prompt: Each year the value is multiplied by 0.85.

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.
  1. A car worth $39000 loses 10% of its value each year. What is it worth after 2 years? Round to the nearest whole number (type the number only). → 31590Prompt: Each year the value is multiplied by 0.9.
  2. $4300 is saved at 5% compound interest per year. How much is in the account after 3 years? Round to 2 decimal places (type the number only). → 4977.79Prompt: Each year the amount is multiplied by 1.05.

Watch out for

  • Thinking 0.45 is bigger than 0.5 because 45 is bigger than 5.
  • Moving the digits the wrong way when multiplying or dividing by 10.

Support and stretch

Support

  • Review first: Percentage increase and decrease.
  • Use concrete materials: place value chart with tenths and hundredths.
  • 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 growth and decay; Compare compounding periods and continuous interest.
  • 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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Compound interest and depreciation

Name

Date

Score/ 8

  1. Question 1

    A car worth $30000 loses 10% of its value each year. What is it worth after 2 years? Round to the nearest whole number (type the number only).

    Answer

  2. Question 2

    $1400 is saved at 2% compound interest per year. How much is in the account after 3 years? Round to 2 decimal places (type the number only).

    Answer

  3. Question 3

    A car worth $22000 loses 20% of its value each year. What is it worth after 2 years? Round to the nearest whole number (type the number only).

    Answer

  4. Question 4

    $1600 is saved at 4% compound interest per year. How much is in the account after 5 years? Round to 2 decimal places (type the number only).

    Answer

  5. Question 5

    A car worth $37000 loses 10% of its value each year. What is it worth after 3 years? Round to the nearest whole number (type the number only).

    Answer

  6. Question 6

    $2200 is saved at 10% compound interest per year. How much is in the account after 3 years? Round to 2 decimal places (type the number only).

    Answer

  7. Question 7

    A car worth $23000 loses 25% of its value each year. What is it worth after 2 years? Round to the nearest whole number (type the number only).

    Answer

  8. Question 8

    $2300 is saved at 5% compound interest per year. How much is in the account after 2 years? Round to 2 decimal places (type the number only).

    Answer

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Answer key: Compound interest and depreciation

  1. 1. 24300

  2. 2. 1485.69

  3. 3. 14080

  4. 4. 1946.64

  5. 5. 26973

  6. 6. 2928.2

  7. 7. 12938

  8. 8. 2535.75