Growth and decay – Year 11 maths lesson
Lesson 17 of 17 in the Year 11 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 11 (ages 15–16) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 11 (ages 15–16)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why does compound interest grow faster than simple interest?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Adding 5% three times (15%) instead of multiplying by 1.05³. Work it year by year to see the difference.
- Using 0.15 for a 15% decrease. What is left is 85%: multiply by 0.85.
Tip for home: Look at how car values or savings change over the years.
What your child will learn
We are learning to use multipliers for repeated percentage change, such as compound interest and depreciation.
Success looks like
- I can use a multiplier for repeated change.
- I can calculate compound interest.
- I can calculate depreciation.
Key words
- compound interest
- interest earned on interest too
- depreciation
- losing value over time
- multiplier
- the decimal you multiply by each time
- exponential
- changing by the same factor each time
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use a spreadsheet or calculator to track savings growing at 4% a year for 10 years.
The big ideas (for the adult)
Repeated percentage change multiplies by the same multiplier each time: 5% growth for 3 years is × 1.05³.
Compound interest adds interest to the total each year, so the interest grows too. Simple interest stays the same each year.
Decay, such as depreciation, uses a multiplier less than 1: losing 15% a year is × 0.85 each year.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 11 maths lessons
- Volume and surface area
- Trigonometry: SOH CAH TOA
- Sine rule, cosine rule and area of a triangle
- Transformations
- Similarity and congruence
- Vectors
- Circle theorems
- Factorising
- Inequalities
- Sequences and the nth term
- Quadratic equations
- Iteration
- Functions
- Algebraic fractions
- Graphs of functions
- Algebraic proof and identities
Curriculum
National Curriculum for England, Year 11: “set up, solve and interpret the answers in growth and decay problems, including compound interest {and work with general iterative processes}”
GCSE subject content R16: “set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes.”
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Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.