Growth and decay – Year 10 maths lesson

Lesson 34 of 37 in the Year 10 maths course

UK version. UK school years, UK spelling and pounds (£). · US Math Department

A complete 45-minute lesson for Year 10 (ages 14–15) 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 10 (ages 14–15)
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

45 minutes in 5 parts
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

All Year 10 maths lessons and tests · Maths Department

Curriculum

National Curriculum for England, Year 10: “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.