Fractions, decimals and recurring decimals – Year 7 maths lesson
Lesson 7 of 18 in the Year 7 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 7 (ages 11–12) 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 7 (ages 11–12)
- 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: “Which fractions give decimals that stop? Look at the denominators.”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Writing 1/3 as 0.3. Divide: 1 ÷ 3 = 0.333… – it keeps going.
- Multiplying by the wrong power of 10 for a two-digit repeat. Two repeating digits: multiply by 100.
Tip for home: Try dividing by 3, 7, 9 and 11 on a calculator and look for patterns.
What your child will learn
We are learning to convert between fractions and decimals, including recurring decimals.
Success looks like
- I can change fractions to decimals.
- I can recognise recurring decimals.
- I can change a recurring decimal to a fraction.
Key words
- terminating decimal
- a decimal that stops
- recurring decimal
- a decimal that repeats for ever
- numerator
- the top of a fraction
- denominator
- the bottom of a fraction
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use short division to change 1/7 to a decimal and spot the repeating pattern.
The big ideas (for the adult)
To change a fraction to a decimal, divide the numerator by the denominator. Some decimals stop; others repeat for ever.
A recurring decimal has a digit or block of digits that repeats: 1/3 = 0.333…, written with a dot over the 3.
To turn a recurring decimal into a fraction, let x be the decimal, multiply by 10 or 100 so the repeating parts line up, and subtract.
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 7 maths lessons
- Ordering numbers, decimals and negatives
- Calculating with negative numbers
- Rounding and estimation
- Powers and roots
- Written methods with decimals
- Calculating with fractions
- Quadrilaterals and symmetry
- 3-D shapes, plans and elevations
- Pie charts and time series graphs
- Probability
- Algebraic notation
- Simplifying expressions
- Solving linear equations
- Sequences and the nth term
- Ratio
- One quantity as a fraction or percentage of another
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 7: “work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and [Fraction:7/2] or 0.375 and [Fraction:3/8])”
GCSE subject content N10: “work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 or 3/8); change recurring decimals into their corresponding fractions and vice versa”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.