One quantity as a fraction or percentage of another – Year 8 maths lesson
Lesson 30 of 35 in the Year 8 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 8 (ages 12–13) 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 8 (ages 12–13)
- 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 is the better test score: 17 out of 20 or 40 out of 50?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Mixing units (30 minutes as a fraction of 2 hours as 30/2). Change both to minutes first.
- Putting the whole on top. Part on top, whole on the bottom.
Tip for home: Work out what percentage of a packet is sugar or fat from the label.
What your child will learn
We are learning to write one quantity as a fraction or percentage of another.
Success looks like
- I can write one amount as a fraction of another.
- I can write it as a percentage.
- I can compare using fractions or percentages.
Key words
- fraction
- part over whole
- percentage
- out of 100
- units
- what each amount is measured in
- simplify
- divide top and bottom by the same number
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Find what fraction and percentage of a day you spend asleep, at school and eating.
The big ideas (for the adult)
To write a as a fraction of b, write a/b and simplify. Make sure both are in the same units.
To write it as a percentage, change the fraction to hundredths, or divide and multiply by 100.
30 minutes as a fraction of 2 hours is 30/120 = 1/4 = 25%.
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 8 maths lessons
- Ordering numbers, decimals and negatives
- Calculating with negative numbers
- Prime factors, HCF and LCM
- Rounding and estimation
- Powers and roots
- Written methods with decimals
- BIDMAS: order of operations
- Calculating with fractions
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Angle facts and parallel lines
- Angles in polygons
- Transformations
- Quadrilaterals and symmetry
- Constructions and loci
- Averages and range
- Scatter graphs and correlation
- Probability
- Relative frequency and expected outcomes
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- Percentages
- Direct and inverse proportion
- Speed, density and pressure
- Best buys and exchange rates
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 8: “define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%”
GCSE subject content R9: “define percentage as ‘number of parts per hundred’; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another; compare two quantities using percentages; work with percentages greater than 100%; solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics”
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.