Home → Curriculum Hub → Maths Lessons → Schemes of Work → Key Stage 3 → Multiplying and Dividing with Fractions
This Key Stage 3 Multiplying and Dividing with Fractions scheme of work is designed for Year 8 work on products and quotients with proper fractions, mixed numbers and top-heavy forms, including visual and written methods and an introduction to algebraic fractions with single brackets.
Use this page to sequence the lessons below, keep cross-simplifying and reciprocal language consistent, and connect fraction arithmetic to area, volume and formula contexts before students move to more formal algebraic manipulation.
For more schemes and topic routes across KS3, GCSE and A-Level, browse the Mr Mathematics Curriculum Hub.
Read the prerequisite and key-concept cards first so ordering and the four operations on fractions are secure. Teach the lessons in the order listed unless your department splits pure number fractions from algebraic fractions—if you reorder, keep multiplying and dividing proper fractions before mixed numbers and visual division before written quotients with reciprocals.
Presentations, worksheets, question generators and video tutorials for the lessons in this unit are available to members. Explore Mr Mathematics membership if you need full access to the library and schemes of work.
If you are comparing options for a department, the membership page sets out exactly what is included so you can align this unit with your wider KS3 number and algebra plan.
Students should be secure with the following before this unit.
Ideas to keep explicit while students multiply and divide with fractions and mixed numbers.
How this unit supports fluency, reasoning and problem solving in Key Stage 3.
Typical slips to address during teaching and marking.
Use it to sequence teaching, align vocabulary and spot likely errors before they become habits. Then use the lessons below as the delivery route for the unit.
They need confident ordering and the four operations on integers, decimals and fractions so new work focuses on structure—cross-simplifying, reciprocals and mixed-number forms—rather than basic arithmetic slips.
Each lesson listed below has its own page with downloadable resources and, where available, online tasks. Access depends on your membership level.
Yes if your timetable requires it—keep multiplying proper fractions and mixed numbers before division with reciprocals, and place the calculations and algebraic-fraction lessons after core number methods are secure.
You can find additional revision lessons, exam-style questions and topic-based practice on the GCSE Maths Revision Hub. This is useful for consolidating learning after teaching the unit or for Year 11 exam preparation.
Students learn how to calculate the product of two fractions by cross-simplifying.
As learning progresses, students are challenged to simplify simple algebraic fractions using the same method.
Students learn how to calculate the product of mixed numbers using cross-simplifying.
As learning progresses, this is linked to finding the area of rectangles with lengths as mixed numbers.
Students learn how to divide with fractions using visual methods and written methods.
Learning progresses to dividing with decimals and algebraic fractions.
Students learn about dividing mixed numbers and top-heavy fractions using visual and written methods.
As learning progresses, students connect dividing fractions with 3D shapes and volume.
Students solve many problems with fractions and mixed numbers.
As learning progresses, students link fractions to formulae.
Students learn how to simplify algebraic fractions using single brackets.
As learning progresses, they set up algebraic fractions to model real-life problems.
Students learn how to simplify the sum and difference of two algebraic fractions.
As learning progresses they solve problems involving the perimeter of rectangles.
Students learn how to simplify the product of two or more algebraic fractions.
As learning progresses, they work with dividing fractions and mixed numbers.
Additional practice dividing with fractions.
The problem-solving activity challenges students to solve a real-life problem involving fractions and capacity.
Additional practice multiplying with fractions.
The problem-solving activity challenges students to use cross-simplifying to find the product of 5 fractions.
Fluency and Mastery: Students practise dividing fractions by mixed numbers, simplifying answers correctly before progressing to dividing mixed numbers by mixed numbers using cross-simplification.
Problem-Solving: Students apply their skills to a real-world proportional reasoning problem involving division with mixed numbers.
Students are challenged to solve various problems involving arithmetic with fractions.
Five problems link to ratio, probability, mean averages and money.
A research-backed case exploring why over-reliance on automated math homework platforms and repetitive worksheets lowers student expectations, and how departments can build genuine mathematical thinking.
How to teach converting between fractions, decimals and percentages.
Four problem solving lessons to develop student’s mathematical reasoning and communication skills.
