Home → Curriculum Hub → Maths Lessons → Schemes of Work → Key Stage 3 → Expressions, Equations and Formulae
This Key Stage 3 Expressions, Equations and Formulae scheme of work is designed for Year 8 work on expanding and factorising algebraic expressions, substituting into formulae, solving linear equations including those with unknowns on both sides and with fractions, changing the subject of a formula, and an introduction to factorising quadratics.
Use this page to sequence the lessons below, keep expanding and factorising vocabulary distinct, and build from single-bracket work through to two-bracket expansion and quadratic factorisation before students encounter formal algebraic proof.
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 algebraic notation, collecting like terms and single-bracket work are secure. Teach the lessons in the order listed unless your timetable requires otherwise — keep single-bracket expansion and substitution before two-bracket work, and equations with unknowns on both sides before equations with fractions.
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 algebra plan.
Students should be secure with the following before this unit.
Ideas to keep explicit while students work with expressions, equations and formulae.
Subject content (Algebra)
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 algebraic notation, the ability to collect like terms and experience of single-bracket expansion so new work focuses on two-bracket products, factorisation strategies and solving more complex equations rather than basic notation.
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 single-bracket expansion and substitution before two-bracket work, and place equations with fractions and changing the subject after students can solve equations with unknowns on both sides confidently.
Additional revision lessons, exam-style questions and topic-based practice are available 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 substitute numbers into formulae using the order of operations.
Later, as learning progresses they are challened to substitute decimal and negative numbers into increasingly complex formulae.
Students learn how to expand a pair of brackets with the constant and unknown on the outside.
As learning progresses, students expand brackets with terms involving powers and multiple unknowns.
Students learn how to find the sum and difference of two algebraic expressions by expanding brackets.
Learning progresses from working with linear to non-linear terms and writing the area of composite shapes as simplified algebraic expressions.
Students learn how to expand and simplify algebraic expressions using the distributive property. They practice expanding brackets, including squared binomials and special products.
Later, they work with algebraic identities and attempt exam-style questions to reinforce their understanding.
Students learn to factorise an algebraic expression into a pair of brackets using the highest common factor.
As learning progresses, students are challenged to factorise expressions involving multiple unknowns and powers.
In this lesson, students are introduced to writing quadratic expressions in the form x2 + bx + c as the product of two polynomials.
As they progress, students explore the difference of two squares and solve simple quadratic identities. The lesson includes examples and exam-style questions to help students build confidence.
Students learn how to solve an equation where the unknown appears on both sides using the balance method.
Later, as learning progresses students solve equations involving positive and negative terms.
Students learn how to solve linear equations where terms include algebraic fractions. They practise clearing denominators by multiplying through, simplifying both sides, and isolating the variable.
As learning progresses, they handle more complex setups, including unknowns in multiple denominators and brackets.
Students learn to form and solve equations from word problems, like balancing book counts or party costs. They connect algebra to real-world scenarios.
Later, they apply these skills to geometric problems, finding missing lengths and verifying perimeters and areas, linking algebra to geometry.
Students learn how to change the subject of a formula using the balance method.
Later, they use formulae to model real-life situations as learning progresses.
Additional practice substituting numbers into formulae.
The problem-solving activity challenges to solve a problem involving a pendulum.
Students gain additional practice solving a linear equation where the unknown appears on both sides.
The problem-solving activity challenges students to set up and solve equations using the properties of 2D shapes.
Additional practice representing changing the subject of a formula.
The problem-solving activity challenges students to rearrange the volume of a sphere to find its radius.
Related Blogs: Changing the Subject of a Formula
Students gain additional practice factorising expressions into a single bracket.
The problem-solving activity challenges students to collect like terms around the perimeter of a hexagon to solve an algebraic identity.
Students gain additional practice expanding a pair of brackets and simplifying the result.
The problem-solving activity challenges students to write the expression for the area of a composite shape.
Students are challenged to solve a range of problems involving substitution into formulae.
Five problems link to
Students are challenged to solve a range of problems involving setting up and solving linear equations.
Five problems link to
GCSE Maths Equation Solving Strategies
Teaching Two-Step Equations with Inverse Operations and Real-Life Contexts
Students revise how to change the subject of a formula using the balance method.
Later, as learning progresses, they use formulae to model real-life and solve problems.
Related Blogs: Changing the Subject of a Formula
Students revise how to use the balance method to solve two-step equations.
Later, as learning progresses, they set up and solve equations to model real-life problems.
Teaching Two-Step Equations with Inverse Operations and Real-Life Contexts
Students revise how to factorise algebraic expressions by taking out the highest common factor.
As learning progresses, they factorise expressions involving powers and solve algebraic identities.
Students revise how to expand a single pair of brackets by a number and term.
Learning progresses to simplifying the sum and difference of multiple brackets while linking to shape and space.
Students revise how to solve equations where the unknown appears on both sides.
Later, as learning progresses, they solve equations involving fractions and brackets.
Students revise how to substitute known values into formulae using the order of operations.
Later, they rearrange formulae to model real-life problems as learning progresses.
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