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This Key Stage 3 Writing with algebraic notation scheme of work introduces students to algebraic conventions, expressions and substitution, building towards manipulation, equations and using formulae in context. The unit focuses on clear notation, collecting like terms, working with products and quotients in algebra, and evaluating expressions systematically using the order of operations.
Use the sections below to align vocabulary and departmental expectations (coefficients, terms, like terms, substitution), and to sequence teaching so diagrams and language develop into fluent manipulation before students meet equations and formulae. The lesson list at the end matches the published sequence for this scheme on Mr Mathematics.
Published: 10 October 2016 | Last updated: April 2026
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Use the prerequisite list to judge whether students need to revisit formulae and sequences from Key Stage 2 before you increase demand. Teach in the order shown under Lessons where possible so notation, simplifying and multiplication skills are secure before substitution, equations and formulae. Use the key concepts and subject content sections to agree notational conventions across your department and to plan mini-whiteboard checks for common errors (like terms, index notation, order of operations).
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Students should be able to do the following before or during early lessons in this unit. Use the list to diagnose gaps and plan short consolidation if needed.
These ideas are central to teaching Key Stage 3 Writing with algebraic notation effectively and to building confidence before more complex algebra.
The scheme supports students to work in line with Key Stage 3 expectations for fluency, reasoning and problem solving in algebra.
Below is the Key Stage 3 algebra content summarised from your original materials.
What is included?
This page summarises the curriculum focus for the unit. Full teaching packs (lessons, questions and answers) are available through the site and membership where applicable.
Which skills are developed?
Students develop confidence with algebraic notation, simplifying expressions, multiplication and division in algebra, substitution, solving simple equations and using formulae—skills that underpin much of later algebra at Key Stage 3 and GCSE.
Can lessons be used independently?
Yes—individual lessons can be taught standalone if you adjust the prior-knowledge check, though teaching in sequence usually gives the smoothest progression.
Does this support GCSE?
Yes. Fluent notation and manipulation are essential for GCSE algebra; this unit establishes conventions and routines that students use throughout later topics.
These lesson titles match the scheme sequence on Mr Mathematics. Link or embed question generators, online lessons and downloadable resources from each lesson page as needed.
Students learn to represent algebraic expressions visually by interpreting diagrams made from shapes with known areas. The lesson introduces collecting like terms and simplifying expressions through visual models.
As learning progresses, students move from identifying and simplifying expressions to creating their own diagrams from given algebraic expressions, strengthening the link between visual and symbolic algebra.
Students learn about writing expressions using keywords.
As learning progresses, students are challenged to write expressions with brackets using more than one unknown.
Students learn about simplifying expressions by collecting like terms.
As learning progresses, they consider a mixture of unknowns and numbers.
Students learn about multiplying and dividing with algebra using the correct notation.
As learning progresses students are challenged to use index notation and brackets.
Students learn about substituting numbers into expressions.
Using the order of operations, they are taught how to break down and evaluate an expression.
Students learn about solving an equation with function machines.
As learning progresses, students can use the balance method to find the unknown.
Students learn how to use formulae to solve problems involving cost, velocity, and distance using the order of operations.
As learning progresses, the formulae become more complex and involve multiple operations.
Fluency questions provide extra practice writing algebraic expressions from written descriptions.
Mastery and Problem Solving questions require students to form expressions with multiple operations and apply to real-life situations.
Students gain additional practice simplifying expressions by collecting like terms.
The problem-solving activity challenges students to write the perimeter of a composite shape as a simplified expression.
The lesson builds from substitution to reasoning and application. In fluency, students practise substituting values and simplifying accurately.
IProblem solving applies formulae in real contexts, interpreting and rearranging simple expressions to model relationships.
Students revise how to simplify expressions by collecting like terms.
As learning progresses they simplify algebraic products and solve problems involving the perimeter of shapes.
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