Algebra
Free algebra lessons and resources for key stage 3 and GCSE maths, whichever board you teach: lesson decks, worksheets with answers, puzzles, exam questions and end of unit tests.
Expressions and formulae
Algebraic notation and vocabulary
- Expression, equation, formula or inequality?Lesson · Support
- Exit ticket: Expression, equation, formula or inequality?Exit ticket
- Expression, equation, formula or inequality?Lesson · Foundation
- Exit ticket: Expression, equation, formula or inequality?Exit ticket
- Key words: algebraWorksheet · Foundation
- Algebraic notation: multiplyingLesson · Support
- Exit ticket: Algebraic notation: multiplyingExit ticket
- Algebraic notation: multiplyingLesson · Foundation
- Exit ticket: Algebraic notation: multiplyingExit ticket
- Four Fours: algebraic notationPuzzle
- Ramp up: algebraic notation and vocabularyWorksheet · Foundation
- Four Fours: expression, equation, formula or identityPuzzle
- Revision mat: algebra 1, Foundation BRevision mat · Foundation
- Revision mat: algebra 1, Foundation ARevision mat · Foundation
- Algebraic expressions: exam questionsExam questions
- Revision mat: linear equations, Higher ARevision mat · Higher
- Algebraic proof: exam questionsExam questions
- Revision mat: sequences, Higher ARevision mat · Higher
Substitution
- SubstitutionLesson · Support
- Exit ticket: SubstitutionExit ticket
- Substitution: a letter stands for a numberLesson · Support
- Exit ticket: Substitution: a letter stands for a numberExit ticket
- SubstitutionLesson · Foundation
- Exit ticket: SubstitutionExit ticket
- Code breaker: substitutionPuzzle
- Revision mat: algebra 1, Foundation BRevision mat · Foundation
- Revision mat: algebra 1, Foundation ARevision mat · Foundation
- Ramp up: substitutionWorksheet · Foundation
- Algebraic expressions: exam questionsExam questions
- Revision mat: formulae, Foundation BRevision mat · Foundation
- Revision mat: formulae, Foundation ARevision mat · Foundation
- Revision mat: inequalities and formulae, Higher ARevision mat · Higher
- Formulae: exam questionsExam questions
Simplifying, expanding and factorising
- Four Fours: index lawsPuzzle
- Collecting like termsLesson · Support
- Exit ticket: Collecting like termsExit ticket
- Collecting like terms: grouping lettersLesson · Support
- Exit ticket: Collecting like terms: grouping lettersExit ticket
- Collecting like termsLesson · Foundation
- Exit ticket: Collecting like termsExit ticket
- Expanding single bracketsLesson · Support
- Exit ticket: Expanding single bracketsExit ticket
- Expanding single bracketsLesson · Foundation
- Exit ticket: Expanding single bracketsExit ticket
- Four Fours: expanding and simplifyingPuzzle
- Expanding double bracketsLesson · Common
- Exit ticket: Expanding double bracketsExit ticket
- Four Fours: expanding double bracketsPuzzle
- Expanding triple bracketsLesson · Higher
- Exit ticket: Expanding triple bracketsExit ticket
- Factorising into a single bracketLesson · Support
- Exit ticket: Factorising into a single bracketExit ticket
- Factorising into a single bracketLesson · Foundation
- Exit ticket: Factorising into a single bracketExit ticket
- Ramp up: simplifying, expanding and factorisingWorksheet · Foundation
- Factorising quadraticsLesson · Common
- Exit ticket: Factorising quadraticsExit ticket
- The difference of two squaresLesson · Common
- Exit ticket: The difference of two squaresExit ticket
- Factorising quadratics: harderLesson · Higher
- Exit ticket: Factorising quadratics: harderExit ticket
- Ramp up: simplifying, expanding and factorisingWorksheet · Higher
- Simplifying algebraic fractionsLesson · Higher
- Exit ticket: Simplifying algebraic fractionsExit ticket
- Adding and subtracting algebraic fractionsLesson · Higher
- Exit ticket: Adding and subtracting algebraic fractionsExit ticket
- Ramp up: algebraic fractionsWorksheet · Higher
- Algebra without solvingProblem solving
- Revision mat: algebra 1, Foundation BRevision mat · Foundation
- Revision mat: algebra 1, Foundation ARevision mat · Foundation
- Algebraic expressions: exam questionsExam questions
- Revision mat: quadratics, rearranging formulae and identities, Foundation BRevision mat · Foundation
- Revision mat: quadratics, rearranging formulae and identities, Foundation ARevision mat · Foundation
- Revision mat: algebraic fractions and algebraic proof, Higher ARevision mat · Higher
- Algebraic fractions: exam questionsExam questions
- Revision mat: expanding brackets, factorising and solving quadratics, Higher ARevision mat · Higher
- Expanding and factorising: exam questionsExam questions
- Quadratic equations: exam questionsExam questions
Using and rearranging formulae
- Rearranging formulaeLesson · Foundation
- Exit ticket: Rearranging formulaeExit ticket
- Four Fours: rearranging formulaePuzzle
- Rearranging formulae: powers, roots and bracketsWorksheet · Foundation
- Revision mat: formulae, Foundation BRevision mat · Foundation
- Revision mat: formulae, Foundation ARevision mat · Foundation
- Ramp up: using and rearranging formulaeWorksheet · Foundation
- Using the formulae sheet: HigherWorksheet · Higher
- Using the formulae sheet: FoundationWorksheet · Foundation
- Changing the subject: the subject appears twiceLesson · Higher
- Exit ticket: Changing the subject: the subject appears twiceExit ticket
- Ramp up: using and rearranging formulaeWorksheet · Higher
- Revision mat: inequalities and formulae, Higher ARevision mat · Higher
- Revision mat: quadratics, rearranging formulae and identities, Foundation BRevision mat · Foundation
- Revision mat: quadratics, rearranging formulae and identities, Foundation ARevision mat · Foundation
- Formulae: exam questionsExam questions
Identities and algebraic proof
- Equation or identity?Lesson · Common
- Exit ticket: Equation or identity?Exit ticket
- Four Fours: expression, equation, formula or identityPuzzle
- Revision mat: quadratics, rearranging formulae and identities, Foundation BRevision mat · Foundation
- Revision mat: quadratics, rearranging formulae and identities, Foundation ARevision mat · Foundation
- Algebraic proofLesson · Higher
- Exit ticket: Algebraic proofExit ticket
- Revision mat: algebraic fractions and algebraic proof, Higher ARevision mat · Higher
- Ramp up: identities and algebraic proofWorksheet · Higher
- Algebraic proof: exam questionsExam questions
- Algebraic proofProblem solving
Function machines and functions
- Function machinesLesson · Support
- Exit ticket: Function machinesExit ticket
- Function machines: forwards and backwardsLesson · Support
- Exit ticket: Function machines: forwards and backwardsExit ticket
- Function machinesLesson · Foundation
- Exit ticket: Function machinesExit ticket
- Answer chain: function machinesPuzzle
- Ramp up: function machines and functionsWorksheet · Foundation
- Inverse functionsLesson · Higher
- Exit ticket: Inverse functionsExit ticket
- Composite functionsLesson · Higher
- Exit ticket: Composite functionsExit ticket
- Revision mat: functions, Higher ARevision mat · Higher
- Ramp up: function machines and functionsWorksheet · Higher
- Functions and iterationProblem solving
- Functions and iteration: exam questionsExam questions
Equations and inequalities
Solving linear equations
- Missing numbers: first equationsLesson · Support
- Exit ticket: Missing numbers: first equationsExit ticket
- Solving one-step equationsWorksheet · Foundation
- Solving two-step equationsLesson · Support
- Exit ticket: Solving two-step equationsExit ticket
- Solving two-step equationsLesson · Foundation
- Exit ticket: Solving two-step equationsExit ticket
- Answer chain: two-step equationsPuzzle
- Equations with bracketsLesson · Support
- Exit ticket: Equations with bracketsExit ticket
- Equations with bracketsLesson · Foundation
- Exit ticket: Equations with bracketsExit ticket
- Equations: the unknown on both sidesLesson · Foundation
- Exit ticket: Equations: the unknown on both sidesExit ticket
- Code breaker: unknowns on both sidesPuzzle
- Ramp up: solving linear equationsWorksheet · Foundation
- Revision mat: linear equations, Higher ARevision mat · Higher
- Revision mat: equations and inequalities, Foundation BRevision mat · Foundation
- Revision mat: equations and inequalities, Foundation ARevision mat · Foundation
- Linear equations: exam questionsExam questions
Forming and solving equations
- Algebraic expressions: exam questionsExam questions
- Forming equations from perimeterLesson · Common
- Exit ticket: Forming equations from perimeterExit ticket
- Code breaker: forming equationsPuzzle
- Revision mat: linear equations, Higher ARevision mat · Higher
- Ramp up: forming and solving equationsWorksheet · Common
- Revision mat: equations and inequalities, Foundation BRevision mat · Foundation
- Revision mat: equations and inequalities, Foundation ARevision mat · Foundation
- Linear equations: exam questionsExam questions
- Simultaneous equations: exam questionsExam questions
- Formulae: exam questionsExam questions
Quadratic equations
- Solving quadratics by factorisingLesson · Common
- Exit ticket: Solving quadratics by factorisingExit ticket
- Code breaker: solving quadratics by factorisingPuzzle
- Revision mat: quadratics, rearranging formulae and identities, Foundation BRevision mat · Foundation
- Revision mat: quadratics, rearranging formulae and identities, Foundation ARevision mat · Foundation
- The quadratic formulaLesson · Higher
- Exit ticket: The quadratic formulaExit ticket
- The quadratic formulaWorksheet · Higher
- Ramp up: quadratic equationsWorksheet · Higher
- Revision mat: expanding brackets, factorising and solving quadratics, Higher ARevision mat · Higher
- Quadratic equations: exam questionsExam questions
- Quadratic and other graphs: exam questionsExam questions
- Geometry puzzles with algebraLesson · Stretch
- Exit ticket: Geometry puzzles with algebraExit ticket
- Probability meets algebraProblem solving
Simultaneous equations
- Simultaneous equationsLesson · Common
- Exit ticket: Simultaneous equationsExit ticket
- Code breaker: simultaneous equationsPuzzle
- Revision mat: simultaneous equations, Foundation BRevision mat · Foundation
- Revision mat: simultaneous equations, Foundation ARevision mat · Foundation
- Solving simultaneous equationsWorksheet · Common
- Simultaneous equations: multiply firstWorksheet · Common
- Simultaneous equations: linear and quadraticLesson · Higher
- Exit ticket: Simultaneous equations: linear and quadraticExit ticket
- Revision mat: simultaneous equations, Higher ARevision mat · Higher
- Ramp up: simultaneous equationsWorksheet · Higher
- Simultaneous equations: exam questionsExam questions
- Quadratic equations: exam questionsExam questions
Inequalities
- Inequalities on a number lineLesson · Common
- Exit ticket: Inequalities on a number lineExit ticket
- Solving inequalitiesLesson · Common
- Exit ticket: Solving inequalitiesExit ticket
- Four Fours: solving inequalitiesPuzzle
- Revision mat: equations and inequalities, Foundation BRevision mat · Foundation
- Revision mat: equations and inequalities, Foundation ARevision mat · Foundation
- Quadratic inequalitiesLesson · Higher
- Exit ticket: Quadratic inequalitiesExit ticket
- Revision mat: inequalities and formulae, Higher ARevision mat · Higher
- Ramp up: inequalitiesWorksheet · Higher
- Inequalities: exam questionsExam questions
Iteration
- Functions and iterationProblem solving
- IterationLesson · Higher
- Exit ticket: IterationExit ticket
- Code breaker: iterationPuzzle
- Ramp up: iterationWorksheet · Higher
- Functions and iteration: exam questionsExam questions
- Revision mat: more graphs and equations, Higher ARevision mat · Higher
Graphs
Coordinates
- CoordinatesLesson · Support
- Exit ticket: CoordinatesExit ticket
- Coordinates in the first quadrantLesson · Support
- Exit ticket: Coordinates in the first quadrantExit ticket
- CoordinatesLesson · Foundation
- Exit ticket: CoordinatesExit ticket
- Mystery picture: coordinatesPuzzle
- Mystery picture: first quadrantPuzzle
- Ramp up: coordinatesWorksheet · Foundation
- Revision mat: graphs 1, Foundation BRevision mat · Foundation
- Revision mat: graphs 1, Foundation ARevision mat · Foundation
- Straight-line graphs: exam questionsExam questions
- Revision mat: graphs, Higher ARevision mat · Higher
Straight-line graphs
- Plotting straight-line graphsLesson · Support
- Exit ticket: Plotting straight-line graphsExit ticket
- Plotting straight-line graphsLesson · Foundation
- Exit ticket: Plotting straight-line graphsExit ticket
- Ramp up: straight line graphsWorksheet · Foundation
- Four Fours: straight line graphsPuzzle
- Revision mat: graphs 1, Foundation BRevision mat · Foundation
- Revision mat: graphs 1, Foundation ARevision mat · Foundation
- Equation of a line through two pointsWorksheet · Common
- Perpendicular linesLesson · Higher
- Exit ticket: Perpendicular linesExit ticket
- Ramp up: straight line graphsWorksheet · Higher
- Straight-line graphs: exam questionsExam questions
- Revision mat: graphs, Higher ARevision mat · Higher
Gradient and y = mx + c
- Gradient of a lineLesson · Foundation
- Exit ticket: Gradient of a lineExit ticket
- The equation of a line from its graphLesson · Foundation
- Exit ticket: The equation of a line from its graphExit ticket
- Four Fours: straight line graphsPuzzle
- Revision mat: graphs 1, Foundation BRevision mat · Foundation
- Revision mat: graphs 1, Foundation ARevision mat · Foundation
- Ramp up: gradient and y = mx + cWorksheet · Foundation
- Straight-line graphs: exam questionsExam questions
- Revision mat: graphs, Higher ARevision mat · Higher
Real-life graphs
- Straight-line graphs: exam questionsExam questions
- Conversion graphsLesson · Support
- Exit ticket: Conversion graphsExit ticket
- Conversion graphsLesson · Foundation
- Exit ticket: Conversion graphsExit ticket
- Code breaker: conversion graphPuzzle
- Distance-time graphsLesson · Support
- Exit ticket: Distance-time graphsExit ticket
- Distance-time graphsLesson · Foundation
- Exit ticket: Distance-time graphsExit ticket
- Code breaker: distance-time graphPuzzle
- Ramp up: real life graphsWorksheet · Foundation
- Real-life graphs: exam questionsExam questions
- Revision mat: graphs 2, Foundation BRevision mat · Foundation
- Revision mat: graphs 2, Foundation ARevision mat · Foundation
- Revision mat: graphs, Higher ARevision mat · Higher
Quadratic graphs
- Completing the squareLesson · Higher
- Exit ticket: Completing the squareExit ticket
- Completing the squareWorksheet · Higher
- Quadratic graphs: roots and turning pointsLesson · Common
- Exit ticket: Quadratic graphs: roots and turning pointsExit ticket
- Code breaker: quadratic graphsPuzzle
- Revision mat: expanding brackets, factorising and solving quadratics, Higher ARevision mat · Higher
- Quadratic equations: exam questionsExam questions
- Revision mat: more graphs and equations, Higher ARevision mat · Higher
- Ramp up: quadratic graphsWorksheet · Higher
- Revision mat: graphs 2, Foundation BRevision mat · Foundation
- Revision mat: graphs 2, Foundation ARevision mat · Foundation
- Quadratic and other graphs: exam questionsExam questions
Recognising and sketching curves
- Real-life graphs: exam questionsExam questions
- Recognising linear and quadratic graphsLesson · Foundation
- Exit ticket: Recognising linear and quadratic graphsExit ticket
- Four Fours: recognising graphsPuzzle
- Plotting quadratic graphsLesson · Foundation
- Exit ticket: Plotting quadratic graphsExit ticket
- Ramp up: recognising and sketching curvesWorksheet · Higher
- Ramp up: recognising and sketching curvesWorksheet · Foundation
- Revision mat: more graphs and equations, Higher ARevision mat · Higher
- Revision mat: graphs 2, Foundation BRevision mat · Foundation
- Revision mat: graphs 2, Foundation ARevision mat · Foundation
- Quadratic and other graphs: exam questionsExam questions
Graph transformations
- Graph transformations: translationsLesson · Higher
- Exit ticket: Graph transformations: translationsExit ticket
- Graph transformations: reflectionsLesson · Higher
- Exit ticket: Graph transformations: reflectionsExit ticket
- Graph transformations: where does the point go?Lesson · Higher
- Exit ticket: Graph transformations: where does the point go?Exit ticket
- Four Fours: transformations of functionsPuzzle
- Revision mat: transformations of functions, Higher ARevision mat · Higher
- Ramp up: graph transformationsWorksheet · Higher
- Quadratic and other graphs: exam questionsExam questions
Gradient of a curve and area under a graph
- Real-life graphs: exam questionsExam questions
- Area under a graphLesson · Higher
- Exit ticket: Area under a graphExit ticket
- Code breaker: gradients and areasPuzzle
- Ramp up: gradients and areas under graphsWorksheet · Higher
- Quadratic and other graphs: exam questionsExam questions
- Revision mat: pre-calculus, Higher ARevision mat · Higher
Equation of a circle
- Simultaneous equations: exam questionsExam questions
- Straight-line graphs: exam questionsExam questions
- Equation of a circleLesson · Higher
- Exit ticket: Equation of a circleExit ticket
- Equation of a tangent to a circleLesson · Higher
- Exit ticket: Equation of a tangent to a circleExit ticket
- Code breaker: equation of a circlePuzzle
- Revision mat: equations of circles, Higher ARevision mat · Higher
- Ramp up: equation of a circleWorksheet · Higher
Sequences
Generating sequences
- Perfect Ten: counting in stepsPuzzle
- Term to term rulesLesson · Support
- Exit ticket: Term to term rulesExit ticket
- Sequences: counting in stepsLesson · Support
- Exit ticket: Sequences: counting in stepsExit ticket
- Term to term rulesLesson · Foundation
- Exit ticket: Term to term rulesExit ticket
- Answer chain: term to term rulesPuzzle
- Ramp up: generating sequencesWorksheet · Foundation
- Revision mat: sequences, Foundation BRevision mat · Foundation
- Revision mat: sequences, Foundation ARevision mat · Foundation
- Revision mat: sequences, Higher ARevision mat · Higher
- Key words: sequencesWorksheet · Foundation
- Sequences: exam questionsExam questions
Special sequences
- Square and triangular numbersLesson · Support
- Exit ticket: Square and triangular numbersExit ticket
- Square and triangular numbersLesson · Foundation
- Exit ticket: Square and triangular numbersExit ticket
- Perfect Ten: square and triangular numbersPuzzle
- Ramp up: special sequencesWorksheet · Foundation
- Fibonacci type sequencesLesson · Common
- Exit ticket: Fibonacci type sequencesExit ticket
- Types of sequencesLesson · Common
- Exit ticket: Types of sequencesExit ticket
- Four Fours: types of sequencesPuzzle
- Revision mat: sequences, Foundation BRevision mat · Foundation
- Revision mat: sequences, Foundation ARevision mat · Foundation
- Revision mat: sequences, Higher ARevision mat · Higher
- Ramp up: special sequencesWorksheet · Higher
- Key words: sequencesWorksheet · Foundation
- Sequences: exam questionsExam questions
- SequencesProblem solving
The nth term
- Revision mat: sequences, Foundation BRevision mat · Foundation
- Revision mat: sequences, Foundation ARevision mat · Foundation
- Revision mat: sequences, Higher ARevision mat · Higher
- The nth term of a linear sequenceLesson · Support
- Exit ticket: The nth term of a linear sequenceExit ticket
- The nth term of a linear sequenceLesson · Foundation
- Exit ticket: The nth term of a linear sequenceExit ticket
- Four Fours: nth termPuzzle
- The nth term of a linear sequenceWorksheet · Foundation
- Ramp up: the nth termWorksheet · Foundation
- Key words: sequencesWorksheet · Foundation
- The nth term of a quadratic sequenceLesson · Higher
- Exit ticket: The nth term of a quadratic sequenceExit ticket
- Ramp up: the nth termWorksheet · Higher
- Sequences: exam questionsExam questions
- SequencesProblem solving
End of unit tests
- Functions test: HigherEnd of unit test
- Algebraic expressions test: Foundation AEnd of unit test
- Algebraic expressions test: Foundation BEnd of unit test
- Linear equations test: HigherEnd of unit test
- Equations and inequalities test: Foundation AEnd of unit test
- Equations and inequalities test: Foundation BEnd of unit test
- Simultaneous equations test: Foundation AEnd of unit test
- Simultaneous equations test: Foundation BEnd of unit test
- Simultaneous equations test: HigherEnd of unit test
- Inequalities and formulae test: HigherEnd of unit test
- Formulae test: Foundation AEnd of unit test
- Quadratics and formulae test: Foundation AEnd of unit test
- Formulae test: Foundation BEnd of unit test
- Quadratics and formulae test: Foundation BEnd of unit test
- Algebraic fractions and proof test: HigherEnd of unit test
- Expressions, functions and formulae test: CoreEnd of unit test
- Expressions, functions and formulae test: ExtensionEnd of unit test
- Sequences test: Foundation AEnd of unit test
- Sequences test: Foundation BEnd of unit test
- Sequences test: HigherEnd of unit test
- Algebra and sequences test: SupportEnd of unit test
- Straight line graphs test: Foundation AEnd of unit test
- Straight line graphs test: Foundation BEnd of unit test
- Real life and quadratic graphs test: Foundation AEnd of unit test
- Real life and quadratic graphs test: Foundation BEnd of unit test
- Expanding, factorising and quadratics test: HigherEnd of unit test
- Expressions, equations and formulae test: CoreEnd of unit test
- Expressions, equations and formulae test: ExtensionEnd of unit test
- Transformations of functions test: HigherEnd of unit test
- Gradients and area under graphs test: HigherEnd of unit test
- Equations of circles test: HigherEnd of unit test
- Curved graphs and iteration test: HigherEnd of unit test
- Graphs test: HigherEnd of unit test
- Graphs test: CoreEnd of unit test
- Sequences and graphs test: CoreEnd of unit test
- Graphs test: ExtensionEnd of unit test
- Sequences and graphs test: ExtensionEnd of unit test