Equations & inequalities
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Stage 4: Equations · Stage 5: Equations A · Stage 5: Equations B (Path) · Stage 5: Equations C (Path) · Mathematics Advanced 11–12 – Year 11: Trigonometric identities and equations
Stage 4 (Year 7, 8)
- Math Playground: Algebraic ReasoningUse it for: Balance puzzles for unknown values.
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolStarterMaths Is Fun: Solving equationsUse it for: Solving linear equations with checks.
- PhET Equality ExplorerUse it for: Use the balance-scale model to justify each step when solving linear equations.
- SimulationStarterPhET Equality Explorer: BasicsUse it for: Introduce equations as balanced scales before any algebra.
- Corbettmaths practice questions: Equations: Think of a numberUse it for: Free printable graded practice questions (with answers) on equations: think of a number for drill or a quick check.
- Corbettmaths practice questions: Equations: angles and perimeterUse it for: Free printable graded practice questions (with answers) on equations: angles and perimeter for drill or a quick check.
- Corbettmaths practice questions: Equations: solvingUse it for: Free printable graded practice questions (with answers) on equations: solving for drill or a quick check.
- Corbettmaths practice questions: Equations: x squaredUse it for: Free printable graded practice questions (with answers) on equations: x squared for drill or a quick check.
- Corbettmaths practice questions: Identities, Formula, Equations etcUse it for: Free printable graded practice questions (with answers) on identities, formula, equations etc for drill or a quick check.
- WorksheetDrillKuta free worksheet: Equations with hanger diagramsUse it for: Printable skills-practice sheet with answer key on equations with hanger diagrams; good for drill or homework.
- WorksheetDrillKuta free worksheet: Equations with tape diagramsUse it for: Printable skills-practice sheet with answer key on equations with tape diagrams; good for drill or homework.
- WorksheetDrillKuta free worksheet: Equations word problemsUse it for: Printable skills-practice sheet with answer key on equations word problems; good for drill or homework.
- WorksheetDrillKuta free worksheet: One-step equations with integersUse it for: Printable skills-practice sheet with answer key on one-step equations with integers; good for drill or homework.
- WorksheetDrillKuta free worksheet: Solutions to equationsUse it for: Printable skills-practice sheet with answer key on solutions to equations; good for drill or homework.
- WorksheetDrillKuta free worksheet: Solving quadratics by taking square rootsUse it for: Printable skills-practice sheet with answer key on solving quadratics by taking square roots; good for drill or homework.
- WorksheetDrillKuta free worksheet: Systems of equations by graphingUse it for: Printable skills-practice sheet with answer key on systems of equations by graphing; good for drill or homework.
- WorksheetDrillKuta free worksheet: Two-step equation word problemsUse it for: Printable skills-practice sheet with answer key on two-step equation word problems; good for drill or homework.
- WorksheetDrillKuta free worksheet: Two-step equations with decimalsUse it for: Printable skills-practice sheet with answer key on two-step equations with decimals; good for drill or homework.
- WorksheetDrillKuta free worksheet: Two-step equations with integersUse it for: Printable skills-practice sheet with answer key on two-step equations with integers; good for drill or homework.
- NRICH: ArithmagonsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: How Old Am I?Use it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- Open Middle: Solving Quadratic Functions using the Square Root MethodUse it for: Fill-the-boxes puzzle using digits 0-9 once; many paths to an optimal answer, good extension.
- Open Middle: problem collectionUse it for: Problems with one answer but many paths; use as low-floor high-ceiling extensions.
- VideoStarterCorbettmaths video: Equations: angles and perimeterUse it for: Short worked-example video on equations: angles and perimeter to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Equations: formingUse it for: Short worked-example video on equations: forming to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Equations: solvingUse it for: Short worked-example video on equations: solving to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Equations: x squaredUse it for: Short worked-example video on equations: x squared to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Identities, Formula, Equations etcUse it for: Short worked-example video on identities, formula, equations etc to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Simultaneous equations (graphical)Use it for: Short worked-example video on simultaneous equations (graphical) to model the method before practice or for flipped revision.
- VideoStarterEddie Woo (WooTube): Basic Equations playlistUse it for: Sydney teacher Eddie Woo's recorded lessons on equations; play a clip to model a method or for revision.
- Unit/PlanningStage 4 Unit 10 – investigating triangles (sample unit of learning)
- Unit/PlanningStage 4 Unit 12 – further multiplicative thinking (sample unit of learning)
- Unit/PlanningStage 4 Unit 15 – exploring circles (sample unit of learning)
- Unit/PlanningStage 4 Unit 16 – constructing cylinders (sample unit of learning)
- Unit/PlanningStage 4 Unit 5 – multiplicative thinking (sample unit of learning)
- Unit/PlanningStage 4 Unit 7 – length and area (sample unit of learning)
Stage 5 (Year 9, 10)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolStarterMathigon: Quadratic equationsUse it for: Visual introduction to parabolas and solving quadratics.
- Interactive toolStarterMaths Is Fun: Completing the squareUse it for: Visual explanation of completing the square.
- Interactive toolStarterMaths Is Fun: Quadratic equationsUse it for: The quadratic formula and discriminant with an interactive graph.
- Interactive toolStarterMaths Is Fun: Solving inequalitiesUse it for: Explains flipping the sign when multiplying by a negative.
- PhET Equality ExplorerUse it for: Use the balance-scale model to justify each step when solving linear equations.
- PhET Equality Explorer: Two VariablesUse it for: Balance model with two unknowns, a lead-in to simultaneous equations.
- Corbettmaths practice questions: Algebra: changing the subjectUse it for: Free printable graded practice questions (with answers) on algebra: changing the subject for drill or a quick check.
- Corbettmaths practice questions: Algebra: changing the subject advancedUse it for: Free printable graded practice questions (with answers) on algebra: changing the subject advanced for drill or a quick check.
- Corbettmaths practice questions: Algebra: completing the squareUse it for: Free printable graded practice questions (with answers) on algebra: completing the square for drill or a quick check.
- Corbettmaths practice questions: Equations: angles and perimeterUse it for: Free printable graded practice questions (with answers) on equations: angles and perimeter for drill or a quick check.
- Corbettmaths practice questions: Equations: cross multiplicationUse it for: Free printable graded practice questions (with answers) on equations: cross multiplication for drill or a quick check.
- Corbettmaths practice questions: Equations: fractional advancedUse it for: Free printable graded practice questions (with answers) on equations: fractional advanced for drill or a quick check.
- Corbettmaths practice questions: Equations: involving fractionsUse it for: Free printable graded practice questions (with answers) on equations: involving fractions for drill or a quick check.
- Corbettmaths practice questions: Equations: solvingUse it for: Free printable graded practice questions (with answers) on equations: solving for drill or a quick check.
- Corbettmaths practice questions: Identities, Formula, Equations etcUse it for: Free printable graded practice questions (with answers) on identities, formula, equations etc for drill or a quick check.
- Corbettmaths practice questions: Inequalities on a number lineUse it for: Free printable graded practice questions (with answers) on inequalities on a number line for drill or a quick check.
- Corbettmaths practice questions: Quadratics: formulaUse it for: Free printable graded practice questions (with answers) on quadratics: formula for drill or a quick check.
- Corbettmaths practice questions: Quadratics: solving (factorising)Use it for: Free printable graded practice questions (with answers) on quadratics: solving (factorising) for drill or a quick check.
- Corbettmaths practice questions: Simultaneous equations (elimination)Use it for: Free printable graded practice questions (with answers) on simultaneous equations (elimination) for drill or a quick check.
- WorksheetDrillKuta free worksheet: Graphing single-variable inequalitiesUse it for: Printable skills-practice sheet with answer key on graphing single-variable inequalities; good for drill or homework.
- WorksheetDrillKuta free worksheet: Literal equations (changing the subject)Use it for: Printable skills-practice sheet with answer key on literal equations (changing the subject); good for drill or homework.
- WorksheetDrillKuta free worksheet: Multi-step equationsUse it for: Printable skills-practice sheet with answer key on multi-step equations; good for drill or homework.
- WorksheetDrillKuta free worksheet: Multi-step inequalitiesUse it for: Printable skills-practice sheet with answer key on multi-step inequalities; good for drill or homework.
- WorksheetDrillKuta free worksheet: Quadratic formulaUse it for: Printable skills-practice sheet with answer key on quadratic formula; good for drill or homework.
- WorksheetDrillKuta free worksheet: Simultaneous equations by eliminationUse it for: Printable skills-practice sheet with answer key on simultaneous equations by elimination; good for drill or homework.
- WorksheetDrillKuta free worksheet: Simultaneous equations by substitutionUse it for: Printable skills-practice sheet with answer key on simultaneous equations by substitution; good for drill or homework.
- WorksheetDrillKuta free worksheet: Simultaneous equations word problemsUse it for: Printable skills-practice sheet with answer key on simultaneous equations word problems; good for drill or homework.
- WorksheetDrillKuta free worksheet: Solving quadratics by completing the squareUse it for: Printable skills-practice sheet with answer key on solving quadratics by completing the square; good for drill or homework.
- WorksheetDrillKuta free worksheet: Solving quadratics by factoringUse it for: Printable skills-practice sheet with answer key on solving quadratics by factoring; good for drill or homework.
- WorksheetDrillKuta free worksheet: Systems of equations by graphingUse it for: Printable skills-practice sheet with answer key on systems of equations by graphing; good for drill or homework.
- WorksheetDrillKuta free worksheet: The discriminantUse it for: Printable skills-practice sheet with answer key on the discriminant; good for drill or homework.
- WorksheetDrillKuta free worksheet: Two-step inequalitiesUse it for: Printable skills-practice sheet with answer key on two-step inequalities; good for drill or homework.
- WorksheetEnrichmentNRICH: Cinema ProblemUse it for: Rich task leading to simultaneous equations reasoning.
- NRICH: ArithmagonsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: How Many Solutions?Use it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: MatchlessUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- Open Middle: Completing the SquareUse it for: Fill-the-boxes puzzle using digits 0-9 once; many paths to an optimal answer, good extension.
- Open Middle: Quadratics and Number of SolutionsUse it for: Fill-the-boxes puzzle using digits 0-9 once; many paths to an optimal answer, good extension.
- VideoStarterCorbettmaths video: Algebra: changing the subjectUse it for: Short worked-example video on algebra: changing the subject to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebra: changing the subject advancedUse it for: Short worked-example video on algebra: changing the subject advanced to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebra: completing the squareUse it for: Short worked-example video on algebra: completing the square to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Equations: cross multiplicationUse it for: Short worked-example video on equations: cross multiplication to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Equations: formingUse it for: Short worked-example video on equations: forming to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Equations: fractional advancedUse it for: Short worked-example video on equations: fractional advanced to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Equations: involving fractionsUse it for: Short worked-example video on equations: involving fractions to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Equations: letters both sidesUse it for: Short worked-example video on equations: letters both sides to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Equations: solvingUse it for: Short worked-example video on equations: solving to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Identities, Formula, Equations etcUse it for: Short worked-example video on identities, formula, equations etc to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Inequalities on a number lineUse it for: Short worked-example video on inequalities on a number line to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Inequalities: solving (one sign)Use it for: Short worked-example video on inequalities: solving (one sign) to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Inequalities: solving (two signs)Use it for: Short worked-example video on inequalities: solving (two signs) to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Quadratics: forming and solvingUse it for: Short worked-example video on quadratics: forming and solving to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Quadratics: formulaUse it for: Short worked-example video on quadratics: formula to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Quadratics: solving (factorising)Use it for: Short worked-example video on quadratics: solving (factorising) to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Simultaneous equations (elimination)Use it for: Short worked-example video on simultaneous equations (elimination) to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Simultaneous equations (graphical)Use it for: Short worked-example video on simultaneous equations (graphical) to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Simultaneous equations (substitution, both linear)Use it for: Short worked-example video on simultaneous equations (substitution, both linear) to model the method before practice or for flipped revision.
- VideoStarterEddie Woo (WooTube): Basic Equations playlistUse it for: Sydney teacher Eddie Woo's recorded lessons on equations; play a clip to model a method or for revision.
- Unit/PlanningStage 5 Unit 10 – expressions and equations (sample unit of learning)
- Unit/PlanningStage 5 Unit 12 – investigating parabolas (sample unit of learning)
- Unit/PlanningStage 5 Unit 3 – prisms and cylinders (sample unit of learning)
- Unit/PlanningStage 5 Unit 5 – financial mathematics (sample unit of learning)
- Unit/PlanningStage 5 Unit 6 – constant rates of change (sample unit of learning)
Standard Year 11 (Year 11)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Corbettmaths practice questions: Algebra: changing the subjectUse it for: Free printable graded practice questions (with answers) on algebra: changing the subject for drill or a quick check.
- Corbettmaths practice questions: Equations: angles and perimeterUse it for: Free printable graded practice questions (with answers) on equations: angles and perimeter for drill or a quick check.
- WorksheetDrillKuta free worksheet: Literal equations (changing the subject)Use it for: Printable skills-practice sheet with answer key on literal equations (changing the subject); good for drill or homework.
- VideoStarterCorbettmaths video: Algebra: changing the subjectUse it for: Short worked-example video on algebra: changing the subject to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Equations: formingUse it for: Short worked-example video on equations: forming to model the method before practice or for flipped revision.
Advanced Year 11 (Year 11)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
Standard Year 12 (Year 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
Extension 1 (Year 11, 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
Advanced Year 12 (Year 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
Extension 2 (Year 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.