Algebraic techniques
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Stage 4: Algebraic techniques · Stage 5: Algebraic techniques A · Stage 5: Algebraic techniques B (Path) · Stage 5: Algebraic techniques C (Path) · Mathematics Standard 11–12 – Year 11: Formulas and equations · Mathematics Standard 11–12 – Year 12 – Standard 1: Algebraic relationships · Mathematics Standard 11–12 – Year 12 – Standard 2: Algebraic relationships
Stage 3 (Year 5, 6)
- Mathigon PolypadUse it for: Virtual manipulatives: fraction bars, algebra tiles, cubes and polygons.
- Interactive toolStarterMathsbot: ManipulativesUse it for: Virtual manipulatives incl. algebra tiles, two-colour counters, fraction walls.
Stage 4 (Year 7, 8)
- PhET Expression ExchangeUse it for: Collect like terms by dragging coins/variables together; game screens for practice.
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
- Mathigon PolypadUse it for: Virtual manipulatives: fraction bars, algebra tiles, cubes and polygons.
- Interactive toolStarterMaths Is Fun: Factoring in algebraUse it for: Factorising by taking out common factors.
- Interactive toolStarterMaths Is Fun: Introduction to algebraUse it for: Gentle introduction to pronumerals.
- Interactive toolStarterMaths Is Fun: Like termsUse it for: Identifying and combining like terms.
- Interactive toolStarterMaths Is Fun: SubstitutionUse it for: Substituting values into expressions.
- Interactive toolStarterMathsbot: Algebra TilesUse it for: Algebra tiles for expanding and factorising.
- Interactive toolStarterMathsbot: ManipulativesUse it for: Virtual manipulatives incl. algebra tiles, two-colour counters, fraction walls.
- Interactive toolStarterPolypad virtual manipulatives (algebra tiles, fraction bars, number lines)Use it for: Free virtual manipulatives; use algebra tiles to model expanding/factorising or fraction bars for equivalence.
- PhET Area Model AlgebraUse it for: Show expanding brackets and binomial products as rectangle areas.
- Corbettmaths practice questions: Algebra: collecting like termsUse it for: Free printable graded practice questions (with answers) on algebra: collecting like terms for drill or a quick check.
- Corbettmaths practice questions: Algebra: dividing termsUse it for: Free printable graded practice questions (with answers) on algebra: dividing terms for drill or a quick check.
- Corbettmaths practice questions: Algebra: expanding bracketsUse it for: Free printable graded practice questions (with answers) on algebra: expanding brackets for drill or a quick check.
- Corbettmaths practice questions: Algebra: expressions – formingUse it for: Free printable graded practice questions (with answers) on algebra: expressions – forming for drill or a quick check.
- Corbettmaths practice questions: Algebra: multiplying termsUse it for: Free printable graded practice questions (with answers) on algebra: multiplying terms for drill or a quick check.
- Corbettmaths practice questions: Algebra: notationUse it for: Free printable graded practice questions (with answers) on algebra: notation for drill or a quick check.
- Corbettmaths practice questions: Algebra: substitutionUse it for: Free printable graded practice questions (with answers) on algebra: substitution 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: FactorisationUse it for: Free printable graded practice questions (with answers) on factorisation for drill or a quick check.
- Corbettmaths practice questions: Speed, distance and timeUse it for: Free printable graded practice questions (with answers) on speed, distance and time for drill or a quick check.
- WorksheetDrillKuta free worksheet: Combining like termsUse it for: Printable skills-practice sheet with answer key on combining like terms; good for drill or homework.
- WorksheetDrillKuta free worksheet: Distributive property with area diagramsUse it for: Printable skills-practice sheet with answer key on distributive property with area diagrams; good for drill or homework.
- WorksheetDrillKuta free worksheet: Evaluating algebraic expressionsUse it for: Printable skills-practice sheet with answer key on evaluating algebraic expressions; good for drill or homework.
- WorksheetDrillKuta free worksheet: Evaluating variable expressions (substitution)Use it for: Printable skills-practice sheet with answer key on evaluating variable expressions (substitution); good for drill or homework.
- WorksheetDrillKuta free worksheet: Factoring monomialsUse it for: Printable skills-practice sheet with answer key on factoring monomials; good for drill or homework.
- WorksheetDrillKuta free worksheet: Simplifying variable expressionsUse it for: Printable skills-practice sheet with answer key on simplifying variable expressions; good for drill or homework.
- WorksheetDrillKuta free worksheet: The distributive propertyUse it for: Printable skills-practice sheet with answer key on the distributive property; good for drill or homework.
- WorksheetDrillKuta free worksheet: Variable and verbal expressionsUse it for: Printable skills-practice sheet with answer key on variable and verbal expressions; good for drill or homework.
- WorksheetDrillKuta free worksheet: Writing algebraic expressionsUse it for: Printable skills-practice sheet with answer key on writing algebraic expressions; good for drill or homework.
- Variation Theory sequences: Algebraic notationUse it for: Intelligent-practice sequences on algebraic notation where one thing changes at a time; ask students to predict before answering.
- Variation Theory sequences: Dividing termsUse it for: Intelligent-practice sequences on dividing terms where one thing changes at a time; ask students to predict before answering.
- Variation Theory sequences: Expand single bracketsUse it for: Intelligent-practice sequences on expand single brackets where one thing changes at a time; ask students to predict before answering.
- Variation Theory sequences: Writing expressionsUse it for: Intelligent-practice sequences on writing expressions where one thing changes at a time; ask students to predict before answering.
- NRICH: Algebra MatchUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Consecutive NumbersUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Crossed EndsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Number PyramidsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Perimeter ExpressionsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- Open Middle: Factoring using Greatest Common FactorUse it for: Fill-the-boxes puzzle using digits 0-9 once; many paths to an optimal answer, good extension.
- VideoStarterCorbettmaths video: Algebra: collecting like termsUse it for: Short worked-example video on algebra: collecting like terms to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebra: dividing termsUse it for: Short worked-example video on algebra: dividing terms to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebra: expanding bracketsUse it for: Short worked-example video on algebra: expanding brackets to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebra: expressions – formingUse it for: Short worked-example video on algebra: expressions – forming to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebra: multiplying termsUse it for: Short worked-example video on algebra: multiplying terms to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebra: notationUse it for: Short worked-example video on algebra: notation to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebra: substitutionUse it for: Short worked-example video on algebra: substitution 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: FactorisationUse it for: Short worked-example video on factorisation to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Speed, distance and timeUse it for: Short worked-example video on speed, distance and time to model the method before practice or for flipped revision.
- VideoStarterEddie Woo (WooTube): Basic Algebraic Techniques playlistUse it for: Sydney teacher Eddie Woo's recorded lessons on algebraic techniques; play a clip to model a method or for revision.
- Unit/PlanningStage 4 Unit 12 – further multiplicative thinking (sample unit of learning)
- Unit/PlanningStage 4 Unit 4 – additive thinking (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 toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
- Interactive toolStarterMaths Is Fun: ExpandingUse it for: Expanding brackets explained with area diagrams.
- Interactive toolStarterMaths Is Fun: Factoring quadraticsUse it for: Methods for factorising quadratic trinomials.
- Interactive toolStarterMathsbot: Algebra TilesUse it for: Algebra tiles for expanding and factorising.
- Interactive toolStarterPolypad virtual manipulatives (algebra tiles, fraction bars, number lines)Use it for: Free virtual manipulatives; use algebra tiles to model expanding/factorising or fraction bars for equivalence.
- PhET Area Model AlgebraUse it for: Show expanding brackets and binomial products as rectangle areas.
- 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: expanding bracketsUse it for: Free printable graded practice questions (with answers) on algebra: expanding brackets for drill or a quick check.
- Corbettmaths practice questions: Algebra: expanding three bracketsUse it for: Free printable graded practice questions (with answers) on algebra: expanding three brackets for drill or a quick check.
- Corbettmaths practice questions: Algebra: expanding two bracketsUse it for: Free printable graded practice questions (with answers) on algebra: expanding two brackets for drill or a quick check.
- Corbettmaths practice questions: Algebraic fractions: additionUse it for: Free printable graded practice questions (with answers) on algebraic fractions: addition 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: Factorisation: bracketsUse it for: Free printable graded practice questions (with answers) on factorisation: brackets for drill or a quick check.
- Corbettmaths practice questions: Factorisation: quadraticsUse it for: Free printable graded practice questions (with answers) on factorisation: quadratics for drill or a quick check.
- Corbettmaths practice questions: Factorisation: splitting the middleUse it for: Free printable graded practice questions (with answers) on factorisation: splitting the middle for drill or a quick check.
- WorksheetDrillKuta free worksheet: Adding and subtracting algebraic fractionsUse it for: Printable skills-practice sheet with answer key on adding and subtracting algebraic fractions; good for drill or homework.
- WorksheetDrillKuta free worksheet: Factoring quadratic trinomials (easy)Use it for: Printable skills-practice sheet with answer key on factoring quadratic trinomials (easy); good for drill or homework.
- WorksheetDrillKuta free worksheet: Factoring quadratic trinomials (hard)Use it for: Printable skills-practice sheet with answer key on factoring quadratic trinomials (hard); good for drill or homework.
- WorksheetDrillKuta free worksheet: Factoring special case polynomialsUse it for: Printable skills-practice sheet with answer key on factoring special case polynomials; 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: Multiplying binomialsUse it for: Printable skills-practice sheet with answer key on multiplying binomials; good for drill or homework.
- WorksheetDrillKuta free worksheet: Multiplying special case polynomialsUse it for: Printable skills-practice sheet with answer key on multiplying special case polynomials; good for drill or homework.
- WorksheetDrillKuta free worksheet: Simplifying algebraic fractionsUse it for: Printable skills-practice sheet with answer key on simplifying algebraic fractions; good for drill or homework.
- Variation Theory sequences: Expand double bracketsUse it for: Intelligent-practice sequences on expand double brackets where one thing changes at a time; ask students to predict before answering.
- Variation Theory sequences: Expand single bracketsUse it for: Intelligent-practice sequences on expand single brackets where one thing changes at a time; ask students to predict before answering.
- NRICH: Pair ProductsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Plus MinusUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: What's Possible?Use it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Why 24?Use it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- 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: expanding bracketsUse it for: Short worked-example video on algebra: expanding brackets to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebra: expanding three bracketsUse it for: Short worked-example video on algebra: expanding three brackets to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebra: expanding two bracketsUse it for: Short worked-example video on algebra: expanding two brackets to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebraic fractions: additionUse it for: Short worked-example video on algebraic fractions: addition to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebraic fractions: divisionUse it for: Short worked-example video on algebraic fractions: division to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebraic fractions: multiplicationUse it for: Short worked-example video on algebraic fractions: multiplication to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Algebraic fractions: simplifyingUse it for: Short worked-example video on algebraic fractions: simplifying 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: Factorisation: difference of 2 squaresUse it for: Short worked-example video on factorisation: difference of 2 squares to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Factorisation: quadraticsUse it for: Short worked-example video on factorisation: quadratics to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Factorisation: quadratics harderUse it for: Short worked-example video on factorisation: quadratics harder to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Factorisation: splitting the middleUse it for: Short worked-example video on factorisation: splitting the middle to model the method before practice or for flipped 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)
Standard Year 11 (Year 11)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
- 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: substitutionUse it for: Free printable graded practice questions (with answers) on algebra: substitution 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: Speed, distance and timeUse it for: Free printable graded practice questions (with answers) on speed, distance and time 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: Algebra: substitutionUse it for: Short worked-example video on algebra: substitution 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: Speed, distance and timeUse it for: Short worked-example video on speed, distance and time to model the method before practice or for flipped revision.
- Unit/PlanningMathematics Standard (2024) Year 11 Unit 1 – getting healthy (9 lessons)
- Unit/PlanningMathematics Standard (2024) Year 11 Unit 2 – show me the money (19 lessons)
- Unit/PlanningMathematics Standard (2024) Year 11 Unit 3 – making things (13 lessons)
- Unit/PlanningMathematics Standard (2024) Year 11 Unit 4 – driving safely (11 lessons)
Advanced Year 11 (Year 11)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Standard Year 12 (Year 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
- Unit/PlanningMathematics Standard (2024) Year 12 Unit 2 – managing events (part 1)
Extension 1 (Year 11, 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Advanced Year 12 (Year 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Extension 2 (Year 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.