Indices, roots & surds
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Focus areas in this topic
Stage 4: Indices · Stage 5: Indices A · Stage 5: Indices B (Path) · Stage 5: Indices C (Path)
Stage 3 (Year 5, 6)
- NRICH: Factors and Multiples GameUse it for: Two-player strategy game chaining factors and multiples.
Stage 4 (Year 7, 8)
- NRICH: Factors and Multiples GameUse it for: Two-player strategy game chaining factors and multiples.
- Interactive toolDrillDesmos ScientificUse it for: Free scientific calculator.
- Interactive toolStarterMathigon: Divisibility rulesUse it for: Discover why the divisibility tests for 2, 3, 4, 5, 6 and 10 work.
- Interactive toolStarterMathigon: Prime numbersUse it for: Sieve of Eratosthenes and prime factorisation.
- Mathigon: Sierpinski triangleUse it for: Enrichment on self-similar patterns and powers.
- Interactive toolStarterMaths Is Fun: Cube rootsUse it for: Cubes and cube roots explained.
- Interactive toolStarterMaths Is Fun: Divisibility rulesUse it for: Divisibility tests with examples.
- Interactive toolStarterMaths Is Fun: ExponentsUse it for: Base, power and index notation.
- Interactive toolStarterMaths Is Fun: Irrational numbersUse it for: What makes a number irrational, with examples.
- Interactive toolStarterMaths Is Fun: Laws of exponentsUse it for: Index laws summarised with reasons.
- Interactive toolStarterMaths Is Fun: Square rootsUse it for: Squares and square roots explained.
- Interactive toolStarterMathsisfun: Prime factorisationUse it for: Factor trees and prime factorisation tool.
- Corbettmaths practice questions: Algebra: indicesUse it for: Free printable graded practice questions (with answers) on algebra: indices for drill or a quick check.
- Corbettmaths practice questions: Decimals: recurring decimalsUse it for: Free printable graded practice questions (with answers) on decimals: recurring decimals for drill or a quick check.
- Corbettmaths practice questions: Indices (numerical)Use it for: Free printable graded practice questions (with answers) on indices (numerical) for drill or a quick check.
- Corbettmaths practice questions: Number: cubing a numberUse it for: Free printable graded practice questions (with answers) on number: cubing a number for drill or a quick check.
- Corbettmaths practice questions: Number: product of primesUse it for: Free printable graded practice questions (with answers) on number: product of primes for drill or a quick check.
- Corbettmaths practice questions: Number: rational/irrationalUse it for: Free printable graded practice questions (with answers) on number: rational/irrational for drill or a quick check.
- Corbettmaths practice questions: Number: squaring a numberUse it for: Free printable graded practice questions (with answers) on number: squaring a number for drill or a quick check.
- WorksheetDrillKuta free worksheet: Divisibility and factorsUse it for: Printable skills-practice sheet with answer key on divisibility and factors; good for drill or homework.
- WorksheetDrillKuta free worksheet: Division property of exponentsUse it for: Printable skills-practice sheet with answer key on division property of exponents; good for drill or homework.
- WorksheetDrillKuta free worksheet: Factoring numbers (prime factorisation)Use it for: Printable skills-practice sheet with answer key on factoring numbers (prime factorisation); good for drill or homework.
- WorksheetDrillKuta free worksheet: Multiplication property of exponentsUse it for: Printable skills-practice sheet with answer key on multiplication property of exponents; good for drill or homework.
- WorksheetDrillKuta free worksheet: Numeric expressions with exponentsUse it for: Printable skills-practice sheet with answer key on numeric expressions with exponents; good for drill or homework.
- WorksheetDrillKuta free worksheet: Powers of products and quotientsUse it for: Printable skills-practice sheet with answer key on powers of products and quotients; good for drill or homework.
- WorksheetDrillKuta free worksheet: Square rootsUse it for: Printable skills-practice sheet with answer key on square roots; good for drill or homework.
- WorksheetDrillTransum: Dr Tim's Indices ChallengeUse it for: Index laws practice by level.
- NRICH: Multiplication ArithmagonsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Power CountdownUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: RepetitiouslyUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- Open Middle: Equivalent ExponentsUse it for: Fill-the-boxes puzzle using digits 0-9 once; many paths to an optimal answer, good extension.
- VideoStarterCorbettmaths video: Algebra: indicesUse it for: Short worked-example video on algebra: indices to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Decimals: recurring decimalsUse it for: Short worked-example video on decimals: recurring decimals to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Indices (numerical)Use it for: Short worked-example video on indices (numerical) to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Number: cube rootUse it for: Short worked-example video on number: cube root to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Number: cubing a numberUse it for: Short worked-example video on number: cubing a number to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Number: product of primesUse it for: Short worked-example video on number: product of primes to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Number: rational/irrationalUse it for: Short worked-example video on number: rational/irrational to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Number: square rootUse it for: Short worked-example video on number: square root to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Number: squaring a numberUse it for: Short worked-example video on number: squaring a number to model the method before practice or for flipped revision.
- VideoStarterEddie Woo (WooTube): Basic Indices playlistUse it for: Sydney teacher Eddie Woo's recorded lessons on indices; 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 5 – multiplicative thinking (sample unit of learning)
Stage 5 (Year 9, 10)
- Mathigon: Sierpinski triangleUse it for: Enrichment on self-similar patterns and powers.
- Interactive toolStarterMaths Is Fun: Fractional exponentsUse it for: Links fractional indices to roots.
- Interactive toolStarterMaths Is Fun: Irrational numbersUse it for: What makes a number irrational, with examples.
- Interactive toolStarterMaths Is Fun: Laws of exponentsUse it for: Index laws summarised with reasons.
- Interactive toolStarterMaths Is Fun: Negative exponentsUse it for: Pattern-based explanation of negative indices.
- Corbettmaths practice questions: Algebra: indicesUse it for: Free printable graded practice questions (with answers) on algebra: indices for drill or a quick check.
- Corbettmaths practice questions: Decimals: recurring decimalsUse it for: Free printable graded practice questions (with answers) on decimals: recurring decimals for drill or a quick check.
- Corbettmaths practice questions: Indices: fractionalUse it for: Free printable graded practice questions (with answers) on indices: fractional for drill or a quick check.
- Corbettmaths practice questions: Indices: negativeUse it for: Free printable graded practice questions (with answers) on indices: negative for drill or a quick check.
- Corbettmaths practice questions: Number: rational/irrationalUse it for: Free printable graded practice questions (with answers) on number: rational/irrational for drill or a quick check.
- Corbettmaths practice questions: Surds: intro, rules, simplifyingUse it for: Free printable graded practice questions (with answers) on surds: intro, rules, simplifying for drill or a quick check.
- WorksheetDrillKuta free worksheet: Adding and subtracting surdsUse it for: Printable skills-practice sheet with answer key on adding and subtracting surds; good for drill or homework.
- WorksheetDrillKuta free worksheet: Dividing surds and rationalisingUse it for: Printable skills-practice sheet with answer key on dividing surds and rationalising; good for drill or homework.
- WorksheetDrillKuta free worksheet: Division property of exponentsUse it for: Printable skills-practice sheet with answer key on division property of exponents; good for drill or homework.
- WorksheetDrillKuta free worksheet: More properties of exponents (negative indices)Use it for: Printable skills-practice sheet with answer key on more properties of exponents (negative indices); good for drill or homework.
- WorksheetDrillKuta free worksheet: Multiplication property of exponentsUse it for: Printable skills-practice sheet with answer key on multiplication property of exponents; good for drill or homework.
- WorksheetDrillKuta free worksheet: Multiplying surdsUse it for: Printable skills-practice sheet with answer key on multiplying surds; good for drill or homework.
- WorksheetDrillKuta free worksheet: Powers of products and quotientsUse it for: Printable skills-practice sheet with answer key on powers of products and quotients; good for drill or homework.
- WorksheetDrillKuta free worksheet: Properties of exponentsUse it for: Printable skills-practice sheet with answer key on properties of exponents; good for drill or homework.
- WorksheetDrillKuta free worksheet: Simplifying fractional indicesUse it for: Printable skills-practice sheet with answer key on simplifying fractional indices; good for drill or homework.
- WorksheetDrillKuta free worksheet: Simplifying radicals (surds)Use it for: Printable skills-practice sheet with answer key on simplifying radicals (surds); good for drill or homework.
- WorksheetDrillKuta free worksheet: Surds and fractional indicesUse it for: Printable skills-practice sheet with answer key on surds and fractional indices; good for drill or homework.
- WorksheetDrillTransum: Dr Tim's Indices ChallengeUse it for: Index laws practice by level.
- NRICH: Irrational ArithmagonsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Multiplication ArithmagonsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Rational RootsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: RepetitiouslyUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Tiny NinesUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- VideoStarterCorbettmaths video: Algebra: indicesUse it for: Short worked-example video on algebra: indices to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Decimals: recurring decimalsUse it for: Short worked-example video on decimals: recurring decimals to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Indices: fractionalUse it for: Short worked-example video on indices: fractional to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Indices: negativeUse it for: Short worked-example video on indices: negative to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Number: rational/irrationalUse it for: Short worked-example video on number: rational/irrational to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Surds: addition/subtractionUse it for: Short worked-example video on surds: addition/subtraction to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Surds: expanding bracketsUse it for: Short worked-example video on surds: expanding brackets to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Surds: intro, rules, simplifyingUse it for: Short worked-example video on surds: intro, rules, simplifying to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Surds: rationalising denominatorsUse it for: Short worked-example video on surds: rationalising denominators to model the method before practice or for flipped revision.
- VideoStarterEddie Woo (WooTube): Basic Indices playlistUse it for: Sydney teacher Eddie Woo's recorded lessons on indices; play a clip to model a method or for revision.
- Unit/PlanningStage 5 Unit 2 – working with triangles (sample unit of learning)
- Unit/PlanningStage 5 Unit 4 – index laws (sample unit of learning)
- Unit/PlanningStage 5 Year 10 – the unit circle elective (sample unit of learning)