We believe **deep understanding** is enhanced with mental hooks onto **historical stories**, hence the Inspiration round and one section of the Confidence round is focused upon the work of twenty-five mathematicians from within a specified century.

For the August 2022 to July 2023 season, focus is on work from the 20th century:

A.N. Whitehead | Andrey Kolmogorov | Emmy Noether | John von Neumann | Paul Erdos |

Alan Turing | Benoit Mandelbrot | G.H. Hardy | Julia Robinson | Srinivasa Ramanujan |

Alanzo Church | Bertrand Russell | Gerd Faltings | Kurt Godel | Thomas Hales |

Alexander Grothendiek | Claude Shannon | J. E. Littlewood | Nicolas Bourbaki | Wolfgang Haken |

Andre Weil | David Hilbert | John Nash | Paul Cohen | Yuri Matiyasevich |

For the August 2021 to July 2022 season, focus was on work from the 19th century:

Adrian-Marie Legendre | Carl Fredrich Gauss | George Cantor | Jean-Robert Argard | Leonard Euler |

Arther Cayley | Charles Babbage | George Peacock | John Venn | Nikolai Lobachevsky |

Augustin-Ferdinand Mobius | Evariste Galois | Gottfried Wilhelm Leibniz | Joseph Fourier | Peter Dirichlet |

Augustin-Louis Cauchy | Felix Klein | Henri Poincare | Joseph-Louise LaGrange | Pierre-Simon LaPlace |

Bernard Riemann | George Boole | Janos Bolyai | Karl Weierstrass | William Hamilton |

This learning content is comprised of conceptual understanding statements, which have been crafted by considering important generic knowledge, for a happier life, of:

- Numeracy
- Pattern spotting
- Logic
- Deductive reasoning

within real-life as well as abstract situations.

Each Championships will feature content at the same level and below.

THEME | LEVEL | EU | DESCRIPTOR |
---|---|---|---|

Arithmetic | Junior | Operations | Understand how rational exponents are short-hand for roots, and simplify number expressions accordingly |

Arithmetic | Junior | Operations | Perform common binary operations on number values |

Arithmetic | Junior | Quotients | Manipulate any quotient raised to any exponent |

Arithmetic | Junior | Exponents | Communicate in base 2 and convert into base 10 |

Arithmetic | Junior | Ratio and Proportion | Use indirect proportion as a constant rate of change for different quantities |

Arithmetic | Junior | Matrices | Use matrices to transform images around a cartesian grid |

Arithmetic | Junior | Operations | Use the factorial operation |

Arithmetic | Junior | Operations | Perform correct order of operation processes involving trigonometric ratios |

Arithmetic | Junior | Rationality | Interpret solutions involving any real-numbers in context |

Arithmetic | Junior | Error | Analyse innaccuracies of compounding rounded values |

Arithmetic | Junior | Sequences and Series | Use conventional notation for geometric sequences in context |

Arithmetic | Junior | Binomial expressions | Use the binomial expansion to solve a problem |

Arithmetic | Junior | Cryptography | Communicate in braille and morse code with precision |

Arithmetic | Junior | Matrices | Use matrices to visualise and draw transformed images of shapes on a cartesian grid |

Arithmetic | Junior | Exponents | Solve simple modular arithmetic problems |

Arithmetic | Junior | Finance | Create and interpret simple accounting documentation |

Arithmetic | Junior | Divisibility | Identify divisibilities of a number written in any base |

Arithmetic | Junior | Relations Mappings and Equations | Identify terms in a sequence pattern CODEBREAKERS |

Arithmetic | Junior | Combinatorics | Calculate simple binomial problems involving combinations |

Arithmetic | Junior | Finance | Solve problems involving amortization and annuity |

Arithmetic | Junior | Exponents | Communicate in base 10 and convert into base 2 |

Arithmetic | Primary | Time | Read from an analog clock |

Arithmetic | Primary | Operations | Understand how multiplication is short-hand for repeated addition and use it accordingly |

Arithmetic | Primary | Divisibility | Identify the divisibility by 10, 5 and 2 of any number |

Arithmetic | Primary | Quotients | Understand how division is short-hand for repeated subtraction and find exact quotients without remainders |

Arithmetic | Primary | Notation | Articulate place value of number digits within words |

Arithmetic | Primary | Exponents | Appreciate the distinction between numbers arranged in a square compared to in an oblong |

Arithmetic | Primary | Finance | Appreciate and recognise 'value for money' involving decimals and percentages |

Arithmetic | Primary | Error | Identify approximations for sums and obvious mis-calculations |

Arithmetic | Primary | Ratio and Proportion | Calculate any percentage of an amount |

Arithmetic | Primary | Sequences and Series | Recite up to the 15 times tables as a fundamental axiom of number patterns |

Arithmetic | Primary | Cryptography | Communicate the phonetic alphabet, Atbash, handphone keypad and dancing men cipher with precision |

Arithmetic | Primary | Directions and Angles | Identify common factors within expressions |

Arithmetic | Primary | Kinematics | Calculate departure, arrival times or distance travelled in context |

Arithmetic | Primary | Time | Solve problems involving all convential formats of time |

Arithmetic | Primary | Directions and Angles | Recognise appropriate units for quantities in context |

Arithmetic | Primary | Divisibility | Identify and label numbers that have a maximum of 2 factors |

Arithmetic | Primary | Rationality | Distinguish between the different possible types of rational number |

Arithmetic | Primary | Notation | Communicate the value of items using words |

Arithmetic | Primary | Exponents | Calculate the value of integers raised to single-digit exponents |

Arithmetic | Primary | Ratio and Proportion | Create group representations for parts of a whole |

Arithmetic | Primary | Exponents | Use everyday contexts to perform exponent calculations with any base number |

Arithmetic | Primary | Finance | Consider costs and expenses when making value judgements within specified budgets |

Arithmetic | Primary | Error | Identify the magnitude of a rounding error |

Arithmetic | Primary | Ratio and Proportion | Use direct proportion as a constant rate of change for different quantities |

Arithmetic | Primary | Divisibility | Decompose any number into its prime factors and compare with others |

Arithmetic | Primary | Sequences and Series | Use conventional notation for common sequences in context |

Arithmetic | Primary | Exponents | Express values in exponent form |

Arithmetic | Primary | Relations Mappings and Equations | Identify terms in a sequence pattern CODEBREAKERS |

Arithmetic | Secondary | Operations | Perform multi-step calculations, involving parentheses and indices, in the correct order |

Arithmetic | Secondary | Quotients | Calculate quotients of values and interpret possible remainders in context |

Arithmetic | Secondary | Divisibility | Identify divisibilities by single-digit numbers |

Arithmetic | Secondary | Rationality | Appreciate there are infinitely many numbers between any two distinct numbers |

Arithmetic | Secondary | Notation | Understand appropriate representations for very small and very large numbers in context |

Arithmetic | Secondary | Cryptography | Communicate morse code, braille, Ceasar and PigPen cipher with precision |

Arithmetic | Secondary | Vectors | Use vectors to translate images around a cartesian grid |

Arithmetic | Secondary | Rationality | Perform calculations involving any real numbers |

Arithmetic | Secondary | Notation | Always communicate using conventional notation, including units of derived values |

Arithmetic | Secondary | Finance | Make financial value judgements within real contexts |

Arithmetic | Secondary | Error | Write answers to appropriate decimal places or significant figures |

Arithmetic | Secondary | Directions and Angles | Convert across common imperial and metric quantities |

Arithmetic | Secondary | Quotients | Express any quotient in terms of the sum of unit fractions |

Arithmetic | Secondary | Finance | Compare results using simple and compound interest |

Arithmetic | Secondary | Divisibility | Solve simple linear concruence problems |

Arithmetic | Secondary | Relations Mappings and Equations | Identify terms in a sequence pattern CODEBREAKERS |

Arithmetic | Secondary | Exponential and Logarithmic | Recognise and compare depreciation rates with absolute drops in value |

Arithmetic | Secondary | Exponential and Logarithmic | Identify and use the multiplier when calculating with increasing and decreasing percentages |

Arithmetic | Secondary | Sequences and Series | Use conventional notation for arithmetic sequences and find simple series in context |

Arithmetic | Senior | Exponents | Manipulate numbers expressed in any form and within any common base |

Arithmetic | Senior | Binomial expressions | Use the binomial expansion with simple rational values |

Arithmetic | Senior | Matrices | Use inverse 2 by 2 matrices to help transform (large) data sets in solving real-life problems |

Arithmetic | Senior | Exponents | Use modular arithmetic and linear congruences to solve number problems |

Arithmetic | Senior | Finance | Solve problems involving amortization |

Arithmetic | Senior | Sequences and Series | Distinguish between recursive and telescoping sequences and use conventional notation to sum their series where possible, in context |

Arithmetic | Senior | Binomial expressions | Use the binomial expansion with any exponent |

Arithmetic | Senior | Complex numbers | Use DeMoivre's Theorem as a tool within calculations |

Arithmetic | Senior | Divisibility | Use Fermat's Little Theorem |

Arithmetic | Senior | Rationality | Use the Ramanujan-Nagell exponential diophantine equation in context |

Arithmetic | Senior | Finance | Solve problems involving annuity |

Arithmetic | Senior | Manipulation | Identify values or quantity of digits within large numbers in any base |

Arithmetic | Senior | Relations Mappings and Equations | Identify terms in a sequence pattern CODEBREAKERS |

Arithmetic | Senior | Combinatorics | Calculate simple problems involving permutations |

Arithmetic | Senior | Divisibility | Identify divisibilities of a number written in any base |

Arithmetic | Senior | Complex numbers | Use Pell's equation in context |

Algebra & Geometry | Junior | Tessellations | Identify tilings that create monohedral tessellations |

Algebra & Geometry | Junior | Relations Mappings and Equations | Graphically solve a small system of equations in context |

Algebra & Geometry | Junior | Perimeter and Area | Use nets and coordinates to calculate perimeter and area |

Algebra & Geometry | Junior | Nets and Volume | Find Volume of composite Polyhedra from their net |

Algebra & Geometry | Junior | Trigonometry | Recognise common ratios between the sides of and angles within a right-angled triangle |

Algebra & Geometry | Junior | Theorems | identify and use the circle theorems in solving problems |

Algebra & Geometry | Junior | Graph Theory | Use the handshaking lemma and komplete graphs in simple cases |

Algebra & Geometry | Junior | Direction and Angles | Calculate and use amounts of turn in radians |

Algebra & Geometry | Junior | Theorems | Know and use Pick's Theorem as a tool within calculations |

Algebra & Geometry | Junior | Tessellations | Recognise the geometric properties of the Torus and Klein bottle are different in cartesian and spherical geometry |

Algebra & Geometry | Junior | Vectors | Represent a scalar product geometrically and use it in calculating intersections and angles of lines |

Algebra & Geometry | Junior | Exponential and Logarithmic | Recognise the effect of increasing interest rates over absolute interest |

Algebra & Geometry | Junior | Polygons and Polyhedra | Solve for measures of angles and segments relating to circles |

Algebra & Geometry | Junior | Polygons and Polyhedra | Calculate perimeters and areas of sectors and segments relating to circles |

Algebra & Geometry | Junior | Area and Surface Area | Calculate the area of any triangle |

Algebra & Geometry | Junior | Proof | Appreciate and follow the logic required in creating direct mathematical proofs, and proof by contradiction |

Algebra & Geometry | Junior | Area and Surface Area | Find the area of compound polygons |

Algebra & Geometry | Junior | Axioms and Logic | Identify when a statement is logical or not (ie tautology) |

Algebra & Geometry | Junior | Matrices | Use matrices to transform images around a cartesian grid |

Algebra & Geometry | Junior | Matrices | Use matrices to visualise and draw transformed images of shapes on a cartesian grid |

Algebra & Geometry | Junior | Nets and Volume | Find the dimensions of composite Polyhedra from the Volume |

Algebra & Geometry | Junior | Vectors | Perform simple transformations within 3D space |

Algebra & Geometry | Junior | Vectors | Identify multiple transformations in 2D |

Algebra & Geometry | Junior | Trigonometry | Recognise common ratios between the sides of and angles within any triangle |

Algebra & Geometry | Junior | Combinatorics | Calculate binomial problems involving simple permutations |

Algebra & Geometry | Junior | Area and Surface Area | Find the SA of compound polyhedra |

Algebra & Geometry | Primary | Directions and Angles | Have an understanding of the estimation of magnitudes |

Algebra & Geometry | Primary | Coordinates | Know and use first quadrant cartesian coordinates in context |

Algebra & Geometry | Primary | Direction and Angles | Provide directions using a 4-point compass rose |

Algebra & Geometry | Primary | Relations Mappings and Equations | Visualise times tables with an arithmetic translation in a mapping |

Algebra & Geometry | Primary | Graphs | Appreciate the graphical representation of a constant input with independent output and vice versa |

Algebra & Geometry | Primary | Nets and Volume | Distinguish between and label common polygon shapes |

Algebra & Geometry | Primary | Area and Surface Area | Find area of right-angled polygons and surface area of right-angled polyhedra |

Algebra & Geometry | Primary | Nets and Volume | Find the volume of right-angled polyhedra |

Algebra & Geometry | Primary | Theorems | Recognise the fundamental axioms of geometry: Amount of turn round a point, vertically opposite and corresponding angles |

Algebra & Geometry | Primary | Vectors | Recognise the spacial effect of a translation slide movement |

Algebra & Geometry | Primary | Tessellations | Maintain a visual appreciation for shapes that create tiling patterns |

Algebra & Geometry | Primary | Operations | Use everyday contexts to create calculations |

Algebra & Geometry | Primary | Polygons and Polyhedra | Distinguish between and label common polyhedron objects |

Algebra & Geometry | Primary | Nets and Volume | Find the volume of right-angled polyhedra |

Algebra & Geometry | Primary | Directions and Angles | Use appropriate metric units when representing quantities |

Algebra & Geometry | Primary | Polynomials | Simplify any expression |

Algebra & Geometry | Primary | Trigonometry | Understand the relationship connecting the perpendicular sides and area of a right-angled triangle |

Algebra & Geometry | Primary | Vectors | Recognise and describe the spacial effect of a spin rotation |

Algebra & Geometry | Primary | Directions and Angles | Use appropriate imperial units when representing quantities |

Algebra & Geometry | Primary | Polygons and Polyhedra | Identify the labels relating to circles |

Algebra & Geometry | Primary | Area and Surface Area | Identify and name angles smaller or larger than multiples of quarter turns |

Algebra & Geometry | Primary | Area and Surface Area | Distinguish triangles from the magnitude of their angles or lengths of sides |

Algebra & Geometry | Primary | Vectors | Recognise the spacial effect of a mirror image reflection |

Algebra & Geometry | Secondary | Direction and Angles | Provide directions using an 8-point compass rose |

Algebra & Geometry | Secondary | Nets and Volume | Classify quadrilaterals by using interior and exterior angles |

Algebra & Geometry | Secondary | Coordinates | Know and use cartesian coordinates in context |

Algebra & Geometry | Secondary | Direction and Angles | Estimate and describe amounts of turn in degrees |

Algebra & Geometry | Secondary | Relations Mappings and Equations | Describe linear relationships from a mapping diagram and solve equivalent equations with rational coefficients |

Algebra & Geometry | Secondary | Polygons and Polyhedra | Recognise the properties of the platonic solids |

Algebra & Geometry | Secondary | Perimeter and Area | Use proportions to calculate area and perimeter |

Algebra & Geometry | Secondary | Area and Surface Area | Find area of common polygons and SA of common Polyhedra |

Algebra & Geometry | Secondary | Factorising | Fully factorise any expression |

Algebra & Geometry | Secondary | Exponential and Logarithmic | Recognise and compare depreciation rates with absolute drops in value |

Algebra & Geometry | Secondary | Theorems | Understand the relationships of angles formed by a transversal over a pair of parallel lines |

Algebra & Geometry | Secondary | Graph Theory | From given information about its faces, edges and vertices, recognise if a solid exists |

Algebra & Geometry | Secondary | Direction and Angles | Use three-figure bearings to describe the direction of an object compared to another |

Algebra & Geometry | Secondary | Nets and Volume | Find the volume of common Polyhedra from their net and vice versa |

Algebra & Geometry | Secondary | Polynomials | Represent and use a linear function graphically and algebraically |

Algebra & Geometry | Secondary | Exponential and Logarithmic | Identify and use the multiplier when calculating with increasing and decreasing percentages |

Algebra & Geometry | Secondary | Trigonometry | Understand and use the relationship connecting the 3 sides of a right-angled triangle and calculate its area |

Algebra & Geometry | Secondary | Vectors | Use the language of constant, increasing and decreasing for the visual rate of change of a graph |

Algebra & Geometry | Secondary | Theorems | Understand the relationship connecting areas around the sides of a right-angled triangle |

Algebra & Geometry | Secondary | Vectors | Perform stretch and sheer transformations on 2D shapes |

Algebra & Geometry | Secondary | Combinatorics | Recognise the pattern of Pascal's triangle as a tool for simple combination poblems |

Algebra & Geometry | Secondary | Vectors | Describe movement around a shape using given vectors |

Algebra & Geometry | Secondary | Direction and Angles | Identify the loci of a situation given conditions |

Algebra & Geometry | Secondary | Vectors | Rotate a 2D shape by any angle amount of turn |

Algebra & Geometry | Secondary | Direction and Angles | Construct and interpret scale drawings, using bearings |

Algebra & Geometry | Secondary | Polygons and Polyhedra | Calculate the perimeter and area relating to circles |

Algebra & Geometry | Secondary | Tessellations | Recognise the geometric properties of the mobius strip |

Algebra & Geometry | Secondary | Vectors | Describe or draw quarter-turn rotation images of shapes and integer scale factor enlargement on a cartesian grid |

Algebra & Geometry | Secondary | Area and Surface Area | Identify mathematically similar shapes |

Algebra & Geometry | Secondary | Area and Surface Area | Understand a proof for the sum of angles in a triangle |

Algebra & Geometry | Secondary | Area and Surface Area | Understand and use the side, angle and area relationships within any cartesian triangle |

Algebra & Geometry | Secondary | Axioms and Logic | Appreciate and recognise Euclid's postulates |

Algebra & Geometry | Secondary | Direction and Angles | Use different 2D planes within 3D spaces |

Algebra & Geometry | Secondary | Nets and Volume | Find the volume of common Polyhedra from their net and vice versa. |

Algebra & Geometry | Secondary | Ratio and Proportion | Construct angle bisectors and find the shortest distance between lines and a point |

Algebra & Geometry | Senior | Nets and Volume | Identify and use bipyramids |

Algebra & Geometry | Senior | Tessellations | Recognise Hirschhorn tilings |

Algebra & Geometry | Senior | Nets and Volume | Use of Euler's characteristic and duality within simple contexts |

Algebra & Geometry | Senior | Trigonometry | Use the compound angle identities as tools |

Algebra & Geometry | Senior | Theorems | Use Ceva's Theorem as a tool within calculations |

Algebra & Geometry | Senior | Graph Theory | Recognise Eulerian cycles in context |

Algebra & Geometry | Senior | Trigonometry | Use the arctrigonometric identities as tools |

Algebra & Geometry | Senior | Theorems | Know and use Carnot's Theorem as a tool within calculations |

Algebra & Geometry | Senior | Polygons and Polyhedra | Recognise Archimedean solids, duals and Kepler-Poinsot polyhedra |

Algebra & Geometry | Senior | Area and Surface Area | Use Heron's Formula as a tool within calculations |

Algebra & Geometry | Senior | Directions and Angles | Use completing the rectangle as a tool within calculations |

Algebra & Geometry | Senior | Tessellations | Recognise Periodic tilings |

Algebra & Geometry | Senior | Tessellations | Recognise Aperiodic tilings |

Algebra & Geometry | Senior | Theorems | Use Menelaus' Theorem as a tool within calculations |

Algebra & Geometry | Senior | Graph Theory | Recognise Eulerian circuits in context |

Algebra & Geometry | Senior | Graph Theory | Recognise Hamiltonian cycles in context |

Algebra & Geometry | Senior | Graph Theory | Recognise Hamiltonian circuits in context |

Algebra & Geometry | Senior | Nets and Volume | Identify and use uniform stars |

Calculus | Junior | Kinematics | Use scalar equivalents of displacement and velocity vectors with time |

Calculus | Junior | Integration | Calculate areas between graphs and axes, where common shapes and objects are generated |

Calculus | Junior | Kinematics | Understand and calculate the linear movement of a particle |

Calculus | Junior | Differentiation | Find minimums for optimsed solutions |

Calculus | Junior | Vectors | Distinguish between increasing and decreasing slope of graphs in context |

Calculus | Junior | Vectors | Use average rate of change in context |

Calculus | Junior | Kinematics | Use scalar equivalents of velocity and acceleration vectors with time |

Calculus | Junior | Differentiation | Know and use the chain rule as a tool to differentiate simple functions in context |

Calculus | Junior | Differentiation | Know and use the product rule as a tool to differentiate simple functions in context |

Calculus | Junior | Differentiation | Know and use the quotient rule as a tool to differentiate simple functions in context |

Calculus | Junior | Integration | Calculate volumes of revolution of simple functions wrt x |

Calculus | Junior | Integration | Calculate volumes of revolution of simple functions wrt y |

Calculus | Junior | Differentiation | Find maximums for optimsed solutions |

Calculus | Junior | Differentiation | Find inflections for optimsed solutions |

Calculus | Junior | Vectors | Use concavity of graphs to identify local behaviour of a particle in context |

Calculus | Junior | Vectors | Use instantaneous rate of change in context |

Calculus | Secondary | Differentiation | Recognise and distinguish between graphs of functions and of their slope functions |

Calculus | Secondary | Vectors | Use the language of constant, increasing or decreasing for the visual rate of change of a graph |

Calculus | Senior | Differentiation | Know and use the chain rule and substitution as tools to differentiate simple functions in context |

Calculus | Senior | Integration | Know and use the inverse chain rule and substitution as tools to integrate simple functions in context |

Calculus | Senior | Kinematics | Use and convert between displacement and velocity functions in context |

Calculus | Senior | Differentiation | Use implicit differentiation and related rates of change as tools on functions in context |

Calculus | Senior | Integration | Know and use integration by parts as tools within calculations |

Calculus | Senior | Limits | Use Eulers Method and slope fields as tools in simple contexts |

Calculus | Senior | Differential Equations | Solve first order linear differential equations |

Calculus | Senior | Differential Equations | Solve separable variable differential equations |

Calculus | Senior | Differential Equations | Solve homogenous differential equations |

Calculus | Senior | Differential Equations | Solve simple linear coupled simultaneous differential equations |

Calculus | Senior | Integration | Know and use the product rule and substitution as tools to differentiate simple functions in context |

Calculus | Senior | Integration | Know and use the inverse product rule and substitution as tools to integrate simple functions in context |

Calculus | Senior | Kinematics | Use and convert between velocity and acceleration functions in context |

Calculus | Senior | Kinematics | Use and convert between displacement and acceleration functions in context |

Calculus | Senior | Limits | Calculate limits to infinity of rational functions |

Calculus | Senior | Integration | Know and use partial fractions as tools within calculations |

Experimental Sciences | Junior | Probability | Appreciate and interpret theoretical probabilities of independent events, in context |

Experimental Sciences | Junior | Regression | Draw and use a line of best fit by hand, passing through the mean value |

Experimental Sciences | Junior | Location and Dispersion | Make comparisons between data sets using cumulative frequency |

Experimental Sciences | Junior | Probability | Know and use the rules for union, intersection as tools within calculations |

Experimental Sciences | Junior | Regression | Calculate simple least squares linear regression by hand |

Experimental Sciences | Junior | Representing Data | Use and graphically represent discrete vs continuous data appropriately |

Experimental Sciences | Junior | Location and Dispersion | Generate and interpret the geometric mean from a dataset |

Experimental Sciences | Junior | Data tests and correlation | Use and interpret the correlation coefficient in context when analysing data |

Experimental Sciences | Junior | Data tests and correlation | Understand the effect of sampling compared to population statistics |

Experimental Sciences | Junior | Location and Dispersion | Generate and interpret the arithmetic mean value from a grouped frequency table |

Experimental Sciences | Junior | Random variables and distributions | Use and interpret binomial probability distributions in context |

Experimental Sciences | Junior | Location and Dispersion | Generate and interpret the arithmetic median value from a grouped frequency table |

Experimental Sciences | Junior | Probability | Know and use the complement of a set as a tool within calculations |

Experimental Sciences | Junior | Combinatorics | Calculate probabilities involving combinations |

Experimental Sciences | Junior | Location and Dispersion | Use and interpret standard deviation |

Experimental Sciences | Junior | Location and Dispersion | Use and interpret variance |

Experimental Sciences | Junior | Location and Dispersion | Generate and interpret the arithmetic modal value from a grouped frequency table |

Experimental Sciences | Primary | Location and Dispersion | Identify the mode (most occurring object) within a group |

Experimental Sciences | Primary | Set Theory | Place objects into given overlapping groups |

Experimental Sciences | Primary | Representing Data | Count frequencies through pictorial representations and interpret in context |

Experimental Sciences | Primary | Location and Dispersion | Calculate the mode, median, mean and range from a list of quantative data |

Experimental Sciences | Primary | Representing Data | Count frequencies from bars and a number line scale, and interpret the results in context. |

Experimental Sciences | Primary | Representing Data | Identify proportions from pie charts and interpret in context |

Experimental Sciences | Primary | Probability | Interpret theoretical probabilities of independent events, in context |

Experimental Sciences | Secondary | Location and Dispersion | Generate and interpret the arithmetic mean, median and modal values from frequency tables |

Experimental Sciences | Secondary | Probability | Interpret experimental probabilities of independent events in context |

Experimental Sciences | Secondary | Set Theory | Identify regions within Venn diagrams using conventianal notation and vice versa |

Experimental Sciences | Secondary | Representing Data | Distinguish between pie, bar charts and histograms and interpret in context |

Experimental Sciences | Secondary | Probability | Interpret theoretical probabilities of dependent events, in context |

Experimental Sciences | Senior | Probability | Know and use Bayes' Theorem as a tool within calculations. |

Experimental Sciences | Senior | Regression | Calculate function regressions using technology |

Experimental Sciences | Senior | Data tests and correlation | Use Chi-square test for independence |

Experimental Sciences | Senior | Matrices | Find the steady state of a real-life Markov Chain system |

Experimental Sciences | Senior | Combinatorics | Calculate probabilities involving permutations |

Experimental Sciences | Senior | Random variables and distributions | Use and interpret the test for the mean in a poisson distribution in context |

Experimental Sciences | Senior | Probability | Use and interpret Expectation of combined independent events in context |

Experimental Sciences | Senior | Representing Data | Use statistical hypothesis testing with real-life datasets |

Experimental Sciences | Senior | Location and Dispersion | Use and interpret transformations of standard deviation |

Experimental Sciences | Senior | Regression | Calculate least squares linear regression |

Experimental Sciences | Senior | Data tests and correlation | Use PPMCC for bivariate data sets |

Experimental Sciences | Senior | Data tests and correlation | Use Spearman's rank correlation coefficient for bivariate data sets |

Experimental Sciences | Senior | Random variables and distributions | Use and interpret z-test for the mean of a normal probability distribution in context |

Experimental Sciences | Senior | Probability | Use and interpret Variance of combined independent events in context |

Experimental Sciences | Senior | Data tests and correlation | Use Chi-square goodness of fit test |

Experimental Sciences | Senior | Location and Dispersion | Use and interpret transformations of variance |

Experimental Sciences | Senior | Data tests and correlation | Use 2-sample t-test in context |

Experimental Sciences | Senior | Data tests and correlation | Use 1-sample t-test in context |

Experimental Sciences | Senior | Data tests and correlation | Use and interpret the correlation coUse and interpret the coefficient of determination in context when analysing data |

History | Junior | Recreational | Appreciate the patterns created from shuffling small packs of cards |

History | Junior | Mathematicians | Know about some prominent 19th century mathematicians |

History | Junior | Mathematicians | Know about some prominent 20th century mathematicians |

History | Primary | Recreational | Identify and complete magic squares |

History | Primary | Mathematicians | Know about some prominent 20th century mathematicians |

History | Primary | Mathematicians | Know about some prominent 19th century mathematicians |

History | Secondary | Axioms and Logic | Appreciate and recognise Euclid's postulates |

History | Secondary | Proof | Create simple geometric proofs involving parallel lines |

History | Secondary | Mathematicians | Know about some prominent 20th century mathematicians |

History | Secondary | Mathematicians | Know about some prominent 19th century mathematicians |

History | Senior | Proof | Follow the logic required in creating nonconstructive mathematical proofs and applications in Graph Theory |

History | Senior | Proof | Think through a larger logic problem and create tests for efficiency and optimization |

History | Senior | Mathematicians | Know about some prominent 20th century mathematicians |

History | Senior | Mathematicians | Know about some prominent 19th century mathematicians |

Algebra and Graphs | Junior | Exponential and Logarithmic | Use and solve exponential equations considering their graphs |

Algebra and Graphs | Junior | Vectors | Use the magnitude of vectors in geometric problems |

Algebra and Graphs | Junior | Polynomials | Use the rational root and sum or product of zeros tools when manipulating polynomials |

Algebra and Graphs | Junior | Polynomials | Represent and use a quadratic function graphically and algebraically |

Algebra and Graphs | Junior | Coordinates | Convert between cartesian and simple polar coordinates |

Algebra and Graphs | Junior | Exponential and Logarithmic | Use exponential functions to linearize graphs of variable relationships |

Algebra and Graphs | Junior | Graphs | Use conventional notation when describing curved graphs |

Algebra and Graphs | Junior | Graphs | Use conventional notation to describe odd functions and key parts of graphs |

Algebra and Graphs | Junior | Graphs | Describe piecewise functions and identify continuity across the domain |

Algebra and Graphs | Junior | Graphs | Know and use the relations that create circles |

Algebra and Graphs | Junior | Limits | Identify vertical asymptotes by taking limits of functions |

Algebra and Graphs | Junior | Relations Mappings and Equations | Manipulate quadratic expressions and graph their relationship |

Algebra and Graphs | Junior | Trigonometry | Identify all possible solutions to trigonometric graphs |

Algebra and Graphs | Junior | Vectors | Recognise the graphical movement of a function manipulation |

Algebra and Graphs | Junior | Trigonometry | Understand the sine graph for more than a full turn |

Algebra and Graphs | Junior | Factorising | Appreciate the graphical representations of the 'difference of 2 squares' identity |

Algebra and Graphs | Junior | Polynomials | Represent and use the 2 distinct roots of a quadratic function graphically |

Algebra and Graphs | Junior | Polynomials | Represent and use the repeated real root of a quadratic function graphically |

Algebra and Graphs | Junior | Polynomials | Understand and represent a quadratic function without any real roots graphically |

Algebra and Graphs | Junior | Exponential and Logarithmic | Use and solve logarithmic equations considering their graphs |

Algebra and Graphs | Junior | Exponential and Logarithmic | Use logarithmic functions to linearize graphs of variable relationships |

Algebra and Graphs | Junior | Graphs | Use conventional notation to describe even functions and key parts of graphs |

Algebra and Graphs | Junior | Limits | Identify horizontal asymptotes by taking limits of functions |

Algebra and Graphs | Junior | Relations Mappings and Equations | Manipulate simple cubic expressions and graph their relationship |

Algebra and Graphs | Junior | Relations Mappings and Equations | Manipulate simple rational expressions and graph their relationship |

Algebra and Graphs | Junior | Trigonometry | Understand the cosine graph for more than a full turn |

Algebra and Graphs | Junior | Polynomials | Relate a vertex-form quadratic equation to its parabola |

Algebra and Graphs | Junior | Trigonometry | Understand the tangent graph for more than a full turn |

Algebra and Graphs | Primary | Relations Mappings and Equations | Identify times tables with an arithmetic translation |

Algebra and Graphs | Primary | Graphs | Use convential notation to describe and draw linear inequalities |

Algebra and Graphs | Primary | Graphs | Identify roots from graphs within context |

Algebra and Graphs | Primary | Graphs | Use convential notation to describe and draw linear inequalities |

Algebra and Graphs | Primary | Inequalities | Solve one simple linear inequality |

Algebra and Graphs | Secondary | Graphs | Describe key features of parabola graphs |

Algebra and Graphs | Secondary | Coordinates | Know and use cartesian coordinates in context |

Algebra and Graphs | Secondary | Graphs | Use conventional notation when describing linear graphs |

Algebra and Graphs | Secondary | Graphs | Graphically solve a small system of equations in context |

Algebra and Graphs | Secondary | Graphs | Use conventional notation to solve 2D inequalities |

Algebra and Graphs | Secondary | Limits | Identify the equations of asymptotes on graphs |

Algebra and Graphs | Secondary | Relations Mappings and Equations | Describe linear relationships from a mapping diagram and solve equivalent equations with rational coefficients |

Algebra and Graphs | Secondary | Relations Mappings and Equations | Graphically solve a small system of equations in context |

Algebra and Graphs | Secondary | Polynomials | Represent and use a linear function graphically and algebraically |

Algebra and Graphs | Secondary | Polynomials | Relate a quadratic equation to its parabola |

Algebra and Graphs | Secondary | Regression | Draw and use a line of best fit by hand, passing through the mean value |

Algebra and Graphs | Senior | Tessellations | Create simple Voronoi tilings using midpoints |

Algebra and Graphs | Senior | Coordinates | Understand when polar coordinates are easier/more efficient than cartesian, and use them in simple contexts |

Algebra and Graphs | Senior | Graphs | Use conventional notation to describe piecewise functions and discuss continuity across the domain |

Algebra and Graphs | Senior | Vectors | Find the volume of composite polyhedra using Vectors |

Algebra and Graphs | Senior | Factorising | Know and use Descartes Rule of Signs as a tool within calculations |

Algebra and Graphs | Senior | Exponential and Logarithmic | Use and solve logistical equations and their graphs |

Algebra and Graphs | Senior | Vectors | Recognise and distinguish between the graphs of functions, their first and second differential graphs |

Algebra and Graphs | Senior | Vectors | Perform transformations within 3D space |

Algebra and Graphs | Senior | Vectors | Represent a vector product geometrically and use it in calculating areas of plane segments |

Algebra and Graphs | Senior | Limits | Calculate limits to any point of rational functions |

Algebra and Graphs | Senior | Matrices | Use eigenvalues and eigenvectors as tools within simple calculations |

Algebra and Graphs | Senior | Coordinates | Use polar coordinates in context |

Algebra and Graphs | Senior | Relations Mappings and Equations | Use parametric equations as a tool within calculations |

Algebra and Graphs | Senior | Polygons and Polyhedra | Know and use the relations that create ellipses |

Algebra and Graphs | Senior | Graphs | Use conventional notation to solve any inequality |

Algebra and Graphs | Senior | Vectors | Find surface areas of composite polyhedra using Vectors |

Algebra and Graphs | Senior | Limits | Identify oblique asymptotes by taking limits of functions |

Pure Algebra | Junior | Polynomials | Solve simple linear diophantine equations |

Pure Algebra | Junior | Axioms and Logic | Use truth tables to solve simple problems |

Pure Algebra | Junior | Binomial expressions | Use the binomial expansion with integer values to work backwards to solve a problem |

Pure Algebra | Junior | Inequalities | Solve a system of three linear inequalities |

Pure Algebra | Junior | Operations | Understand how rational exponents are short-hand for roots, and simplify algebraic expressions accordingly |

Pure Algebra | Junior | Quotients | Manipulate any algebraic quotient raised to any exponent |

Pure Algebra | Junior | Operations | Perform multi-step algebraic calculations, involving parentheses and indices, in the correct order |

Pure Algebra | Junior | Operations | Perform binary operations on algebraic values |

Pure Algebra | Junior | Proof | Create simple constructive mathematical proofs |

Pure Algebra | Junior | Factorising | Know and use the Factor Theorem |

Pure Algebra | Junior | Factorising | Know and use Remainder Theorem |

Pure Algebra | Junior | Polynomials | Use the 2 distinct roots of a quadratic function algebraically |

Pure Algebra | Junior | Polynomials | Use the repeated real root of a quadratic function algebraically |

Pure Algebra | Junior | Polynomials | Recognise quadratic functions without any real roots algebraically |

Pure Algebra | Junior | Trigonometry | Identify all possible solutions to sine ratio equations |

Pure Algebra | Junior | Trigonometry | Identify all possible solutions to cosine ratio equations |

Pure Algebra | Junior | Trigonometry | Identify all possible solutions to tangent ratio equations |

Pure Algebra | Secondary | Directions and Angles | Manipulate expressions involving parenthesis |

Pure Algebra | Secondary | Directions and Angles | Solve a small system of equations in context |

Pure Algebra | Secondary | Inequalities | Solve a system of linear inequalities |

Pure Algebra | Senior | Axioms and Logic | Use truth tables to solve problems |

Pure Algebra | Senior | Proof | Appreciate and follow the logic required in Fermat's infinite descent proof |

Pure Algebra | Senior | Quotients | Understand the use for and manipulate partial fraction expressions |

Pure Algebra | Senior | Sequences and Series | Find the nth term rule for recurrence relations |

Pure Algebra | Senior | Axioms and Logic | Use digital logic gates to solve Boolean algebra problems |

Pure Algebra | Senior | Axioms and Logic | Use Venn diagrams to solve Boolean algebra logic problems |

Pure Algebra | Senior | Complex numbers | Recognise the existence of non-real solutions to mathematical problems |

Pure Algebra | Senior | Polynomials | Solve linear diophantine equations |

Pure Algebra | Senior | Sequences and Series | Distinguish between infinite, iterative and recurrence relation sequences |

Pure Algebra | Senior | Factorising | Use the Factor Theorem as a tool to help solve problems |

Pure Algebra | Senior | Factorising | Use the Remainder Theorem as a tool to help solve problems |