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Number N1a - Ordering positive and negative integers with GeoGebra applet 1-3 Numbers, place value, ascending, descending, whole numbers, compares, comparing, comparisons
Number N1b - Ordering decimals 1-3 Numbers, place values, ascending, descending, compares, comparing, comparisons
Number N1c - Equivalent fractions and simplifying fractions with GeoGebra applet 1-3 Improper fractions, Mixed numbers, Converting between, numerators, denominators, vulgar, top-heavy
Number N1d - Ordering fractions 1-3 Ascending, descending, numerators, denominators, common, compares, comparing, comparisons
Number N1e - Ordering integers, decimals and fractions and using inequality symbols 3-5 Numbers, place value, ascending, descending, improper fraction, vulgar, mixed number, greater than , less than, or equal to, equals, not equals, compares, comparing, comparisons, whole numbers
Number N2a - Adding and subtracting positive integers 1-3 additions, adding to, subtractions from, subtracting, take away, totals, sums, differences, wholes numbers, four operations,
Number N2b - Multiplying positive integers 1-3 Products, multiplications, multiplying by, four operations, whole numbers
Number N2c - Dividing with positive integers 1-3 Dividing, divisions, sharing, bus stops, chunking, methods, four operations, whole numbers remainders
Number Multiplication & Division assorted problems 1-3 Multiplication, Multiplying, Division, Dividing, remainders, context, sharing, share, ssdd
Number N2d - Applying the four operations to decimals 1-3 additions, adding to, subtractions from, subtracting, multiplications, multiplying by, divisions, dividing, wholes, numbers, four operations
Number N2e - Applying the four operations to negative numbers 1-3 positives, negatives, directed numbers, adding, additions to, subtracting, subtractions from, multiplying by, multiplications, dividing, divisions
Number N2f - Applying the four operations to fractions with GeoGebra applet 3-5 additions, adding to, subtractions, subtracting from, multiplications, multiplying by, divisions, dividing improper, mixed numbers, vulgar, top-heavy, keep, kiss and flip, reciprocal
Number N2g - Reading and interpreting scales with GeoGebra applet 1-3 Number lines missing
Number N3a - Relationships between operations, including inverse operations 1-3 BIDMAS, BODMAS, PEMDAS, PEDMAS, BOMDAS, BIMDAS, Brackets, indexes, indices, order, exponents, powers, parenthesis, parentheses, additions, adding to, subtractions, subtracting from, multiplications, multiplying by, divisions, dividing
Number N3b - Order of operations, including brackets, powers, roots and reciprocals 1-3 BIDMAS, BODMAS, PEMDAS, PEDMAS, BOMDAS, BIMDAS, Brackets, indexes, indices, order, exponents, powers, parenthesis, parentheses, additions, adding to, subtractions from, subtracting, multiplications, multiplying by, divisions, dividing
Number N4a - Factors and highest common factors 1-3 HCFs
Number N4b - Multiples and lowest common multiples 1-3 LCMs
Number N4c - Prime numbers and prime factorisation with GeoGebra applet 3-5 Primes, Unique, factorizes, factorizations, factorising, factorizing,HCFs, LCMs, highest, lowest, common, multiples, factorises, factors, decompose, decomposition, decomposing, fundamental theorem of arithmetic
Number Factors, multiples and primes assorted problems 3-5 Factors, multiples, primes, prime numbers, powers, indices, ssdd
Number N5a - Systematic listing strategies and the product rule for counting 5-7 rules
Number N6a - Using powers and roots 3-5 Squares roots, Cubes roots, Indices, Indexes of a numbers
Number N6b - Estimating powers and roots 5-7 Square roots, Cube roots, Indices, Index, powers, estimates of a numbers
Number N7a - Calculating with positive and negative integer indices 3-5 Squares roots, Cubes roots, Indices, Indexes, powers of a numbers
Number N7b - Calculating with fractional indices 5-7 Squares roots, Cubes roots, Indices, Indexes, powers, fractions of a numbers
Number N8a - Calculating exactly with fractions and with multiples of pi 3-5 Pi, exact form,
Number N8b - Surds 5-7 Roots, rationals numbers, irrationals numbers, rationalising rationalizing denominators
Number N9a - Converting between normal numbers and standard form 3-5 Standard index form, Scientific notation
Number N9b - Multiplying and dividing in standard form 3-5 Standard index form, Scientific notation, multiplication by, division
Number N9c - Adding and subtracting in standard form 3-5 Standard index form, Scientific notation, additions to, subtractions from
Number N10a - Converting terminating decimals into fractions and vice versa 3-5 terminates, expansions
Number N10b - Converting recurring decimals into fractions and vice versa 5-7 infinite, expansion, infinity, for ever, forever
Number N11a - Identifying and working with fractions in ratio problems 3-5
Number N12a - Interpreting fractions and percentages as operators 3-5 Finding a fraction of a quantity, numbers amounts
Number N13a - Using standards units of measure 1-3 grams, metres, litres, km, kg, kilometres, kilograms, years, days, hours, minutes, hrs, mins, seconds, secs
Number N14a - Estimating answers and checking calculations 1-3 Estimating, approximating, rounding, calculators, calculating, technology, estimates, estimations, figures, significant
Number N15a - Rounding and truncating 1-3 truncate, truncation, Decimals places, significant figures, place values Rounding numbers and measures to an appropriate degree of accuracy, 1 2 3 4 5 dp d.p. sf s.f. sigfig
Number N15b - Using inequality notation to specify simple error intervals 3-5 Truncate, truncation, truncating, rounding, inequalities, errors, rounding, significant figures, decimal places, dp d.p. s.f. sf sigfig
Number N16a - Applying and interpreting limits of accuracy, including upper and lower bounds 5-7 UB, LB, error intervals
Algebra A1a - Using and interpreting algebraic notation 1-3 Coefficients, brackets, fractions, division, simplifying
Algebra A2a - Substituting numerical values into formulae and expressions 1-3 Substitutes, substitution, substituting
Algebra A3a - Understanding and using the concepts of expressions, equations, formulas, identities, inequalities, terms and factors 3-5 Inequality, formulae, identity,
Algebra A4a - Simplifying and manipulating algebraic expressions by collecting like terms (basic) 1-3
Algebra A4b - Multiplying a single term over a bracket 3-5 Expanding, out, expansions, by
Algebra A4c - Factorising (basic) 3-5 Taking out common factors, factorise, factorizing, factorize, brackets
Algebra A4d - Multiplying two or more brackets 3-5 Expanding products of two or more binomials, out, expansions, by, dots, difference of two squares, triple brackets, three brackets, products of, trinomials
Algebra A4e - Factorising quadratics 3-5 expressions, coefficient, factorise, factorizing, factorize, dots, difference of two squares, brackets
Algebra A4f - Simplifying, multiplying and dividing algebraic fractions 7-9 Multiplications by, Divisions
Algebra A4g - Adding and subtracting algebraic fractions 7-9 Additions to, Subtractions from
Algebra A4h - Algebraic manipulation involving surds 7-9 Powers, indexes, indices
Algebra A4i - Index laws and solving equations involving indices 3-5, 7-9 Indices, powers, indexes, bases, power, exponents, solving, solutions, equations, rewriting different bases, rebasing, rebase
Algebra A5a - Rearranging formulas to change the subject with GeoGebra applet 3-5, 5-7 Rearranges, make the subject, rearrangement, formulae, making, changing, of a
Algebra Rearranging formulas to change the subject assorted problems 3-5, 5-7 Rearranges, make the subject, rearrangement, formulae, making, changing, of a, rearranging, ssdd
Algebra A6a - Arguing mathematically 3-5 Equivalent, Equivalence, algebraic expressions, Equations, identities, argument, constructing, proofs, constructions, prove that, show, proving with
Algebra A6b - Using algebra to construct proofs 7-9 Equivalent, Equivalence, algebraic expressions, Equations, identities, argument, constructing, proofs, constructions, show that, prove, proving with
Algebra A7a - Interpreting functions and composite functions 5-7 Inputs, outputs
Algebra A7b - Interpreting inverse functions 7-9
Algebra A7c - Solving equations involving functions 7-9 inverse, composite, solving, solve, linear, quadratic
Algebra A8a - Working with coordinates in all four quadrants 1-3 Graphs
Algebra A9a - Plotting straight-line graphs with GeoGebra applets 3-5 Gradients, y- intercepts, horizontal, vertical, slopes, lines, y=mx+c, y = mx + c, x = k, ax+by=c ax+by=k ax + by = c k - 0
Algebra A9b - Identifying parallel and perpendicular lines with GeoGebra applet 5-7 Gradients, intercepts, horizontal, vertical, slope, straight lines graphs, y = mx + c
Algebra A9c - Finding the equation of a line through two given points or through one point with a given gradient (e.g. parallel or perpendicular to another line) with GeoGebra applet 3-5 Gradients, intercepts, slopes, straight, graphs, lines, parallel, perpendicular to
Algebra A10a - Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically 1-3 slopes, graphs, straight lines
Algebra A11a - Identifying roots, intercepts and turning points of quadratic functions graphically with GeoGebra applet 3-5 solutions, parabolas, parabolic, curves, curved, graphs, quadratics, sketching, equations, sketches
Algebra A11b - Identifying turning points of quadratic functions by completing the square with GeoGebra applet 5-7 Minimum, minima, maximum, maxima, parabolas, parabolic, complete, curves, curved, graphs, quadratics, sketching, equations, sketches
Algebra A11c - Sketching quadratics with GeoGebra applet 5-7 Minimum, minima, maximum, maxima, parabolas, parabolic, complete, curves, curved, graphs, functions, equations, y=,sketches, turning points, complete completing the square solving, curves, curved, graphs, sketches
Algebra A12a - Graphs of linear functions, quadratic functions, simple cubic functions, and the reciprocal function with GeoGebra applet 3-5 parabolas, parabolic, asymptotes, curved, curves, straight lines, plotting, quadratics
Algebra A12b - Graphs of exponential functions 5-7 curved, cures
Algebra A12c - Graphs of trigonometric functions 7-9 sin, sine, cos, cosine, tan, tangent, wave
Algebra A13a - Sketch translations and reflections of a given function 7-9 transformations of functions graphs curves lines move slide shift mirroring transforming
Algebra A14a - Plotting and interpreting graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions 3-5 asymptotes, curved, curves
Algebra A14b - Plotting and interpreting graphs in real contexts to find approximate solutions to problems such as simple kinematic problems 3-5 speeds, distances, times, depth-time graphs containers liquid water jars filling
Algebra A15a - Calculating or estimating gradients of graphs 5-7 Estimates, chords, tangents, slopes, rates of changes, curves, curved, straight lines
Algebra A15b - Estimating the area under a graph 7-9 Estimates, trapezium rule, estimations, curved, curves, straight lines, graphs
Algebra A15c - Interpreting gradients and areas under graphs 7-9 distances, velocity, times, kinematics, slopes, velocities, rates of changes, curved, curves, straight lines,
Algebra Kinematics graphs assorted problems 3-5,5-7 distances, velocity, times, kinematics, slopes, velocities, rates of changes, curved, curves, straight lines, graphs, ssdd
Algebra A16a - Recognising and using the equation of a circle with the centre at the origin 7-9 equations of circles, centre radiuses radii
Algebra A16b - Finding the equation of a tangent to a circle at a given point 7-9 equations of circles, a tangents to, finding the with the centre at the origin
Algebra A17a - Solving simple linear equations in one unknown algebraically 3-5 balances, balancing, solves, method, algebraic fractions
Algebra A17b - Solving linear equations in one unknown algebraically where the unknown is on both sides of the equation 3-5 balances, balancing, solves, method, algebraic fractions
Algebra A17c - Finding solutions to linear equations using graphs 3-5 intersection, solves, straight lines, solving graphically, intersecting, intersects, lines
Algebra A18a - Solving quadratic equations by factorising 3-5, 7-9 factorises, factorizse, factorizing, parabolas, parabolic, solves, quadratics, algebraic fractions
Algebra A18b - Solving quadratic equations by completing the square 7-9 completes, parabolas, parabolic, turning points, minimums, maximums, solves, minima, maxima, quadratics, algebraic fractions, vertex form
Algebra A18c - Solving quadratic equations using the quadratic formula 5-7 discriminants, parabolas, parabolic, roots, solutions, solves, quadratics, algebraic fractions
Algebra Quadratic functions—putting it all together (with dynamic algebra tiles) 5-7 discriminants, parabolas, parabolic, roots, solutions, solves, quadratics, algebraic fractions, graphs, completes, parabolas, parabolic, turning points, minimums, maximums, solves, minima, maxima, quadratics, algebraic fractions, vertex form completing the square completes,factorises, factorizse, factorizing, dynamic algebra tiles
Algebra Expanding, simplifying, factorising, and solving equations assorted problems 3-5, 5-7 Expanding, multiplying out, simplifying, collecting like terms, factorise, factorize, factorizing, solve, both sides, quadratics, ssdd
Algebra A19a - Solving two linear simultaneous equations algebraically by elimination 3-5 eliminates, elimination, eliminating substitutes, substitution, solves, worded problems, substituting
Algebra A19b - Solving two linear simultaneous equations graphically or algebraically by substitution 3-5 intersections, intersects, intersecting, solves, straight lines graphs, substituting
Algebra A19c - Solving two simultaneous equations (linear/ quadratic) algebraically 7-9 substitutes, substitution, solves, substituting, quadratics
Algebra A19d - Solving two simultaneous equations (linear/ quadratic) graphically 7-9 intersections, intersects, intersecting, parabolas, parabolic, solutions, solves, graphs straight lines curves curved, quadratics
Algebra A20a - Finding approximate solutions to equations numerically using iteration 5-7 trial, solve, and error, improvement, sign change, solution to an equation by, iterate, iterating, repeating, repeated, converge converging diverge diverging
Algebra A21a - Representing simple situations using algebraic expressions or formulae 3-5 Writing, write, describes, describing, writes, writing, worded problems
Algebra A21b - Deriving and solving an equation or simultaneous equations to describe a situation 3-5, 5-7 solves, derives, writing, writes, describes, worded problems, equate, equating
Algebra A22a - Solving linear inequalities in one variable 3-5 Greater, less, than, equal to, solves, unknowns, inequality
Algebra A22b - Solving linear inequalities in two variables 5-7 Greater, less, than, equal to, solves, unknowns, graphs, graphically, regions, shaded shades, shading by, inequality
Algebra A22c - Solving quadratic inequalities in one variable 7-9 Greater, less, than, equal to, solves, inequality, quadratics
Algebra A23a - Generating terms of a sequence from either a term-to-term or a position-to-term rule 1-3 nth term, number, linear arithmetic progressions, sequences
Algebra A24a - Recognising and using triangular, square and cube numbers 3-5 sequences, triangle, cubic
Algebra A24b - Recognising and using arithmetic, geometric and quadratic sequences 1-3 sequences, linear arithmetic progressions, quadratics
Algebra A24c - Recognising and using Fibonacci type sequences 3-5 sequences, fibonnaci numbers
Algebra A25a - Finding the nth term of a linear sequence 3-5 expression for, linear arithmetic progressions, sequences
Algebra A25b - Finding the nth term of a quadratic sequence 7-9 expression for, quadratics, sequences
Algebra Sequences assorted problems 3-5, 5-7 Arithmetic, linear, geometric, sequences, progression, quadratics, nth term, position to term, term to term -, ssdd
Ratio and proportion R1a - Changing between standard units and compound units in numerical and algebraic contexts 3-5 times, lengths, areas, volumes, capacity, capacities, masses, speeds, rates of pay, prices, density, densities, pressures, mass/
Ratio and proportion R2a - Using scale diagrams and maps 3-5 scales diagrams, maps, scales factors
Ratio and proportion R3a - Expressing one quantity as a fraction of another 3-5 fractions writing, writes
Ratio and proportion R4a - Using ratio notation, and reducing ratios to simplest form 1-3 reduction, reduces, simplifying
Ratio and proportion R5a - Dividing a quantity in a given ratio, and expressing the division of a quantity as a ratio with GeoGebra applet 3-5 divides, shares, sharing, ratios, quantities
Ratio and proportion R5b - Applying ratio to real contexts 3-5 ratios, mixing, mixes, converting, conversions, paints, dilutes, diluting, mixtures, squash, colours
Ratio and proportion R6a - Expressing a multiplicative relationship between two quantities as a ratio or a fraction 3-5 fractions
Ratio and proportion R7a - Understanding and using proportion as equality of ratios 3-5 the unitary method, scale, scaling recipes, up down
Ratio and proportion R8a - Relating ratios to fractions and to linear functions 3-5
Ratio and proportion Ratio assorted problems 3-5 divides, shares, sharing, ratios, given, quantity, quantities, ssdd
Ratio and proportion R9a - Converting between fractions, decimals and percentages 3-5 FDP
Ratio and proportion R9b - Finding percentages and percentage changes (basic) 3-5 of a number amount quantity
Ratio and proportion R9c - Finding percentages and percentage changes multiplicatively using decimals 3-5 of a number amount quantity increase decrease, multipliers
Ratio and proportion R9d - Solving problems involving percentage change 3-5 reverse, percentages, reversing, undoing, original value, original amount, original quantity
Ratio and proportion R9e - Comparing two quantities using percentages 3-5 compares, comparisons
Ratio and proportion Percentages assorted problems 3-5 FDP, of a number amount quantity, increase decrease, multipliers, reverse, percentages, reversing, undoing, compares, comparisons, ssdd
Ratio and proportion R10a - Solving problems involving direct proportion with GeoGebra applet 3-5 inverse, including graphical and algebraic representations, imperial, metric, converting between to from miles kilometres centimetres cm km yards inches
Ratio and proportion R10b - Solving problems involving inverse proportion with GeoGebra applet 5-7 direct, graphs, including graphical and algebraic representations
Ratio and proportion R11a - Using compound units with GeoGebra applet 3-5 speeds, density, densities, pressures, rates of pay, mass / volume, distance time divided by formula triangles
Ratio and proportion R12a - Ratios and similar shapes; scale, area and volume factors 3-5 similarity
Ratio and proportion R13a - Constructing and interpreting equations that describe direct and inverse proportion 3-5 directly, inversely, proportions
Ratio and proportion R14a - Recognising and interpreting graphs that illustrate direct and inverse proportion 3-5
Ratio and proportion R15a - Gradient as a rate of change (straight line and curved graphs) 7-9 Lines
Ratio and proportion R16a - Growth and decay problems 5-7 gradients, compound, interest, exponential, rates, borrowing, simple, depreciates, depreciation, banks, banking,
Ratio and proportion Compound and simple interest assorted problems 5-7 growth, decay, ssdd, compounding, percentage, roots, powers, indices
Geometry G1a - 2D geometry - terms and notation 1-3 parallel, perpendiculars, edges, vertex, vertices, angles, straight lines, corners, sides, names of polygons regular n-gons ngons, triangles, quadirlaterals, pentagons, hexagons, heptagons, septagons, octagons, nonagons, decagons, hendecagons, undecagons, dodecagons triskadecagons
Geometry G1b - 3D geometry - terms 3-5 edges, vertex, vertices, faces, corners, sides, surfaces, nets, polyhedra, polyhedrons, curved shapes, 3-d three dimensions dimensional
Geometry G1c - Reflection symmetry 1-3 lines ofs mirrors
Geometry G1d - Rotation symmetry with GeoGebra applet 1-3 order of rotate, rotational
Geometry G1e - Conventions for labelling the sides and angles of triangles 3-5 labels how to name, naming edges, corners, vertices
Geometry G1f - Drawing diagrams from a written description 1-3 how to parallel, perpendicular, equal, edges, vertices, corners, sides, faces, shapes, polygons, 2D, squares, rhombuses, rhombi, parallelograms, rectangles, trapeziums, trapezia, kites, triangles, equilateral, scalene, symmetries, symmetry, reflection, reflects, reflective, order of, rotations, rotational,
Geometry G2a - Constructing perpendicular bisectors, angle bisectors, and perpendiculars to or from a point 3-5 constructions, using rulers and straight edges, compasses, without protractors, bisecting
Geometry G2b - Constructing triangles 3-5 constructions, equilateral, scalene, SSS,SAS,ASA, isosceles, right angled , using rulers and straight edges, compasses, without protractors
Geometry G2c - Mixed loci problems with GeoGebra applet 3-5 constructions, locus, rulers and straight edges, compasses, without protractors
Geometry G3a - Angles at a point, angles at a point on a straight line, vertically opposite angles 1-3 rules, 180, 360, º, degrees, around, meeting, points
Geometry G3b - Alternate and corresponding angles on parallel lines with GeoGebra applet 3-5 F Z degrees, forresponding, zalternate, co-interior, supplementary, complementary, º
Geometry G3c - The sum of angles in a triangle and the angle properties of polygons with GeoGebra applet 3-5 180, 360, quadrilateral, interior, exterior, degrees, º
Geometry G4a - Properties of special triangles and quadrilaterals 3-5 equilateral, isosceles, right angles, squares, rectangles, parallelograms, trapeziums, trapezia, kites, rhombuses rhombi, symmetries, symmetry, reflection, reflects, reflective, order of, rotations, rotational,
Geometry G5a - Congruence criteria for triangles (SSS, SAS, ASA, RHS) 3-5 Congruent, Side, angle, congruency, similarity
Geometry G6a - Simple geometric proofs 3-5 Prove that show
Geometry G7a - Coordinates with GeoGebra applet 1-3 Cartesian, planes, co-ordinates, x, y, axis, axes, along the corridor and up the stairs, is across high
Geometry G7b - Rotation with GeoGebra applet 3-5 Rotates, transformations, centres of, clockwise, anticlockwise, rotations, rotating, transforming
Geometry G7c - Reflection with GeoGebra applet 3-5 transformations, mirrors, lines reflects, reflecting, mirroring, transforming
Geometry G7d - Translation with GeoGebra applet 1-3 Translates, transformations, column vectors, translating, transforming
Geometry G7e - Enlargement with GeoGebra applet 3-5 transformations, scale factors, negative, fractional, fractions, enlarging, centre of, transforming
Geometry G7f - Congruence, similarity and transformations 3-5 congruent
Geometry G8a - Combinations of transformations 5-7 reflections, rotations, rotates, translates, translations, enlargements, scale factors, column vectors, mirrors, centres of, clockwise, anticlockwise, direction, anti-clockwise, reflecting, rotating, translating, enlarging, mirroring, transforming lines of
Geometry G9a - Circle parts - definitions and properties 3-5 arcs, sectors, segments, chords, tangents, diameters, radius, circles, parts of
Geometry G10a - Circle theorems with GeoGebra applets 7-9 alternate segments, centres, opposites, semicircles, angles, tangents, radius, chords, diameters, radii, radiuses
Geometry G11a - Solve geometrical problems on coordinate axes 3-5 Lengths of lines segments, shortest distances from a points to, Pythagoras, perpendiculars, gradients, graphs, y = mx + c, between two, on the planes, cartesian, coordinates, co-ordinates, midpoints, mid-points, halfway, finding, calculating, calculate, work out, working
Geometry G12a - Properties of 3D shapes with GeoGebra applets 3-5 cubes, cuboids, prisms, cylinders, pyramids, cones, spheres, nets, vertices, faces, edges, corners, surfaces, sides, polyhedrons, polyhedra, curved, triangular, 3-d three dimensions dimensional
Geometry G13a - Plans and elevations of 3D shapes 3-5 constructions, isometric, 3-d, hexagonal, hexagons, triangles, triangular, dotty, side view, overhead view, birdseye bird's eye top perspectives
Geometry G14a - Converting between metric units of measures of length and mass 1-3 length, area, volume, capacity, mass, time, money, km, kg, kilometres, kilograms, metres, grams, cm, centimetres, mm, millimetres
Geometry G14b - Converting between metric units of measures of area and volume 5-7 square mm cm m millimetres, centimetres, metres, squared, cube, cubed, cubic
Geometry G14c - Money 1-3 £, pounds, penny, pence, currency, currencies, conversion, converting, exchanges rates, euros, cents between different, best buys
Geometry G14d - Time with GeoGebra applet 1-3 years, months, days, hours, minutes, seconds 24-hours 12-hours military clocks clockfaces - converting telling the between digital analogue watch and, hrs, mins, secs
Geometry G15a - Measuring line segments and angles in geometric figures with GeoGebra applet 1-3 measure using a protractors rulers length size of lines, acute, right, obtuse, straight, reflex angles
Geometry G15b - Scale drawings 3-5 maps, diagrams, scales
Geometry G15c - Bearings with GeoGebra applet 3-5 angles, North South East West North-east, South-west, South-east, North-west NW NE SW SE NNE ENE ESE SSE WSW SSW NNW WNW anticlockwise anti-clockwise from north
Geometry G16a - Area of rectangles with GeoGebra applet 1-3 squares, quadrialterals
Geometry G16b - Area of parallelograms with GeoGebra applet 1-3 bases heights quadrilaterals
Geometry G16c - Area of triangles with GeoGebra applet 1-3 bases heights
Geometry G16d - Area of trapezia with GeoGebra applet 3-5 trapeziums, quadriaterals
Geometry G16e - Volume of cuboids, prisms and cylinders with GeoGebra applet 1-3 triangular, volumes
Geometry G17a - Perimeter of polygons 1-3 perimeters, shapes, 2D
Geometry G17b - Circumference of a circle 1-3 perimeters, diameters, pi, radius, radii, radiuses, circumferences, circles
Geometry G17c - Area of a circle with GeoGebra applet 1-3 diameters, pi, radius, radii, radiuses, circles
Geometry G17d - Perimeter and area of composite shapes made up of polygons 3-5 Perimeters, areas, compound, 2d shapes, edges, sides, many, with
Geometry G17e - Perimeter and area of composite shapes made up of polygons and sectors of circles 3-5 pi, radius, diameters, radii, radiuses,
Geometry G17f - Surface area of cuboids, prisms and pyramids with GeoGebra applet 3-5 Cubes, square-based, squares, tetrahedrons, tetrahedra triangle-based, sa
Geometry G17g - Volume of spheres, pyramids, and cones 5-7 pi, radius, diameters, composite solids, hemispheres, frustums, square based, radii, radiuses
Geometry G17h - Surface area of cylinders, spheres, and cones with GeoGebra applet 5-7 pi, radius, radii, radiuses, diameters, composite solids, hemispheres, frustums, square based, sa
Geometry G18a - Arcs and sectors of circles with GeoGebra applet 3-5 pi, radiuses, radii, diameters, lengths, areas, circumferences, finding, calculating, calculate, parts of
Geometry G19a - Lengths, areas and volumes in similar shapes 5-7 similarity, areas, volumes factors
Geometry G20a - Pythagoras' theorem with GeoGebra applets 5-7 Right angled triangles, Pythagoras's, Pythagorean, 90º, degrees, triple, a ^2 = b c, hypotenuse 3d, 3-d in dimensions dimensional
Geometry Pythagoras and surds assorted problems 3-5 Surds, Pythagoras' Theorem, Pythagorean, radicals, roots, surd exact form, ssdd
Geometry G20b - Trigonometric ratios - sin, cos and tan with GeoGebra applets 3-5 Trigonometry, sine, cosine, tangent, Right angled triangles, degrees, opposite, adjacent, hypotenuse SOHCAHTOA
Geometry G20c - Inverse trigonometric functions 3-5 Trigonometry, sine, cosine, tangent, Right angled triangles, opposite, adjacent, hypotenuse SOHCAHTOA, inverse sin-1 cos-1 tan-1 sin^-1 cos^-1 tan^-1 arcsin arccos arctan arc
Geometry G20d - Trigonometry with right-angled triangles
in 3D shapes with GeoGebra applets 5-7 Trigonometry, sine, cosine, tangent, Right angled triangles, opposite, adjacent, hypotenuse SOHCAHTOA, inverse sin-1 cos-1 tan-1 sin^-1 cos^-1 tan^-1 arcsin arccos arctan arc, Pythagoras, 3D three dimensional, angles of elevation depression, cube cuboid, prism, triangular, pyramid
Geometry Pythagoras, sin, cos, or tan? method selection (right-angled triangles only) 3-5 Trigonometry, sine, cosine, tangent, Right angled triangles, opposite, adjacent, hypotenuse SOHCAHTOA, inverse sin-1 cos-1 tan-1 sin^-1 cos^-1 tan^-1 arcsin arccos arctan arc
Geometry G21a - Exact values of sin, cos and tan for special angles 5-7 0, 30, 45, 60, 90, Trigonometry, sine, cosine, tangent, Right angled triangles, º, degrees, opposite, adjacent, hypotenuse, SOHCAHTOA
Geometry G22a - The sine rule 7-9 Trigonometry, sine, cosine, tangent, triangles, opposite, lengths angles any triangles
Geometry G22b - The cosine rule 7-9 Trigonometry, sine, cosine, tangent, triangles, angle between, opposite, lengths angles any triangles
Geometry G23a - Area of a triangle using sine 7-9 Trigonometry, sine, cosine, tangent, triangles, opposite, adjacent, hypotenuse, angle between, opposite, any triangles, base, height
Geometry G23b - Mixed problems using trigonometric formulas 7-9 Trigonometry, sine, cosine, tangent, Right angled triangles, opposite, adjacent, hypotenuse, lengths angles any triangles, SOHCAHTOA
Geometry Right-angled triangles assorted problems 3-5, 5-7, 7-9 Trigonometry, sine, cosine, tangent, Right angled triangles, Pythagoras' Pythagorean, Theorem, SOH CAH TOA, SOHCAHTOA, ssdd
Geometry G24a - Describing translations as 2D vectors 3-5 column
Geometry G25a - Adding and subtracting column vectors with GeoGebra applets 3-5 Addition to, subtraction from
Geometry G25b - Multiplying column vectors by a scalar 3-5 scalars, multiplication of, by
Geometry G25c - Proofs using vectors 7-9 parallel, on a line, show that points straight, direction, magnitude, size, prove
Probability P1a - Frequency trees 1-3
Probability P2a - Theoretical probability 1-3
Probability P2b - Relative frequency 3-5 Experimental probability, outcomes, events, probabilities
Probability P3a - Expected frequency 3-5 Expectation, value, trials, frequencies, probabilities
Probability P4a - Properties of probability 3-5 Mutually exclusive, exhaustive, outcomes, events, probabilities
Probability P5a - Probability and sampling 3-5 bias, unbiased, samples size, probabilities, capture-recapture recapturing releasing wild estimate populations size
Probability P6a - Enumerating sets and combinations of sets systematically, using tables, grids and Venn diagrams 3-5 probabilities, unions, intersections, empty set, null set, universal set, xi, complement, and, or, not
Probability P7a - Constructing theoretical possibility spaces for combined experiments with equally likely outcomes and use these to calculate theoretical probabilities 3-5
Probability P8a - Tree diagrams 3-5 independent dependendent events
Probability P9a - Conditional probabilities 5-7
Statistics S1a - Sampling 3-5 populations, samples
Statistics S2a - Frequency tables and two-way tables 1-3 Diagrams, frequencies, grouped
Statistics S2b - Pictograms 1-3 tally, tallies, charts, tables, diagrams
Statistics S2c - Bar charts, vertical line charts and basic histograms 1-3 bar graphs, discrete, continuous, categorical, diagrams
Statistics S2d - Pie charts 1-3 Angles, 360, degrees, º, emma, diagrams
Statistics S2e - Tables, conversion graphs, line graphs and time series 3-5 diagrams,
Statistics S2f - Stem and leaf diagrams 3-5 plot, ordered, unordered, non, back-to-back back to back
Statistics S3a - Histograms 7-9 classes intervals, unequal, widths, diagrams, frequency density, densities, fd
Statistics S3b - Cumulative frequency graphs 5-7 interquartile range, lower upper quartiles median, Q1, Q2, Q3, LQ, UQ, IQR, diagrams, curves
Statistics S4a - Median 1-3 averages, classes intervals, estimates, estimation, frequency tables grouped from, finding the median using a, estimating
Statistics S4b - Mean with GeoGebra applet 1-3 averages, classes intervals, estimates, estimation, frequency tables grouped from, finding the mode using a, estimating, artihmetic
Statistics S4c - Mode and modal class 1-3 averages, classes intervals, frequency tables grouped from, finding the using a,
Statistics S4d - Range 1-3 spreads
Statistics S4e - Interquartile range and box plots with GeoGebra applet 5-7 spread, interquartile range, lower upper quartiles median, Q1, Q2, Q3, LQ, UQ, IQR, boxplots, whisker, diagrams
Statistics S4f - Comparing data sets 3-5 compares, comparisons, of
Statistics S5a - Applying statistics to describe a population 3-5
Statistics S6a - Scatter graphs, correlation and causation 3-5 lines of best fit, predictions, predicting, interpolating interpolates, interpolations, extrapolating extrapolates, extrapolations
Ideas Knowing the whole without knowing the parts All theme, information, limited, not all, total, sum, details, big picture
Manipulative Customisable double number line All Algebra, Number, Proportion
Manipulative Multi-base zooming number line All Number
Manipulative Interactive counting stick All Number
Manipulative Algebra discs (with ability to group and turn over groups) All Algebra, Number
Manipulative Double-sided counters (with ability to group and turn over groups) All Algebra, Number
Animation Inner solar system animation demonstrating relative motion All
Animation Pale Blue Dot—our insignificance in time and space All
| Strand | Topic (click for search box) | Target grades | Other key words |
|---|---|---|---|
| Number | N1a - Ordering positive and negative integers with GeoGebra applet | 1-3 | Numbers, place value, ascending, descending, whole numbers, compares, comparing, comparisons |
| Number | N1b - Ordering decimals | 1-3 | Numbers, place values, ascending, descending, compares, comparing, comparisons |
| Number | N1c - Equivalent fractions and simplifying fractions with GeoGebra applet | 1-3 | Improper fractions, Mixed numbers, Converting between, numerators, denominators, vulgar, top-heavy |
| Number | N1d - Ordering fractions | 1-3 | Ascending, descending, numerators, denominators, common, compares, comparing, comparisons |
| Number | N1e - Ordering integers, decimals and fractions and using inequality symbols | 3-5 | Numbers, place value, ascending, descending, improper fraction, vulgar, mixed number, greater than , less than, or equal to, equals, not equals, compares, comparing, comparisons, whole numbers |
| Number | N2a - Adding and subtracting positive integers | 1-3 | additions, adding to, subtractions from, subtracting, take away, totals, sums, differences, wholes numbers, four operations, |
| Number | N2b - Multiplying positive integers | 1-3 | Products, multiplications, multiplying by, four operations, whole numbers |
| Number | N2c - Dividing with positive integers | 1-3 | Dividing, divisions, sharing, bus stops, chunking, methods, four operations, whole numbers remainders |
| Number | Multiplication & Division assorted problems | 1-3 | Multiplication, Multiplying, Division, Dividing, remainders, context, sharing, share, ssdd |
| Number | N2d - Applying the four operations to decimals | 1-3 | additions, adding to, subtractions from, subtracting, multiplications, multiplying by, divisions, dividing, wholes, numbers, four operations |
| Number | N2e - Applying the four operations to negative numbers | 1-3 | positives, negatives, directed numbers, adding, additions to, subtracting, subtractions from, multiplying by, multiplications, dividing, divisions |
| Number | N2f - Applying the four operations to fractions with GeoGebra applet | 3-5 | additions, adding to, subtractions, subtracting from, multiplications, multiplying by, divisions, dividing improper, mixed numbers, vulgar, top-heavy, keep, kiss and flip, reciprocal |
| Number | N2g - Reading and interpreting scales with GeoGebra applet | 1-3 | Number lines missing |
| Number | N3a - Relationships between operations, including inverse operations | 1-3 | BIDMAS, BODMAS, PEMDAS, PEDMAS, BOMDAS, BIMDAS, Brackets, indexes, indices, order, exponents, powers, parenthesis, parentheses, additions, adding to, subtractions, subtracting from, multiplications, multiplying by, divisions, dividing |
| Number | N3b - Order of operations, including brackets, powers, roots and reciprocals | 1-3 | BIDMAS, BODMAS, PEMDAS, PEDMAS, BOMDAS, BIMDAS, Brackets, indexes, indices, order, exponents, powers, parenthesis, parentheses, additions, adding to, subtractions from, subtracting, multiplications, multiplying by, divisions, dividing |
| Number | N4a - Factors and highest common factors | 1-3 | HCFs |
| Number | N4b - Multiples and lowest common multiples | 1-3 | LCMs |
| Number | N4c - Prime numbers and prime factorisation with GeoGebra applet | 3-5 | Primes, Unique, factorizes, factorizations, factorising, factorizing,HCFs, LCMs, highest, lowest, common, multiples, factorises, factors, decompose, decomposition, decomposing, fundamental theorem of arithmetic |
| Number | Factors, multiples and primes assorted problems | 3-5 | Factors, multiples, primes, prime numbers, powers, indices, ssdd |
| Number | N5a - Systematic listing strategies and the product rule for counting | 5-7 | rules |
| Number | N6a - Using powers and roots | 3-5 | Squares roots, Cubes roots, Indices, Indexes of a numbers |
| Number | N6b - Estimating powers and roots | 5-7 | Square roots, Cube roots, Indices, Index, powers, estimates of a numbers |
| Number | N7a - Calculating with positive and negative integer indices | 3-5 | Squares roots, Cubes roots, Indices, Indexes, powers of a numbers |
| Number | N7b - Calculating with fractional indices | 5-7 | Squares roots, Cubes roots, Indices, Indexes, powers, fractions of a numbers |
| Number | N8a - Calculating exactly with fractions and with multiples of pi | 3-5 | Pi, exact form, |
| Number | N8b - Surds | 5-7 | Roots, rationals numbers, irrationals numbers, rationalising rationalizing denominators |
| Number | N9a - Converting between normal numbers and standard form | 3-5 | Standard index form, Scientific notation |
| Number | N9b - Multiplying and dividing in standard form | 3-5 | Standard index form, Scientific notation, multiplication by, division |
| Number | N9c - Adding and subtracting in standard form | 3-5 | Standard index form, Scientific notation, additions to, subtractions from |
| Number | N10a - Converting terminating decimals into fractions and vice versa | 3-5 | terminates, expansions |
| Number | N10b - Converting recurring decimals into fractions and vice versa | 5-7 | infinite, expansion, infinity, for ever, forever |
| Number | N11a - Identifying and working with fractions in ratio problems | 3-5 | |
| Number | N12a - Interpreting fractions and percentages as operators | 3-5 | Finding a fraction of a quantity, numbers amounts |
| Number | N13a - Using standards units of measure | 1-3 | grams, metres, litres, km, kg, kilometres, kilograms, years, days, hours, minutes, hrs, mins, seconds, secs |
| Number | N14a - Estimating answers and checking calculations | 1-3 | Estimating, approximating, rounding, calculators, calculating, technology, estimates, estimations, figures, significant |
| Number | N15a - Rounding and truncating | 1-3 | truncate, truncation, Decimals places, significant figures, place values Rounding numbers and measures to an appropriate degree of accuracy, 1 2 3 4 5 dp d.p. sf s.f. sigfig |
| Number | N15b - Using inequality notation to specify simple error intervals | 3-5 | Truncate, truncation, truncating, rounding, inequalities, errors, rounding, significant figures, decimal places, dp d.p. s.f. sf sigfig |
| Number | N16a - Applying and interpreting limits of accuracy, including upper and lower bounds | 5-7 | UB, LB, error intervals |
| Algebra | A1a - Using and interpreting algebraic notation | 1-3 | Coefficients, brackets, fractions, division, simplifying |
| Algebra | A2a - Substituting numerical values into formulae and expressions | 1-3 | Substitutes, substitution, substituting |
| Algebra | A3a - Understanding and using the concepts of expressions, equations, formulas, identities, inequalities, terms and factors | 3-5 | Inequality, formulae, identity, |
| Algebra | A4a - Simplifying and manipulating algebraic expressions by collecting like terms (basic) | 1-3 | |
| Algebra | A4b - Multiplying a single term over a bracket | 3-5 | Expanding, out, expansions, by |
| Algebra | A4c - Factorising (basic) | 3-5 | Taking out common factors, factorise, factorizing, factorize, brackets |
| Algebra | A4d - Multiplying two or more brackets | 3-5 | Expanding products of two or more binomials, out, expansions, by, dots, difference of two squares, triple brackets, three brackets, products of, trinomials |
| Algebra | A4e - Factorising quadratics | 3-5 | expressions, coefficient, factorise, factorizing, factorize, dots, difference of two squares, brackets |
| Algebra | A4f - Simplifying, multiplying and dividing algebraic fractions | 7-9 | Multiplications by, Divisions |
| Algebra | A4g - Adding and subtracting algebraic fractions | 7-9 | Additions to, Subtractions from |
| Algebra | A4h - Algebraic manipulation involving surds | 7-9 | Powers, indexes, indices |
| Algebra | A4i - Index laws and solving equations involving indices | 3-5, 7-9 | Indices, powers, indexes, bases, power, exponents, solving, solutions, equations, rewriting different bases, rebasing, rebase |
| Algebra | A5a - Rearranging formulas to change the subject with GeoGebra applet | 3-5, 5-7 | Rearranges, make the subject, rearrangement, formulae, making, changing, of a |
| Algebra | Rearranging formulas to change the subject assorted problems | 3-5, 5-7 | Rearranges, make the subject, rearrangement, formulae, making, changing, of a, rearranging, ssdd |
| Algebra | A6a - Arguing mathematically | 3-5 | Equivalent, Equivalence, algebraic expressions, Equations, identities, argument, constructing, proofs, constructions, prove that, show, proving with |
| Algebra | A6b - Using algebra to construct proofs | 7-9 | Equivalent, Equivalence, algebraic expressions, Equations, identities, argument, constructing, proofs, constructions, show that, prove, proving with |
| Algebra | A7a - Interpreting functions and composite functions | 5-7 | Inputs, outputs |
| Algebra | A7b - Interpreting inverse functions | 7-9 | |
| Algebra | A7c - Solving equations involving functions | 7-9 | inverse, composite, solving, solve, linear, quadratic |
| Algebra | A8a - Working with coordinates in all four quadrants | 1-3 | Graphs |
| Algebra | A9a - Plotting straight-line graphs with GeoGebra applets | 3-5 | Gradients, y- intercepts, horizontal, vertical, slopes, lines, y=mx+c, y = mx + c, x = k, ax+by=c ax+by=k ax + by = c k - 0 |
| Algebra | A9b - Identifying parallel and perpendicular lines with GeoGebra applet | 5-7 | Gradients, intercepts, horizontal, vertical, slope, straight lines graphs, y = mx + c |
| Algebra | A9c - Finding the equation of a line through two given points or through one point with a given gradient (e.g. parallel or perpendicular to another line) with GeoGebra applet | 3-5 | Gradients, intercepts, slopes, straight, graphs, lines, parallel, perpendicular to |
| Algebra | A10a - Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically | 1-3 | slopes, graphs, straight lines |
| Algebra | A11a - Identifying roots, intercepts and turning points of quadratic functions graphically with GeoGebra applet | 3-5 | solutions, parabolas, parabolic, curves, curved, graphs, quadratics, sketching, equations, sketches |
| Algebra | A11b - Identifying turning points of quadratic functions by completing the square with GeoGebra applet | 5-7 | Minimum, minima, maximum, maxima, parabolas, parabolic, complete, curves, curved, graphs, quadratics, sketching, equations, sketches |
| Algebra | A11c - Sketching quadratics with GeoGebra applet | 5-7 | Minimum, minima, maximum, maxima, parabolas, parabolic, complete, curves, curved, graphs, functions, equations, y=,sketches, turning points, complete completing the square solving, curves, curved, graphs, sketches |
| Algebra | A12a - Graphs of linear functions, quadratic functions, simple cubic functions, and the reciprocal function with GeoGebra applet | 3-5 | parabolas, parabolic, asymptotes, curved, curves, straight lines, plotting, quadratics |
| Algebra | A12b - Graphs of exponential functions | 5-7 | curved, cures |
| Algebra | A12c - Graphs of trigonometric functions | 7-9 | sin, sine, cos, cosine, tan, tangent, wave |
| Algebra | A13a - Sketch translations and reflections of a given function | 7-9 | transformations of functions graphs curves lines move slide shift mirroring transforming |
| Algebra | A14a - Plotting and interpreting graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions | 3-5 | asymptotes, curved, curves |
| Algebra | A14b - Plotting and interpreting graphs in real contexts to find approximate solutions to problems such as simple kinematic problems | 3-5 | speeds, distances, times, depth-time graphs containers liquid water jars filling |
| Algebra | A15a - Calculating or estimating gradients of graphs | 5-7 | Estimates, chords, tangents, slopes, rates of changes, curves, curved, straight lines |
| Algebra | A15b - Estimating the area under a graph | 7-9 | Estimates, trapezium rule, estimations, curved, curves, straight lines, graphs |
| Algebra | A15c - Interpreting gradients and areas under graphs | 7-9 | distances, velocity, times, kinematics, slopes, velocities, rates of changes, curved, curves, straight lines, |
| Algebra | Kinematics graphs assorted problems | 3-5,5-7 | distances, velocity, times, kinematics, slopes, velocities, rates of changes, curved, curves, straight lines, graphs, ssdd |
| Algebra | A16a - Recognising and using the equation of a circle with the centre at the origin | 7-9 | equations of circles, centre radiuses radii |
| Algebra | A16b - Finding the equation of a tangent to a circle at a given point | 7-9 | equations of circles, a tangents to, finding the with the centre at the origin |
| Algebra | A17a - Solving simple linear equations in one unknown algebraically | 3-5 | balances, balancing, solves, method, algebraic fractions |
| Algebra | A17b - Solving linear equations in one unknown algebraically where the unknown is on both sides of the equation | 3-5 | balances, balancing, solves, method, algebraic fractions |
| Algebra | A17c - Finding solutions to linear equations using graphs | 3-5 | intersection, solves, straight lines, solving graphically, intersecting, intersects, lines |
| Algebra | A18a - Solving quadratic equations by factorising | 3-5, 7-9 | factorises, factorizse, factorizing, parabolas, parabolic, solves, quadratics, algebraic fractions |
| Algebra | A18b - Solving quadratic equations by completing the square | 7-9 | completes, parabolas, parabolic, turning points, minimums, maximums, solves, minima, maxima, quadratics, algebraic fractions, vertex form |
| Algebra | A18c - Solving quadratic equations using the quadratic formula | 5-7 | discriminants, parabolas, parabolic, roots, solutions, solves, quadratics, algebraic fractions |
| Algebra | Quadratic functions—putting it all together (with dynamic algebra tiles) | 5-7 | discriminants, parabolas, parabolic, roots, solutions, solves, quadratics, algebraic fractions, graphs, completes, parabolas, parabolic, turning points, minimums, maximums, solves, minima, maxima, quadratics, algebraic fractions, vertex form completing the square completes,factorises, factorizse, factorizing, dynamic algebra tiles |
| Algebra | Expanding, simplifying, factorising, and solving equations assorted problems | 3-5, 5-7 | Expanding, multiplying out, simplifying, collecting like terms, factorise, factorize, factorizing, solve, both sides, quadratics, ssdd |
| Algebra | A19a - Solving two linear simultaneous equations algebraically by elimination | 3-5 | eliminates, elimination, eliminating substitutes, substitution, solves, worded problems, substituting |
| Algebra | A19b - Solving two linear simultaneous equations graphically or algebraically by substitution | 3-5 | intersections, intersects, intersecting, solves, straight lines graphs, substituting |
| Algebra | A19c - Solving two simultaneous equations (linear/ quadratic) algebraically | 7-9 | substitutes, substitution, solves, substituting, quadratics |
| Algebra | A19d - Solving two simultaneous equations (linear/ quadratic) graphically | 7-9 | intersections, intersects, intersecting, parabolas, parabolic, solutions, solves, graphs straight lines curves curved, quadratics |
| Algebra | A20a - Finding approximate solutions to equations numerically using iteration | 5-7 | trial, solve, and error, improvement, sign change, solution to an equation by, iterate, iterating, repeating, repeated, converge converging diverge diverging |
| Algebra | A21a - Representing simple situations using algebraic expressions or formulae | 3-5 | Writing, write, describes, describing, writes, writing, worded problems |
| Algebra | A21b - Deriving and solving an equation or simultaneous equations to describe a situation | 3-5, 5-7 | solves, derives, writing, writes, describes, worded problems, equate, equating |
| Algebra | A22a - Solving linear inequalities in one variable | 3-5 | Greater, less, than, equal to, solves, unknowns, inequality |
| Algebra | A22b - Solving linear inequalities in two variables | 5-7 | Greater, less, than, equal to, solves, unknowns, graphs, graphically, regions, shaded shades, shading by, inequality |
| Algebra | A22c - Solving quadratic inequalities in one variable | 7-9 | Greater, less, than, equal to, solves, inequality, quadratics |
| Algebra | A23a - Generating terms of a sequence from either a term-to-term or a position-to-term rule | 1-3 | nth term, number, linear arithmetic progressions, sequences |
| Algebra | A24a - Recognising and using triangular, square and cube numbers | 3-5 | sequences, triangle, cubic |
| Algebra | A24b - Recognising and using arithmetic, geometric and quadratic sequences | 1-3 | sequences, linear arithmetic progressions, quadratics |
| Algebra | A24c - Recognising and using Fibonacci type sequences | 3-5 | sequences, fibonnaci numbers |
| Algebra | A25a - Finding the nth term of a linear sequence | 3-5 | expression for, linear arithmetic progressions, sequences |
| Algebra | A25b - Finding the nth term of a quadratic sequence | 7-9 | expression for, quadratics, sequences |
| Algebra | Sequences assorted problems | 3-5, 5-7 | Arithmetic, linear, geometric, sequences, progression, quadratics, nth term, position to term, term to term -, ssdd |
| Ratio and proportion | R1a - Changing between standard units and compound units in numerical and algebraic contexts | 3-5 | times, lengths, areas, volumes, capacity, capacities, masses, speeds, rates of pay, prices, density, densities, pressures, mass/ |
| Ratio and proportion | R2a - Using scale diagrams and maps | 3-5 | scales diagrams, maps, scales factors |
| Ratio and proportion | R3a - Expressing one quantity as a fraction of another | 3-5 | fractions writing, writes |
| Ratio and proportion | R4a - Using ratio notation, and reducing ratios to simplest form | 1-3 | reduction, reduces, simplifying |
| Ratio and proportion | R5a - Dividing a quantity in a given ratio, and expressing the division of a quantity as a ratio with GeoGebra applet | 3-5 | divides, shares, sharing, ratios, quantities |
| Ratio and proportion | R5b - Applying ratio to real contexts | 3-5 | ratios, mixing, mixes, converting, conversions, paints, dilutes, diluting, mixtures, squash, colours |
| Ratio and proportion | R6a - Expressing a multiplicative relationship between two quantities as a ratio or a fraction | 3-5 | fractions |
| Ratio and proportion | R7a - Understanding and using proportion as equality of ratios | 3-5 | the unitary method, scale, scaling recipes, up down |
| Ratio and proportion | R8a - Relating ratios to fractions and to linear functions | 3-5 | |
| Ratio and proportion | Ratio assorted problems | 3-5 | divides, shares, sharing, ratios, given, quantity, quantities, ssdd |
| Ratio and proportion | R9a - Converting between fractions, decimals and percentages | 3-5 | FDP |
| Ratio and proportion | R9b - Finding percentages and percentage changes (basic) | 3-5 | of a number amount quantity |
| Ratio and proportion | R9c - Finding percentages and percentage changes multiplicatively using decimals | 3-5 | of a number amount quantity increase decrease, multipliers |
| Ratio and proportion | R9d - Solving problems involving percentage change | 3-5 | reverse, percentages, reversing, undoing, original value, original amount, original quantity |
| Ratio and proportion | R9e - Comparing two quantities using percentages | 3-5 | compares, comparisons |
| Ratio and proportion | Percentages assorted problems | 3-5 | FDP, of a number amount quantity, increase decrease, multipliers, reverse, percentages, reversing, undoing, compares, comparisons, ssdd |
| Ratio and proportion | R10a - Solving problems involving direct proportion with GeoGebra applet | 3-5 | inverse, including graphical and algebraic representations, imperial, metric, converting between to from miles kilometres centimetres cm km yards inches |
| Ratio and proportion | R10b - Solving problems involving inverse proportion with GeoGebra applet | 5-7 | direct, graphs, including graphical and algebraic representations |
| Ratio and proportion | R11a - Using compound units with GeoGebra applet | 3-5 | speeds, density, densities, pressures, rates of pay, mass / volume, distance time divided by formula triangles |
| Ratio and proportion | R12a - Ratios and similar shapes; scale, area and volume factors | 3-5 | similarity |
| Ratio and proportion | R13a - Constructing and interpreting equations that describe direct and inverse proportion | 3-5 | directly, inversely, proportions |
| Ratio and proportion | R14a - Recognising and interpreting graphs that illustrate direct and inverse proportion | 3-5 | |
| Ratio and proportion | R15a - Gradient as a rate of change (straight line and curved graphs) | 7-9 | Lines |
| Ratio and proportion | R16a - Growth and decay problems | 5-7 | gradients, compound, interest, exponential, rates, borrowing, simple, depreciates, depreciation, banks, banking, |
| Ratio and proportion | Compound and simple interest assorted problems | 5-7 | growth, decay, ssdd, compounding, percentage, roots, powers, indices |
| Geometry | G1a - 2D geometry - terms and notation | 1-3 | parallel, perpendiculars, edges, vertex, vertices, angles, straight lines, corners, sides, names of polygons regular n-gons ngons, triangles, quadirlaterals, pentagons, hexagons, heptagons, septagons, octagons, nonagons, decagons, hendecagons, undecagons, dodecagons triskadecagons |
| Geometry | G1b - 3D geometry - terms | 3-5 | edges, vertex, vertices, faces, corners, sides, surfaces, nets, polyhedra, polyhedrons, curved shapes, 3-d three dimensions dimensional |
| Geometry | G1c - Reflection symmetry | 1-3 | lines ofs mirrors |
| Geometry | G1d - Rotation symmetry with GeoGebra applet | 1-3 | order of rotate, rotational |
| Geometry | G1e - Conventions for labelling the sides and angles of triangles | 3-5 | labels how to name, naming edges, corners, vertices |
| Geometry | G1f - Drawing diagrams from a written description | 1-3 | how to parallel, perpendicular, equal, edges, vertices, corners, sides, faces, shapes, polygons, 2D, squares, rhombuses, rhombi, parallelograms, rectangles, trapeziums, trapezia, kites, triangles, equilateral, scalene, symmetries, symmetry, reflection, reflects, reflective, order of, rotations, rotational, |
| Geometry | G2a - Constructing perpendicular bisectors, angle bisectors, and perpendiculars to or from a point | 3-5 | constructions, using rulers and straight edges, compasses, without protractors, bisecting |
| Geometry | G2b - Constructing triangles | 3-5 | constructions, equilateral, scalene, SSS,SAS,ASA, isosceles, right angled , using rulers and straight edges, compasses, without protractors |
| Geometry | G2c - Mixed loci problems with GeoGebra applet | 3-5 | constructions, locus, rulers and straight edges, compasses, without protractors |
| Geometry | G3a - Angles at a point, angles at a point on a straight line, vertically opposite angles | 1-3 | rules, 180, 360, º, degrees, around, meeting, points |
| Geometry | G3b - Alternate and corresponding angles on parallel lines with GeoGebra applet | 3-5 | F Z degrees, forresponding, zalternate, co-interior, supplementary, complementary, º |
| Geometry | G3c - The sum of angles in a triangle and the angle properties of polygons with GeoGebra applet | 3-5 | 180, 360, quadrilateral, interior, exterior, degrees, º |
| Geometry | G4a - Properties of special triangles and quadrilaterals | 3-5 | equilateral, isosceles, right angles, squares, rectangles, parallelograms, trapeziums, trapezia, kites, rhombuses rhombi, symmetries, symmetry, reflection, reflects, reflective, order of, rotations, rotational, |
| Geometry | G5a - Congruence criteria for triangles (SSS, SAS, ASA, RHS) | 3-5 | Congruent, Side, angle, congruency, similarity |
| Geometry | G6a - Simple geometric proofs | 3-5 | Prove that show |
| Geometry | G7a - Coordinates with GeoGebra applet | 1-3 | Cartesian, planes, co-ordinates, x, y, axis, axes, along the corridor and up the stairs, is across high |
| Geometry | G7b - Rotation with GeoGebra applet | 3-5 | Rotates, transformations, centres of, clockwise, anticlockwise, rotations, rotating, transforming |
| Geometry | G7c - Reflection with GeoGebra applet | 3-5 | transformations, mirrors, lines reflects, reflecting, mirroring, transforming |
| Geometry | G7d - Translation with GeoGebra applet | 1-3 | Translates, transformations, column vectors, translating, transforming |
| Geometry | G7e - Enlargement with GeoGebra applet | 3-5 | transformations, scale factors, negative, fractional, fractions, enlarging, centre of, transforming |
| Geometry | G7f - Congruence, similarity and transformations | 3-5 | congruent |
| Geometry | G8a - Combinations of transformations | 5-7 | reflections, rotations, rotates, translates, translations, enlargements, scale factors, column vectors, mirrors, centres of, clockwise, anticlockwise, direction, anti-clockwise, reflecting, rotating, translating, enlarging, mirroring, transforming lines of |
| Geometry | G9a - Circle parts - definitions and properties | 3-5 | arcs, sectors, segments, chords, tangents, diameters, radius, circles, parts of |
| Geometry | G10a - Circle theorems with GeoGebra applets | 7-9 | alternate segments, centres, opposites, semicircles, angles, tangents, radius, chords, diameters, radii, radiuses |
| Geometry | G11a - Solve geometrical problems on coordinate axes | 3-5 | Lengths of lines segments, shortest distances from a points to, Pythagoras, perpendiculars, gradients, graphs, y = mx + c, between two, on the planes, cartesian, coordinates, co-ordinates, midpoints, mid-points, halfway, finding, calculating, calculate, work out, working |
| Geometry | G12a - Properties of 3D shapes with GeoGebra applets | 3-5 | cubes, cuboids, prisms, cylinders, pyramids, cones, spheres, nets, vertices, faces, edges, corners, surfaces, sides, polyhedrons, polyhedra, curved, triangular, 3-d three dimensions dimensional |
| Geometry | G13a - Plans and elevations of 3D shapes | 3-5 | constructions, isometric, 3-d, hexagonal, hexagons, triangles, triangular, dotty, side view, overhead view, birdseye bird's eye top perspectives |
| Geometry | G14a - Converting between metric units of measures of length and mass | 1-3 | length, area, volume, capacity, mass, time, money, km, kg, kilometres, kilograms, metres, grams, cm, centimetres, mm, millimetres |
| Geometry | G14b - Converting between metric units of measures of area and volume | 5-7 | square mm cm m millimetres, centimetres, metres, squared, cube, cubed, cubic |
| Geometry | G14c - Money | 1-3 | £, pounds, penny, pence, currency, currencies, conversion, converting, exchanges rates, euros, cents between different, best buys |
| Geometry | G14d - Time with GeoGebra applet | 1-3 | years, months, days, hours, minutes, seconds 24-hours 12-hours military clocks clockfaces - converting telling the between digital analogue watch and, hrs, mins, secs |
| Geometry | G15a - Measuring line segments and angles in geometric figures with GeoGebra applet | 1-3 | measure using a protractors rulers length size of lines, acute, right, obtuse, straight, reflex angles |
| Geometry | G15b - Scale drawings | 3-5 | maps, diagrams, scales |
| Geometry | G15c - Bearings with GeoGebra applet | 3-5 | angles, North South East West North-east, South-west, South-east, North-west NW NE SW SE NNE ENE ESE SSE WSW SSW NNW WNW anticlockwise anti-clockwise from north |
| Geometry | G16a - Area of rectangles with GeoGebra applet | 1-3 | squares, quadrialterals |
| Geometry | G16b - Area of parallelograms with GeoGebra applet | 1-3 | bases heights quadrilaterals |
| Geometry | G16c - Area of triangles with GeoGebra applet | 1-3 | bases heights |
| Geometry | G16d - Area of trapezia with GeoGebra applet | 3-5 | trapeziums, quadriaterals |
| Geometry | G16e - Volume of cuboids, prisms and cylinders with GeoGebra applet | 1-3 | triangular, volumes |
| Geometry | G17a - Perimeter of polygons | 1-3 | perimeters, shapes, 2D |
| Geometry | G17b - Circumference of a circle | 1-3 | perimeters, diameters, pi, radius, radii, radiuses, circumferences, circles |
| Geometry | G17c - Area of a circle with GeoGebra applet | 1-3 | diameters, pi, radius, radii, radiuses, circles |
| Geometry | G17d - Perimeter and area of composite shapes made up of polygons | 3-5 | Perimeters, areas, compound, 2d shapes, edges, sides, many, with |
| Geometry | G17e - Perimeter and area of composite shapes made up of polygons and sectors of circles | 3-5 | pi, radius, diameters, radii, radiuses, |
| Geometry | G17f - Surface area of cuboids, prisms and pyramids with GeoGebra applet | 3-5 | Cubes, square-based, squares, tetrahedrons, tetrahedra triangle-based, sa |
| Geometry | G17g - Volume of spheres, pyramids, and cones | 5-7 | pi, radius, diameters, composite solids, hemispheres, frustums, square based, radii, radiuses |
| Geometry | G17h - Surface area of cylinders, spheres, and cones with GeoGebra applet | 5-7 | pi, radius, radii, radiuses, diameters, composite solids, hemispheres, frustums, square based, sa |
| Geometry | G18a - Arcs and sectors of circles with GeoGebra applet | 3-5 | pi, radiuses, radii, diameters, lengths, areas, circumferences, finding, calculating, calculate, parts of |
| Geometry | G19a - Lengths, areas and volumes in similar shapes | 5-7 | similarity, areas, volumes factors |
| Geometry | G20a - Pythagoras' theorem with GeoGebra applets | 5-7 | Right angled triangles, Pythagoras's, Pythagorean, 90º, degrees, triple, a ^2 = b c, hypotenuse 3d, 3-d in dimensions dimensional |
| Geometry | Pythagoras and surds assorted problems | 3-5 | Surds, Pythagoras' Theorem, Pythagorean, radicals, roots, surd exact form, ssdd |
| Geometry | G20b - Trigonometric ratios - sin, cos and tan with GeoGebra applets | 3-5 | Trigonometry, sine, cosine, tangent, Right angled triangles, degrees, opposite, adjacent, hypotenuse SOHCAHTOA |
| Geometry | G20c - Inverse trigonometric functions | 3-5 | Trigonometry, sine, cosine, tangent, Right angled triangles, opposite, adjacent, hypotenuse SOHCAHTOA, inverse sin-1 cos-1 tan-1 sin^-1 cos^-1 tan^-1 arcsin arccos arctan arc |
| Geometry | G20d - Trigonometry with right-angled triangles in 3D shapes with GeoGebra applets | 5-7 | Trigonometry, sine, cosine, tangent, Right angled triangles, opposite, adjacent, hypotenuse SOHCAHTOA, inverse sin-1 cos-1 tan-1 sin^-1 cos^-1 tan^-1 arcsin arccos arctan arc, Pythagoras, 3D three dimensional, angles of elevation depression, cube cuboid, prism, triangular, pyramid |
| Geometry | Pythagoras, sin, cos, or tan? method selection (right-angled triangles only) | 3-5 | Trigonometry, sine, cosine, tangent, Right angled triangles, opposite, adjacent, hypotenuse SOHCAHTOA, inverse sin-1 cos-1 tan-1 sin^-1 cos^-1 tan^-1 arcsin arccos arctan arc |
| Geometry | G21a - Exact values of sin, cos and tan for special angles | 5-7 | 0, 30, 45, 60, 90, Trigonometry, sine, cosine, tangent, Right angled triangles, º, degrees, opposite, adjacent, hypotenuse, SOHCAHTOA |
| Geometry | G22a - The sine rule | 7-9 | Trigonometry, sine, cosine, tangent, triangles, opposite, lengths angles any triangles |
| Geometry | G22b - The cosine rule | 7-9 | Trigonometry, sine, cosine, tangent, triangles, angle between, opposite, lengths angles any triangles |
| Geometry | G23a - Area of a triangle using sine | 7-9 | Trigonometry, sine, cosine, tangent, triangles, opposite, adjacent, hypotenuse, angle between, opposite, any triangles, base, height |
| Geometry | G23b - Mixed problems using trigonometric formulas | 7-9 | Trigonometry, sine, cosine, tangent, Right angled triangles, opposite, adjacent, hypotenuse, lengths angles any triangles, SOHCAHTOA |
| Geometry | Right-angled triangles assorted problems | 3-5, 5-7, 7-9 | Trigonometry, sine, cosine, tangent, Right angled triangles, Pythagoras' Pythagorean, Theorem, SOH CAH TOA, SOHCAHTOA, ssdd |
| Geometry | G24a - Describing translations as 2D vectors | 3-5 | column |
| Geometry | G25a - Adding and subtracting column vectors with GeoGebra applets | 3-5 | Addition to, subtraction from |
| Geometry | G25b - Multiplying column vectors by a scalar | 3-5 | scalars, multiplication of, by |
| Geometry | G25c - Proofs using vectors | 7-9 | parallel, on a line, show that points straight, direction, magnitude, size, prove |
| Probability | P1a - Frequency trees | 1-3 | |
| Probability | P2a - Theoretical probability | 1-3 | |
| Probability | P2b - Relative frequency | 3-5 | Experimental probability, outcomes, events, probabilities |
| Probability | P3a - Expected frequency | 3-5 | Expectation, value, trials, frequencies, probabilities |
| Probability | P4a - Properties of probability | 3-5 | Mutually exclusive, exhaustive, outcomes, events, probabilities |
| Probability | P5a - Probability and sampling | 3-5 | bias, unbiased, samples size, probabilities, capture-recapture recapturing releasing wild estimate populations size |
| Probability | P6a - Enumerating sets and combinations of sets systematically, using tables, grids and Venn diagrams | 3-5 | probabilities, unions, intersections, empty set, null set, universal set, xi, complement, and, or, not |
| Probability | P7a - Constructing theoretical possibility spaces for combined experiments with equally likely outcomes and use these to calculate theoretical probabilities | 3-5 | |
| Probability | P8a - Tree diagrams | 3-5 | independent dependendent events |
| Probability | P9a - Conditional probabilities | 5-7 | |
| Statistics | S1a - Sampling | 3-5 | populations, samples |
| Statistics | S2a - Frequency tables and two-way tables | 1-3 | Diagrams, frequencies, grouped |
| Statistics | S2b - Pictograms | 1-3 | tally, tallies, charts, tables, diagrams |
| Statistics | S2c - Bar charts, vertical line charts and basic histograms | 1-3 | bar graphs, discrete, continuous, categorical, diagrams |
| Statistics | S2d - Pie charts | 1-3 | Angles, 360, degrees, º, emma, diagrams |
| Statistics | S2e - Tables, conversion graphs, line graphs and time series | 3-5 | diagrams, |
| Statistics | S2f - Stem and leaf diagrams | 3-5 | plot, ordered, unordered, non, back-to-back back to back |
| Statistics | S3a - Histograms | 7-9 | classes intervals, unequal, widths, diagrams, frequency density, densities, fd |
| Statistics | S3b - Cumulative frequency graphs | 5-7 | interquartile range, lower upper quartiles median, Q1, Q2, Q3, LQ, UQ, IQR, diagrams, curves |
| Statistics | S4a - Median | 1-3 | averages, classes intervals, estimates, estimation, frequency tables grouped from, finding the median using a, estimating |
| Statistics | S4b - Mean with GeoGebra applet | 1-3 | averages, classes intervals, estimates, estimation, frequency tables grouped from, finding the mode using a, estimating, artihmetic |
| Statistics | S4c - Mode and modal class | 1-3 | averages, classes intervals, frequency tables grouped from, finding the using a, |
| Statistics | S4d - Range | 1-3 | spreads |
| Statistics | S4e - Interquartile range and box plots with GeoGebra applet | 5-7 | spread, interquartile range, lower upper quartiles median, Q1, Q2, Q3, LQ, UQ, IQR, boxplots, whisker, diagrams |
| Statistics | S4f - Comparing data sets | 3-5 | compares, comparisons, of |
| Statistics | S5a - Applying statistics to describe a population | 3-5 | |
| Statistics | S6a - Scatter graphs, correlation and causation | 3-5 | lines of best fit, predictions, predicting, interpolating interpolates, interpolations, extrapolating extrapolates, extrapolations |
| Ideas | Knowing the whole without knowing the parts | All | theme, information, limited, not all, total, sum, details, big picture |
| Manipulative | Customisable double number line | All | Algebra, Number, Proportion |
| Manipulative | Multi-base zooming number line | All | Number |
| Manipulative | Interactive counting stick | All | Number |
| Manipulative | Algebra discs (with ability to group and turn over groups) | All | Algebra, Number |
| Manipulative | Double-sided counters (with ability to group and turn over groups) | All | Algebra, Number |
| Animation | Inner solar system animation demonstrating relative motion | All | |
| Animation | Pale Blue Dot—our insignificance in time and space | All |
Shortcut and Mashup problems
What are Shortcut problems?
Shortcut problems can be solved with very little working if students have a good understanding of the relevant concepts. It is often possible to solve these without such an understanding, but students will find it far more laborious. Here is an example of a Shortcut resource:
What are Mashup problems?
Our Mashup problems interweave different topics within a single question, and generally require a significant amount of written working. Here is an example of a Mashup problem, requiring knowledge of circle theorems, ratios, and trigonometry:
You can filter these resources by topic, BossMaths lesson code (e.g. G20a for Pythagoras’ Theorem) or any relevant key word:
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Problem Topics (click for search box) Type & Difficulty Other key words
Swaps Addition, subtraction, multiplication, division reciprocals, inverses Shortcut ★ N2a - Adding and subtracting positive integers N2b - Multiplying positive integers N2d - Applying the four operations to decimals subtracting multiplying times product minus take away difference N2f - Applying the four operations to fractions N3a - Relationships between operations, including inverse operations N2e - Applying the four operations to negative numbers
How wrong? Subtraction, Multiplication, decimals Shortcut ★ N2d - Applying the four operations to decimals subtracting multiplying times product minus take away difference distributive law property distributivity
Multiplication primetime Multiplication, prime factorisation, time Shortcut ★ N2b N4c G14d numbers Multiplying positive integers, multiply, times, remainders, divide, division, residue, modular arithmetic, modulo, clock, am, pm. hours, days, minutes, unique prime factors, factorization, factorise, factorize, factoring, money, £, pounds, and relationships, fundamental theorem of arithmetic, composite
A tricky slope? Gradient, coordinates, decimals, fractions Shortcut ★ A9a A9c A10a Plotting straight-line graphs, Finding the equation of a line through two given points or through one point with a given gradient (e.g. parallel or perpendicular to another line), gradient, Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically, slope, intercept, y=mx+c, adding and subtracting fractions and decimals, addition, subtraction
Pedestrian pair power Speed, prime factorisation, indices, inequalities Shortcut ★ N4c N7a A4i R11a A22a Solving linear inequalities in one variable Using compound units, Prime numbers, Calculating with positive and negative integer indices, Index laws and solving equations involving indices, distance time Root, prime factors, factorize, factorise, factorization, factorisation, speed, metres second, hour, minutes time, composite, indices, index laws, powers, base rebase, changing base, inequality, less greater more than
Tutti frutti 🔒 Scaling, simultaneous equations, money Shortcut ★ A19a G14c, Solving two linear simultaneous equations algebraically by elimination, simultaneous equations, scale
Change 🔒 Money, symmetry Shortcut ★ G14c Money, coins, change
Complementary cards 🔒 Systematic listing strategies, symmetry Shortcut ★ N5a Systematic listing strategies and the product rule for counting
Similar rectangles 🔒 Similar shapes, enlargement Shortcut ★ G19a Lengths, areas and volumes in similar shapes G7e Enlargement Dilation R12a Ratios and similar shapes; scale, area and volume factors
Parallelogram 🔒 Straight line graphs, Area of parallelogram Shortcut ★ A9a Plotting straight-line graphs A9b Identifying parallel and perpendicular lines G16b Area of parallelograms
Six-digit numbers 🔒 Systematic lisiting strategies, probability Shortcut ★ Structure, N5a - Systematic listing strategies and the product rule for counting P2a Theoretical probability
Products of primes 🔒 Properties of multiplication, products of primes Shortcut ★ N2b - Multiplying positive integers N4c - Prime numbers and prime factorisation factors numbers
Cube 🔒 3D geometry definitions, percentages Mashup ★ G13a Plans and elevations of 3D shapes G12a Properties of 3D shapes with GeoGebra applets G1b 3D geometry terms R9a - Converting between fractions and percentages
Perimeter, pi, and fractions 🔒 Area, perimeter, fractions Mashup ★ G17a - Perimeter of polygons, G17b - Circumference of a circle, G16a - Area of rectangles, G17c - Area of a circle, N12a - Interpreting fractions and percentages as operators, R3a - Expressing one quantity as a fraction of another
Prism density 🔒 Density, prisms Mashup ★ G13a Plans and elevations of 3D shapes, R11a - Using compound units, R1a - Changing between standard units and compound units in numerical and algebraic contexts
Fractions and simultaneous equations 🔒 Adding fractions, simultaneous equations Mashup ★ N2f Applying the four operations to fraction A19a Solving two linear simultaneous equations algebraically by elimination
Pattern product proof 🔒 Multiplication, division, rearranging, spotting patterns Shortcut ★★ A5a A17a N2c Dividing with positive integers, N3a Relationships between operations, including inverse operations, Pattern-spotting, proofs, rearranging, rearrange, multiply and divide relationships, rewrite
Solutions required? 🔒 Substitution, completing the square, index laws Shortcut ★★ Powers, indices, base, rebasing rebase, substitute substituting A2a A11b A4i A17a A18a A18b Solving quadratic equations by factorising Solving quadratic equations by completing the square N7a Calculating with positive and negative integer indices
Easy expanding 🔒 Expanding brackets, symmetry Shortcut ★★ A4d Multiplying two or more brackets, symmetric
Generating simultaneous equations 🔒 Simultaneous equations, substitution Shortcut ★★ A2a Substituting numerical values into formulae and expressions A19a - Solving two linear simultaneous equations algebraically by elimination A19b - Solving two linear simultaneous equations graphically or algebraically by substitution
Simultaneous symmetry 🔒 Simultaneous equations, symmetry Shortcut ★★ A19a - Solving two linear simultaneous equations algebraically by elimination A19b - Solving two linear simultaneous equations graphically or algebraically by substitution
Prime calculations 🔒 Prime factorisation, indices, sums, products, differences Shortcut ★★ N4c A4c Subtraction, Addition, Multiplication, multiplying, adding, subtracting, finding a differences, minus, plus, times, take away, Prime numbers and prime factorisation, distributive law distributivity property factorising factorizing factoring factorise factorize
Rhombi 🔒 Angles on parallel lines, Special quadrilaterals Shortcut ★★ G4a Properties of special quadrilaterals, Rhombuses, G3b Alternate angles on parallel lines
Two out of three ain't bad 🔒 Simultaneous equations, symmetry Shortcut ★★ A19a - Solving two linear simultaneous equations algebraically by elimination
Don't expand Quadratic equations, Shortcut ★★ N4c Prime numbers and prime factorisationA18a Solving quadratic equations by factorising
Exterior equations Exterior angles and solving equations Mashup ★★ A17a, A17b Solving linear equations in one unknown algebraically where the unknown is on both sides of the equation,G3c The sum of angles in a triangle and the angle properties of polygons, polygons, exterior, sides, edges, writing setting up solve linear
Gradients Gradients of straight lines, surds, rearranging Mashup ★★ A5a Rearranging formulas to change the subject N8b Surds A10a Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically slope standard
Not one in a million 🔒 Standard form, multiples, probability Mashup ★★ N4b, N9c Adding and subtracting in standard form, P2a Theoretical probability, inequalities, integers, inequality, probabilities
Not standard form 🔒 Standard form, Indices Mashup ★★ N9b Multiplying and dividing in standard form, A4i Index laws, powers, abases
Subprime 🔒 Prime factorisation, algebraic fractions, index laws Mashup ★★ N4c Prime numbers and prime factorisation, A4f Simplifying, multiplying and dividing algebraic fractions, A4i Index laws and solving equations involving indices, Prime factors, factorize, factorise, factorization, factorisation, factoring, powers, indices, simplifying, lowest terms, substitute, substitution, substituting, cancelling
Prime terms 🔒 Arithmetic, quadratic, and Fibonacci-type sequences, prime numbers Mashup ★★ N4c Prime numbers and prime factorisation, A24b - Recognising and using arithmetic, geometric and quadratic sequences, A24c - Recognising and using Fibonacci type sequences
Transforming sequences 🔒 Arithmetic and quadratic sequences, squaring, finding square roots, expanding, factorising Mashup ★★ A24b - Recognising and using arithmetic, geometric and quadratic sequences, A24c - Recognising and using Fibonacci type sequences A25a - Finding the nth term of a linear sequence A25b - Finding the nth term of a quadratic sequence
Don't be a surd 🔒 Surds, geometric sequences Mashup ★★ N8b Surds simplifying rationalising denominators, rationalizing, rationalise, rationalize
Irrational stats 🔒 Surds, median, mode, range Mashup ★★ N8b Surds simplifying. rationalising denominators, rationalizing, rationalise, rationalize, Statistics, S4a S4b S4c S4d
Points 🔒 Sequences, coordinates Mashup ★★ A25a - Finding the nth term of a linear sequence G7a - Coordinates
Symmetry and probability 🔒 Lines of symmetry, probability Mashup ★★ G1c - Reflection symmetry, probability, P7a - Constructing theoretical possibility spaces for combined experiments with equally likely outcomes and use these to calculate theoretical probabilities, sample
Tiles 🔒 Area, perimeter, simultaneous equations Mashup ★★ G16a G16b G16c Area of rectangles triangles parallelograms G17a Perimeter of polygons composite shapes made up of G17d
Rounding and inequalities 🔒 Rounding, error intervals, inequalities Mashup ★★ N15a - Rounding and truncating N15b - Using inequality notation to specify simple error intervals A22a - Solving linear inequalities in one variable
Investments 🔒 Compound interest, non-calculator skills Shortcut ★★★ R16a Growth and decay problems
Powerplay 🔒 Index laws, simultaneous equations Shortcut ★★★ Powers, indices, A19a Solving two linear simultaneous equations algebraically by elimination A19b Solving two linear simultaneous equations graphically or algebraically by substitution A4i Index laws and solving equations involving indices
Round a rectangle 🔒 Perimeter, circumference, circle theorems, Pythagoras' Theorem Shortcut ★★★ G10a, N8a, G20a, A21b, A18a, Solving quadratic by factorising Deriving and solving an equation or simultaneous equations to describe a situation, Perimeter, circumference, circle theorems, obling, rectangles, diagonals, pi, exact values, cyclic quadrilateral, angles in a semicircle 90º degrees, factorize, factorise, factorization, factorisation
Factorised fun 🔒 Quadratic curves, roots, turning points, factorisation Shortcut ★★★ A18a A18b A18c Solving quadratic equations formula, A11b Identifying turning points of quadratic functions, A4e Factorising quadratics, Quadratic factors, factorize, factorise, factorization, factorisation, factorizing, solve solving equations completed completing the square form, turning minimum point maximum curve coordinates, parabolas
Not quite congruent 🔒 Congruent triangles, sine rule Shortcut ★★★ G5a Congruence criteria for triangles (SSS, SAS, ASA, RHS), trigonometry, G22a The sine rule
Fib 🔒 Fibonacci sequences, estimation Shortcut ★★★ A24c - Recognising and using Fibonacci type sequences, golden ratio, section, phi, N14a - Estimating answers and checking calculations
A quadratic sequence 🔒 Quadratic sequences, quadratic equations Shortcut ★★★ A25b - Finding the nth term of a quadratic sequence, A18a - Solving quadratic equations by factorising A18b A18c completing the square using the quadratic formula
Widening range 🔒 Mean, range, percentages Mashup ★★★ A21b Deriving and solving an equation or simultaneous equations to describe a situation, S4a S4b R9c Finding percentages and percentage changes multiplicatively using decimals, Average, spread, increase decrease percentage change
Square 🔒 Area, coordinates, Pythagoras, surds, midpoints, circle theorems Mashup ★★★ G10a circle theorems angle in a semicircle 90º degrees G20a Pythagoras' theorem Pythagorean G11a Solve geometrical problems on coordinate axes Surds
In a spin 🔒 Rotation, gradient Mashup ★★★ Perpendicular lines segments rotate rotating angle centre of
Perimeter bounds 🔒 Perimeter, bounds, arithmetic sequences Mashup ★★★ Squares, rectangles, linear sequences, nth term, upper bounds, lower bounds, and, error intervals N15b Using inequality notation to specify simple error intervals N16a Applying and interpreting limits of accuracy, including upper and lower bounds G17a Perimeter of polygons A25a Finding the nth term of a linear sequence A23a
A24b
A triangle and a circle 🔒 Trigonometry, circle theorems Mashup ★★★ G10a circle theorems Segment angles G20b G20c inverse trigonometric functions right-angled triangles
Probability pi 🔒 Trigonometry, circle theorems, probability Mashup ★★★ G10a circle theorems Segment angles G22b G23a cosine rule area of triangle using sine 1/2 absinC probability fraction P2a
Congruent chords 🔒 Circle theorems, congruence, symmetry Mashup ★★★ G10a circle theorems Segment angles G5a G7a reflection rotation G1c G1d
From radius to angles to area Circle theorems, ratios, trigonometry Mashup ★★★ G10a R5a Dividing a ratio in a given quantity, G23a area of triangle using sine ratio, radius, shaded area, triangle, sine 1/2 ab sinC 1/2absinc
Frusta 🔒 Quadratic sequences, volume of a cone Mashup ★★★ G17g - Volume of spheres, pyramids, and cones A25b - Finding the nth term of a quadratic sequence A24b - Recognising and using arithmetic, geometric and quadratic sequences, frustums
Square and semicircle 🔒 Circle theorems, Pythagoras, prime factors Mashup ★★★ G10a Circle theorems, G20a Pythagoras' theorem, N4c Prime numbers and prime factorisation, product decomposition Pythagorean
Intervowen area (dynamic) Area of triangles, multiplying decimals, fractions, surds, algebraic expressions Mashup ★★★ N2b Multiplying positive integers N2f Applying the four operations to fractions N8b Surds A4b Multiplying a single term over a bracket A4d Multiplying two or more brackets G16c Area of triangles
| Problem | Topics (click for search box) | Type & Difficulty | Other key words |
|---|---|---|---|
| Swaps | Addition, subtraction, multiplication, division reciprocals, inverses | Shortcut ★ | N2a - Adding and subtracting positive integers N2b - Multiplying positive integers N2d - Applying the four operations to decimals subtracting multiplying times product minus take away difference N2f - Applying the four operations to fractions N3a - Relationships between operations, including inverse operations N2e - Applying the four operations to negative numbers |
| How wrong? | Subtraction, Multiplication, decimals | Shortcut ★ | N2d - Applying the four operations to decimals subtracting multiplying times product minus take away difference distributive law property distributivity |
| Multiplication primetime | Multiplication, prime factorisation, time | Shortcut ★ | N2b N4c G14d numbers Multiplying positive integers, multiply, times, remainders, divide, division, residue, modular arithmetic, modulo, clock, am, pm. hours, days, minutes, unique prime factors, factorization, factorise, factorize, factoring, money, £, pounds, and relationships, fundamental theorem of arithmetic, composite |
| A tricky slope? | Gradient, coordinates, decimals, fractions | Shortcut ★ | A9a A9c A10a Plotting straight-line graphs, Finding the equation of a line through two given points or through one point with a given gradient (e.g. parallel or perpendicular to another line), gradient, Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically, slope, intercept, y=mx+c, adding and subtracting fractions and decimals, addition, subtraction |
| Pedestrian pair power | Speed, prime factorisation, indices, inequalities | Shortcut ★ | N4c N7a A4i R11a A22a Solving linear inequalities in one variable Using compound units, Prime numbers, Calculating with positive and negative integer indices, Index laws and solving equations involving indices, distance time Root, prime factors, factorize, factorise, factorization, factorisation, speed, metres second, hour, minutes time, composite, indices, index laws, powers, base rebase, changing base, inequality, less greater more than |
| Tutti frutti 🔒 | Scaling, simultaneous equations, money | Shortcut ★ | A19a G14c, Solving two linear simultaneous equations algebraically by elimination, simultaneous equations, scale |
| Change 🔒 | Money, symmetry | Shortcut ★ | G14c Money, coins, change |
| Complementary cards 🔒 | Systematic listing strategies, symmetry | Shortcut ★ | N5a Systematic listing strategies and the product rule for counting |
| Similar rectangles 🔒 | Similar shapes, enlargement | Shortcut ★ | G19a Lengths, areas and volumes in similar shapes G7e Enlargement Dilation R12a Ratios and similar shapes; scale, area and volume factors |
| Parallelogram 🔒 | Straight line graphs, Area of parallelogram | Shortcut ★ | A9a Plotting straight-line graphs A9b Identifying parallel and perpendicular lines G16b Area of parallelograms |
| Six-digit numbers 🔒 | Systematic lisiting strategies, probability | Shortcut ★ | Structure, N5a - Systematic listing strategies and the product rule for counting P2a Theoretical probability |
| Products of primes 🔒 | Properties of multiplication, products of primes | Shortcut ★ | N2b - Multiplying positive integers N4c - Prime numbers and prime factorisation factors numbers |
| Cube 🔒 | 3D geometry definitions, percentages | Mashup ★ | G13a Plans and elevations of 3D shapes G12a Properties of 3D shapes with GeoGebra applets G1b 3D geometry terms R9a - Converting between fractions and percentages |
| Perimeter, pi, and fractions 🔒 | Area, perimeter, fractions | Mashup ★ | G17a - Perimeter of polygons, G17b - Circumference of a circle, G16a - Area of rectangles, G17c - Area of a circle, N12a - Interpreting fractions and percentages as operators, R3a - Expressing one quantity as a fraction of another |
| Prism density 🔒 | Density, prisms | Mashup ★ | G13a Plans and elevations of 3D shapes, R11a - Using compound units, R1a - Changing between standard units and compound units in numerical and algebraic contexts |
| Fractions and simultaneous equations 🔒 | Adding fractions, simultaneous equations | Mashup ★ | N2f Applying the four operations to fraction A19a Solving two linear simultaneous equations algebraically by elimination |
| Pattern product proof 🔒 | Multiplication, division, rearranging, spotting patterns | Shortcut ★★ | A5a A17a N2c Dividing with positive integers, N3a Relationships between operations, including inverse operations, Pattern-spotting, proofs, rearranging, rearrange, multiply and divide relationships, rewrite |
| Solutions required? 🔒 | Substitution, completing the square, index laws | Shortcut ★★ | Powers, indices, base, rebasing rebase, substitute substituting A2a A11b A4i A17a A18a A18b Solving quadratic equations by factorising Solving quadratic equations by completing the square N7a Calculating with positive and negative integer indices |
| Easy expanding 🔒 | Expanding brackets, symmetry | Shortcut ★★ | A4d Multiplying two or more brackets, symmetric |
| Generating simultaneous equations 🔒 | Simultaneous equations, substitution | Shortcut ★★ | A2a Substituting numerical values into formulae and expressions A19a - Solving two linear simultaneous equations algebraically by elimination A19b - Solving two linear simultaneous equations graphically or algebraically by substitution |
| Simultaneous symmetry 🔒 | Simultaneous equations, symmetry | Shortcut ★★ | A19a - Solving two linear simultaneous equations algebraically by elimination A19b - Solving two linear simultaneous equations graphically or algebraically by substitution |
| Prime calculations 🔒 | Prime factorisation, indices, sums, products, differences | Shortcut ★★ | N4c A4c Subtraction, Addition, Multiplication, multiplying, adding, subtracting, finding a differences, minus, plus, times, take away, Prime numbers and prime factorisation, distributive law distributivity property factorising factorizing factoring factorise factorize |
| Rhombi 🔒 | Angles on parallel lines, Special quadrilaterals | Shortcut ★★ | G4a Properties of special quadrilaterals, Rhombuses, G3b Alternate angles on parallel lines |
| Two out of three ain't bad 🔒 | Simultaneous equations, symmetry | Shortcut ★★ | A19a - Solving two linear simultaneous equations algebraically by elimination |
| Don't expand | Quadratic equations, | Shortcut ★★ | N4c Prime numbers and prime factorisationA18a Solving quadratic equations by factorising |
| Exterior equations | Exterior angles and solving equations | Mashup ★★ | A17a, A17b Solving linear equations in one unknown algebraically where the unknown is on both sides of the equation,G3c The sum of angles in a triangle and the angle properties of polygons, polygons, exterior, sides, edges, writing setting up solve linear |
| Gradients | Gradients of straight lines, surds, rearranging | Mashup ★★ | A5a Rearranging formulas to change the subject N8b Surds A10a Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically slope standard |
| Not one in a million 🔒 | Standard form, multiples, probability | Mashup ★★ | N4b, N9c Adding and subtracting in standard form, P2a Theoretical probability, inequalities, integers, inequality, probabilities |
| Not standard form 🔒 | Standard form, Indices | Mashup ★★ | N9b Multiplying and dividing in standard form, A4i Index laws, powers, abases |
| Subprime 🔒 | Prime factorisation, algebraic fractions, index laws | Mashup ★★ | N4c Prime numbers and prime factorisation, A4f Simplifying, multiplying and dividing algebraic fractions, A4i Index laws and solving equations involving indices, Prime factors, factorize, factorise, factorization, factorisation, factoring, powers, indices, simplifying, lowest terms, substitute, substitution, substituting, cancelling |
| Prime terms 🔒 | Arithmetic, quadratic, and Fibonacci-type sequences, prime numbers | Mashup ★★ | N4c Prime numbers and prime factorisation, A24b - Recognising and using arithmetic, geometric and quadratic sequences, A24c - Recognising and using Fibonacci type sequences |
| Transforming sequences 🔒 | Arithmetic and quadratic sequences, squaring, finding square roots, expanding, factorising | Mashup ★★ | A24b - Recognising and using arithmetic, geometric and quadratic sequences, A24c - Recognising and using Fibonacci type sequences A25a - Finding the nth term of a linear sequence A25b - Finding the nth term of a quadratic sequence |
| Don't be a surd 🔒 | Surds, geometric sequences | Mashup ★★ | N8b Surds simplifying rationalising denominators, rationalizing, rationalise, rationalize |
| Irrational stats 🔒 | Surds, median, mode, range | Mashup ★★ | N8b Surds simplifying. rationalising denominators, rationalizing, rationalise, rationalize, Statistics, S4a S4b S4c S4d |
| Points 🔒 | Sequences, coordinates | Mashup ★★ | A25a - Finding the nth term of a linear sequence G7a - Coordinates |
| Symmetry and probability 🔒 | Lines of symmetry, probability | Mashup ★★ | G1c - Reflection symmetry, probability, P7a - Constructing theoretical possibility spaces for combined experiments with equally likely outcomes and use these to calculate theoretical probabilities, sample |
| Tiles 🔒 | Area, perimeter, simultaneous equations | Mashup ★★ | G16a G16b G16c Area of rectangles triangles parallelograms G17a Perimeter of polygons composite shapes made up of G17d |
| Rounding and inequalities 🔒 | Rounding, error intervals, inequalities | Mashup ★★ | N15a - Rounding and truncating N15b - Using inequality notation to specify simple error intervals A22a - Solving linear inequalities in one variable |
| Investments 🔒 | Compound interest, non-calculator skills | Shortcut ★★★ | R16a Growth and decay problems |
| Powerplay 🔒 | Index laws, simultaneous equations | Shortcut ★★★ | Powers, indices, A19a Solving two linear simultaneous equations algebraically by elimination A19b Solving two linear simultaneous equations graphically or algebraically by substitution A4i Index laws and solving equations involving indices |
| Round a rectangle 🔒 | Perimeter, circumference, circle theorems, Pythagoras' Theorem | Shortcut ★★★ | G10a, N8a, G20a, A21b, A18a, Solving quadratic by factorising Deriving and solving an equation or simultaneous equations to describe a situation, Perimeter, circumference, circle theorems, obling, rectangles, diagonals, pi, exact values, cyclic quadrilateral, angles in a semicircle 90º degrees, factorize, factorise, factorization, factorisation |
| Factorised fun 🔒 | Quadratic curves, roots, turning points, factorisation | Shortcut ★★★ | A18a A18b A18c Solving quadratic equations formula, A11b Identifying turning points of quadratic functions, A4e Factorising quadratics, Quadratic factors, factorize, factorise, factorization, factorisation, factorizing, solve solving equations completed completing the square form, turning minimum point maximum curve coordinates, parabolas |
| Not quite congruent 🔒 | Congruent triangles, sine rule | Shortcut ★★★ | G5a Congruence criteria for triangles (SSS, SAS, ASA, RHS), trigonometry, G22a The sine rule |
| Fib 🔒 | Fibonacci sequences, estimation | Shortcut ★★★ | A24c - Recognising and using Fibonacci type sequences, golden ratio, section, phi, N14a - Estimating answers and checking calculations |
| A quadratic sequence 🔒 | Quadratic sequences, quadratic equations | Shortcut ★★★ | A25b - Finding the nth term of a quadratic sequence, A18a - Solving quadratic equations by factorising A18b A18c completing the square using the quadratic formula |
| Widening range 🔒 | Mean, range, percentages | Mashup ★★★ | A21b Deriving and solving an equation or simultaneous equations to describe a situation, S4a S4b R9c Finding percentages and percentage changes multiplicatively using decimals, Average, spread, increase decrease percentage change |
| Square 🔒 | Area, coordinates, Pythagoras, surds, midpoints, circle theorems | Mashup ★★★ | G10a circle theorems angle in a semicircle 90º degrees G20a Pythagoras' theorem Pythagorean G11a Solve geometrical problems on coordinate axes Surds |
| In a spin 🔒 | Rotation, gradient | Mashup ★★★ | Perpendicular lines segments rotate rotating angle centre of |
| Perimeter bounds 🔒 | Perimeter, bounds, arithmetic sequences | Mashup ★★★ | Squares, rectangles, linear sequences, nth term, upper bounds, lower bounds, and, error intervals N15b Using inequality notation to specify simple error intervals N16a Applying and interpreting limits of accuracy, including upper and lower bounds G17a Perimeter of polygons A25a Finding the nth term of a linear sequence A23a A24b |
| A triangle and a circle 🔒 | Trigonometry, circle theorems | Mashup ★★★ | G10a circle theorems Segment angles G20b G20c inverse trigonometric functions right-angled triangles |
| Probability pi 🔒 | Trigonometry, circle theorems, probability | Mashup ★★★ | G10a circle theorems Segment angles G22b G23a cosine rule area of triangle using sine 1/2 absinC probability fraction P2a |
| Congruent chords 🔒 | Circle theorems, congruence, symmetry | Mashup ★★★ | G10a circle theorems Segment angles G5a G7a reflection rotation G1c G1d |
| From radius to angles to area | Circle theorems, ratios, trigonometry | Mashup ★★★ | G10a R5a Dividing a ratio in a given quantity, G23a area of triangle using sine ratio, radius, shaded area, triangle, sine 1/2 ab sinC 1/2absinc |
| Frusta 🔒 | Quadratic sequences, volume of a cone | Mashup ★★★ | G17g - Volume of spheres, pyramids, and cones A25b - Finding the nth term of a quadratic sequence A24b - Recognising and using arithmetic, geometric and quadratic sequences, frustums |
| Square and semicircle 🔒 | Circle theorems, Pythagoras, prime factors | Mashup ★★★ | G10a Circle theorems, G20a Pythagoras' theorem, N4c Prime numbers and prime factorisation, product decomposition Pythagorean |
| Intervowen area (dynamic) | Area of triangles, multiplying decimals, fractions, surds, algebraic expressions | Mashup ★★★ | N2b Multiplying positive integers N2f Applying the four operations to fractions N8b Surds A4b Multiplying a single term over a bracket A4d Multiplying two or more brackets G16c Area of triangles |
Enrichment course
The course is made up of fourteen sessions, which need to be delivered by a teacher. The sessions mainly cover areas of mathematics, science and philosophy that are not part of most schools’ curricula but are fascinating in their own right. Many of these underpin the great technological advances made over the last century.
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- Session 1: Start at zero, not one
- Session 2: Binary and the amazing quality of twoness
- Session 3: Three dimensions – and more
- Session 4: Pythagoras, Fermat, Wiles
- Session 5: Prime numbers and cryptography
- Session 6: Honeycombs
- Session 7: Lucky seven
- Session 8: Infinity
- Session 9: Proof
- Session 10: Elections and voting systems
- Session 11: Imaginary numbers
- Session 12: Time with Newton and Einstein
- Session 13: Beauty
- Session 14: Chaos and the weather in a fortnight
Quizzes
ompetitive team quizzes for the end of term!Christmas Quiz 2019Available to logged in users only  | Estimation QuizAvailable to logged in users only  |
Christmas Quiz 2018Available to all users – no login required!  |