# Printable Cards - Landscape!

These are the statements, each one preceeded with the words "Pupils should be taught to:". Print onto card (landscape) then cut them out for your sorting or grouping activities.

### Number (01)

...apply systematic listing strategies, {including use of the product rule for counting}

### Number (02)

...{estimate powers and roots of any given positive number}

### Number (03)

...calculate with roots, and with integer {and fractional} indices

### Number (04)

...calculate exactly with fractions, {surds} and multiples of π ; {simplify surd expressions involving squares [for example √12 = √(4 × 3) = √4 × √3 = 2√3] and rationalise denominators}

### Number (05)

...calculate with numbers in standard form A × 10n, where 1≤A<10 and n is an integer

### Number (06)

...{change recurring decimals into their corresponding fractions and vice versa}

### Number (07)

...identify and work with fractions in ratio problems

### Number (08)

...apply and interpret limits of accuracy when rounding or truncating, {including upper and lower bounds}

### Algebra (01)

...simplify and manipulate algebraic expressions (including those involving surds {and algebraic fractions}) by: factorising quadratic expressions of the form x2 + bx + c, including the difference of 2 squares; {factorising quadratic expressions of the form ax2 + bx + c} and by simplifying expressions involving sums, products and powers, including the laws of indices

### Algebra (02)

...know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments {and proofs}

### Algebra (03)

...where appropriate, interpret simple expressions as functions with inputs and outputs; {interpret the reverse process as the ‘inverse function’; interpret the succession of 2 functions as a ‘composite function’}

### Algebra (04)

...use the form y = mx + c to identify parallel {and perpendicular} lines; find the equation of the line through 2 given points, or through 1 point with a given gradient

### Algebra (05)

...identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square}

### Algebra (06)

...recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y =  with x not equal to 0, {the exponential function y = kx for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size}

### Algebra (07)

...{sketch translations and reflections of the graph of a given function}

### Algebra (08)

...plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration

### Algebra (09)

...{calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts}

### Algebra (10)

...{recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point}

### Algebra (11)

...solve quadratic equations {including those that require rearrangement} algebraically by factorising, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph

### Algebra (12)

...solve 2 simultaneous equations in 2 variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph

### Algebra (13)

...{find approximate solutions to equations numerically using iteration}

### Algebra (14)

...translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or 2 simultaneous equations), solve the equation(s) and interpret the solution

### Algebra (15)

...solve linear inequalities in 1 {or 2} variable {s}, {and quadratic inequalities in 1 variable}; represent the solution set on a number line, {using set notation and on a graph}

### Algebra (16)

...recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (rn where n is an integer, and r is a positive rational number {or a surd}) {and other sequences}

### Algebra (17)

...deduce expressions to calculate the nth term of linear {and quadratic} sequences.

### Ratio and Proportion (01)

...compare lengths, areas and volumes using ratio notation and/or scale factors; make links to similarity (including trigonometric ratios)

### Ratio and Proportion (02)

...convert between related compound units (speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts

### Ratio and Proportion (03)

...understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y ; {construct and} interpret equations that describe direct and inverse proportion

### Ratio and Proportion (04)

...interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion

### Ratio and Proportion (05)

...{interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of instantaneous and average rate of change (gradients of tangents and chords) in numerical, algebraic and graphical contexts}

### Ratio and Proportion (06)

...set up, solve and interpret the answers in growth and decay problems, including compound interest {and work with general iterative processes}

### Geometry and measures (01)

...interpret and use fractional {and negative} scale factors for enlargements

### Geometry and measures (02)

...{describe the changes and invariance achieved by combinations of rotations, reflections and translations}

### Geometry and measures (03)

...identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

### Geometry and measures (04)

...{apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results}

### Geometry and measures (05)

...construct and interpret plans and elevations of 3D shapes

### Geometry and measures (06)

...interpret and use bearings

### Geometry and measures (07)

...calculate arc lengths, angles and areas of sectors of circles

### Geometry and measures (08)

...calculate surface areas and volumes of spheres, pyramids, cones and composite solids

### Geometry and measures (09)

...apply the concepts of congruence and similarity, including the relationships between lengths, {areas and volumes} in similar figures

### Geometry and measures (10)

...apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in 2 {and 3} dimensional figures

### Geometry and measures (11)

...know the exact values of the sine and cosine of 30, 45, 60 and 90 degrees; know the exact value of the tangent of 30, 45, and 60 degrees

### Geometry and measures (12)

...{know and apply the sine and cosine rules to find unknown lengths and angles}

### Geometry and measures (13)

...{know and apply Area =  ½ ab sin C to calculate the area, sides or angles of any triangle}

### Geometry and measures (14)

...describe translations as 2D vectors

### Geometry and measures (15)

...apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; {use vectors to construct geometric arguments and proofs}

### Probability (01)

...apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to 1

### Probability (02)

...use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size

### Probability (03)

...calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions

### Probability (04)

...{calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams}

### Statistics (01)

...infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling

### Statistics (02)

...interpret and construct tables and line graphs for time series data

### Statistics (03)

...{construct and interpret diagrams for grouped discrete data and continuous data, ie, histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use}

### Statistics (04)

...interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate graphical representation involving discrete, continuous and grouped data, {including box plots} and appropriate measures of central tendency (including modal class) and spread {including quartiles and inter-quartile range}

### Statistics (05)

...apply statistics to describe a population

### Statistics (06)

...use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing.

For Students:

For All: