·         Recall the properties and definitions of special types of quadrilaterals, including symmetry properties;

·         List the properties of each special type of quadrilateral, or identify (name) a given shape;

·         Draw sketches of shapes;

·         Name all quadrilaterals that have a specific property;

·         Identify quadrilaterals from everyday usage;

·         Given some information about a shape on coordinate axes, complete the shape;

·         Classify quadrilaterals by their geometric properties;

·         Understand and use the angle properties of quadrilaterals;

·         Use the fact that angle sum of a quadrilateral is 360°;

·         Use geometrical language appropriately and give reasons for angle calculations;

·         Recall and use properties of angles at a point, angles at a point on a straight line, right angles, and vertically opposite angles;

·         Distinguish between scalene, equilateral, isosceles and right-angled triangles;

·         Derive and use the sum of angles in a triangle;

·         Find a missing angle in a triangle, using the angle sum of a triangle is 180°;

·         Understand and use the angle properties of triangles, use the symmetry property of isosceles triangle to show that base angles are equal;

·         Use the side/angle properties of isosceles and equilateral triangles;

·         Show step-by-step deduction when solving problems;

·         Understand and use the angle properties of intersecting lines;

·         Understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices;

·         Solve linear equations which contain brackets, including those that have negative signs occurring anywhere in the equation, and those with a negative solution;

·         Solve linear equations in one unknown, with integer or fractional coefficients;

·         Rearrange simple equations;

·         Substitute into a formula, and solve the resulting equation;

·         Find an approximate solution to a linear equation using a graph;

·         Solve angle or perimeter problems using algebra.

·         Write an equation to solve a word problem.

·         Calculate the mean, mode, median and range for discrete data;

·         Can interpret and find a range of averages as follows:

·         median, mean and range from a (discrete) frequency table;

·         range, modal class, interval containing the median, and estimate of the mean from a grouped data frequency table;

·         mode and range from a bar chart;

·         median, mode and range from stem and leaf diagrams;

·         mean from a bar chart;

·         Understand that the expression 'estimate' will be used where appropriate, when finding the mean of grouped data using mid-interval values;

·         Compare the mean, median, mode and range (as appropriate) of two distributions using bar charts, dual bar charts, pictograms and back-to-back stem and leaf;

·         Recognise the advantages and disadvantages between measures of average.

·         Use input/output diagrams;

·         Use axes and coordinates to specify points in all four quadrants in 2D;

·         Identify points with given coordinates and coordinates of a given point in all four quadrants;

·         Find the coordinates of points identified by geometrical information in 2D (all four quadrants);

·         Find the coordinates of the midpoint of a line segment;

·         Draw, label and scale axes;

·         Read values from straight-line graphs for real-life situations;

·         Derive a simple formula, including those with squares, cubes and roots;

·         Substitute numbers into a word formula;

·         Substitute numbers into a formula.

·         Find missing angles using properties of corresponding and alternate angles;

·         Understand and use the angle properties of parallel lines.

       ·         Write expressions to solve problems representing a situation;

·         Substitute numbers in simple algebraic expressions;

·         Substitute numbers into expressions involving brackets and powers;

·         Substitute positive and negative numbers into expressions;

·         Add and subtract mixed number fractions;

·         Multiply mixed number fractions;

·         Divide mixed numbers by whole numbers and vice versa;

·         Find the reciprocal of an integer, decimal or fraction;

·         Understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number multiplied by its reciprocal is 1 (and that zero has no reciprocal because division by zero is not defined).

·         Show inequalities on number lines;

·         Write down whole number values that satisfy an inequality;

·         Solve an inequality such as –3 < 2x + 1 <7 and show the solution set on a number line;

·         Solve two inequalities in x, find the solution sets and compare them to see which value of x satisfies both;

·         Use the correct notation to show inclusive and exclusive inequalities;

·         Construct inequalities to represent a set shown on a number line;

·         Solve simple linear inequalities in one variable, and represent the solution set on a number line;

·         Round answers to a given degree of accuracy.

·         Use the nth term of an arithmetic sequence to decide if a given number is a term in the sequence, or find the first term over a certain number;

·         Use the nth term of an arithmetic sequence to find the first term greater/less than a certain number;

·         Continue a geometric progression and find the term-to-term rule, including negatives, fraction and decimal terms;

·         Continue a quadratic sequence and use the nth term to generate terms;

Distinguish between arithmetic and geometric sequences 

·         Find the area of a trapezium and recall the formula;

·         Find the area of a parallelogram;

·         Calculate areas and perimeters of compound shapes made from triangles and rectangles;

·         Estimate surface areas by rounding measurements to 1 significant figure;

·         Find the surface area of a prism;

·         Find surface area using rectangles and triangles;

·         Convert between metric area measures.

·         Draw scatter graphs;

·         Interpret points on a scatter graph;

·         Identify outliers and ignore them on scatter graphs;

·         Draw the line of best fit on a scatter diagram by eye, and understand what it represents;

·         Use the line of best fit make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing;

·         Distinguish between positive, negative and no correlation using lines of best fit;

·         Use a line of best fit to predict values of a variable given values of the other variable;

·         Interpret scatter graphs in terms of the relationship between two variables;

·         Interpret correlation in terms of the problem;

·         Understand that correlation does not imply causality;

·         State how reliable their predictions are, i.e. not reliable if extrapolated.

•         Generate points and plot graphs of simple quadratic functions, then more general quadratic functions;

•         Identify the line of symmetry of a quadratic graph;

•         Find approximate solutions to quadratic equations using a graph;

•         Interpret graphs of quadratic functions from real-life problems;

•         Identify and interpret roots, intercepts and turning points of quadratic graphs.

·         Recognise when values are in direct proportion by reference to the graph form;

·         Understand inverse proportion: as x increases, y decreases (inverse graphs done in later unit);

·         Recognise when values are in direct proportion by reference to the graph form;

·         Understand direct proportion ---> relationship y = kx.

·         Understand and express the division of a quantity into a of number parts as a ratio;

·         Write ratios in their simplest form;

·         Write/interpret a ratio to describe a situation;

·         Share a quantity in a given ratio including three-part ratios;

·         Solve a ratio problem in context:

·         use a ratio to find one quantity when the other is known;

·         use a ratio to compare a scale model to a real-life object;

·         use a ratio to convert between measures and currencies;

·         problems involving mixing, e.g. paint colours, cement and drawn conclusions;

·         Compare ratios;

·         Write ratios in form 1 : m or m : 1;

·         Write a ratio as a fraction;

·         Use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integer powers, fractions and powers of a power;

·         Use numbers raised to the power zero, including the zero power of 10;

·         Understand clockwise and anticlockwise;

·         Draw circles and arcs to a given radius or given the diameter;

·         Measure and draw lines, to the nearest mm;

·         Measure and draw angles, to the nearest degree;

·         Know and use compass directions;

·         Draw sketches of 3D solids;

·         Know the terms face, edge and vertex;

·         Identify and sketch planes of symmetry of 3D solids;

·         Use isometric grids to draw 2D representations of 3D solids;

·         Make accurate drawings of triangles and other 2D shapes using a ruler and a protractor;

·         Construct diagrams of everyday 2D situations involving rectangles, triangles, perpendicular and parallel lines;

·         Understand and draw front and side elevations and plans of shapes made from simple solids;

·         Given the front and side elevations and the plan of a solid, draw a sketch of the 3D solid.

·         Understand and use proportion as equality of ratios;

·         Solve word problems involving direct and indirect proportion;

·         Work out which product is the better buy;

·         Scale up recipes;

·         Convert between currencies;

·         Find amounts for 3 people when amount for 1 given;

·         Solve proportion problems using the unitary method;

·         Identify congruent shapes by eye;

·         Understand clockwise and anticlockwise;

·         Understand that rotations are specified by a centre, an angle and a direction of rotation;

·         Find the centre of rotation, angle and direction of rotation and describe rotations;

·         Describe a rotation fully using the angle, direction of turn, and centre;

·         Rotate a shape about the origin or any other point on a coordinate grid;

·         Draw the position of a shape after rotation about a centre (not on a coordinate grid);

·         Identify correct rotations from a choice of diagrams;

·         Understand that translations are specified by a distance and direction using a vector;

·         Translate a given shape by a vector;

·         Describe and transform 2D shapes using single translations on a coordinate grid;

·         Use column vectors to describe translations;

·         Understand that distances and angles are preserved under rotations and translations, so that any figure is congruent under either of these transformations.

·         Find the original amount given the final amount after a percentage increase or decrease (reverse percentages), including VAT;

·         Use calculators for reverse percentage calculations by doing an appropriate division;

·         Use percentages in real-life situations, including percentages greater than 100%;

·         Describe percentage increase/decrease with fractions, e.g. 150% increase means  times as big;

·         Understand that fractions are more accurate in calculations than rounded percentage or decimal equivalents, and choose fractions, decimals or percentages appropriately for calculations.

·         Understand that reflections are specified by a mirror line;

·         Identify correct reflections from a choice of diagrams;

·         Understand that reflections are specified by a mirror line;

·         Identify the equation of a line of symmetry;

·         Transform 2D shapes using single reflections (including those not on coordinate grids) with vertical, horizontal and diagonal mirror lines;

·         Describe reflections on a coordinate grid;

·         Scale a shape on a grid (without a centre specified);

·         Understand that an enlargement is specified by a centre and a scale factor;

·         Enlarge a given shape using (0, 0) as the centre of enlargement, and enlarge shapes with a centre other than (0, 0);

·         Find the centre of enlargement by drawing;

·         Describe and transform 2D shapes using enlargements by:

·         a positive integer scale factor;

·         a fractional scale factor;

·         Identify the scale factor of an enlargement of a shape as the ratio of the lengths of two corresponding sides, simple integer scale factors, or simple fractions;

·         Understand that distances and angles are preserved under reflections, so that any figure is congruent under this transformation;

·         Understand that similar shapes are enlargements of each other and angles are preserved – define similar in this unit;

·         Describe and transform 2D shapes using combined rotations, reflections, translations, or enlargements.

•         construct the perpendicular bisector of a given line;

•         construct the perpendicular from a point to a line;

•         construct the bisector of a given angle;

•         construct angles of 90°, 45°;

·         Select an expression/equation/formula/identity from a list;

·         Write expressions and set up simple equations;

·         Use function machines;

·         Solve simple equations;

·         Solve linear equations, with integer coefficients, in which the unknown appears on either side or on both sides of the equation;

·         Multiply a single number term over a bracket;

·         Write and simplify expressions using squares and cubes;

·         Simplify expressions involving brackets, i.e. expand the brackets, then add/subtract;

·         Argue mathematically to show algebraic expressions are equivalent;

·         Recognise factors of algebraic terms involving single brackets;

·         Factorise algebraic expressions by taking out common factors.

·         Calculate perimeters and areas of composite shapes made from circles and parts of circles;

·         Calculate arc lengths, angles and areas of sectors of circles;

·         Find the surface area of a cylinder;

·         Find the volume of a cylinder;

·         Find the surface area and volume of spheres, pyramids, cones and composite solids;

·         Round answers to a given degree of accuracy.

 ·         Add and subtract mixed number fractions;

·         Multiply mixed number fractions;

·         Divide mixed numbers by whole numbers and vice versa;

·         Find the reciprocal of an integer, decimal or fraction;

·         Understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number multiplied by its reciprocal is 1 (and that zero has no reciprocal because division by zero is not defined).

·         Recall the definition of a circle;

·         Identify, name and draw parts of a circle including tangent, chord and segment;

·         Recall and use formulae for the circumference of a circle and the area enclosed by a circle circumference of a circle = 2πr = πd, area of a circle = πr2;

·         Find circumferences and areas enclosed by circles;

·         Use π ≈ 3.142 or use the π button on a calculator;

·         Give an answer to a question involving the circumference or area of a circle in terms of π;

·         Find radius or diameter, given area or perimeter of a circles;

·         Find the perimeters and areas of semicircles and quarter-circles;

·         Find the probability of an event happening using relative frequency;

·         Estimate the number of times an event will occur, given the probability and the number of trials – for both experimental and theoretical probabilities;

·         List all outcomes for combined events systematically;

·         Use and draw sample space diagrams;

·         Draw straight line graphs for real-life situations, including ready reckoner graphs, conversion graphs, fuel bills graphs, fixed charge and cost per unit;

·         Draw distance–time graphs and velocity–time graphs;

·         Work out time intervals for graph scales;

·         Interpret distance–time graphs, and calculate: the speed of individual sections, total distance and total time;

·         Interpret information presented in a range of linear and non-linear graphs;

·         Interpret graphs with negative values on axes;

·         Interpret gradient as the rate of change in distance–time and speed–time graphs, graphs of containers filling and emptying, and unit price graphs.