Key Stage 2 Step 1- Step 2 Key Stage 2 Key Stage 3 Step 3 - Step 4 Key Stage 3 Key Stage 4 Step 5 - Step 6 ≈ GCSE grade 3 - 4 Key Stage 4 Step 7 - Step 8 ≈ GCSE grade 4 - 7 Key Stage 4 Step 9 - Step 12 ≈ GCSE grade 7 - 9

Step 1

 Topic: Lesson: Topic: Lesson: Number Read and write large numbers Number Indentify numbers Number Round positive whole numbers to the nearest 10, 100 or 1000 Number Round using decimal places Number Round using significant figures Number Estimate numbers Number Using an empty number line Number Use standard column procedures to add and subtract whole numbers Number Multiply and divide integers by 10 and 100, and explain the effect Number Long and short multiplication Number Long and short division Number Know and use the order of operations Number Apply simple tests of divisibility Number order positive and negative integers Statistics Find range from a set of ordered data Geometry and measures Know the names of 2d shapes Geometry and measures Identify and name common solids: cube, cuboid, cylinder, prism, pyramid, sphere and cone Geometry and measures Know the terms face, edge and vertex Geometry and measures Use a protractor to measure acute angles to the nearest degree Geometry and measures Distinguish between acute, obtuse and reflex angles Geometry and measures Know the sum of angles on a straight line Geometry and measures Find the perimeter of a square/rectangle by counting Geometry and measures Identify complex arrangements of a net of a cube Geometry and measures Work out time intervals Geometry and measures Read and interpret scales on a range of measuring instruments Geometry and measures Suggest suitable units to estimate or measure length, mass and capacity Geometry and measures Identify all the symmetries of 2-D shapes

Step 2

 Topic: Lesson: Topic: Lesson: Number Understand addition and subtraction as they apply to whole numbers and decimals Number Be able to use > or < correctly between two positive decimals. Decimals should be to 4 or 5 significant figures Number Be able to order positive decimals. Decimals should be to 4 or 5 significant figures Geometry and measures Know the sum of angles round a point Geometry and measures Explain why some shapes tessellate and why other shapes do not Geometry and measures Find the perimeter of a shape Geometry and measures Choose suitable metric units to estimate length and area Geometry and measures Identify quadrilaterals from their properties Geometry and measures Know the sum of angles in a triangle is 180° Geometry and measures Know the sum of angles in a quadrilateral is 360° Geometry and measures Translate a shape on a square/coordinate grid Geometry and measures Recognise and visualise the reflection in a mirror line of a 2-D shape Ratio, proportion and rates of change Read and construct scale drawings Statistics Calculate Mode Statistics Calculate Median Statistics Calulate mean

Step 3

 Topic: Lesson: Topic: Lesson: Number Understand multiplication as it applies to decimals Number Understand division as it applies to decimals Number Recognise and use multiples Number Recognise and use factors Number Identify numbers with exactly 2 factors (primes) Number Understand how to find common multiples Number Understand how to find the common factors Number Knowing simple Fraction, Decimal and Percentage equivalents Number Convert percentages to fractions out of 100 Number Convert percentage to decimals Number Convert terminating decimals to fractions, e.g. 0.23 = 23/100 Number Calculating simple percentages without a calculator Number Find roots of square numbers upto 100 (i.e. roots upto 10) Algebra Find outputs and inputs of more complex functions expressed in words (e.g. add 6 then multiply by 3) Algebra Use function machines to find coordinates Algebra Read values from straight-line graphs for real-life situations Algebra Drawing straight-line graphs for real-life situations Algebra Read and plot co-ordinates in all four quadrants Algebra Be able to interpret inequalities and show on a number line Algebra Generate terms of a simple sequence using term to term rule Algebra Generate and describe simple integer sequences – square and triangle numbers Algebra Generate terms of a simple sequence arising from practical contexts (Pictorial) Probability Use a probability scale with words Probability Mark events and/or probabilities on a probability scale of 0 to 1 Statistics Represent data in a table (Tally chart) Statistics Extract data and interpret discrete bar charts Statistics Construct simple bar charts to represent discrete data Statistics Produce dual bar charts Statistics Produce pictograms Statistics Find the mode and range from a bar chart Statistics Interpret simple pie charts using simple fractions and percentages Geometry and measures Using correct notation to label lines, angles and triangles Geometry and measures Use the formula for the area of a rectangle/square Geometry and measures Use the formula for the area of a triangle Geometry and measures Calculate the surface area of cubes with a net Geometry and measures Calculate perimeter and area of compound shapes made from triangles, rectangles Geometry and measures Identify simple angle, side and symmetry properties of triangles Geometry and measures Identify angle, side and symmetry properties of simple quadrilaterals Geometry and measures Recognise and visualise – rotation about a given point (rotation point must be outside the shape) Geometry and measures Begin to estimate the size of angles Ratio, proportion and rates of change Use fraction notation to describe parts of shapes Ratio, proportion and rates of change Recognise the equivalence of percentages, fractions and decimals

Step 4

 Topic: Lesson: Topic: Lesson: Number Multiply three-digit by two-digit whole numbers Number Begin to add and subtract simple fractions and those with simple common denominators Number Add and subtract positive integers from negative integers Number Multiply and divide negative integers by a positive and negative numbers Number Add and subtract integers - positive and negative numbers Number Use inverse operations Number Simplify fractions by cancelling all common factors Number primes factor decomposition Number Calculate simple fractions of quantities and measurements (whole-number answers) Number Extend the percentage calculation strategies with jottings to find any percentage, e.g. 17.5% by finding 10%, 5% and 2.5%, and adding Number Use index notation for squares and cubes and for positive integer powers of 10 (e.g. write 27 as 3³ and 1000 as 10³) Number Be able to order negative decimals with the smallest on the left. Decimals should be to 2 or 3 significant figures Number Order fractions, decimals and percentages Algebra Substitute positive integers into simple formulae expressed in letter symbols, e.g. a+/- b, a × b Algebra Substitute integers into more complex formulae expressed in letter symbols, e.g. a/b, ax +/- b Algebra simplify algebraic expressions by collecting like terms Algebra Form expression from words Algebra Plot a simple distance-time graph (straight-line graphs) Algebra Plot and draw vertical and horizontal line graphs Algebra Generate terms of a linear sequence using term-to-term using positive or negative integers Algebra Multiply together two simple algebraic expressions, e.g. 2a × 3b Probability Apply the property that the probabilities of an exhaustive set of outcomes sum to 1 Probability Identify all possible mutually exclusive outcomes of a single event Probability Know that if the probability of an event is p, the probability of it not occurring is 1-p Probability Compare experimental and theoretical probabilities Statistics Extract data and interpret frequency tables Statistics Find the modal class for a small set of grouped discrete data Statistics Use information provided to complete a two-way table Statistics Produce pie-charts Statistics Compare two simple distributions using the range and the median Statistics Calculate the mean from a simple frequency table Statistics Compare two simple distributions using the mean Statistics Interpret data from simple compound and comparative bar charts Statistics find the range and modal class interval from grouped data Statistics Calculate the interval from grouped data containing the median Statistics Estimate the mean from a grouped frequency table Geometry and measures Identify interior and exterior angles in a shape Geometry and measures Recognise and use vertically opposite angles Geometry and measures Derive and use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles Geometry and measures Calculate the surface area of simple cuboids (without use of nets) Geometry and measures Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) Geometry and measures Begin to use plans and elevations Geometry and measures Solve simple problems involving units of measurement in the context of length and area Geometry and measures Draw or complete diagrams with a given number of lines of symmetry Probability Mutually exclusive outcomes Ratio, proportion and rates of change Recognise and visualise the rotational symmetry of a 2-D shape Geometry and measures Solve geometric problems using side and angle properties of equilateral and isosceles triangles Geometry and measures Solve simple geometrical problems using properties of quadrilaterals Geometry and measures Give a bearing between 2 points Ratio, proportion and rates of change Express the division of a quantity into a number of parts as a ratio Ratio, proportion and rates of change Convert between simple metric units Ratio, proportion and rates of change Express one number as a fraction of another Ratio, proportion and rates of change Divide a quantity into two parts in a given ratio, where ratio given in ratio notation Ratio, proportion and rates of change Use percentages to compare simple proportions Ratio, proportion and rates of change Express one given number as a percentage of another Ratio, proportion and rates of change Find a percentage of a quantity using a multiplier Ratio, proportion and rates of change Interpet percentages and percentage change as a fraction or a decimal Ratio, proportion and rates of change Use ratio notation Ratio, proportion and rates of change Reduce a ratio to its simplest form

Step 6

 Topic: Lesson: Topic: Lesson: Number Identify upper and lower bounds for rounding of discrete and continuous data Number Write numbers as a decimal number of millions or thousands, e.g. 23 600 000 as 23.6 million Number Divide an integer by a fraction Number Understand which part of an expression is raised to a power by knowing the difference between 3 × (7 + 8)² and 3² × (7 + 8) and (3 × (7 + 8))² Number Calculate average speed, distance, time - in mph as well as metric measures Number Understand the effect of multiplying or dividing any number between 0 and 1 Number Multiply simple fractions (proper and improper) - Number Divide simple fractions (proper and improper) Number Use halving and doubling strategies on fractions to find decimal equivalents of other fractions, e.g. 1/4 = 0.25 so 1/8 is half of 0.25 etc. Original fact is given Number Establish multiplying and dividing index laws Number index laws for powers of 1 and 0 Number Use an extended range of calculator functions, including +, -, x, , x², √x, memory, xy, x1/y, brackets Algebra Substitute positive integers into expressions involving small powers (up to 3) Algebra Expand single brackets Algebra Expand two single brackets and simplify Algebra Manipulate expressions by taking out common factors, not necessarily the highest e.g. 4x + 8 = 2(2x + 4) Algebra Change the subject of a formula in one step e.g. y = x + 4 Algebra Begin to consider the features of graphs of simple linear functions, where y is given explicitly in terms of x, e.g. y = x, y = 2x, y = 3x are all straight lines that pass through the origin, vary in steepness depending on the function Algebra Draw velocity-time graphs Algebra Find the coordinates of the midpoint of a line from a given graph Algebra Recognise that equations of the form y = mx + c correspond to straight-line graphs in the coordinate plane Algebra Write down whole number values that satisfy an inequality Algebra Find a specific term in the sequence using position-to-term rules Probability complete a probability tree diagram based on given information (no more than 3 branches per event) Probability Use tree diagrams to calculate the probability of two independent events Statistics Produce ordered back-to-back stem and leaf diagrams Statistics Recognise when it is appropriate to use mean, median or mode in more complex cases (put in extreme values) Statistics Construct and use frequency polygons to compare sets of data Statistics Identify and explain anomalies (outliers) in a data set Statistics Recognise types of quantitative and qualitative data Statistics Understand what is meant by a sample and a population Statistics Understand primary and secondary data sources Geometry and measures Identify co-interior angles and their values Geometry and measures Calculate exterior angles of any polygon using the sum is 360° Geometry and measures Calculate the interior angles of polygons Geometry and measures Use a formula to calculate the area of trapezia Geometry and measures Use the formula for the circumference of a circle Geometry and measures Use the formulae for area of a circle, given the radius or diameter Geometry and measures Use straight edge and compasses to construct the bisector of an angle Geometry and measures Use straight edge and compasses to construct a triangle given three sides (SSS) Geometry and measures Construct an equilateral triangle Geometry and measures Construct a regular hexagon inside a circle Geometry and measures Begin to use the trigonometric ratios to find the size of an angle in a right-angled triangle Geometry and measures Enlarge 2-D shapes, given a centre of enlargement and a positive whole number scale factor Geometry and measures Find the centre of enlargement Ratio, proportion and rates of change Write ratios in the form 1: m or m: 1 Ratio, proportion and rates of change Know rough metric equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons) Ratio, proportion and rates of change Convert between area measures (e.g. mm² to cm², cm² to m², and vice versa) Ratio, proportion and rates of change Convert between metric measures of volume and capacity eg 1 cm³ = 1 ml Ratio, proportion and rates of change Use a unitary method, e.g. if £40 is 60%, find 1% by dividing by 60 and then 100% by multiplying by 100. Give them the scaffolding to answer the question Ratio, proportion and rates of change Use percentages in real life simple interest, income tax calculations Ratio, proportion and rates of change Use and interpret maps, using proper map scales (1 : 25 000)

Step 7

 Topic: Lesson: Topic: Lesson: Number Find the reciprocal of simple numbers/fractions mentally, e.g. 10 and 1/10, 1/3 and 3 etc. Know that a number multiplied by its reciprocal is 1 Number Understand and use compound measures: density; pressure; speed Number Use the index laws to include negative power answers Number Convert between currencies Number Write numbers greater than 10 in standard index form Algebra Use systematic trial and improvement to find the approximate solution to one decimal place of equations such as x³ = 29 Algebra solve equations that involves multiplying out brackets by a negative number (e.g. 4(2a - 1) = 32 - 3(2a - 2)) Algebra Multiply out double brakets and collect like terms Algebra Substitute positive and negative integers into linear expressions and expressions involving powers Algebra Factorise to one bracket by taking out the highest common factors for all terms e.g. 2x²y + 6xy² = 2xy(x + 3y) Algebra Find an unknown where it is not the subject of the formula and where an equation must be solved Algebra Identify parallel lines from their equations Algebra Generate points and plot graphs of simple quadratic functions Algebra Construct a table of values, including negative values of x for a function such as y = ax² Algebra Recognise that linear functions can be rearranged to give y explicitly in terms of x e.g. rearrange y + 3x - 2 = 0 in the form y = 2 - 3x Algebra Solve simple linear inequalities in one variable and represent the solution on a number line Probability Record outcomes of events in a Venn Diagram Statistics Find the median, mode and range from a stem and leaf diagram Statistics Understand that the frequency represented by corresponding sectors in two pie charts is dependent upon the total populations represented by each of the pie charts Statistics Know the definition and methods of random sampling Statistics Scattergraphs - Use a line of best fit, or otherwise, to predict values of one variable given values of the other variable Geometry and measures Calculate the volume of prisms Geometry and measures Calculate the surface area of prisms Geometry and measures Calculate the lengths and areas given the volumes in right prisms Geometry and measures Calculated volumes in cylinders Geometry and measures Find the perimeters and areas of semicircles and quarter circles Geometry and measures Use the information given about the length of sides and sizes of angles to determine whether triangles are congruent Geometry and measures Use straight edge and compass to construct the perpendicular from a point on a line segment Geometry and measures Understand loci about a point, line and corner Geometry and measures Construct angles of 60°, 90°, 30°, 45° Geometry and measures Know the formula for Pythagoras' theorem and use to find the hypotenuse Geometry and measures describe and Use vector notation for translations Geometry and measures describe an enlargement Geometry and measures Describe a rotation transformation Geometry and measures Describe reflections transformaion Ratio, proportion and rates of change Use algebraic methods to solve problems involving variables in direct proportion Ratio, proportion and rates of change Use expressions of the form y α 1/x Ratio, proportion and rates of change Calculate compound interest Ratio, proportion and rates of change Use measures in ratio and proportion problems (best value)

Step 8

 Topic: Lesson: Topic: Lesson: Number Multiply and divide simple fractions (mixed) - Number Calculate with roots (surds - exact values) Number Write numbers less than 10 in standard index form Number Order numbers written in standard index form Number Add and subtract in standard form Number Multiply and divide numbers in standard form Algebra Find the equation of a straight-line from its graph Algebra Recognise that when the linear and inverse of a linear function such as y = 2x, y = 3x are plotted, they are a reflection in the line y = x Algebra Interpret distance-time graphs and calculate the speed of individual sections, total distance and total time Algebra Interpret gradient as rate of change in distance-time and speed-time graphs, containers emptying and filling and unit price graphs Algebra Identify and interpret roots, intercepts and turning points of a quadratic graph Algebra Given the coordinates of points A and B, calculate the length of AB Algebra Plot and draw graphs of straight lines WITHOUT using a table of values (use intercept and gradient) Algebra Recognise a quadratic function from its equation and explain the shape of it's graph Algebra Solve more complex linear inequalities in one variable and represent the solution on a number line Algebra Use algebra to support proofs e.g. show that the volume of a cube with side lengths of (2x - 1)cm is (8x³ - 12x² + 6x - 1)cm³ Algebra Identify which terms cannot be in a sequence Algebra Recognise and use simple geometric progressions (rn where n is an integer and r is a rational number number Algebra By looking at the spatial patterns of triangular numbers, deduce that the nth term is 1/2n(n + 1) Algebra Solve linear/linear simultaneous equations graphically Algebra Solve simultaneous equations where neither or one equation needs multiplying Algebra Set up and solve a pair of simultaneous equations in two variables Algebra Solve simultaneous equations representing a real-life situation Probability Use tree diagrams to calculate the probability of two dependent events Statistics Construct cumulative frequency tables and draw the graph Statistics Interpret box plots to find median, quartiles, range and interquartile range Statistics Produce box plots from raw data and identify outliers when given quartiles and median Geometry and measures Find the surface area and volumes of compound solids constructed from cubes, cuboids, cones, pyramids, spheres, hemispheres, cylinders Geometry and measures Recognise the formulae for length of arcs in a circle Geometry and measures Recognise the formulae for area of sectors in a circle Geometry and measures Use simple examples of the relationship between enlargement and areas and volumes of simple shapes and solids Geometry and measures Know the formula for Pythagoras' theorem and use to find a shorter side Geometry and measures Use Trigonometry to find unknown sides of a right angled triangle Geometry and measures Use Trigonometry to find missing angles of a right angled triangle Geometry and measures Add and Subtract vectors

Step 9

 Topic: Lesson: Topic: Lesson: Algebra Change the subject of a complex formula that involves fractions, e.g. make u or v the subject of the formula 1/v + 1/u =1/t Algebra Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function Algebra Recognise, sketch and interpret graphs of simple cubic functions Algebra Recognise, sketch and interpret reciprocal graphs Algebra Solve linear inequalities in two variables graphically Algebra Answer simple proof and 'show that' questions using consecutive integers (n, n+ 1), squares a², b², even numbers 2n, and odd numbers 2n + 1 Algebra Continue a quadratic sequence and use the nth term to generate terms Algebra Cube a linear expression and simplify Statistics Interpret cumulative frequency graphs Statistics Compare the measures of spread between a pair of box plots/cumulative frequency graphs Geometry and measures Prove and use the fact that the angle in a semicircle is a right angle ; Geometry and measures Prove and use the fact that opposite angles of a cyclic quadrilateral sum to 180° Geometry and measures Prove and use the fact that angles in the same segment are equal Geometry and measures Prove and use facts about the angle subtended at the centre and at the circumference; Geometry and measures Know that the tangent at any point on a circle is perpendicular to the radius at that point Geometry and measures Find angles of elevation and angles of depression Ratio, proportion and rates of change Use expressions of the form y α x²

Step 10

 Topic: Lesson Topic: Lesson: Number Use the product rule for counting (i.e. if there are m ways of doing one task and for each of these, there are n ways of doing another task, then the total number of ways the two tasks can be done is m × n ways) Number Convert a recurring decimal to a fraction in simple cases Algebra Deduce turning points by completing the square Algebra Sketch a graph of a quadratic by factorising, identifying roots and y-intercept , turning point Algebra Find the equation of the line through two given points Algebra Find the equation of the line through one point with a given gradient Algebra Know that a line perpendicular to the line y = mx + c, will have a gradient of -1/m Algebra Finding the equation of a circle on a graph Algebra Simplify and manipulate algebraic expressions involving surds and algebraic fractions Algebra Find approximate solutions to simultaneous equations formed from one linear function and one non-linear ( quadratic or circle) function using a graphical approach Probability Use Venn diagrams to calculate conditional probability Statistics Stratified sampling - know the definition and state in terms of proportion, fraction, percentage or ratio Geometry and measures Prove and use the alternate segment theorem Geometry and measures Understand, recall and use Pythagoras' theorem in 3-D problems Geometry and measures Enlarge 2D shapes, given a negative, fractional scale factor Geometry and measures Know and apply the sine rule a/sin A = b/sin B = c/sin C to find unknown lengths and angles Geometry and measures know and apply the cosine rule a² = b² + c² – 2bc cos A to find unknown lengths Geometry and measures Calculate the area of a triangle given the length of two sides and the included angle Geometry and measures Work out the magnitude of a vector Algebra Solve a quadratic equation by completing the square Algebra Solve quadratic equations using the formula

Step 11

 Topic: Lesson: Topic: Lesson: Number Calculate the upper and lower bounds of 2-D measurements e.g. area Number Write (3 - √3)² in the form a + b√3 Number Rationalise a denominator Algebra Apply to the graph of y = f(x) the transformations y = f(x) + a y = f(ax) y = f(x + a) y = af(x) for linear, quadratic Algebra Apply to the graph of y = f(x) the transformations cubic, sine and cosine functions f(x) Algebra Find the gradient of the radius that meets the circle at a given point Algebra Find the nth term of a quadratic sequence of the form n² ,an², an² ± b, an² ± bn ± c, Algebra Solve exactly, by elimination of an unknown, linear/x² + y² = r² simultaneous equations Statistics Construct and interpret histograms from class intervals with unequal width and From a histogram complete a grouped frequency table Geometry and measures know and apply the cosine rule a² = b² + c² – 2bc cos A to find unknown angles

Step 12

 Topic: Lesson: Topic: Lesson: Algebra Interpret the gradient of linear or non-linear graphs, and estimate the gradient of a quadratic or non-linear graph at a given point by sketching the tangent and finding its gradient Algebra Interpret coodinates for trigonometric graphs Algebra Plot graphs of the exponential function y = abx for integer values of x and simple positive values of a and b Algebra Use iteration with simple converging sequences Algebra Recursive Iteration Geometry and measures Solve problems involving more complex shapes and solids, including segments of circles and frustums of cones Geometry and measures Find the area of a segment of a circle given the radius and length of the chord Geometry and measures Solve problems for areas and volumes of similar shapes and solids Geometry and measures Use the trigonometric ratios to solve 3-D problems Geometry and measures Apply vector methods for simple geometrical proofs