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

# Step 1

 Topic: Lesson: Topic: Lesson: Number Read and write large numbers Statistics Range Number Identifying values Geometry and measures Naming 2D shapes Number Rounding whole numbers Geometry and measures Features of 3D shapes Number Rounding to decimal places Geometry and measures Know the terms face, edge and vertex Number Rounding to significant figures Geometry and measures Measuring angles using a protractor Number Rounding to estimation Geometry and measures Recognising types of angles Number Using an empty number line Geometry and measures Angles on a straight line Number Column addition and subtraction Geometry and measures Area and perimeter of a rectangle counting squares Number Multiply and divide by powers of 10, 100, and 1000 Geometry and measures The net of a cube Number Standard methods for multiplication Geometry and measures Calculating time intervals Number Standard methods for division Geometry and measures Reading units on scales Number BIDMAS Geometry and measures Units to estimate length, mass and capacity Number Divisibility tests Geometry and measures Identify lines of symmetry on 2D shapes Number Introducing negative numbers

# Step 2

 Topic: Lesson: Topic: Lesson: Number Adding and subtracting decimals Geometry and measures Choosing appropriate metric units for measuring Number Introducing inequality signs Geometry and measures Identifying quadrilaterals Number Ordering decimals Ratio, proportion and rates of change Translating a shape on a grid Geometry and measures Angles around a point Statistics Mode Geometry and measures Tessellation Statistics Calculate median Geometry and measures Perimeter of a shape Statistics Mean average

# Step 3

 Topic: Lesson: Topic: Lesson: Number Multiplying decimals Algebra Generate terms of a pictorial sequence Number Dividing decimals Probability Use a probability scale with words Number Recognise and use multiples Probability Use a probability scale with 0 to 1 Number Factors Statistics Tally charts Number Prime numbers Statistics Extract data and interpret discrete bar Number Common multiples Statistics Construct simple bar charts Number Commonfactors Statistics Dual bar charts Number Knowing simple fraction, decimal and percentage equivalents Statistics Pictograms Number Convert percentages to fractions out of 100 Statistics Find range and mode from a bar chart Number Convert percentages to decimals Statistics Interpret simple pie charts Number Convert terminating decimals to fractions Geometry and measures Labelling lines, angles, and triangles Number Calculate simple percentages Geometry and measures Area of squares and rectangles using the formula Number Roots of square numbers Geometry and measures Use the formula for the area of a triangle Algebra Inputs and outputs of more complex functions expressed in words Geometry and measures Surface area of a cube using nets Algebra Using function machines to find coordinates Geometry and measures Perimeter of compound shapes Algebra Read values from straight line graphs Geometry and measures Properties of triangles Algebra Drawing and plotting straight line graphs Geometry and measures Properties of quadrilaterals Algebra Read and plot coordinates in all four quadrants Geometry and measures Rotation around a point Algebra Interpret inequalities and show on a number line Geometry and measures Begin to estimate the size of angles Algebra Generate terms of a simple sequence using term to term rules Ratio, proportion and rates of change To identify fractions Algebra Generate sequences of square and triangle numbers Ratio, proportion and rates of change Simple fraction, decimal and percentage equivalents

# Step 4

 Topic: Lesson: Topic: Lesson: Number Multiply 3 digit by 2 digit numbers Statistics Calculate the mean from a frequency table Number Adding and subtracting simple fractions Statistics Compare distributions using mean Number Add and subtract from negatives Statistics Compound and comparative bar charts Number Multiply and divide negative numbers Statistics Find range and mode from grouped data Number Add and subtract integers from positive and negative numbers Statistics Calculate the interval from grouped data containing median Number Inverse operations Statistics Estimate the mean Number Simplifying fractions Geometry and measures Interior and exterior angles Number Prime factor decomposition Geometry and measures Vertically opposite angles Number Fractions of quantities and measurements Geometry and measures Exterior angles in a triangle Number 17.5% Geometry and measures Calculate the surface area of a cuboid Number Index notation Geometry and measures Congruent triangles Number Ordering negative numbers Geometry and measures Plans and elevations Number Order fractions, decimals and percentages Geometry and measures Solve simple problems with length and area Algebra Substitute positive integers into simple formulae Geometry and measures Draw diagrams with lines of symmetry Algebra Substitute positive and negative integers into simple formulae Geometry and measures Rotational symmetry Algebra Collecting like terms Geometry and measures Identify the order of rotational symmetry Algebra Forming expressions from words Geometry and measures Solving problems using properties of triangles Algebra Plot a simple time distance graph Geometry and measures Solving problems using properties of quadrilaterals Algebra Plot and draw simple vertical and horizontal line graphs Geometry and measures Give a bearing between two points Algebra Generate terms of a linear sequence Ratio, proportion and rates of change Compare quantities using ratio Algebra Simplify by multiplying terms Ratio, proportion and rates of change Convert between metric units Probability Probabilities sum to 1 whole Ratio, proportion and rates of change One number as a fraction of another Probability Mutually exclusive outcomes Ratio, proportion and rates of change Share quantities in a given ratio Probability Probability of something not occurring Ratio, proportion and rates of change Proportion Probability Experimental and theoretical probabilities Ratio, proportion and rates of change Find percentages Statistics Interpret frequency tables Ratio, proportion and rates of change Find percentages using a calculator Statistics Find the mode from frequency tables Ratio, proportion and rates of change To increase or decrease a quantity by a percentage Statistics Two-way tables Ratio, proportion and rates of change Equivalent ratios Statistics Produce pie charts Ratio, proportion and rates of change Simplify ratio Statistics Compare distributions using range and median

# Step 5

 Topic: Lesson: Topic: Lesson: Number Adding and subtracting fractions with different denominators Probability Write probabilities in words, fractions, decimals and percentages Number Multiply a fraction by an integer Probability Work out probability from a frequency table Number Multiply by 0.1 and 0.01 Probability Work out probabilities from two way tables Number Divide by 0.1 and 0.01 Statistics Recognise misleading graphs and statistics Number Adding three or more fractions Statistics Design good questions for questionnaires Number Add mixed numbers Statistics Use grouped frequency tables for continuous data Number Work interchangeably with terminating decimals and their corresponding fractions Statistics Construct and interpret compound bar charts Number Learn fractional equivalents to key recurring decimals Statistics Interpret a scatter graph Number Find fractions of quantities Geometry and measures Alternate and corresponding angles Algebra Substitute positive and negative numbers into simple formulae Geometry and measures Use angle facts to calculate missing angles Algebra Forming expressions from geometry Geometry and measures Calculate the volume of a cuboid Algebra Use graphs to solve distance time problems Geometry and measures Calculate the area of a parallelogram Algebra Interpret information from a complex real life graph Geometry and measures Construct the perpendicular bisector of a line Algebra Plot coordinates in four quadrants Geometry and measures Name parts of a circle Algebra Plot a graph from the equation Geometry and measures Draw a circle Algebra Find the nth term of an expression Ratio, proportion and rates of change Simple unitary ratio and proportion Probability Use probability to estimate the number of outcomes Ratio, proportion and rates of change Divide a quantity into more than two parts in a given ratio Probability Apply probabilities from experimental data to a different experiment Ratio, proportion and rates of change Use a ratio to find one quantity when the other is known Probability Identify all mutually exclusive outcomes for successive events Ratio, proportion and rates of change Use proportion to solve a problem Probability Record outcomes of events in tables and grids Ratio, proportion and rates of change Calculate percentage profit and loss Probability Find the probability of an event happening using relative frequency

# Step 6

 Topic: Lesson: Topic: Lesson: Number Calculating upper and lower bounds Statistics Recognise when to use mean, median and mode Number Write numbers as a decimal number of millions or thousands Statistics Frequency polygons Number Divide an integer by a fraction Statistics Identify and explain outliers in a data set Number Understand which part of an expression is raised to a power Statistics Quantitative and qualitative data Number Calculate average speed, distance and time Statistics Sample and population Number Multiplying and dividing any number between 0 and 1 Statistics Primary and secondary data sources Number Multiply simple fractions (proper and improper) - Geometry and measures Co-interior angles Number Divide simple fractions Geometry and measures Exterior angles of polygons Number Use halving and doubling strategies on fractions to find decimal equivalents Geometry and measures Interior angles of polygons Number Establish multiplying and dividing index laws for positive powers Geometry and measures Area of a trapezium Number Index laws for powers of 1 and 0 Geometry and measures Circumference of a circle Number Use an extended range of calculator functions Geometry and measures Area of a circle Algebra Substitute positive integers into expressions involving powers Geometry and measures Construct the bisector of an angle Algebra Expanding single brackets Geometry and measures Construct a triangle Algebra Expanding single brackets and simplifying answers Geometry and measures Construct an equilateral triangle Algebra Common factors of expressions Geometry and measures Construct a hexagon Algebra Change the subject of a formula Geometry and measures Calculate an angle in a right angled triangle Algebra Features of graphs of linear functions Geometry and measures Enlarge a shape by a positive scale factor Algebra Interpret velocity, time graphs Geometry and measures Identify the centre of an enlargement Algebra Find the coordinates of the mid-point of a line Ratio, proportion and rates of change Ratios in the form of 1: n and n:1 Algebra Straight line graphs Ratio, proportion and rates of change Rough metric and imperial equivalents Algebra Whole number values that satisfy an inequality Ratio, proportion and rates of change Convert between area measures Algebra Position-to-term rules Ratio, proportion and rates of change Convert between metric measures of volume and capacity Probability Probability tree diagrams Ratio, proportion and rates of change Use a unitary method to calculate 100% Probability Calculate probability of individual events Ratio, proportion and rates of change Percentages in real life Statistics Produce back-to-back stem and leaf diagrams Ratio, proportion and rates of change Map scales

# Step 7

 Topic: Lesson: Topic: Lesson: Number Find the reciprocal of a number Geometry and measures Area and perimeter of semicircles and quadrants Number Compound measures Geometry and measures Congruent triangles Number Index laws and negative powers Geometry and measures Construct a perpendicular from a point Number Write numbers in standard index form Geometry and measures Loci about a point, line, or corner Number Calculating compound interest Geometry and measures Construct angles of 90º, 60º, 30º, and 45º Algebra Find an unknown where it is not the subject of the formula Geometry and measures Pythagoras theorem Algebra Identify parallel lines from their equation Geometry and measures Describe a translation Algebra Quadratic functions Geometry and measures Describe an enlargement Algebra Construct a table of values of x Geometry and measures Describe a rotation Algebra Re-arrange linear functions in terms of x Geometry and measures Describe a reflection Algebra Linear inequalities Ratio, proportion and rates of change Find best value using ratio and proportion Algebra Trial and improvement to solve equations Ratio, proportion and rates of change Convert between currencies Algebra Multiplying brackets by a negative number Ratio, proportion and rates of change Direct proportion with algebra Algebra Multiplying double brackets Ratio, proportion and rates of change Inversely proportionate expressions Algebra Substituting into expressions involving powers Statistics Venn diagrams Algebra Factorising expressions into single brackets Statistics Median, mode and range from stem and leaf diagrams Geometry and measures Volume of a prism Statistics Comparing data in pie charts Geometry and measures Surface area of a prism Statistics Random sampling Geometry and measures Calculate lengths and area of a prism given the volume Statistics Scatter graphs and line of best fit Geometry and measures Volume of a cylinder

# Step 8

 Topic: Lesson: Topic: Lesson: Number Multiply mixed fractions Algebra Triangular numbers Number To manipulate and simplify surds Algebra Solve simultaneous equations graphically Number Write numbers less than 1 in standard form Algebra Solve simultaneous equations where neither or one equation needs multiplying Number Order numbers in standard form Algebra Setup and solve a pair of simultaneous equations in two variables Number Calculations involving numbers in standard form Algebra Solve simultaneous equations representing a real-life situation Number Multiply and divide numbers in standard form Algebra Add and subtract vectors Algebra Find the equation of a line from its graph Geometry and measures Find the surface area and volume of compound solids Algebra Graphs of inverse Geometry and measures Recognise the formula for length of arc of a circle Algebra Interpret distance time graphs Geometry and measures Recognise the formula for area of a sector of a circle Algebra Interpret gradients Geometry and measures Enlarged areas and volumes Algebra Identify and interpret roots, intercepts and turning points of a quadratic graph Geometry and measures Calculate the short side of a triangle using Pythagoras theorem Algebra Calculate the length of AB from their given coordinates Geometry and measures Use trigonometry to find missing sides of a right-angle triangle Algebra Plot & draw graphs of straight lines without using a table of values Geometry and measures Use trigonometry to find missing angle of a right-angle triangle Algebra Recognise a quadratic function from its equation Statistics Use tree diagrams to calculate the probability of two dependent events Algebra Solve more complex inequalities Statistics Construct cumulative frequency tables Algebra Use algebra to support proofs Statistics Interpret box plots Algebra Identify which terms cannot be in a sequence Statistics Produce box plots from raw data Algebra Recognise and use simple geometric progressions

# Step 9

 Topic: Lesson: Topic: Lesson: Number Use inequality notation to specify simple error intervals Algebra Cube a linear expression and simplify Number Estimate powers and roots of a positive number Statistics Interpret cumulative frequency graphs Number Recall that n0 = 1 and n-1 = 1/n for any positive number n Statistics Compare the measures  between a pair of box plots/cumulative frequency graphs Algebra Change the subject of a complex formula that involves fractions Statistics Select and justify a sampling scheme and a method to investigate a population Algebra Identify and interpret gradient from ax+by=c Geometry and measures Prove and use the fact that the angle in a semicircle is a right angle Algebra Quadratic equation from the graph of the corresponding quadratic function Geometry and measures Prove and use the fact that angles in the same segment are equal Algebra Graphs of simple cubic functions Geometry and measures Prove and use the fact that opposite angles of a cyclic quadrilateral sum to 180° Algebra Reciprocal graphs Geometry and measures Prove and use facts about the angle subtended at the centre and at the circumference; Algebra Find the coordinates of the midpoint of a line Geometry and measures Use the sine, cosine and tangent ratios to find the lengths of unknown sides in a right-angled triangle Algebra Solve linear inequalities graphically Geometry and measures Use the appropriate ratio to find a length or angle Algebra Solve two simultaneous inequalities algebraically Geometry and measures Find angles of elevation and angles of depression Algebra Answer simple proof and 'show that' questions using consecutive integers Geometry and measures Know that the tangent on a circle is perpendicular to the radius at that point. Algebra Continue a quadratic sequence and use the nth term to generate terms Geometry and measures Know that the perpendicular from the centre to the chord bisects the chord. Algebra Use finite/infinite and ascending/ descending to describe sequences Geometry and measures Complete a formal geometric proof of similarity of two triangles Algebra Arithmetic and geometric sequences Ratio, proportion and rates of change Use expressions of the form y α x² Algebra Continue geometric progression and find term to term rule Ratio, proportion and rates of change Identify direct proportion from a table of values by comparing ratios of values Algebra Expand double brackets and simplify

# Step 10

 Topic: Lesson Topic: Lesson: Number Use the product rule for counting Probability Use a tree diagram to calculate conditional probability Number Convert a recurring decimal to a fraction in simple cases Statistics Appropriate use of Histograms Number Understand a recurring decimal to fraction proof Statistics Compare distributions and make inferences Number Value of calculations using indices Statistics Compare median and inter-quartile range of two distributions Number The inverse operation of raising a positive number to a power n Statistics From a cumulative frequency graph Number Simplify surd expressions involving squares Statistics Estimate the mean from a histogram Number Use fractions, surds and pi in exact calculations, without a calculator Statistics Stratified sampling Algebra Use function notation Geometry and measures Prove and use the alternate segment theorem Algebra Deduce turning points by completing the square Geometry and measures Use congruence to show that translations, rotations and reflections preserve length and angle Algebra Sketch a graph of a quadratic by factorising, identifying roots and y-intercept Geometry and measures Use Pythagoras' theorem in 3-D problems Algebra Find the equation of the line through two given points Geometry and measures Calculate the length of a diagonal of a cuboid Algebra The equation of the line through one point with a given gradient Geometry and measures Enlarge 2D shapes, given a negative, fractional scale factor Algebra A line perpendicular to the line y = mx + c, will have a gradient of -1/m Geometry and measures Apply the sine rule a/sin A = b/sin B = c/sin C to find unknown lengths and angles Algebra Write  the equation of a line perpendicular to a given line Geometry and measures Apply the cosine rule a² = b² + c² - 2bc cos A to find unknown lengths Algebra Analyse a straight-line graph Geometry and measures Area of a triangle given the length of two sides and the included angle Algebra Solve quadratic inequalities in one variable Geometry and measures Magnitude of a vector Algebra Simplify and manipulate algebraic expressions Geometry and measures Calculate, the sum of, and the difference of two vectors and a scalar multiple of a vector Algebra Solve exactly linear/quadratic simultaneous equations Geometry and measures Calculate the resultant of two vectors Algebra Find approximate solutions to simultaneous equations Ratio, proportion and rates of change Solve problems involving inverse proportion using graphs Probability Calculate conditional probability Ratio, proportion and rates of change Solve problems involving inverse proportionality Probability Use a tree diagram to calculate conditional probability Ratio, proportion and rates of change Calculate an unknown quantity Probability Use Venn diagrams to calculate conditional probability Ratio, proportion and rates of change Set up and use equations to solve word and other problems involving direct or inverse proportion Probability Understand  probabilities to decide if two events are independent Ratio, proportion and rates of change Calculate the new area of a shape after enlargement Probability Understand selection with or without replacement

# Step 11

 Topic: Lesson: Topic: Lesson: Number Calculate the upper and lower bounds of 2-D measurements Statistics Use and understand frequency density Number Calculate the upper and lower bounds of other compound measurements Statistics Construct and interpret histograms from class intervals with unequal width Number Write (3 - √3) ² in the form a + b√3 Statistics From a histogram complete a grouped frequency table Number Rationalise a denominator Statistics From a histogram understand and define frequency density Algebra Apply transformations to the graph of y = f(x) for linear, quadratic, cubic, sine and cosine functions Statistics Estimate the median from a histogram with unequal class width Algebra Apply to the graph of y = f(x) the transformations Geometry and measures Use the formulae for length of arcs and area of sectors of circles to solve problems. Algebra y = f(x) + a Geometry and measures Give reasons for angle sizes using mathematical language Algebra y = f(ax) Geometry and measures Give reasons for angle and length calculations involving the use of tangent theorems Statistics y = f(x + a) Geometry and measures Understand and use the fact that tangents from an external point are equal in length Statistics y = af(x) for linear, quadratic, cubic, sine and cosine functions f(x) Geometry and measures Apply the cosine rule a² = b² + c² - 2bc cos A to find unknown angles Algebra Construct the graphs of simple loci including the circle x² + y² = r² Geometry and measures Apply Area = 1/2 ab sin C to calculate the sides or angles of any triangle Algebra Find the gradient of the radius that meets the circle at a given point Geometry and measures Prove lines are parallel / co linear Algebra Find the nth term of a quadratic sequence of the form n² ,an², an² ± b, an² ± bn ± c, Ratio, proportion and rates of change Recognise sketch and interpret graphs of exponential functions y = kx Algebra Solve linear/x² + y² = r² simultaneous equations Ratio, proportion and rates of change Find points that divide a line in a given ratio, using the properties of similar triangles

# 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 Geometry and measures Solve problems for areas and volumes Algebra Find the equation of a tangent to a circle at a given point Geometry and measures Use the trigonometric ratios to solve 3-D problems Algebra Interpret coordinates for trigonometric graphs Geometry and measures Find the angle between a line and a task