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 |