Topic summaries
Year Five – Addition & Subtraction
Column Addition (5+ digits)
Add whole numbers with more than four digits using the formal column method.
Year Five – Addition & Subtraction
Column Subtraction (5+ digits)
Subtract whole numbers with more than four digits using the formal column method, including multiple exchanges and exchanges through zeros.
Year Five – Addition & Subtraction
Mental Strategies with Large Numbers
Add and subtract increasingly large numbers mentally using efficient strategies.
Year Five – Addition & Subtraction
Rounding to Check
Use rounding to check answers to calculations and determine, in context, levels of accuracy.
Year Five – Fractions, Decimals & Percentages
Adding & Subtracting (related denominators)
Add and subtract fractions whose denominators are multiples of the same number, including mixed numbers.
Year Five – Fractions, Decimals & Percentages
Comparing & Ordering Fractions (related denominators)
Compare and order fractions whose denominators are multiples of the same number.
Year Five – Fractions, Decimals & Percentages
Decimal Equivalents by Division
Read and write decimal numbers as fractions and find decimal equivalents of simple fractions by division.
Year Five – Fractions, Decimals & Percentages
FDP Equivalents (½, ¼, ⅕, ⅖, ⅘)
Solve problems requiring knowing percentage and decimal equivalents of ½, ¼, ⅕, ⅖, ⅘ and fractions with a denominator that is a multiple of 10 or 25.
Year Five – Fractions, Decimals & Percentages
Mixed Numbers & Improper Fractions
Recognise mixed numbers and improper fractions and convert from one form to the other.
Year Five – Fractions, Decimals & Percentages
Multiplying Fractions by Whole Numbers
Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.
Year Five – Fractions, Decimals & Percentages
Ordering Decimals to 3dp
Read, write, order and compare numbers with up to three decimal places.
Year Five – Fractions, Decimals & Percentages
Percentages
Recognise the per cent symbol and understand that per cent relates to 'number of parts per hundred'; write percentages as fractions and decimals.
Year Five – Fractions, Decimals & Percentages
Rounding Decimals to 1 and 2 dp
Round decimals with two or three places to the nearest whole number and to one or two decimal places.
Year Five – Fractions, Decimals & Percentages
Thousandths
Recognise and use thousandths, relating them to tenths, hundredths and decimal equivalents.
Year Five – Geometry: Position & Direction
Reflection in Lines Parallel to the Axes
Identify, describe and represent the position of a shape following a reflection in a line parallel to an axis.
Year Five – Geometry: Position & Direction
Translation on a Grid
Identify, describe and represent the position of a shape following a translation, using the appropriate language, and know that the shape has not changed.
Year Five – Geometry: Properties of Shapes
3-D Shapes from 2-D Drawings
Identify 3-D shapes, including cubes and other cuboids, from 2-D representations.
Year Five – Geometry: Properties of Shapes
Angles on a Straight Line & at a Point
Identify angles at a point and one whole turn (360°), angles at a point on a straight line and half a turn (180°), and other multiples of 90°.
Year Five – Geometry: Properties of Shapes
Degrees, Reflex Angles & Estimating
Know angles are measured in degrees; estimate and compare acute, obtuse and reflex angles.
Year Five – Geometry: Properties of Shapes
Measuring & Drawing with a Protractor
Draw given angles and measure them in degrees, using a protractor.
Year Five – Geometry: Properties of Shapes
Properties of Rectangles: Missing Lengths & Angles
Use the properties of rectangles to deduce related facts and find missing lengths and angles.
Year Five – Geometry: Properties of Shapes
Regular & Irregular Polygons
Distinguish between regular and irregular polygons based on reasoning about equal sides and angles.
Year Five – Measurement
Area of Rectangles (formula)
Calculate and compare the area of rectangles using standard units, including using the formula length × width.
Year Five – Measurement
Converting Metric Units
Convert between different units of metric measure, including with decimals.
Year Five – Measurement
Estimating Area of Irregular Shapes
Estimate the area of irregular shapes by counting whole and part squares.
Year Five – Measurement
Imperial Equivalents
Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints.
Year Five – Measurement
Perimeter of Composite Shapes
Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres.
Year Five – Measurement
Volume & Capacity
Estimate volume using 1 cm³ blocks and capacity using water, and understand the difference between them.
Year Five – Multiplication & Division
Factors & Common Factors
Identify all factor pairs of a number and common factors of two numbers.
Year Five – Multiplication & Division
Multiples & Common Multiples
Identify multiples and common multiples of two numbers, including the lowest common multiple.
Year Five – Multiplication & Division
Multiplying & Dividing by 10, 100 and 1000
Multiply and divide whole numbers and decimals by 10, 100 and 1000 by shifting digits across place value.
Year Five – Multiplication & Division
Prime & Composite Numbers
Know and use the vocabulary of prime numbers, prime factors and composite numbers.
Year Five – Multiplication & Division
Remainders as Fractions, Decimals & Rounding
Express remainders appropriately as fractions, as decimals or by rounding, according to the context.
Year Five – Multiplication & Division
Short Multiplication & Division (4-digit by 1-digit)
Multiply and divide numbers up to four digits by a one-digit number using formal short methods.
Year Five – Multiplication & Division
Square & Cube Numbers
Recognise and use square and cube numbers and the notation for squared and cubed.
Year Five – Multiplication & Division
Stretch Grammar – Divisibility Rules
Stretch (universal 11+): use divisibility rules for 2, 3, 4, 5, 6, 9 and 10 to test numbers quickly.
Year Five – Multiplication & Division
Stretch Grammar – Square Roots
Stretch (universal 11+): find square roots of square numbers to 144 and use the √ notation.
Year Five – Multiplication & Division
Stretch Independent – Powers & Index Notation
Stretch (independent-school 11+): read and evaluate small powers such as 2⁵ and 10⁴ and use index notation.
Year Five – Number & Place Value
Comparing & Ordering to 1,000,000
Compare and order numbers to at least 1,000,000.
Year Five – Number & Place Value
Counting in Powers of 10
Count forwards and backwards in steps of powers of 10 from any number up to 1,000,000.
Year Five – Number & Place Value
Negative Numbers in Context
Interpret negative numbers in context and count forwards and backwards through zero.
Year Five – Number & Place Value
Reading, Writing & Digit Value to 1,000,000
Read and write numbers to 1,000,000 and determine the value of each digit.
Year Five – Number & Place Value
Roman Numerals to 1000
Read Roman numerals to 1000 (M) and recognise years written in Roman numerals.
Year Five – Number & Place Value
Rounding to 100,000
Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 or 100,000.
Year Five – Statistics
Line Graphs
Solve comparison, sum and difference problems using information presented in a line graph.
Year Five – Statistics
Timetables & Choosing Representations
Complete, read and interpret information in tables, including timetables, and decide which representation best suits a set of data.
Year Four – Addition & Subtraction
Column Addition (4-digit)
Add numbers with up to four digits using the formal column method.
Year Four – Addition & Subtraction
Column Subtraction (4-digit, exchange through zero)
Subtract numbers with up to four digits using the formal column method, including exchanging across a zero.
Year Four – Addition & Subtraction
Estimating & Checking Two-Step Problems
Estimate and use inverse operations to check the answers to two-step problems.
Year Four – Addition & Subtraction
Two-Step Problems
Solve two-step addition and subtraction problems in context, deciding which operations to use.
Year Four – Fractions, Decimals & Percentages
Adding & Subtracting beyond One Whole
Add and subtract fractions with the same denominator, including totals greater than one whole.
Year Four – Fractions, Decimals & Percentages
Decimal Equivalents of ¼, ½ and ¾
Recognise and write the decimal equivalents of one quarter, one half and three quarters.
Year Four – Fractions, Decimals & Percentages
Dividing by 10 and 100 into Decimals
Divide one- and two-digit numbers by 10 and 100, identifying the value of the digits as tenths and hundredths.
Year Four – Fractions, Decimals & Percentages
Families of Equivalent Fractions
Recognise and show families of common equivalent fractions.
Year Four – Fractions, Decimals & Percentages
Hundredths
Recognise that hundredths arise when dividing an object by a hundred and dividing tenths by ten, and count in hundredths.
Year Four – Fractions, Decimals & Percentages
Non-Unit Fractions of Quantities
Find non-unit fractions of quantities where the answer is a whole number, in context including measures and money.
Year Four – Fractions, Decimals & Percentages
Rounding & Comparing Decimals
Round decimals with one decimal place to the nearest whole number, and compare numbers with the same number of decimal places up to two places.
Year Four – Fractions, Decimals & Percentages
Tenths & Hundredths as Decimals
Recognise and write decimal equivalents of tenths and hundredths, understanding the decimal point and place value.
Year Four – Geometry: Position & Direction
Plotting Points & Completing Shapes
Plot specified points and draw sides to complete a given polygon.
Year Four – Geometry: Position & Direction
Reading Coordinates (along then up)
Describe positions on a 2-D grid as coordinates in the first quadrant.
Year Four – Geometry: Position & Direction
Translation
Describe movements between positions as translations of a given unit to the left/right and up/down.
Year Four – Geometry: Properties of Shapes
Acute, Obtuse & Right Angles
Identify acute and obtuse angles and compare and order angles up to two right angles by size.
Year Four – Geometry: Properties of Shapes
Stretch Grammar – Rotational Symmetry
Stretch (universal 11+): recognise rotational symmetry and find the order of rotational symmetry of a shape.
Year Four – Geometry: Properties of Shapes
Symmetry
Identify lines of symmetry in 2-D shapes presented in different orientations, and complete a simple symmetric figure with respect to a specific line of symmetry.
Year Four – Geometry: Properties of Shapes
Types of Quadrilateral
Compare and classify quadrilaterals — square, rectangle, rhombus, parallelogram, trapezium, kite — based on their properties.
Year Four – Geometry: Properties of Shapes
Types of Triangle
Compare and classify triangles as equilateral, isosceles, scalene or right-angled, based on their properties and sizes.
Year Four – Measurement
Area by Counting Squares
Find the area of rectilinear shapes by counting squares.
Year Four – Measurement
Converting Between Clocks
Read, write and convert time between analogue and digital 12- and 24-hour clocks.
Year Four – Measurement
Converting Length, Mass & Capacity
Convert between different units of measure: kilometres and metres, metres and centimetres, centimetres and millimetres, kilograms and grams, litres and millilitres.
Year Four – Measurement
Converting Units of Time
Convert between hours and minutes, minutes and seconds, years and months, weeks and days.
Year Four – Measurement
Perimeter of Rectilinear Shapes
Measure and calculate the perimeter of rectilinear figures, including squares, in centimetres and metres.
Year Four – Multiplication & Division
Factor Pairs & the Distributive Law
Recognise factor pairs of a number and use the distributive law to multiply.
Year Four – Multiplication & Division
Interpreting Remainders
Interpret remainders appropriately in the context of a problem.
Year Four – Multiplication & Division
Short Division
Divide two- and three-digit numbers by a one-digit number using formal short division.
Year Four – Multiplication & Division
Short Multiplication
Multiply two- and three-digit numbers by a one-digit number using formal short multiplication.
Year Four – Multiplication & Division
The 11 and 12 Times Tables
Recall and use the 11 and 12 times tables to complete all tables to 12 × 12.
Year Four – Multiplication & Division
The 6, 7 and 9 Times Tables
Recall and use multiplication and division facts for the 6, 7 and 9 times tables.
Year Four – Number & Place Value
Comparing & Ordering beyond 1000
Compare and order numbers beyond 1000 using place value.
Year Four – Number & Place Value
Negative Numbers
Count backwards through zero to include negative numbers.
Year Four – Number & Place Value
Roman Numerals to 100
Read Roman numerals from I to C, including the subtractive pairs.
Year Four – Number & Place Value
Rounding to 10, 100 and 1000
Round any number to the nearest 10, 100 or 1000.
Year Four – Number & Place Value
Thousands, Hundreds, Tens & Ones
Recognise the value of each digit in a four-digit number.
Year Four – Statistics
Graphs with Larger Scales
Interpret and present discrete and continuous data using bar charts and time graphs with larger scales.
Year Four – Statistics
Reading Tables
Solve comparison, sum and difference problems using information presented in tables, including two-way tables.
Year Four – Statistics
Stretch Grammar – Venn & Carroll Diagrams
Stretch (universal 11+): sort data into Venn diagrams with two overlapping sets and Carroll diagrams with two criteria, and read them.
Year Four – Statistics
Timetables
Read and interpret timetables, including 24-hour times, and find durations and connections.
Year One – Addition & Subtraction
Adding within 20
Add one-digit and two-digit numbers to 20, including zero, by counting on and using bonds.
Year One – Addition & Subtraction
Missing Number Problems
Solve missing-number problems such as 7 = ▢ − 9, understanding = as balance.
Year One – Addition & Subtraction
Number Bonds to 10
Represent and recall the pairs of numbers that make 10, and their subtraction facts.
Year One – Addition & Subtraction
Number Bonds within 20
Represent and use number bonds and related subtraction facts within 20.
Year One – Addition & Subtraction
Subtracting within 20
Subtract within 20 by counting back, using bonds and subtracting through ten.
Year One – Fractions, Decimals & Percentages
Halves
Recognise, find, name and write one half of an object, shape, set of objects or quantity.
Year One – Fractions, Decimals & Percentages
Quarters
Recognise, find, name and write one quarter of an object, shape, set of objects or quantity.
Year One – Geometry: Position & Direction
Position & Direction Words
Describe position, direction and movement using everyday language: left, right, above, below, between, next to, forwards, backwards.
Year One – Geometry: Position & Direction
Whole, Half & Quarter Turns
Describe movement including whole, half, quarter and three-quarter turns.
Year One – Geometry: Properties of Shapes
Naming 2-D Shapes
Recognise and name common 2-D shapes: rectangles (including squares), circles and triangles.
Year One – Geometry: Properties of Shapes
Naming 3-D Shapes
Recognise and name common 3-D shapes: cuboids (including cubes), pyramids and spheres.
Year One – Measurement
Coins & Notes
Recognise and know the value of different denominations of coins and notes.
Year One – Measurement
Comparing Capacity
Compare, describe and solve practical problems for capacity and volume using words such as full, empty, more than, less than.
Year One – Measurement
Comparing Length & Height
Compare, describe and solve practical problems for lengths and heights using words such as longer, shorter, taller.
Year One – Measurement
Comparing Mass
Compare, describe and solve practical problems for mass using words such as heavier, lighter.
Year One – Measurement
Days, Weeks & Months
Sequence events in chronological order and recognise the days of the week and months of the year.
Year One – Measurement
O'clock & Half Past
Tell the time to the hour and half past the hour, and draw the hands on a clock face to show these times.
Year One – Multiplication & Division
Making Equal Groups
Solve one-step multiplication problems using objects, pictures and arrays, with support.
Year One – Multiplication & Division
Sharing Equally
Solve one-step division problems by sharing equally and by grouping, using objects and pictures.
Year One – Number & Place Value
Counting Forwards & Backwards to 100
Count forwards and backwards to and across 100 from any starting number, including across the tens.
Year One – Number & Place Value
Counting in 2s, 5s and 10s
Count forwards in steps of 2, 5 and 10 from zero and spot the patterns.
Year One – Number & Place Value
More, Less & Equal
Compare two or three amounts using more, fewer, less, most, least and equal to.
Year One – Number & Place Value
Numbers on a Number Line
Read and find numbers on a number line and jump along it in steps.
Year One – Number & Place Value
Odd & Even Numbers
Recognise odd and even numbers by making pairs and by looking at the last digit.
Year One – Number & Place Value
One More, One Less
Find one more and one less than any number to 100, including across a tens boundary.
Year One – Number & Place Value
Reading & Writing Numbers to 20
Read and write numbers from 1 to 20 in numerals and in words.
Year Six – Addition & Subtraction
Estimation & Degree of Accuracy
Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.
Year Six – Addition & Subtraction
Multi-Step Problems
Solve multi-step addition and subtraction problems in context, deciding which operations and methods to use and why.
Year Six – Algebra
Cipher's Final Mission (Mixed Problems)
Solve mixed algebra problems drawing on formulae, sequences, expressions, equations and systematic listing.
Year Six – Algebra
Equations with Two Unknowns
Find pairs of numbers that satisfy an equation with two unknowns.
Year Six – Algebra
Finding the Term-to-Term Rule
Describe a linear sequence by its term-to-term rule and continue it, including finding missing terms.
Year Six – Algebra
Formulae in Symbols & Substitution
Use simple formulae written in symbols, substituting values for letters.
Year Six – Algebra
Formulae in Words
Use simple formulae expressed in words, and find outputs from inputs.
Year Six – Algebra
Generating Sequences from a Rule
Generate linear number sequences from a term-to-term rule and a start number.
Year Six – Algebra
Letters for Unknowns (expressions)
Express missing number problems algebraically, using letters for unknowns and writing expressions.
Year Six – Algebra
Listing All Possibilities Systematically
Enumerate possibilities of combinations of two variables systematically.
Year Six – Algebra
Solving One-Step Equations
Solve one-step equations by using inverse operations, and check solutions.
Year Six – Algebra
Stretch Grammar – Forming Equations from Word Problems
Stretch (universal 11+): translate a word problem into an equation, solve it, and interpret the answer.
Year Six – Algebra
Stretch Grammar – Position-to-Term Rule (nth term)
Stretch (universal 11+): find and use the position-to-term rule (nth term) of a linear sequence.
Year Six – Algebra
Stretch Grammar – Special Sequences
Stretch (universal 11+): recognise and continue square, triangular, cube and Fibonacci-type sequences, and sequences with changing differences.
Year Six – Algebra
Stretch Grammar – Two-Step Equations
Stretch (universal 11+): solve two-step equations by undoing operations in reverse order.
Year Six – Algebra
Stretch Independent – Simplifying Expressions: Collecting Like Terms
Stretch (independent-school 11+): simplify expressions by collecting like terms and expanding a single bracket.
Year Six – Fractions, Decimals & Percentages
Adding & Subtracting Mixed Numbers
Add and subtract mixed numbers with different denominators.
Year Six – Fractions, Decimals & Percentages
Adding & Subtracting with Different Denominators
Add and subtract fractions with different denominators using equivalent fractions.
Year Six – Fractions, Decimals & Percentages
Common Denominators & Ordering
Compare and order fractions with any denominators by finding a common denominator.
Year Six – Fractions, Decimals & Percentages
Dividing a Fraction by a Whole Number
Divide proper fractions by whole numbers.
Year Six – Fractions, Decimals & Percentages
Dividing to Decimal Places & Rounding
Use written division methods where the answer has up to two decimal places, and round as required.
Year Six – Fractions, Decimals & Percentages
FDP Equivalence in Context
Solve problems involving fractions, decimals and percentages in context, including percentages of amounts and comparisons across forms.
Year Six – Fractions, Decimals & Percentages
Fractions to Decimals by Division
Convert any fraction to a decimal by dividing the numerator by the denominator, including recurring decimals.
Year Six – Fractions, Decimals & Percentages
Multiplying & Dividing Decimals by 10, 100 and 1000
Multiply and divide decimal numbers by 10, 100 and 1000, giving answers up to three decimal places.
Year Six – Fractions, Decimals & Percentages
Multiplying Decimals by Whole Numbers
Multiply one-digit numbers with up to two decimal places by whole numbers.
Year Six – Fractions, Decimals & Percentages
Multiplying Fractions
Multiply simple pairs of proper fractions, writing the answer in its simplest form.
Year Six – Fractions, Decimals & Percentages
Simplifying Fractions
Use common factors to simplify fractions to their simplest form.
Year Six – Fractions, Decimals & Percentages
Stretch Grammar – Reverse Fractions: Finding the Whole
Stretch (universal 11+): find the whole amount when a fraction of it is known, including multi-step contexts.
Year Six – Fractions, Decimals & Percentages
Stretch Independent – Dividing by a Decimal
Stretch (independent-school 11+): divide by a decimal by scaling both numbers to whole numbers.
Year Six – Fractions, Decimals & Percentages
Stretch Independent – Multiplying Decimals by Decimals
Stretch (independent-school 11+): multiply decimals by decimals, placing the point by counting total decimal places.
Year Six – Geometry: Position & Direction
Predicting Missing Vertices
Predict missing coordinates of shapes using their properties, including across quadrants.
Year Six – Geometry: Position & Direction
Stretch Independent – Midpoints on a Coordinate Grid
Stretch (independent-school 11+): find the midpoint of a line segment from the coordinates of its ends, and find an endpoint from the midpoint.
Year Six – Geometry: Position & Direction
Stretch Independent – Rotation of Shapes on a Grid
Stretch (independent-school 11+): rotate points and shapes by 90° and 180° about the origin on the coordinate grid.
Year Six – Geometry: Position & Direction
The Four Quadrants
Describe positions on the full coordinate grid (all four quadrants).
Year Six – Geometry: Position & Direction
Translating & Reflecting in Four Quadrants
Draw and translate simple shapes on the coordinate plane, and reflect them in the axes.
Year Six – Geometry: Properties of Shapes
Angles in Quadrilaterals
Find unknown angles in quadrilaterals using the angle sum of 360°.
Year Six – Geometry: Properties of Shapes
Angles in Regular Polygons & Vertically Opposite
Find unknown angles in regular polygons, and recognise vertically opposite angles and find missing values.
Year Six – Geometry: Properties of Shapes
Angles in Triangles
Find unknown angles in triangles using the angle sum of 180°.
Year Six – Geometry: Properties of Shapes
Drawing Shapes with Given Dimensions
Draw 2-D shapes using given dimensions and angles.
Year Six – Geometry: Properties of Shapes
Nets of 3-D Shapes
Recognise, describe and build simple 3-D shapes, including making nets.
Year Six – Geometry: Properties of Shapes
Parts of a Circle
Illustrate and name parts of circles, including radius, diameter and circumference, and know that the diameter is twice the radius.
Year Six – Geometry: Properties of Shapes
Stretch Grammar – Angles in Parallel Lines
Stretch (universal 11+): use alternate, corresponding and co-interior angles between parallel lines to find missing angles.
Year Six – Geometry: Properties of Shapes
Stretch Grammar – Counting Cubes & 3-D Views
Stretch (universal 11+): count cubes in a 3-D stack, including hidden ones, and match a stack to its plan, front and side views.
Year Six – Geometry: Properties of Shapes
Stretch Independent – Circumference & Area of Circles
Stretch (independent-school 11+): calculate the circumference and area of a circle using π ≈ 3.14.
Year Six – Measurement
Area of Parallelograms
Calculate the area of parallelograms.
Year Six – Measurement
Area of Triangles
Calculate the area of triangles.
Year Six – Measurement
Converting Units with Decimal Notation
Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit to a larger unit and vice versa, using decimal notation to up to three decimal places.
Year Six – Measurement
Miles & Kilometres
Convert between miles and kilometres.
Year Six – Measurement
Same Area, Different Perimeter
Recognise that shapes with the same areas can have different perimeters and vice versa.
Year Six – Measurement
Stretch Independent – Calendar & Day-Counting Problems
Stretch (independent-school 11+): solve problems counting days across months, using days-in-month facts, leap years and 'inclusive' counting.
Year Six – Measurement
Stretch Independent – Surface Area of Cuboids
Stretch (independent-school 11+): find the surface area of cubes and cuboids by adding the areas of the six faces.
Year Six – Measurement
Volume of Cuboids
Calculate, estimate and compare volume of cubes and cuboids using standard units, including cm³ and m³, and extending to other units.
Year Six – Multiplication & Division
HCF & LCM in Problems
Apply common factors and common multiples to solve problems.
Year Six – Multiplication & Division
Long Division
Divide numbers up to four digits by a two-digit number using long division.
Year Six – Multiplication & Division
Long Multiplication
Multiply numbers up to four digits by a two-digit number using formal long multiplication.
Year Six – Multiplication & Division
Order of Operations
Use the order of operations, including brackets, to carry out calculations involving the four operations, and understand the meaning of '='.
Year Six – Multiplication & Division
Remainders in Context
Interpret remainders in context, including rounding up, when dividing by two-digit numbers.
Year Six – Multiplication & Division
Stretch Grammar – Missing-Digit Problems
Stretch (universal 11+): find missing digits in multiplication and division calculations by reasoning.
Year Six – Multiplication & Division
Stretch Independent – Prime Factor Trees
Stretch (independent-school 11+): write a number as a product of its prime factors using a factor tree, and use it for HCF and LCM.
Year Six – Number & Place Value
Comparing & Ordering to 10,000,000
Order and compare numbers up to 10,000,000.
Year Six – Number & Place Value
Intervals Across Zero
Use negative numbers in context and calculate intervals across zero.
Year Six – Number & Place Value
Reading, Writing & Digit Value to 10,000,000
Read and write numbers to 10,000,000 and determine the value of each digit.
Year Six – Number & Place Value
Rounding to Any Degree of Accuracy
Round any whole number to a required degree of accuracy.
Year Six – Number & Place Value
Stretch Grammar – Calculating with Negative Numbers
Stretch (universal 11+): add and subtract with negative numbers and multiply a negative by a positive.
Year Six – Ratio & Proportion
Comparing with Percentages
Use percentages for comparison, converting fractions and scores to percentages.
Year Six – Ratio & Proportion
Percentages of Amounts
Solve problems involving the calculation of percentages, such as 15% of 360, and use percentages for comparison.
Year Six – Ratio & Proportion
Ratio, Difference & Fractions
Solve ratio problems where the difference between shares is given, or a fraction of the whole, using the relationship between ratio and fraction.
Year Six – Ratio & Proportion
Scale Factors
Solve problems involving similar shapes where the scale factor is known or can be found.
Year Six – Ratio & Proportion
Scaling Ratios
Scale a ratio up or down to find a missing quantity, including recipe and mixture problems.
Year Six – Ratio & Proportion
Sharing in a Ratio
Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.
Year Six – Ratio & Proportion
Similar Shapes
Solve problems involving similar shapes, finding missing lengths from corresponding sides.
Year Six – Ratio & Proportion
Stretch Grammar – Best Buy & Unit Pricing
Stretch (universal 11+): compare value for money using unit prices or a common quantity.
Year Six – Ratio & Proportion
Stretch Grammar – Map Scales & Scale Drawings
Stretch (universal 11+): use map scales (1 : n and '1 cm represents…') and scale drawings to convert between map and real distances.
Year Six – Ratio & Proportion
Stretch Grammar – Percentage Increase & Decrease
Stretch (universal 11+): increase or decrease an amount by a percentage, and find a percentage change.
Year Six – Ratio & Proportion
Stretch Grammar – Reverse Percentages
Stretch (universal 11+): find the original amount after a percentage change, or from a known percentage of it.
Year Six – Ratio & Proportion
Stretch Grammar – Speed, Distance & Time
Stretch (universal 11+): use speed = distance ÷ time and rearrangements to solve journey problems.
Year Six – Ratio & Proportion
The Grand Brew (Mixed Problems)
Solve mixed problems drawing on ratio, proportion, percentages and scale, choosing the method for each.
Year Six – Ratio & Proportion
Times as Many
Solve problems involving the relative sizes of two quantities, using multiplication and division facts — 'times as many'.
Year Six – Ratio & Proportion
Writing & Simplifying Ratios
Write a ratio from a description or picture and simplify it using common factors.
Year Six – Statistics
Constructing & Interpreting Line Graphs
Construct line graphs from tables and interpret them, including reading between points and comparing two lines.
Year Six – Statistics
Pie Charts, Angles & Percentages
Interpret and construct pie charts using angles and percentages.
Year Six – Statistics
Reading Pie Charts
Interpret pie charts and use them to solve problems, reading sectors as fractions of the whole.
Year Six – Statistics
Stretch Grammar – Mean: Reverse & Combined Problems
Stretch (universal 11+): find a missing value from a mean, and find the mean of combined groups.
Year Six – Statistics
Stretch Grammar – Median, Mode & Range
Stretch (universal 11+): find the median, mode and range of a set of data and choose the most appropriate average.
Year Six – Statistics
Stretch Independent – Conversion Graphs
Stretch (independent-school 11+): read and draw conversion graphs (miles–km, £–€, °C–°F) and use them to convert both ways.
Year Six – Statistics
Stretch Independent – Distance–Time Graphs
Stretch (independent-school 11+): read distance–time graphs — steepness as speed, flat as stopped, return journeys — and find speeds and times.
Year Six – Statistics
Stretch Independent – Simple Probability
Stretch (independent-school 11+): describe probability in words and as a fraction from 0 to 1, for equally likely outcomes.
Year Six – Statistics
The Mean
Calculate and interpret the mean as an average.
Year Three – Addition & Subtraction
Adding & Subtracting Hundreds Mentally
Add and subtract a three-digit number and hundreds mentally.
Year Three – Addition & Subtraction
Adding & Subtracting Ones and Tens Mentally
Add and subtract a three-digit number and ones or tens mentally, including across boundaries.
Year Three – Addition & Subtraction
Checking with the Inverse
Use inverse operations to check answers to additions and subtractions with three-digit numbers.
Year Three – Addition & Subtraction
Column Addition (3-digit)
Add numbers with up to three digits using the formal column method, including exchange.
Year Three – Addition & Subtraction
Column Subtraction with Exchange (3-digit)
Subtract numbers with up to three digits using the formal column method with exchange.
Year Three – Addition & Subtraction
Estimating Answers
Estimate the answer to an addition or subtraction by rounding before calculating.
Year Three – Fractions, Decimals & Percentages
Adding & Subtracting (same denominator)
Add and subtract fractions with the same denominator within one whole.
Year Three – Fractions, Decimals & Percentages
Comparing & Ordering Fractions
Compare and order unit fractions, and fractions with the same denominator.
Year Three – Fractions, Decimals & Percentages
Equivalent Fractions with Diagrams
Recognise and show, using diagrams, equivalent fractions with small denominators.
Year Three – Fractions, Decimals & Percentages
Fractions as Numbers on a Number Line
Use fractions as numbers and place them on a number line.
Year Three – Fractions, Decimals & Percentages
Tenths
Recognise that tenths arise from dividing an object into ten equal parts, and count up and down in tenths.
Year Three – Fractions, Decimals & Percentages
Unit & Non-Unit Fractions of a Set
Recognise, find and write unit and non-unit fractions of a set of objects.
Year Three – Geometry: Properties of Shapes
Angles as Turns
Recognise angles as a property of shape or a description of a turn; identify quarter, half, three-quarter and whole turns, clockwise and anticlockwise.
Year Three – Geometry: Properties of Shapes
Drawing & Making Shapes
Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them.
Year Three – Geometry: Properties of Shapes
Horizontal & Vertical Lines
Identify horizontal and vertical lines.
Year Three – Geometry: Properties of Shapes
Perpendicular & Parallel Lines
Identify pairs of perpendicular and parallel lines.
Year Three – Geometry: Properties of Shapes
Right Angles & Comparing Angles
Identify right angles, recognise that two right angles make a half turn and four make a complete turn, and identify whether angles are greater than or less than a right angle.
Year Three – Measurement
am, pm & the 24-Hour Clock
Use am and pm, and tell and write the time in 12-hour and 24-hour clock notation.
Year Three – Measurement
Capacity in l and ml
Measure, compare, add and subtract capacity in litres and millilitres, using mixed units.
Year Three – Measurement
Durations & Time Facts
Know the number of seconds in a minute and days in each month, year and leap year; compare durations of events.
Year Three – Measurement
Length in m, cm and mm
Measure, compare, add and subtract lengths in metres, centimetres and millimetres, using mixed units.
Year Three – Measurement
Mass in kg and g
Measure, compare, add and subtract mass in kilograms and grams, using mixed units.
Year Three – Measurement
Money: Adding, Subtracting & Change
Add and subtract amounts of money to give change, using both £ and p in practical contexts.
Year Three – Measurement
Perimeter of 2-D Shapes
Measure the perimeter of simple 2-D shapes.
Year Three – Measurement
Time to the Minute
Tell and write the time from an analogue clock to the nearest minute, including using Roman numerals.
Year Three – Multiplication & Division
Scaling & Correspondence Problems
Solve scaling problems and correspondence problems in which n objects are connected to m objects.
Year Three – Multiplication & Division
The 3 Times Table
Recall and use multiplication and division facts for the 3 times table.
Year Three – Multiplication & Division
The 4 Times Table (doubling the 2s)
Recall the 4 times table by doubling the 2 times table, and use the related division facts.
Year Three – Multiplication & Division
The 8 Times Table (doubling the 4s)
Recall the 8 times table by doubling the 4 times table, and use the related division facts.
Year Three – Multiplication & Division
Two-Digit × One-Digit (partitioning)
Multiply a two-digit number by a one-digit number mentally by partitioning.
Year Three – Multiplication & Division
Written Layout for Two-Digit × One-Digit
Progress from partitioning to a formal written layout for two-digit × one-digit multiplication.
Year Three – Number & Place Value
10 or 100 More or Less
Find 10 or 100 more or less than any number to 1000, including across boundaries.
Year Three – Number & Place Value
Comparing & Ordering to 1000
Compare and order numbers to 1000 using place value.
Year Three – Number & Place Value
Counting in 4s, 8s, 50s and 100s
Count from zero in multiples of 4, 8, 50 and 100.
Year Three – Number & Place Value
Estimating & Representing to 1000
Represent numbers to 1000 in different ways and estimate positions on a number line to 1000.
Year Three – Number & Place Value
Hundreds, Tens & Ones
Recognise the value of each digit in a three-digit number.
Year Three – Number & Place Value
Partitioning Three-Digit Numbers
Partition three-digit numbers into hundreds, tens and ones in more than one way.
Year Three – Statistics
Bar Charts with Scaled Axes
Interpret and present data using bar charts and pictograms with scaled axes.
Year Three – Statistics
Comparison, Sum & Difference Problems
Solve one-step and two-step questions such as 'how many more?' and 'how many fewer?' using information presented in scaled bar charts, pictograms and tables.
Year Three – Statistics
Time Graphs
Interpret simple time graphs, reading values at given times and describing change.
Year Two – Addition & Subtraction
Adding Three One-Digit Numbers
Add three one-digit numbers, using pairs that make ten.
Year Two – Addition & Subtraction
Any Order? Commutativity
Show that addition can be done in any order but subtraction cannot.
Year Two – Addition & Subtraction
Checking with the Inverse
Use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems.
Year Two – Addition & Subtraction
Deriving Facts to 100
Use known facts to 20 to derive related facts to 100.
Year Two – Addition & Subtraction
Fluent Facts to 20
Recall addition and subtraction facts to 20 fluently.
Year Two – Addition & Subtraction
Two Two-Digit Numbers (with exchange)
Add and subtract two two-digit numbers, exchanging where needed.
Year Two – Addition & Subtraction
Two-Digit Numbers and Ones
Add and subtract a two-digit number and ones, including crossing a ten.
Year Two – Addition & Subtraction
Two-Digit Numbers and Tens
Add and subtract a two-digit number and tens.
Year Two – Fractions, Decimals & Percentages
Equivalence (2/4 = ½) & Counting in Fractions
Recognise the equivalence of 2/4 and ½, and count in halves and quarters up to and beyond 1.
Year Two – Fractions, Decimals & Percentages
Three Quarters & Non-Unit Fractions
Find ¾ and other simple non-unit fractions of shapes and sets, understanding numerator and denominator.
Year Two – Fractions, Decimals & Percentages
Unit Fractions of a Set
Find ⅓, ¼ and other unit fractions of a set of objects, and write simple fraction statements.
Year Two – Geometry: Position & Direction
Patterns & Sequences of Shapes
Order and arrange combinations of mathematical objects in patterns and sequences.
Year Two – Geometry: Position & Direction
Rotation through Right Angles
Use mathematical vocabulary to describe position, direction and movement, including distinguishing rotation as a turn and in terms of right angles for quarter, half and three-quarter turns.
Year Two – Geometry: Properties of Shapes
Faces, Edges & Vertices
Identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces, and identify 2-D shapes on their surfaces.
Year Two – Geometry: Properties of Shapes
Lines of Symmetry
Identify and describe the properties of 2-D shapes including a vertical line of symmetry.
Year Two – Geometry: Properties of Shapes
Sides & Vertices
Identify and describe the properties of 2-D shapes, including the number of sides and vertices.
Year Two – Geometry: Properties of Shapes
Sorting & Comparing Shapes
Compare and sort common 2-D and 3-D shapes and everyday objects by their properties.
Year Two – Measurement
Adding, Subtracting & Giving Change
Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change.
Year Two – Measurement
Capacity & Temperature (l, ml, °C)
Choose and use appropriate standard units to estimate and measure capacity in litres and millilitres, and temperature in degrees Celsius.
Year Two – Measurement
Making Amounts with Coins
Find different combinations of coins that equal the same amounts of money.
Year Two – Measurement
Measuring Length (m, cm)
Choose and use appropriate standard units to estimate and measure length and height in metres and centimetres, using rulers.
Year Two – Measurement
Measuring Mass (kg, g)
Choose and use appropriate standard units to estimate and measure mass in kilograms and grams, using scales.
Year Two – Measurement
Pounds & Pence
Recognise and use symbols for pounds (£) and pence (p), and combine amounts to make a particular value.
Year Two – Measurement
Quarter Past & Quarter To
Tell and write the time to quarter past and quarter to the hour, and draw the hands on a clock face.
Year Two – Measurement
Time to Five Minutes
Tell and write the time to five minutes, and know the number of minutes in an hour and hours in a day.
Year Two – Multiplication & Division
Commutativity of Multiplication
Show that multiplication of two numbers can be done in any order, and division of one number by another cannot.
Year Two – Multiplication & Division
Division: Grouping & Sharing with ÷
Write and calculate division statements using ÷ for grouping and sharing.
Year Two – Multiplication & Division
Multiplication: Repeated Addition & Arrays
Write and calculate multiplication statements using ×, arrays and repeated addition.
Year Two – Multiplication & Division
The 10 Times Table
Recall and use the 10 times table and connect multiplying by 10 to place value.
Year Two – Multiplication & Division
The 2 Times Table
Recall and use multiplication and division facts for the 2 times table.
Year Two – Multiplication & Division
The 5 Times Table
Recall and use multiplication and division facts for the 5 times table.
Year Two – Number & Place Value
Comparing with <, > and =
Compare two numbers to 100 using the symbols <, > and =.
Year Two – Number & Place Value
Counting in 2s, 3s and 5s
Count in steps of 2, 3 and 5 from zero, forwards and backwards.
Year Two – Number & Place Value
Counting in Tens from Any Number
Count forwards and backwards in tens from any starting number.
Year Two – Number & Place Value
Estimating on a Number Line
Estimate the position of a number on a number line marked only in tens.
Year Two – Number & Place Value
Numbers to 100 in Words & Numerals
Read and write numbers to 100 in numerals and in words.
Year Two – Number & Place Value
Ordering Numbers to 100
Order sets of numbers to 100 from least to greatest and greatest to least.
Year Two – Number & Place Value
Partitioning Flexibly
Partition two-digit numbers into tens and ones in more than one way.
Year Two – Number & Place Value
Tens & Ones
Recognise the tens and ones in a two-digit number and use zero as a placeholder.
Year Two – Statistics
Block Diagrams
Interpret and construct simple block diagrams.
Year Two – Statistics
Pictograms
Interpret and construct simple pictograms.
Year Two – Statistics
Sorting & Comparing Data
Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity; ask and answer questions about totalling and comparing categorical data.
Year Two – Statistics
Tally Charts & Tables
Interpret and construct simple tally charts and tables.