All curriculums

Mathematics

Mathematics

283 topic summaries

Topic summaries

Year Five – Addition & Subtraction

Column Addition (5+ digits)

Add whole numbers with more than four digits using the formal column method.

Age 11+

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.

Age 11+

Year Five – Addition & Subtraction

Mental Strategies with Large Numbers

Add and subtract increasingly large numbers mentally using efficient strategies.

Age 11+

Year Five – Addition & Subtraction

Rounding to Check

Use rounding to check answers to calculations and determine, in context, levels of accuracy.

Age 11+

Year Five – Fractions, Decimals & Percentages

Adding & Subtracting (related denominators)

Add and subtract fractions whose denominators are multiples of the same number, including mixed numbers.

Age 11+

Year Five – Fractions, Decimals & Percentages

Comparing & Ordering Fractions (related denominators)

Compare and order fractions whose denominators are multiples of the same number.

Age 11+

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.

Age 11+

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.

Age 11+

Year Five – Fractions, Decimals & Percentages

Mixed Numbers & Improper Fractions

Recognise mixed numbers and improper fractions and convert from one form to the other.

Age 11+

Year Five – Fractions, Decimals & Percentages

Multiplying Fractions by Whole Numbers

Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.

Age 11+

Year Five – Fractions, Decimals & Percentages

Ordering Decimals to 3dp

Read, write, order and compare numbers with up to three decimal places.

Age 11+

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.

Age 11+

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.

Age 11+

Year Five – Fractions, Decimals & Percentages

Thousandths

Recognise and use thousandths, relating them to tenths, hundredths and decimal equivalents.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

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°.

Age 11+

Year Five – Geometry: Properties of Shapes

Degrees, Reflex Angles & Estimating

Know angles are measured in degrees; estimate and compare acute, obtuse and reflex angles.

Age 11+

Year Five – Geometry: Properties of Shapes

Measuring & Drawing with a Protractor

Draw given angles and measure them in degrees, using a protractor.

Age 11+

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.

Age 11+

Year Five – Geometry: Properties of Shapes

Regular & Irregular Polygons

Distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

Age 11+

Year Five – Measurement

Area of Rectangles (formula)

Calculate and compare the area of rectangles using standard units, including using the formula length × width.

Age 11+

Year Five – Measurement

Converting Metric Units

Convert between different units of metric measure, including with decimals.

Age 11+

Year Five – Measurement

Estimating Area of Irregular Shapes

Estimate the area of irregular shapes by counting whole and part squares.

Age 11+

Year Five – Measurement

Imperial Equivalents

Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints.

Age 11+

Year Five – Measurement

Perimeter of Composite Shapes

Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres.

Age 11+

Year Five – Measurement

Volume & Capacity

Estimate volume using 1 cm³ blocks and capacity using water, and understand the difference between them.

Age 11+

Year Five – Multiplication & Division

Factors & Common Factors

Identify all factor pairs of a number and common factors of two numbers.

Age 11+

Year Five – Multiplication & Division

Multiples & Common Multiples

Identify multiples and common multiples of two numbers, including the lowest common multiple.

Age 11+

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.

Age 11+

Year Five – Multiplication & Division

Prime & Composite Numbers

Know and use the vocabulary of prime numbers, prime factors and composite numbers.

Age 11+

Year Five – Multiplication & Division

Remainders as Fractions, Decimals & Rounding

Express remainders appropriately as fractions, as decimals or by rounding, according to the context.

Age 11+

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.

Age 11+

Year Five – Multiplication & Division

Square & Cube Numbers

Recognise and use square and cube numbers and the notation for squared and cubed.

Age 11+

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.

Age 11+

Year Five – Multiplication & Division

Stretch Grammar – Square Roots

Stretch (universal 11+): find square roots of square numbers to 144 and use the √ notation.

Age 11+

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.

Age 11+

Year Five – Number & Place Value

Comparing & Ordering to 1,000,000

Compare and order numbers to at least 1,000,000.

Age 11+

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.

Age 11+

Year Five – Number & Place Value

Negative Numbers in Context

Interpret negative numbers in context and count forwards and backwards through zero.

Age 11+

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.

Age 11+

Year Five – Number & Place Value

Roman Numerals to 1000

Read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Age 11+

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.

Age 11+

Year Five – Statistics

Line Graphs

Solve comparison, sum and difference problems using information presented in a line graph.

Age 11+

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.

Age 11+

Year Four – Addition & Subtraction

Column Addition (4-digit)

Add numbers with up to four digits using the formal column method.

Age 9+

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.

Age 9+

Year Four – Addition & Subtraction

Estimating & Checking Two-Step Problems

Estimate and use inverse operations to check the answers to two-step problems.

Age 9+

Year Four – Addition & Subtraction

Two-Step Problems

Solve two-step addition and subtraction problems in context, deciding which operations to use.

Age 9+

Year Four – Fractions, Decimals & Percentages

Adding & Subtracting beyond One Whole

Add and subtract fractions with the same denominator, including totals greater than one whole.

Age 9+

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.

Age 9+

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.

Age 9+

Year Four – Fractions, Decimals & Percentages

Families of Equivalent Fractions

Recognise and show families of common equivalent fractions.

Age 9+

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.

Age 9+

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.

Age 9+

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.

Age 9+

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.

Age 9+

Year Four – Geometry: Position & Direction

Plotting Points & Completing Shapes

Plot specified points and draw sides to complete a given polygon.

Age 9+

Year Four – Geometry: Position & Direction

Reading Coordinates (along then up)

Describe positions on a 2-D grid as coordinates in the first quadrant.

Age 9+

Year Four – Geometry: Position & Direction

Translation

Describe movements between positions as translations of a given unit to the left/right and up/down.

Age 9+

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.

Age 9+

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.

Age 9+

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.

Age 9+

Year Four – Geometry: Properties of Shapes

Types of Quadrilateral

Compare and classify quadrilaterals — square, rectangle, rhombus, parallelogram, trapezium, kite — based on their properties.

Age 9+

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.

Age 9+

Year Four – Measurement

Area by Counting Squares

Find the area of rectilinear shapes by counting squares.

Age 9+

Year Four – Measurement

Converting Between Clocks

Read, write and convert time between analogue and digital 12- and 24-hour clocks.

Age 9+

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.

Age 9+

Year Four – Measurement

Converting Units of Time

Convert between hours and minutes, minutes and seconds, years and months, weeks and days.

Age 9+

Year Four – Measurement

Perimeter of Rectilinear Shapes

Measure and calculate the perimeter of rectilinear figures, including squares, in centimetres and metres.

Age 9+

Year Four – Multiplication & Division

Factor Pairs & the Distributive Law

Recognise factor pairs of a number and use the distributive law to multiply.

Age 9+

Year Four – Multiplication & Division

Interpreting Remainders

Interpret remainders appropriately in the context of a problem.

Age 9+

Year Four – Multiplication & Division

Short Division

Divide two- and three-digit numbers by a one-digit number using formal short division.

Age 9+

Year Four – Multiplication & Division

Short Multiplication

Multiply two- and three-digit numbers by a one-digit number using formal short multiplication.

Age 9+

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.

Age 9+

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.

Age 9+

Year Four – Number & Place Value

Comparing & Ordering beyond 1000

Compare and order numbers beyond 1000 using place value.

Age 9+

Year Four – Number & Place Value

Negative Numbers

Count backwards through zero to include negative numbers.

Age 9+

Year Four – Number & Place Value

Roman Numerals to 100

Read Roman numerals from I to C, including the subtractive pairs.

Age 9+

Year Four – Number & Place Value

Rounding to 10, 100 and 1000

Round any number to the nearest 10, 100 or 1000.

Age 9+

Year Four – Number & Place Value

Thousands, Hundreds, Tens & Ones

Recognise the value of each digit in a four-digit number.

Age 9+

Year Four – Statistics

Graphs with Larger Scales

Interpret and present discrete and continuous data using bar charts and time graphs with larger scales.

Age 9+

Year Four – Statistics

Reading Tables

Solve comparison, sum and difference problems using information presented in tables, including two-way tables.

Age 9+

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.

Age 9+

Year Four – Statistics

Timetables

Read and interpret timetables, including 24-hour times, and find durations and connections.

Age 9+

Year One – Addition & Subtraction

Adding within 20

Add one-digit and two-digit numbers to 20, including zero, by counting on and using bonds.

Age 7+

Year One – Addition & Subtraction

Missing Number Problems

Solve missing-number problems such as 7 = ▢ − 9, understanding = as balance.

Age 7+

Year One – Addition & Subtraction

Number Bonds to 10

Represent and recall the pairs of numbers that make 10, and their subtraction facts.

Age 7+

Year One – Addition & Subtraction

Number Bonds within 20

Represent and use number bonds and related subtraction facts within 20.

Age 7+

Year One – Addition & Subtraction

Subtracting within 20

Subtract within 20 by counting back, using bonds and subtracting through ten.

Age 7+

Year One – Fractions, Decimals & Percentages

Halves

Recognise, find, name and write one half of an object, shape, set of objects or quantity.

Age 7+

Year One – Fractions, Decimals & Percentages

Quarters

Recognise, find, name and write one quarter of an object, shape, set of objects or quantity.

Age 7+

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.

Age 7+

Year One – Geometry: Position & Direction

Whole, Half & Quarter Turns

Describe movement including whole, half, quarter and three-quarter turns.

Age 7+

Year One – Geometry: Properties of Shapes

Naming 2-D Shapes

Recognise and name common 2-D shapes: rectangles (including squares), circles and triangles.

Age 7+

Year One – Geometry: Properties of Shapes

Naming 3-D Shapes

Recognise and name common 3-D shapes: cuboids (including cubes), pyramids and spheres.

Age 7+

Year One – Measurement

Coins & Notes

Recognise and know the value of different denominations of coins and notes.

Age 7+

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.

Age 7+

Year One – Measurement

Comparing Length & Height

Compare, describe and solve practical problems for lengths and heights using words such as longer, shorter, taller.

Age 7+

Year One – Measurement

Comparing Mass

Compare, describe and solve practical problems for mass using words such as heavier, lighter.

Age 7+

Year One – Measurement

Days, Weeks & Months

Sequence events in chronological order and recognise the days of the week and months of the year.

Age 7+

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.

Age 7+

Year One – Multiplication & Division

Making Equal Groups

Solve one-step multiplication problems using objects, pictures and arrays, with support.

Age 7+

Year One – Multiplication & Division

Sharing Equally

Solve one-step division problems by sharing equally and by grouping, using objects and pictures.

Age 7+

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.

Age 7+

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.

Age 7+

Year One – Number & Place Value

More, Less & Equal

Compare two or three amounts using more, fewer, less, most, least and equal to.

Age 7+

Year One – Number & Place Value

Numbers on a Number Line

Read and find numbers on a number line and jump along it in steps.

Age 7+

Year One – Number & Place Value

Odd & Even Numbers

Recognise odd and even numbers by making pairs and by looking at the last digit.

Age 7+

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.

Age 7+

Year One – Number & Place Value

Reading & Writing Numbers to 20

Read and write numbers from 1 to 20 in numerals and in words.

Age 7+

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.

Age 11+

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.

Age 11+

Year Six – Algebra

Cipher's Final Mission (Mixed Problems)

Solve mixed algebra problems drawing on formulae, sequences, expressions, equations and systematic listing.

Age 11+

Year Six – Algebra

Equations with Two Unknowns

Find pairs of numbers that satisfy an equation with two unknowns.

Age 11+

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.

Age 11+

Year Six – Algebra

Formulae in Symbols & Substitution

Use simple formulae written in symbols, substituting values for letters.

Age 11+

Year Six – Algebra

Formulae in Words

Use simple formulae expressed in words, and find outputs from inputs.

Age 11+

Year Six – Algebra

Generating Sequences from a Rule

Generate linear number sequences from a term-to-term rule and a start number.

Age 11+

Year Six – Algebra

Letters for Unknowns (expressions)

Express missing number problems algebraically, using letters for unknowns and writing expressions.

Age 11+

Year Six – Algebra

Listing All Possibilities Systematically

Enumerate possibilities of combinations of two variables systematically.

Age 11+

Year Six – Algebra

Solving One-Step Equations

Solve one-step equations by using inverse operations, and check solutions.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

Year Six – Algebra

Stretch Grammar – Two-Step Equations

Stretch (universal 11+): solve two-step equations by undoing operations in reverse order.

Age 11+

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.

Age 11+

Year Six – Fractions, Decimals & Percentages

Adding & Subtracting Mixed Numbers

Add and subtract mixed numbers with different denominators.

Age 11+

Year Six – Fractions, Decimals & Percentages

Adding & Subtracting with Different Denominators

Add and subtract fractions with different denominators using equivalent fractions.

Age 11+

Year Six – Fractions, Decimals & Percentages

Common Denominators & Ordering

Compare and order fractions with any denominators by finding a common denominator.

Age 11+

Year Six – Fractions, Decimals & Percentages

Dividing a Fraction by a Whole Number

Divide proper fractions by whole numbers.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

Year Six – Fractions, Decimals & Percentages

Multiplying Decimals by Whole Numbers

Multiply one-digit numbers with up to two decimal places by whole numbers.

Age 11+

Year Six – Fractions, Decimals & Percentages

Multiplying Fractions

Multiply simple pairs of proper fractions, writing the answer in its simplest form.

Age 11+

Year Six – Fractions, Decimals & Percentages

Simplifying Fractions

Use common factors to simplify fractions to their simplest form.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

Year Six – Geometry: Position & Direction

Predicting Missing Vertices

Predict missing coordinates of shapes using their properties, including across quadrants.

Age 11+

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.

Age 11+

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.

Age 11+

Year Six – Geometry: Position & Direction

The Four Quadrants

Describe positions on the full coordinate grid (all four quadrants).

Age 11+

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.

Age 11+

Year Six – Geometry: Properties of Shapes

Angles in Quadrilaterals

Find unknown angles in quadrilaterals using the angle sum of 360°.

Age 11+

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.

Age 11+

Year Six – Geometry: Properties of Shapes

Angles in Triangles

Find unknown angles in triangles using the angle sum of 180°.

Age 11+

Year Six – Geometry: Properties of Shapes

Drawing Shapes with Given Dimensions

Draw 2-D shapes using given dimensions and angles.

Age 11+

Year Six – Geometry: Properties of Shapes

Nets of 3-D Shapes

Recognise, describe and build simple 3-D shapes, including making nets.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

Year Six – Measurement

Area of Parallelograms

Calculate the area of parallelograms.

Age 11+

Year Six – Measurement

Area of Triangles

Calculate the area of triangles.

Age 11+

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.

Age 11+

Year Six – Measurement

Miles & Kilometres

Convert between miles and kilometres.

Age 11+

Year Six – Measurement

Same Area, Different Perimeter

Recognise that shapes with the same areas can have different perimeters and vice versa.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

Year Six – Multiplication & Division

HCF & LCM in Problems

Apply common factors and common multiples to solve problems.

Age 11+

Year Six – Multiplication & Division

Long Division

Divide numbers up to four digits by a two-digit number using long division.

Age 11+

Year Six – Multiplication & Division

Long Multiplication

Multiply numbers up to four digits by a two-digit number using formal long multiplication.

Age 11+

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 '='.

Age 11+

Year Six – Multiplication & Division

Remainders in Context

Interpret remainders in context, including rounding up, when dividing by two-digit numbers.

Age 11+

Year Six – Multiplication & Division

Stretch Grammar – Missing-Digit Problems

Stretch (universal 11+): find missing digits in multiplication and division calculations by reasoning.

Age 11+

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.

Age 11+

Year Six – Number & Place Value

Comparing & Ordering to 10,000,000

Order and compare numbers up to 10,000,000.

Age 11+

Year Six – Number & Place Value

Intervals Across Zero

Use negative numbers in context and calculate intervals across zero.

Age 11+

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.

Age 11+

Year Six – Number & Place Value

Rounding to Any Degree of Accuracy

Round any whole number to a required degree of accuracy.

Age 11+

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.

Age 11+

Year Six – Ratio & Proportion

Comparing with Percentages

Use percentages for comparison, converting fractions and scores to percentages.

Age 11+

Year Six – Ratio & Proportion

Percentages of Amounts

Solve problems involving the calculation of percentages, such as 15% of 360, and use percentages for comparison.

Age 11+

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.

Age 11+

Year Six – Ratio & Proportion

Scale Factors

Solve problems involving similar shapes where the scale factor is known or can be found.

Age 11+

Year Six – Ratio & Proportion

Scaling Ratios

Scale a ratio up or down to find a missing quantity, including recipe and mixture problems.

Age 11+

Year Six – Ratio & Proportion

Sharing in a Ratio

Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

Age 11+

Year Six – Ratio & Proportion

Similar Shapes

Solve problems involving similar shapes, finding missing lengths from corresponding sides.

Age 11+

Year Six – Ratio & Proportion

Stretch Grammar – Best Buy & Unit Pricing

Stretch (universal 11+): compare value for money using unit prices or a common quantity.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

Year Six – Ratio & Proportion

Stretch Grammar – Speed, Distance & Time

Stretch (universal 11+): use speed = distance ÷ time and rearrangements to solve journey problems.

Age 11+

Year Six – Ratio & Proportion

The Grand Brew (Mixed Problems)

Solve mixed problems drawing on ratio, proportion, percentages and scale, choosing the method for each.

Age 11+

Year Six – Ratio & Proportion

Times as Many

Solve problems involving the relative sizes of two quantities, using multiplication and division facts — 'times as many'.

Age 11+

Year Six – Ratio & Proportion

Writing & Simplifying Ratios

Write a ratio from a description or picture and simplify it using common factors.

Age 11+

Year Six – Statistics

Constructing & Interpreting Line Graphs

Construct line graphs from tables and interpret them, including reading between points and comparing two lines.

Age 11+

Year Six – Statistics

Pie Charts, Angles & Percentages

Interpret and construct pie charts using angles and percentages.

Age 11+

Year Six – Statistics

Reading Pie Charts

Interpret pie charts and use them to solve problems, reading sectors as fractions of the whole.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

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.

Age 11+

Year Six – Statistics

The Mean

Calculate and interpret the mean as an average.

Age 11+

Year Three – Addition & Subtraction

Adding & Subtracting Hundreds Mentally

Add and subtract a three-digit number and hundreds mentally.

Age 9+

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.

Age 9+

Year Three – Addition & Subtraction

Checking with the Inverse

Use inverse operations to check answers to additions and subtractions with three-digit numbers.

Age 9+

Year Three – Addition & Subtraction

Column Addition (3-digit)

Add numbers with up to three digits using the formal column method, including exchange.

Age 9+

Year Three – Addition & Subtraction

Column Subtraction with Exchange (3-digit)

Subtract numbers with up to three digits using the formal column method with exchange.

Age 9+

Year Three – Addition & Subtraction

Estimating Answers

Estimate the answer to an addition or subtraction by rounding before calculating.

Age 9+

Year Three – Fractions, Decimals & Percentages

Adding & Subtracting (same denominator)

Add and subtract fractions with the same denominator within one whole.

Age 9+

Year Three – Fractions, Decimals & Percentages

Comparing & Ordering Fractions

Compare and order unit fractions, and fractions with the same denominator.

Age 9+

Year Three – Fractions, Decimals & Percentages

Equivalent Fractions with Diagrams

Recognise and show, using diagrams, equivalent fractions with small denominators.

Age 9+

Year Three – Fractions, Decimals & Percentages

Fractions as Numbers on a Number Line

Use fractions as numbers and place them on a number line.

Age 9+

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.

Age 9+

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.

Age 9+

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.

Age 9+

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.

Age 9+

Year Three – Geometry: Properties of Shapes

Horizontal & Vertical Lines

Identify horizontal and vertical lines.

Age 9+

Year Three – Geometry: Properties of Shapes

Perpendicular & Parallel Lines

Identify pairs of perpendicular and parallel lines.

Age 9+

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.

Age 9+

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.

Age 9+

Year Three – Measurement

Capacity in l and ml

Measure, compare, add and subtract capacity in litres and millilitres, using mixed units.

Age 9+

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.

Age 9+

Year Three – Measurement

Length in m, cm and mm

Measure, compare, add and subtract lengths in metres, centimetres and millimetres, using mixed units.

Age 9+

Year Three – Measurement

Mass in kg and g

Measure, compare, add and subtract mass in kilograms and grams, using mixed units.

Age 9+

Year Three – Measurement

Money: Adding, Subtracting & Change

Add and subtract amounts of money to give change, using both £ and p in practical contexts.

Age 9+

Year Three – Measurement

Perimeter of 2-D Shapes

Measure the perimeter of simple 2-D shapes.

Age 9+

Year Three – Measurement

Time to the Minute

Tell and write the time from an analogue clock to the nearest minute, including using Roman numerals.

Age 9+

Year Three – Multiplication & Division

Scaling & Correspondence Problems

Solve scaling problems and correspondence problems in which n objects are connected to m objects.

Age 9+

Year Three – Multiplication & Division

The 3 Times Table

Recall and use multiplication and division facts for the 3 times table.

Age 9+

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.

Age 9+

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.

Age 9+

Year Three – Multiplication & Division

Two-Digit × One-Digit (partitioning)

Multiply a two-digit number by a one-digit number mentally by partitioning.

Age 9+

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.

Age 9+

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.

Age 9+

Year Three – Number & Place Value

Comparing & Ordering to 1000

Compare and order numbers to 1000 using place value.

Age 9+

Year Three – Number & Place Value

Counting in 4s, 8s, 50s and 100s

Count from zero in multiples of 4, 8, 50 and 100.

Age 9+

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.

Age 9+

Year Three – Number & Place Value

Hundreds, Tens & Ones

Recognise the value of each digit in a three-digit number.

Age 9+

Year Three – Number & Place Value

Partitioning Three-Digit Numbers

Partition three-digit numbers into hundreds, tens and ones in more than one way.

Age 9+

Year Three – Statistics

Bar Charts with Scaled Axes

Interpret and present data using bar charts and pictograms with scaled axes.

Age 9+

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.

Age 9+

Year Three – Statistics

Time Graphs

Interpret simple time graphs, reading values at given times and describing change.

Age 9+

Year Two – Addition & Subtraction

Adding Three One-Digit Numbers

Add three one-digit numbers, using pairs that make ten.

Age 7+

Year Two – Addition & Subtraction

Any Order? Commutativity

Show that addition can be done in any order but subtraction cannot.

Age 7+

Year Two – Addition & Subtraction

Checking with the Inverse

Use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems.

Age 7+

Year Two – Addition & Subtraction

Deriving Facts to 100

Use known facts to 20 to derive related facts to 100.

Age 7+

Year Two – Addition & Subtraction

Fluent Facts to 20

Recall addition and subtraction facts to 20 fluently.

Age 7+

Year Two – Addition & Subtraction

Two Two-Digit Numbers (with exchange)

Add and subtract two two-digit numbers, exchanging where needed.

Age 7+

Year Two – Addition & Subtraction

Two-Digit Numbers and Ones

Add and subtract a two-digit number and ones, including crossing a ten.

Age 7+

Year Two – Addition & Subtraction

Two-Digit Numbers and Tens

Add and subtract a two-digit number and tens.

Age 7+

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.

Age 7+

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.

Age 7+

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.

Age 7+

Year Two – Geometry: Position & Direction

Patterns & Sequences of Shapes

Order and arrange combinations of mathematical objects in patterns and sequences.

Age 7+

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.

Age 7+

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.

Age 7+

Year Two – Geometry: Properties of Shapes

Lines of Symmetry

Identify and describe the properties of 2-D shapes including a vertical line of symmetry.

Age 7+

Year Two – Geometry: Properties of Shapes

Sides & Vertices

Identify and describe the properties of 2-D shapes, including the number of sides and vertices.

Age 7+

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.

Age 7+

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.

Age 7+

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.

Age 7+

Year Two – Measurement

Making Amounts with Coins

Find different combinations of coins that equal the same amounts of money.

Age 7+

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.

Age 7+

Year Two – Measurement

Measuring Mass (kg, g)

Choose and use appropriate standard units to estimate and measure mass in kilograms and grams, using scales.

Age 7+

Year Two – Measurement

Pounds & Pence

Recognise and use symbols for pounds (£) and pence (p), and combine amounts to make a particular value.

Age 7+

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.

Age 7+

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.

Age 7+

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.

Age 7+

Year Two – Multiplication & Division

Division: Grouping & Sharing with ÷

Write and calculate division statements using ÷ for grouping and sharing.

Age 7+

Year Two – Multiplication & Division

Multiplication: Repeated Addition & Arrays

Write and calculate multiplication statements using ×, arrays and repeated addition.

Age 7+

Year Two – Multiplication & Division

The 10 Times Table

Recall and use the 10 times table and connect multiplying by 10 to place value.

Age 7+

Year Two – Multiplication & Division

The 2 Times Table

Recall and use multiplication and division facts for the 2 times table.

Age 7+

Year Two – Multiplication & Division

The 5 Times Table

Recall and use multiplication and division facts for the 5 times table.

Age 7+

Year Two – Number & Place Value

Comparing with <, > and =

Compare two numbers to 100 using the symbols <, > and =.

Age 7+

Year Two – Number & Place Value

Counting in 2s, 3s and 5s

Count in steps of 2, 3 and 5 from zero, forwards and backwards.

Age 7+

Year Two – Number & Place Value

Counting in Tens from Any Number

Count forwards and backwards in tens from any starting number.

Age 7+

Year Two – Number & Place Value

Estimating on a Number Line

Estimate the position of a number on a number line marked only in tens.

Age 7+

Year Two – Number & Place Value

Numbers to 100 in Words & Numerals

Read and write numbers to 100 in numerals and in words.

Age 7+

Year Two – Number & Place Value

Ordering Numbers to 100

Order sets of numbers to 100 from least to greatest and greatest to least.

Age 7+

Year Two – Number & Place Value

Partitioning Flexibly

Partition two-digit numbers into tens and ones in more than one way.

Age 7+

Year Two – Number & Place Value

Tens & Ones

Recognise the tens and ones in a two-digit number and use zero as a placeholder.

Age 7+

Year Two – Statistics

Block Diagrams

Interpret and construct simple block diagrams.

Age 7+

Year Two – Statistics

Pictograms

Interpret and construct simple pictograms.

Age 7+

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.

Age 7+

Year Two – Statistics

Tally Charts & Tables

Interpret and construct simple tally charts and tables.

Age 7+