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Created on 31 May 2013 by ncetm_administrator
Updated on 04 June 2014 by ncetm_administrator

# The National Curriculum for Mathematics - Resource Tool

Topic titles link to Progression Maps and Glossary
Topic

Content will appear in this pane, after making one or more selections from the above grid and clicking on the "Show selection" button.

Content will appear in this pane, after making one or more selections from the above grid and clicking on the "Show selection" button.

## Y1: Number and Place Value

ID 01

• count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number
• count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens
• given a number, identify one more and one less
• identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least
• read and write numbers from 1 to 20 in numerals and words.

## Y2: Number and Place Value

ID 02

• count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward
• recognise the place value of each digit in a two-digit number (tens, ones)
• identify, represent and estimate numbers using different representations, including the number line
• compare and order numbers from 0 up to 100; use <, > and = signs
• read and write numbers to at least 100 in numerals and in words
• use place value and number facts to solve problems.

## Y3: Number and Place Value

ID 03

• count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number
• recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
• compare and order numbers up to 1000
• identify, represent and estimate numbers using different representations
• read and write numbers up to 1000 in numerals and in words
• solve number problems and practical problems involving these ideas.

## Y4: Number and Place Value

ID 04

• count in multiples of 6, 7, 9, 25 and 1000
• find 1000 more or less than a given number
• count backwards through zero to include negative numbers
• recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
• order and compare numbers beyond 1000
• identify, represent and estimate numbers using different representations
• round any number to the nearest 10, 100 or 1000
• solve number and practical problems that involve all of the above and with increasingly large positive numbers
• read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value.

## Y5: Number and place value

ID 05

• read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
• count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
• interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
• round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
• solve number problems and practical problems that involve all of the above
• read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

## Y6: Number – number and place value

ID 06

• read, write, order and compare numbers up to 10 000 000 and determine the value of each digit
• round any whole number to a required degree of accuracy
• use negative numbers in context, and calculate intervals across zero
• solve number problems and practical problems that involve all of the above.

## KS3: Number

ID 07

Pupils should be taught to:

• understand and use place value for decimals, measures and integers of any size
• order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
• use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property
• use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
• use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
• recognise and use relationships between operations including inverse operations
• use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations
• interpret and compare numbers in standard form A × 10n 1≤A>10, where n is a positive or negative integer or zero
• work interchangeably with terminating decimals and their corresponding fractions
(such as 3.5 and 72 or 0.375 and 38)
• define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%
• interpret fractions and percentages as operators
• use standard units of mass, length, time, money and other measures, including with decimal quantities
• round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
• use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xb
• use a calculator and other technologies to calculate results accurately and then interpret them appropriately
• appreciate the infinite nature of the sets of integers, real and rational numbers

ID 08

• read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs
• represent and use number bonds and related subtraction facts within 20
• add and subtract one-digit and two-digit numbers to 20, including zero
• solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ☐ – 9.

ID 09

• solve problems with addition and subtraction:
• using concrete objects and pictorial representations, including those involving numbers, quantities and measures
• applying their increasing knowledge of mental and written methods
• recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
• add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
• a two-digit number and ones
• a two-digit number and tens
• two two-digit numbers
• show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
• recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.

ID 10

• add and subtract numbers mentally, including:
• a three-digit number and ones
• a three-digit number and tens
• a three-digit number and hundreds
• add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction
• estimate the answer to a calculation and use inverse operations to check answers
• solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

ID 11

• add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
• estimate and use inverse operations to check answers to a calculation
• solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

ID 12

• add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
• add and subtract numbers mentally with increasingly large numbers
• use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
• solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

## Y6: Number - Addition and Subtraction, Multiplication and Division

ID 13

• multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
• divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
• divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
• perform mental calculations, including with mixed operations and large numbers
• identify common factors, common multiples and prime numbers
• use their knowledge of the order of operations to carry out calculations involving the four operations
• solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
• solve problems involving addition, subtraction, multiplication and division
• use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

## KS3: Number

ID 14

Pupils should be taught to:

• understand and use place value for decimals, measures and integers of any size
• order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
• use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property
• use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
• use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
• recognise and use relationships between operations including inverse operations
• use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations
• interpret and compare numbers in standard form A × 10n 1≤A>10, where n is a positive or negative integer or zero
• work interchangeably with terminating decimals and their corresponding fractions
(such as 3.5 and 72 or 0.375 and 38)
• define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%
• interpret fractions and percentages as operators
• use standard units of mass, length, time, money and other measures, including with decimal quantities
• round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
• use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xb
• use a calculator and other technologies to calculate results accurately and then interpret them appropriately
• appreciate the infinite nature of the sets of integers, real and rational numbers

## Y1: Multiplication and Division

ID 15

• solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

## Y2: Multiplication and Division

ID 16

• recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
• calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
• show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
• solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

## Y3: Multiplication and Division

ID 17

• recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
• write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods
• solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.

## Y4: Multiplication and Division

ID 18

• recall multiplication and division facts for multiplication tables up to 12 × 12
• use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
• recognise and use factor pairs and commutativity in mental calculations
• multiply two-digit and three-digit numbers by a one-digit number using formal written layout
• solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

## Y5: Multiplication and Division

ID 19

identify multiples and factors:

• identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers
• know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
• establish whether a number up to 100 is prime and recall prime numbers up to 19
• multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
• multiply and divide numbers mentally, drawing upon known facts
• divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
• multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
• recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
• solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes
• solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
• solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

## Y6: Number - Addition and Subtraction, Multiplication and Division

ID 20

• multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
• divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
• divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
• perform mental calculations, including with mixed operations and large numbers
• identify common factors, common multiples and prime numbers
• use their knowledge of the order of operations to carry out calculations involving the four operations
• solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
• solve problems involving addition, subtraction, multiplication and division
• use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

## KS3: Number

ID 21

Pupils should be taught to:

• understand and use place value for decimals, measures and integers of any size
• order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
• use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property
• use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
• use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
• recognise and use relationships between operations including inverse operations
• use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations
• interpret and compare numbers in standard form A × 10n 1≤A>10, where n is a positive or negative integer or zero
• work interchangeably with terminating decimals and their corresponding fractions
(such as 3.5 and 72 or 0.375 and 38)
• define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%
• interpret fractions and percentages as operators
• use standard units of mass, length, time, money and other measures, including with decimal quantities
• round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
• use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<xb
• use a calculator and other technologies to calculate results accurately and then interpret them appropriately
• appreciate the infinite nature of the sets of integers, real and rational numbers

## Y1: Fractions

ID 22

• recognise, find and name a half as one of two equal parts of an object, shape or quantity
• recognise, find and name a quarter as one of four equal parts of an object, shape or quantity

## Y2: Fractions

ID 23

• recognise, find, name and write fractions ⅓, ¼, 24 and ¾ of a length, shape, set of objects or quantity
• write simple fractions e.g. ½ of 6 = 3 and recognise the equivalence of two quarters and one half.

## Y3: Fractions

ID 24

• count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10
• recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
• recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
• recognise and show, using diagrams, equivalent fractions with small denominators
• add and subtract fractions with the same denominator within one whole [for example, 57 + 17 = 67 ]
• compare and order unit fractions, and fractions with the same denominator
• solve problems that involve all of the above.

## Y4: Fractions (including decimals)

ID 25

• recognise and show, using diagrams, families of common equivalent fractions
• count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
• solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
• add and subtract fractions with the same denominator
• recognise and write decimal equivalents of any number of tenths or hundredths
• recognise and write decimal equivalents to ¼, ½, ¾
• find the effect of dividing a one- or two-digit number by 10 and 100, identifying the  value of the digits in the answer as ones, tenths and hundredths
• round decimals with one decimal place to the nearest whole number
• compare numbers with the same number of decimal places up to two decimal places
• solve simple measure and money problems involving fractions and decimals to two decimal places.

## Y5: Fractions (including decimals and percentages)

ID 26

• compare and order fractions whose denominators are all multiples of the same number
• identify, name and write equivalent fractions of a given fraction, represented visually,including tenths and hundredths
• recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements >1 as a mixed number[for example,25+45=65= 115]
• add and subtract fractions with the same denominator and denominators that are multiples of the same number
• multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
• read and write decimal numbers as fractions [for example, 0.71 =71100]
• recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
• round decimals with two decimal places to the nearest whole number and to one decimal place
• read, write, order and compare numbers with up to three decimal places
• solve problems involving number up to three decimal places
• recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal
• solve problems which require knowing percentage and decimal equivalents of 12, 14,15, 25 and those fractions with a denominator of a multiple of 10 or 25.

## Y6: Number - fractions (including decimals and percentages)

ID 27

• use common factors to simplify fractions; use common multiples to express fractions in the same denomination
• compare and order fractions, including fractions >1
• add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
• multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, ¼ × ½ = 18]
• divide proper fractions by whole numbers [for example, 13 ÷ 2 = 16]
• associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 38]
• identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places
• multiply one-digit numbers with up to two decimal places by whole numbers
• use written division methods in cases where the answer has up to two decimal places.
• solve problems which require answers to be rounded to specified degrees of accuracy
• recall and use equivalences between simple fractions, decimals and percentages including in different contexts.

## Y6: Ratio and Proportion

ID 34

• solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
• solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and use percentages for comparison
• solve problems involving similar shapes where the scale factor is known or can be found
• solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

## KS3: Ratio, Proportion and Rates of Change

ID 35

Pupils should be taught to:

• change freely between related standard units (for example time, length, area, volume/capacity, mass)
• use scale factors, scale diagrams and maps
• express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
• use ratio notation, including reduction to simplest form
• divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
• understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
• relate the language of ratios and the associated calculations to arithmetic of fractions and to linear functions
• solve problems involving percentage change, including: percentage increase, decrease and the original value problems and simple interest in financial mathematics
• solve problems involving direct and inverse proportion, including graphical and algebraic representations
• use compound units such as speed, unit pricing and density to solve problems

## Y1: Measurement

ID 36

• compare, describe and solve practical problems for:
• lengths and heights [for example, long/short, longer/shorter, tall/short, double/half]
• mass/weight [for example, heavy/light, heavier than, lighter than]
• capacity and volume [for example, full/empty, more than, less than, half, half full, quarter]
• time [for example, quicker, slower, earlier, later]
• measure and begin to record the following:
• lengths and heights
• mass/weight
• capacity and volume
• time (hours, minutes, seconds)
• recognise and know the value of different denominations of coins and notes
• sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening]
• recognise and use language relating to dates, including days of the week, weeks, months and years
• tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

## Y2: Measurement

ID 37

• choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels
• compare and order lengths, mass, volume/capacity and record the results using >, < and =
• recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value
• find different combinations of coins that equal the same amounts of money
• solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change
• compare and sequence intervals of time
• tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times
• know the number of minutes in an hour and the number of hours in a day.

## Y3: Measurement

ID 38

• measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
• measure the perimeter of simple 2-D shapes
• add and subtract amounts of money to give change, using both £ and p in practical contexts
• tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks
• estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o’clock, a.m./p.m., morning, afternoon, noon and midnight
• know the number of seconds in a minute and the number of days in each month, year and leap year
• compare durations of events [for example to calculate the time taken by particular events or tasks].

## Y4: Measurement

ID 39

• Convert between different units of measure [for example, kilometre to metre; hour to minute]
• measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
• find the area of rectilinear shapes by counting squares
• estimate, compare and calculate different measures, including money in pounds and pence
• read, write and convert time between analogue and digital 12- and 24-hour clocks
• solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.

## Y5: Measurement

ID 40

• convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
• understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
• measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
• calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes
• estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]
• solve problems involving converting between units of time
• use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling.

## Y6: Measurement

ID 41

• solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
• use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places
• convert between miles and kilometres
• recognise that shapes with the same areas can have different perimeters and vice versa
• recognise when it is possible to use the formulae for area and volume of shapes
• calculate the area of parallelograms and triangles
• calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units [for example, mm3 and km3]

## KS3: Geometry and Measures

ID 42

Pupils should be taught to:

• derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)
• calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
• draw and measure line segments and angles in geometric figures, including interpreting scale drawings
• derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line
• describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
• use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
• derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
• identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
• identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
• apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
• understand and use the relationship between parallel lines and alternate and corresponding angles
• derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons
• apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs
• use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
• use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
• interpret mathematical relationships both algebraically and geometrically

## Y1: Geometry: Properties of Shapes

ID 43

• recognise and name common 2-D and 3-D shapes, including:
• 2-D shapes [for example, rectangles (including squares), circles and triangles]
• 3-D shapes [for example, cuboids (including cubes), pyramids and spheres].

## Y2: Geometry: Properties of Shapes

ID 44

• identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line
• identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
• identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
• compare and sort common 2-D and 3-D shapes and everyday objects.

## Y3: Geometry: Properties of Shapes

ID 45

• draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them
• recognise angles as a property of shape or a description of a turn
• identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle
• identify horizontal and vertical lines and pairs of perpendicular and parallel lines.

## Y4: Geometry: Properties of Shapes

ID 46

• compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
• identify acute and obtuse angles and compare and order angles up to two right angles by size
• identify lines of symmetry in 2-D shapes presented in different orientations
• complete a simple symmetric figure with respect to a specific line of symmetry.

## Y5: Geometry: Properties of Shapes

ID 47

• identify 3-D shapes, including cubes and other cuboids, from 2-D representations
• know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
• draw given angles, and measure them in degrees (°)
• identify:
• angles at a point and one whole turn (total 360°)
• angles at a point on a straight line and ½ a turn (total 180°)
• other multiples of 90°
• use the properties of rectangles to deduce related facts and find missing lengths and angles
• distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

## Y6: Geometry: Properties of Shapes

ID 48

• draw 2-D shapes using given dimensions and angles
• recognise, describe and build simple 3-D shapes including making nets
• compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
• illustrate and name parts of circle, including radius, diameter and circumference and know that the diameter is twice the radius
• recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

## KS3: Geometry and Measures

ID 49

Pupils should be taught to:

• derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)
• calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
• draw and measure line segments and angles in geometric figures, including interpreting scale drawings
• derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line
• describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
• use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
• derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
• identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
• identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
• apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
• understand and use the relationship between parallel lines and alternate and corresponding angles
• derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons
• apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs
• use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
• use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
• interpret mathematical relationships both algebraically and geometrically

## Y1: Geometry: Position and Direction

ID 50

• describe position, direction and movement, including whole, half, quarter and three-quarter turns.

## Y2: Geometry: Position and Direction

ID 51

• order and arrange combinations of mathematical objects in patterns and sequences
• use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise).

## Y4: Geometry: Position and Direction

ID 53

• describe positions on a 2-D grid as coordinates in the first quadrant
• describe movements between positions as translations of a given unit to the left/right and up/down
• plot specified points and draw sides to complete a given polygon.

## Y5: Geometry: Position and Direction

ID 54

• identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed.

## Y6: Geometry: Position and Direction

ID 55

• describe positions on the full coordinate grid (all four quadrants)
• draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

## KS3: Geometry and Measures

ID 56

Pupils should be taught to:

• derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)
• calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
• draw and measure line segments and angles in geometric figures, including interpreting scale drawings
• derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line
• describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
• use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
• derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
• identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
• identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
• apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
• understand and use the relationship between parallel lines and alternate and corresponding angles
• derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons
• apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs
• use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
• use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
• interpret mathematical relationships both algebraically and geometrically

## Y2: Statistics

ID 58

• interpret and construct simple pictograms, tally charts, block diagrams and simple tables
• ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity

## Y3: Statistics

ID 59

• interpret and present data using bar charts, pictograms and tables
• solve one-step and two-step questions [for example, ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables.

## Y4: Statistics

ID 60

• interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs.
• solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

## Y5: Statistics

ID 61

• solve comparison, sum and difference problems using information presented in a line graph
• complete, read and interpret information in tables, including timetables.

## Y6: Statistics

ID 62

• interpret and construct pie charts and line graphs and use these to solve problems
• calculate and interpret the mean as an average

ID 63

## Probability

Pupils should be taught to:

• record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
• understand that the probabilities of all possible outcomes sum to 1
• enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
• generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities

## Statistics

Pupils should be taught to:

• describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)
• construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
• describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs

## Y6: Algebra

ID 69

• use simple formulae
• generate and describe linear number sequences
• express missing number problems algebraically
• find pairs of numbers that satisfy number sentences involving two unknowns
• enumerate possibilities of combinations of two variables

## KS3: Algebra

ID 70

Pupils should be taught to:

• Use and interpret algebraic notation, including:
• ab in place of a × b
• 3y in place of y + y + y and 3 × y
• a2 in place of a × a, a3 in place of a × a × a; a2b in place of a × a × b
• ab in place of a ÷ b
• coefficients written as fractions rather than as decimals
• brackets
• substitute numerical values into formulae and expressions, including scientific formulae
• understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
• simplify and manipulate algebraic expressions to maintain equivalence by:
• collecting like terms
• multiplying a single term over a bracket
• taking out common factors
• expanding products of two or more binominals
• understand and use standard mathematical formulae; rearrange formulae to change the subject
• model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
• use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
• work with coordinates in all four quadrants
• recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
• interpret mathematical relationships both algebraically and graphically
• reduce a given linear equation in two variables to the standard form y=mx+c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
• use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
• find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
• generate terms of a sequence from either a term-to-term or position-to-term rule
• recognise arithmetic sequences and find the nth term
• recognise geometric sequences and appreciate other sequences that arise. Add to your NCETM favourites Remove from your NCETM favourites Add a note on this item Recommend to a friend Comment on this item Send to printer Request a reminder of this item Cancel a reminder of this item

09 December 2017 11:09
Hi I have an interview on Monday but before that they want me to teach mastery maths focused on literacy text followed by a lesson on reasoning to 30 children different abilities. any ideas
23 October 2017 15:33
Sorry: this isn't available in print format, as it would make updating difficult, and users wouldn't always be sure that they had the most up-to-date version.
23 October 2017 15:22
This is great - thank you. It would be really usefull to have the examplification for each area on a printable sheet - alongside the obectives - Is this available anywhere?
14 June 2017 10:33
Brilliant. Puposeful and useful - such a greats tarting point. Could you add further resources for times tables for Y4/5/6. I know there is lots of stuff out there for drilling, but there is a lot less that promtes fluency with meaning. I love the teachers TV activity with arrays/multilink. Any more like this?
17 March 2017 11:25
Thank you :-) Very useful
17 March 2017 09:38
And this article in the Primary Magazine looks at misconceptions in the National Curriculum https://www.ncetm.org.uk/resources/47958
17 March 2017 09:36
You may want to look at this document for common misconceptions https://www.ncetm.org.uk/public/files/2042723/Misconceptions+with+the+Key+Objectives2.doc
17 March 2017 07:37
Hi, could anyone please let me know where the 'Common misconceptions' for each topic are? Thanks
08 December 2016 14:33
Interesting...
05 December 2016 10:17
For year 5 to solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes, choose the year 5 multiplication and division button. In particular you may want to look at activity F on https://www.ncetm.org.uk/resources/42605
03 December 2016 10:48
Hi - I'd like some help planning for year 5 relating to this requirement in the 2014NC -

solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors .... but I can't find any reference to it on your website. Can you help?
09 October 2016 11:05
Lynn... the White Rose maths hub planning is pretty useful but I wouldn't take it as scheme of its own right, it will need adapting to fit your class / school.
30 August 2016 13:15
Hi Lynn, the NCETM doesn't provide lesson plans so I would suggest instead contacting your local Maths Hubs. Details of each of the Hubs, including location and contact details, can be found here on the Maths Hubs website http://www.mathshubs.org.uk/find-your-hub/

Best wishes, Natasha
30 August 2016 11:17
As a school we are just beginning to use your comprehensive resource so weekly lesson plans may be located somewhere that I haven't found yet. Please could you advise me as to where I can locate weekly planning for primary year groups
22 August 2016 08:39
Hi Margaret, could you email us at info@ncetm.org.uk and let us know a bit more about what it is you're looking for please so that we can try to help with your query. Thanks, Natasha
19 August 2016 18:56
Wondering how i can access lesson info for GCSE maths lessons. Teaching at home, so I need some help. Thanks
26 June 2016 15:09
Fantastic resouce for teaching ideas, curriculum info and subject knowledge development ; thank you!
04 February 2016 15:35
fbeedie - which questions do you mean?
04 February 2016 14:41
Are there any answers to these brilliant questions? Thanks
13 October 2015 15:55
I’m afraid we do not plan in the near future to extent the treatment we’ve given to Key Stages 1, 2 and 3 to the EYFS.
13 October 2015 13:23
This looks really useful, are there any materials like this for the EYFS?
05 October 2015 18:15
The resource should match the curriculum. If it doesn't then this is an error, please point out where this is and we will correct it
05 October 2015 16:23
Is there a reason that it says 'recognise the place value of each digit in a three-digit number (hundreds, tens, ones)', but on the National Curriculum children are assessed on numbers beyond this e.g. 979 + 100?
19 May 2015 13:25
compare and order unit fractions with the same denominator

Is this not the same thing? 1/2=1/2

Should it be small denominators?
22 January 2015 16:55
At a maths coordinator meeting today, I was told you may have some government approved plans for Year 1 and 2 on the site. Is this true....I can't find them?
22 January 2015 15:36
Sorry, I've just found them.
22 January 2015 15:34
On 12 May last year Debbie Morgan posted 'The assessing reasoning documents are complete and will go live on the site very shortly. They will appear as a link on the main curriculum page, the page you land on after clicking on the National Curriculum box on the home page' Where are they please? Or are they the same assessment materials that Steve mentions on 19 Jan 2015?
19 January 2015 15:35
The development work is underway, but it will be later this (school) year before it is completed.
19 January 2015 12:22
On some training in the Autumn Term we were advised that the NCETM were developing some assessment materials for the new curriculum. Have these been completed yet and if so where abouts would I find them? Thanks
20 November 2014 12:48
You have an error on the Year 4 fractions page of activities. The grid is incomplete for the objectives and incorrectly labelled. It states that F is for recognising decimal equivalents of some fractions but further down the page it says that F is for finding the effect of dividing by 10 and 100. Furthermore it refers to activites H which are not shown in the grid. The grid does not include finding the effect of dividing by 10 and 100. Other than this, I find this a really useful document, thanks.
12 October 2014 11:00
I show this tool to teachers in school a lot but several have told me that 'the blue box' on the home page doesn't look like something to click on - that it just looks like a graphic and that if I hadn't told them to click on it, they wouldn't have done. I wonder if skralj1 above has a point and that this amzing tool is actually not nearly obvious enough. Should the blue box say something like 'click here for'. From my time at NCETM I know this was something that you tried to avoid but, if the blue box is not doing it ..... ? You'll think of something.
09 October 2014 14:25
The blue 'National Curriculum: latest news and support' button on our homepage links to the resource tool, as well as to the suite of NCETM videos and many other resources. We hope you find the tool useful, and that you'll also explore the other materials.
09 October 2014 14:05
This is a really useful tool so why is it so well hidden on this site? I have spent 20minutes looking for it!
17 September 2014 00:15
A simply superb resource - WELL DONE NCETM!!! Y1 statement: Counting in multiples of 2, 5 and 10. Am I going cuckoo here - doesn't this mean that if Year 1 pupils are expected to count in "multiples of 2" then they are expected to count in 4's, 8's etc. Shouldn't this statement be Count "the" multiples of 2, or count in steps of 2... Or am I just being plain old silly?
14 September 2014 16:51
A great resource, making the planning of a new curriculum much more accessible.
01 September 2014 21:24
Excellent, very helpful. Impressive range of U & A activities
29 June 2014 20:10
Hi

click on rlevant strand / year of resource tool, the nshow selection, it gives a range of options including resources, links and assessment. Progression in reasoning maps, also useful
25 June 2014 17:11
I can locate the progression maps but am looking for practical ideas/activities to support my teaching of the new curriculum and subject knowledge....where can i find this on the mircosite? Can anyone help?? I was told that this is available on the site.
12 June 2014 19:39
Ignore that. Have just found the answer above.
12 June 2014 19:34
I absolutely love this tool but have had trouble navigating the site to find it. I only managed it this time by clicking on a link in the latest newsletter. It is now saved in my favourites. However, I want to show colleagues how to find it for themselves. Is there an easy way to navigate here from the home page?
12 May 2014 08:53
The assessing reasoning documents are complete and will go live on the site very shortly. They will appear as a link on the main curriculum page, the page you land on after clicking on the National Curriculum box on the home page
10 May 2014 20:24
These are fantastic! When will the assessment question rows be added to the progression maps (such as the draft example shown at the 2Day Conference in London)? Thanks.
06 May 2014 09:29
Developing a school curriculum for mathematics, scheme of work and calculation policy materials are currently awaiting review and should be published shortly.
04 May 2014 16:06
I know that you are working are flat out on new materials, but are you able to give us a date when planning/scheme of work support will be available? I want to plan staff training after the materials are published.
30 April 2014 09:18
We are currently working on some material to go along side this resource which deal with developing a school curriculum for mathematics, a scheme of work and a calculation policy.
30 April 2014 09:06
I will be sharing this with all staff to support the implementation of the new Maths curriculum. Many thanks. Support for planning would be very welcome too.
24 April 2014 20:52
This resource is fantastic. What a lot of work must have gone into it and it is very much appreciated. Many thanks.
24 April 2014 09:58
We hope to have materials fro KS3 available later in the summer term.
22 April 2014 20:56
Fantastic resource. Is this being created for KS3 too?
22 April 2014 14:05
The direct link to this page is https://www.ncetm.org.uk/resources/41211. We have now added a link from the microsites page as suggested. Alternatively you can reach this page from the blue National Curriculum button, which takes you to the National Curriculum page, then the button with the coloured squares at the top of the right column which will bring you here.
22 April 2014 12:24
Can you explain how I can navigate to this site from the home screen, without clicking on the home screen link that will presumably vanish at some point. The 'route' appears to be resources > microsites > The National Curriculum for Mathematics but I cant find the link from microsites. Cheers
14 April 2014 21:51
Click on the name of the topic and the progression maps are there
14 April 2014 11:36
Hi. I am looking for tracking of strands from EYFS to Yr 6. I am sure that I've seen this, but cannot now find it again! I would be most grateful for your help.
09 April 2014 18:54
Thanks for adding the year 4 stuff, this is a great tool.
03 April 2014 10:13
We are producing some materials to support schools in thinking about planning. This should be available in the summer term.
02 April 2014 21:28
Hi. Is there a medium term planning tool/template anywhere?
28 February 2014 09:42
To use the navigation, click on the coloured button for the year and topic you want to view. Then click on the show selection button. This will show the results below the navigation. In the results are some further coloured boxes with links to different types of resources for that year and topic: Subject Knowledge, Making Connections, Articles, Activities, Exemplification, Video
27 February 2014 19:32
Fantastic resources but I can't seem to navigate to the pages I want. If I use search for Year group exemplars and videos they come up but I can't find the link from resources/ micro-sites. Can you help?
16 February 2014 18:50
There is a document on The Key which outlines the changes; also one on the TES but I personally prefer the one on the key