The National Curriculum for Mathematics - Resource Tool

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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.

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<x≤b

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

read, write and interpret mathematical statements involving addition (+), subtraction (â€“) 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 = ☐ â€“ 9.

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.

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<x≤b

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

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.

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 (Ã—), division (Ã·) 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.

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.

recall multiplication and division facts for multiplication tables up to 12 Ã— 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.

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 (Â²) and cubed (Â³)

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

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.

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<x≤b

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

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, ^{5}⁄_{7} + ^{1}⁄_{7} = ^{6}⁄_{7} ]

compare and order unit fractions, and fractions with the same denominator

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 â€¨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.

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,^{2}⁄_{5}+^{4}⁄_{5}=^{6}⁄_{5}= 1^{1}⁄_{5}]

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 =^{71}⁄_{100}]

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 â€˜number of parts per hundredâ€™, and write percentages as a fraction with denominator 100, and as a decimal

solve problems which require knowing percentage and decimal equivalents of ^{1}⁄_{2}, ^{1}⁄_{4},^{1}⁄_{5}, ^{2}⁄_{5} and those fractions with a denominator of a multiple of 10 or 25.

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 Ã— ½ = ^{1}⁄_{8}]

divide proper fractions by whole numbers [for example, ^{1}⁄_{3} Ã· 2 = ^{1}⁄_{6}]

associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, ^{3}⁄_{8}]

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.

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

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.

choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (Â°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 (Â£) 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.

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 Â£ 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 oâ€™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].

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 (cm^{2}) and square metres (m^{2}) and estimate the area of irregular shapes

estimate volume [for example, using 1 cm^{3} 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.

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 (cm^{3}) and cubic metres (m^{3}), and extending to other units [for example, mm^{3} and km^{3}]

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

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.

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.

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

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).

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.

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

interpret and present data using bar charts, pictograms and tables

solve one-step and two-step questions [for example, â€˜How many more?â€™ and â€˜How many fewer?â€™] using information presented in scaled bar charts and pictograms and tables.

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

a^{2} in place of a × a, a^{3} in place of a × a × a; a^{2}b 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.

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?

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/

If we can be of any further assistance please don't hesitate to contact us at info@ncetm.org.uk

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

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?

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 15:34 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 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.

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?

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 19:34 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.

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 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.

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?

13 February 2014 18:09 The content on the resource tool matches exactly the statutory requirments of the new curriculum, which was published in its final form in September 2013. Clearly much, in fact most, of that content is very similar to the 'old' curriculum. But I'm afraid we have not included annotations to this tool to point out exactly where the differences lie.

13 February 2014 12:38 Hi I have just changed my role as secondary maths adviser to a cross phase maths adviser. This toolkit of resources activities and links are great. However, what would be really useful to include would be to indicate which parts are the NEW NC bits (added) to the old. Is that anywhere? Cheers

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