This document is for use in planning for the teaching of mathematics. These are the basic expectations of what all children in the class will be able to do in mathematics by the end of each school year. These skills build year on year. They should be taught, practiced and consolidated throughout the year with the aim that they become completely embedded for all children.
Year R Numbers To be able to count reliably from 1-20. To be able to place the numbers from 1-20 in order. To be able to say one more or one less than a number to 20. To add and subtract two 1-digit numbers using quantities and objects. To count on or back to find an answer. To be able to solve problems including halving, doubling and sharing. Shape, Space and Measures To use everyday language to talk about size, weight, capacity, position, distance, time and money. To be able to compare quantities and objects using everyday language. To solve problems involving measures. To be able to recognise, create and describe patterns. To explore the characteristics of everyday objects and shapes and begin to use simple mathematical language to describe them.
Year 1 Number Addition and Subtraction Multiplication and Division Fractions Geometry To be able to count beyond 100 forwards and backwards, starting at zero or any given number. To be able to read and write 0-100 in numerals. To be able to count in multiples 1s, 2s, 5s, 10s. To be able to say one more and one less than a given number. To identify and represent numbers using objects and pictorial representations. To fluently use the language of equal to; more than; less than; fewer; most; least. To read and write numbers from 1 to 20 in numerals (correctly formed) and words. To use the symbols +, -, =. To add and subtract 1-digit and 2-digit numbers to 20. To know and use number bonds within 20 (including subtraction facts). To solve one-step and word problems than involve addition and subtraction, using concrete objects and pictorial representations. To be able to solve missing number problems. To multiply and divide with teacher using concrete objects, pictorial representations and arrays. To solve word problems using multiplication and division with the teacher. To recognise, find and name a half as one of two equal parts of an object, shape or quantity. To recognise, find and name a quarter as one of four equal parts of an object, shape or quantity. To recognise and name common 2-D and 3-D shapes. To relate everyday objects to common 2-D and 3-D shapes. To be able to fluently and accurately use the language of position and direction. To describe position, direction and movements including whole, ½, ¼ and ¾ turns.
Measurement To compare, describe and solve practical problems for lengths and heights; mass/weight; capacity and volume; time. To measure and begin to record lengths and heights; mass/weight; capacity and volume; time using nonstandard then standard units. To recognise and use the language of dates. To sequence events in chronological order using related language. To tell the time to the hour and half hour. To be able to draw hands on a clock face to show the time to the hour and half hour.
Year 2 Number Addition and Subtraction Multiplication and Division To be able to read and write the numbers to at least 100 in numerals and words. To recognise place value in 2-digit numbers (T,U). To be able to count in steps of 2,3 and 5 from zero number forwards and backwards. To be able to count in tens from any number forwards and backwards. To say 10 more and 10 less. To be able to compare and order numbers to 100 and use the symbols <, >, =. To use place value and number facts to solve problems. To identify, represent and estimate numbers using different representations, including the number line. To fluently recall and use addition and subtraction facts to 20. To mentally add and subtract: 2-digit and 1-digit; 2-digit with tens; add three 1-digit numbers. To use concrete and pictorial representations to add and subtract 2-digit and 1-digit; 2-digit and tens; two 2- digit numbers. To begin to add and subtract two 2-digit numbers with column addition by recording addition and subtraction in columns. To know addition can be done in any order and that subtraction cannot. To recognise that addition and subtraction are inverse operations and use this to check calculations. To solve missing number problems. To solve word problems with up to 2-digits. To recall and use multiplication and division facts for 2, 5, 10 tables. To recognise odd and even numbers. To use the symbols x,, and = to write mathematical statements. To write and calculate multiplication and division within the times tables. To recognise and use the inverse relationship between multiplication and division. To know multiplication can be done in any order and division cannot. To solve simple problems involving multiplication and division using practical resources, arrays, repeated addition, mental methods, multiplication and division facts.
Fractions Geometry To recognise, find, write and name 1/3, ¼, ½, ¾ of a length, shape, set of objects or quantity. To write simple fractions e.g. ½ of 6 = 3. To recognise simple equivalence of fractions e.g. ½ = 2/4 To count in halves and quarters to 10. To be able to recognise and name common 2-D and 3-D shapes. To identify and describe properties of 2-D shapes (including sides, right angles and line symmetry). To identify and describe properties of 3-D shapes (including edges, vertices and faces) To identify 2-D shapes on the surface of 3-D shapes. To be able to compare and sort 2-D and 3-D shapes. To order and arrange combinations of mathematical objects in patterns and sequences. To use mathematical vocabulary to describe position, movement, and direction. Measurement To choose and use appropriate standard units. To be able to measure to nearest unit (length, height, mass, temp, volume, capacity). To use the symbols <, >, = to compare and order measurements. To be able to read scales to nearest numbered unit. To be able to tell and write time to 5 minutes (including quarter past/to) To be able to recognise and use, p, all coins and notes. To be able to combine coins to make a value. To find different combinations of coins that make the same value. To know the number of minutes in an hour and the number of hours in a day. To solve simple problems involving addition and subtraction of money, including giving change. Statistics To construct and interpret pictograms, tables, tally charts, block diagrams and simple graphs. To ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity. To ask and answer questions about totalling and comparing categories.
Year 3 Number Addition and Subtraction Multiplication and Division To be able to read and write 0-1000 in numerals and words. To recognise place value in a 3-digit number(h,t,u). To compare and order numbers to 1000. To fluently count in multiples 2,3,4,5,8,10.50,100 from 0. To be able to say10 or 100 more or less than a given number. To be able to solve number and practical problems involving number and place value. To add and subtract mentally: Pairs of 1&2-digit 3-digit & ones 3-digit & tens 3-digit & hundreds. To estimate the answer to calculations. To use inverse operations to check answers. To add and subtract up to 3-digit numbers using formal column addition and subtraction method. To solve problems including missing numbers using number facts, place value and more complex additions and subtraction up to 3-digits. To recall and use multiplication and division facts for 2,3,4,5,8,10 times tables. To write and calculate multiplication and division within the multiplication tables, and 2-digit x 1-digit, using mental and formal written methods. To solve word problems with multiplication and division including missing numbers, positive integer scaling problems and correspondence problems where n objects are connected to m objects.
Fractions Geometry To recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators. To recognise and use fractions as numbers; unit fractions and non-unit fractions with small denominators. To compare and order unit fractions and fractions with the same denominators. To recognise and show using diagrams equivalent fractions with small denominators. To recognise fractions equivalent to 1, and pairs of fractions which add to 1 whole. To add and subtract fractions with same denominator within 1 whole. To be able to count up and down in tenths and recognise that tenths arise from dividing an object into 10 equal parts and in dividing 1-digit numbers or quantities by 10. To draw 2-D & make 3-D shapes. To recognise 2-D and 3-D shapes in different orientations and describe them. To recognise angles as a property of shape, and as a description of a turn. To be able to identify right angles and know 2 right angles make a half turn, 3 a three quarter turn and 4 a full turn. To be able to identify whether angles are greater than or less than a right angle. To recognise horizontal and vertical lines, and pairs of perpendicular and parallel lines. Measurement To use full names and abbreviations of metric units of measurement. To measure, compare, add and subtract lengths(mm, cm, m), mass (g, kg), volume/capacity (l, ml) and time. To be able to measure the perimeter of a simple 2-D shape. To be able to tell and write time using analogue (incl. roman numerals) and 12/ 24hour clocks. To be able to measure and record time to nearest minute. To compare time (am/pm, times of the day). To know the number of seconds in a minute; days in each month; days in a year and leap year. To compare durations of events/tasks. To be able to add and subtract money to give change including & p. Data To be able to read, interpret and present data using pictograms, bar charts and tables. To solve one-step and two-step problems using information presented in pictograms, bar charts and tables.
Year 4 Number Addition and Subtraction Multiplication and Division To be able to recognise place value in 4-digit number (ThHTU) To order and compare numbers beyond 1000. To be able to count in multiples 2,3,4,5,6,7,8,9,10, 25,50, 100, 1000. To say 1000 more or less than any number. To be able to round any number to the nearest ten, hundred or thousand. To be able to read and write negative numbers, and count in whole numbers through 0. To read roman numerals to 100. To know that over time the numeral system changed to include the concept of zero and place value. To identify, represent and estimate numbers using different representations. To solve word problems including negative and large, positive numbers. To be able to add & subtract up to 4-digits using formal written methods. To be able to add and subtract up to 2-digits mentally. To estimate within a range. To use the reverse operation to check calculations. To solve addition and subtraction two-step problems in contexts, deciding which methods to use and why. To recall multiplication and division facts for times tables to 12 x 12. To mentally multiply and divide including using known facts and x0 and 1. To multiply and divide 2-digit & 3-digit by 1-digit numbers using formal written methods. To be able to interpret remainders appropriately. To recognise and use factor pairs within 144. To solve word problems involving multiplying and adding, including using the distributive law to multiply 2-digits by 1-digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.
Fractions and Decimals Geometry To recognise and show, using diagrams, families of common equivalent fractions. To count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten. To 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. To be able to add and subtract two fractions with common denominators. To compare numbers with the same number of decimal places up to 2 decimal places. To divide1-digit or 2-digit numbers by 10 or 100 and give the answer in ones, Tenths and Hundredths. To recognise and write decimals equivalent to ¼. ½, ¾, and tenths/hundredths. To be able to identify lines of symmetry in 2-D shapes. To compare and classify geometric shapes including quadrilaterals and triangles, based on properties and sizes. To identify acute and obtuse angles, and compare the sizes of different angles. To describe positions on a 2-D grid and as co-ordinates in 1 st quadrant. To describe movements between positions as translations of a given unit to the left/right and up/down. To be able to plot specified points draw sides to a given polygon. To identify lines of symmetry in 2-D shapes presented in different orientations. To complete a simple symmetric figure with respect to a specific line of symmetry. Measurement To be able to convert between units of measurement. To measure and calculate perimeter of a rectilinear figure with sides labelled cm/mm/m. To find the area of rectilinear shapes by counting squares. To be able to read and convert time between analogue & digital; 12/24hr clocks. To estimate, compare and calculate using different measures including & p. To solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days. Data To be able to interpret and present discrete and continuous data using appropriate graphical methods, including bar charts, and time graphs. To solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.
Year 5 Number Addition and Subtraction Multiplication and Division To read, write, order and compare numbers to 1,000, 000 and determine the value of each digit. To be able to count forwards and backwards in steps of 100,1000, 10,000. To round to the nearest 10, 100, 1000, 10000, 100000. To estimate answers to calculations using all four operations. To be able to read roman numerals to 1000 and recognise years written in roman numerals. To add and subtract whole numbers to 5-digits including using formal written methods. To add and subtract mentally with increasingly large numbers. To be able to identify multiples including common multiples and factors including common factors. To recognise prime numbers, prime factors and composite (non-prime) numbers To be able to establish whether a number up to 100 is prime and recall prime numbers to 19. To multiply up to 4-digit x 1or 2-digit by formal written method including long multiplication. To multiply and divide mentally drawing on known facts. To divide up to 4-digit numbers by 1-digit and 10 and interpret remainders appropriately. To multiply and divide by 10, 100, 1000. To recognise and use square numbers and square roots. To be able to solve word problems with all four operations.
Fractions, decimals and Percentages Shape Measures Data To compare and order fractions with different denominators. To recognise mixed numbers and improper fractions and convert between the two. To add and subtract fractions with the same denominator and related fractions. To be able to write mathematical statements that exceed 1 as a mixed number. To multiply proper fractions and mixed numbers by whole numbers. To be able to read and write decimals as fractions. To recognise and use thousandths. To read, write and order numbers with up to 3 decimal places. To add and subtract numbers with up to 3 decimal places. To recognise the symbol % and understand that per cent refers to parts per 100. To write simple fractions as percentages and decimals as percentages. To be able to measure angles in degrees and draw a given angle. To know that angles are measured in degrees and identify: right angles; angles at a point on a straight line; angles at a point; reflex angles; and to compare angles. To recognise, name and compare different triangles. To be able to identify and name parallelogram, rhombus, trapezium. To be able to construct shapes from given dimensions. To state and use properties of squares and rectangles. To identify 3-D shapes from 2-D representations. To identify, describe and represent the position of a shape following reflection or translations. To add, subtract, multiply and divide units of measure using decimal notation. To understand basic equivalencies between metric and imperial units. To measure force in Newtons. To be able to calculate, estimate and compare areas of squares, rectangles and related composite shapes using standard units including cm 2 and m 2. To complete tables and bar graphs from given information. To solve problems using data represented in bar graphs, tables and simple pie charts.
Year 6 Number The Four Operations Fractions, Decimals, Percentages, Ratio and Algebra. To read, write and order numbers up to 10million and determine value of each digit. To be able to round any number to required degree of accuracy. To recognise binary numerals to 15 (1111) and convert between binary and decimal numerals. To add and subtract negative integers. To multiply numbers with at least 4-digits by a 2-digit number using long multiplication. To divide numbers up to 4-digits by 2-digits using long division and to interpret remainders as whole numbers; fractions; decimals or by rounding. To perform mental calculations including mixed operations and large numbers. To use estimation to check answers to calculations and to determine, in the context of a problem whether an answer should be rounded or written as a fraction or decimal. To carry out combined operations involving the four operations accurately and state the order of operations. To be able to solve word problems involving addition, subtraction, multiplication and division. To add and subtract mixed numbers and fractions with different denominators. To multiply simple unit fractions by fractions and pairs of proper fractions, writing the answer in its simplest form. To be able to divide proper fractions by whole numbers To associate a fraction with division to calculate decimal fraction equivalents. To identify the value of each digit to 3 decimal places. To multiply and divide numbers with up to 2 decimal places by 1&2 digit whole numbers. To use percentages for comparison. To calculate percentages of whole numbers To recall and use equivalences between fractions, decimals and percentages. To use ratio to show relative sizes of two quantities.
Fractions, Decimals, Percentages, Ratio and Algebra (cont) Shape Measures Data To recognise equivalent ratios. To recognise and use division in the context of fractions, decimals and percentages. To be able to solve linea missing number problems and find pairs of numbers that satisfy number sentences involving two unknowns. To use simple formulae expressed in words. To generate and describe linea number sequences including negative and decimal numbers. To compare and classify geometric shapes based on properties and sizes. To be able to find unknown angles in triangles, quadrilaterals and regular polygons. To illustrate and name parts of circles. To be able to recognise, describe and build 3-D shapes including making nets. To describe properties of cuboids and other common 3-D shapes. To estimate the size of angles. To find unknown angles involving angles at a point, in a triangle, in a quadrilateral, and vertically opposite angles. To describe positions on the full co-ordinate grid. To construct, translate and reflect simple shapes on the co-ordinate plane. To use, read, write and convert between measures. To recognise that shapes with the same area can have different perimeters and vice versa. To be able to calculate the area of parallelograms and triangles. To recognise when it is necessary to use formula for the area and volume of shapes. To calculate, estimate and compare volume of cubes and cuboids. To use decimal notation to 3 decimal places to solve problems. To be able to draw, read and interpret line graphs and use these to solve problems. To use and interpret averages including mean, median and mode to solve simple problems using different kinds of averages. To be able to use the language associated with probability.