# Our Curriculum – Maths

This table details what will be taught and when, though since children develop at different speeds, some will be more proficient than others against these YEAR-END expectations for learning in Maths.                                                                  Back to our Curriculum Wheel –>

 Key stage Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Number: Number and Place Value read and write numbers from 1 to 20 in numerals and words. read and write numbers to at least 100 in numerals and in words read and write numbers up to 1000 in numerals and in words 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 read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit read, write, order and compare numbers up to 10 000 000 and determine the value of each digit recognise the place value of each digit in a two-digit number (tens, ones) recognise the place value of each digit in a three-digit number (hundreds, tens, ones) recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones) read Roman numerals to 1000 (M) and recognise years written in Roman numerals identify and represent numbers using objects and pictorial representations including the number line identify, represent and estimate numbers using different representations, including the number line identify, represent and estimate numbers using different representations identify, represent and estimate numbers using different representations count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number count in multiples of 6, 7, 9, 25 and 1000 count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 use negative numbers in context, and calculate intervals across zero 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 find 1000 more or less than a given numberr count backwards through zero to include negative numbers interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero use the language of: equal to, more than, less than (fewer), most, least compare and order numbers from 0 up to 100; use <, > and = signs compare and order numbers up to 1000 order and compare numbers beyond 1000 round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000 round any whole number to a required degree of accuracy round any number to the nearest 10, 100 or 1000 use place value and number facts to solve problems solve number problems and practical problems involving these ideas solve number and practical problems that involve all of the above and with increasingly large positive numbers solve number problems and practical problems that involve all of the above solve number and practical problems that involve all of the above Number: Addition and Subtraction Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 represent and use number bonds and related subtraction facts within 20 recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 add and subtract one-digit and two-digit numbers to 20, including zero 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 – adding three one-digit numbers 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 mentally with increasingly large numbers perform mental calculations, including with mixed operations and large numbers read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot 4 add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ☐ – 9 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 solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why 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 solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. estimate the answer to a calculation and use inverse operations to check answers estimate and use inverse operations to check answers to a calculation use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy Number: Multiplication and Division Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables recall multiplication and division facts for multiplication tables up to 12 × 12 multiply and divide numbers mentally drawing upon known facts perform mental calculations, including with mixed operations and large numbers calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs 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 show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot 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 multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 multiply two-digit and three-digit numbers by a one-digit number using formal written layout 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 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 one-digit number using the formal written method of short division and interpret remainders appropriately for the context 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 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 solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts 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 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 solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign solve problems involving addition, subtraction, multiplication and division solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates use their knowledge of the order of operations to carry out calculations involving the four operations use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy recognise and use factor pairs and commutativity in mental calculations identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers identify common factors, common multiples and prime 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 recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³) Fractions, Decimals and Percentages Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 recognise, find and name a half as one of two equal parts of an object, shape or quantity recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity 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 count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten compare and order fractions whose denominators are all multiples of the same number compare and order fractions, including fractions > 1 recognise, find and name a quarter as one of four equal parts of an object, shape or quantity write simple fractions for example, 1/2 of 6 = 3 recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators 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 recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators compare and order unit fractions, and fractions with the same denominators use common factors to simplify fractions; use common multiples to express fractions in the same denomination add and subtract fractions with the same denominator within one whole [for example, 5/7 + 1/7 = 6/7] add and subtract fractions with the same denominator add and subtract fractions with the same denominator and denominators that are multiples of the same number add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions 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 multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 × 1/2 = 1/8] divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6] round decimals with one decimal place to the nearest whole number round decimals with two decimal places to the nearest whole number and to one decimal place solve problems which require answers to be rounded to specified degrees of accuracy compare numbers with the same number of decimal places up to two decimal places read, write, order and compare numbers with up to three decimal places identifying the value of the digits in the answer as ones, tenths and hundredths identify the value of each digit in numbers given to three decimal places find the effect of dividing a one- or two-digit number by 10 and 100, 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 recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’ recognise the equivalence of 2/4 and 1/2 recognise and show, using diagrams, equivalent fractions with small denominators recognise and show, using diagrams, families of common equivalent fractions identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths use common factors to simplify fractions; use common multiples to express fractions in the same denomination recognise and write decimal equivalents of any number of tenths or hundredths read and write decimal numbers as fractions [for example, 0.71 = 71/100] associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 ] recognise and write decimal equivalents to 1/4,1/2, 3/4 recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents write percentages as a fraction with denominator 100, and as a decimal recall and use equivalences between simple fractions, decimals and percentages, including in different contexts solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25. solve problems that involve all of the above solve simple measure and money problems involving fractions and decimals to two decimal places solve problems involving number up to three decimal places Measurement Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening] compare and sequence intervals of time tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks read, write and convert time between analogue and digital 12- and 24-hour clocks recognise and use language relating to dates, including days of the week, weeks, months and years 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 seconds in a minute and the number of days in each month, year and leap year solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days tell the time to the hour and half past 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. compare durations of events [for example to calculate the time taken by particular events or tasks] 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 recognise and know the value of different denominations of coins and notes recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value add and subtract amounts of money to give change, using both £ and p in practical contexts estimate, compare and calculate different measures, including money in pounds and pence 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, 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] 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 measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml) solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate measure and begin to record the following: – lengths and heights – mass/weight – capacity and volume – time (hours, minutes, seconds) Convert between different units of measure [for example, kilometre to metre; hour to minute] convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre) 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 understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints convert between miles and kilometres use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling measure the perimeter of simple 2-D shapes measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres recognise that shapes with the same areas can have different perimeters and vice versa find the area of rectilinear shapes by counting squares 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 calculate the area of parallelograms and triangles recognise when it is possible to use formulae for area and volume of shapes estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water] 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] 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 Geometry: Properties of Shapes Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 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] identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line identify horizontal and vertical lines and pairs of perpendicular and parallel lines identify lines of symmetry in 2-D shapes presented in different orientations draw 2-D shapes using given dimensions and angles identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces complete a simple symmetric figure with respect to a specific line of symmetry illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid] draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them identify 3-D shapes, including cubes and other cuboids, from 2-D representations recognise, describe and build simple 3-D shapes, including making nets compare and sort common 2-D and 3-D shapes and everyday objects compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes use the properties of rectangles to deduce related facts and find missing lengths and angles compare and classify geometric shapes based on their properties and sizes distinguish between regular and irregular polygons based on reasoning about equal sides and angles. … and find unknown angles in any triangles, quadrilaterals, and regular polygons recognise angles as a property of shape or a description of a turn identify acute and obtuse angles and compare and order angles up to two right angles by size know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles 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 draw given angles, and measure them in degrees (o) identify: – angles at a point and one whole turn (total 360°) – angles at a point on a straight line and 1/2 a turn (total 180°) – other multiples of 90° recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles Geometry: Position and Direction Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 describe positions on a 2-D grid as coordinates in the first quadrant describe positions on the full coordinate grid (all four quadrants) plot specified points and draw sides to complete a given polygon describe position, direction and movement, including whole, half, quarter and three-quarter turns 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) describe movements between positions as translations of a given unit to the left/right and up/down 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 draw and translate simple shapes on the coordinate plane, and reflect them in the axes Statistics Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity 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 solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs complete, read and interpret information in tables, including timetables ask and answer questions about totalling and comparing categorical data interpret and construct simple pictograms, tally charts, block diagrams and simple tables interpret and present data using bar charts, pictograms and tables 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 a line graph interpret and construct pie charts and line graphs and use these to solve problems calculate and interpret the mean as an average Algebra Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit (Non-statutory guidance: Measurement) use simple formulae recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³) Number: Multiplication and Division generate and describe linear number sequences solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ☐ – 9 (Number: Addition & Subtraction) recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems (Number: Addition & Subtraction) solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction (Number: Addition & Subtraction) express missing number problems algebraically 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 (Number: Multiplication & Division) recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 (Number: Addition & Subtraction) find pairs of numbers that satisfy an equation with two unknowns represent and use number bonds and related subtraction facts within 20 (Number: Addition & Subtraction) enumerate possibilities of combinations of two variables Ratio and Proportion Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 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 the use of 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

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