Pupils should be taught to: Number – number and place value - 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 2s, 5s and 10s
- given a number, identify 1 more and 1 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.
Number – addition and subtractionPupils should be taught to:- 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 0
- solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ? – 9.
- 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.
Number – fractionsPupils should be taught to:- recognise, find and name a half as 1 of 2 equal parts of an object, shape or quantity
- recognise, find and name a quarter as 1 of 4 equal parts of an object, shape or quantity.
- 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.
Geometry - properties of shapesPupils should be taught to:- 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]
Pupils should be taught to:Geometry - position and direction - describe position, direction and movement, including whole, half, quarter and three-quarter turns.
Pupils should be taught to:Number – number and place value - count in steps of 2, 3, and 5 from 0, and in 10s from any number, forward and backward
- recognise the place value of each digit in a two-digit number (10s, 1s)
- 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
Number – addition and subtractionPupils should be taught to:- 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 1s
– a two-digit number and 10s – 2 two-digit numbers – adding 3 one-digit numbers
- show that addition of 2 numbers can be done in any order (commutative) and subtraction of 1 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
Pupils should be taught to: · 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 2 numbers can be done in any order (commutative) and division of 1 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
Pupils should be taught to: · recognise, find, name and write fractions , , and of a length, shape, set of objects or quantity · write simple fractions, for example of 6 = 3 and recognise the equivalence of and
Pupils should be taught to: · 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
Pupils should be taught to: · 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
Pupils should be taught to: · 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)
Pupils should be taught to: · interpret and construct simple pictograms, tally charts, block diagrams and tables · ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity · ask-and-answer questions about totalling and comparing categorical data
Pupils should be taught to: · 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 3-digit number (100s, 10s, 1s) · compare and order numbers up to 1,000 · identify, represent and estimate numbers using different representations · read and write numbers up to 1,000 in numerals and in words · solve number problems and practical problems involving these ideas
Pupils should be taught to: · add and subtract numbers mentally, including: · a three-digit number and 1s · a three-digit number and 10s · a three-digit number and 100s · add and subtract numbers with up to 3 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
Pupils should be taught to: · 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
Pupils should be taught to: · 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, + = ] · compare and order unit fractions, and fractions with the same denominators · solve problems that involve all of the above
Pupils should be taught to: · count in multiples of 6, 7, 9, 25 and 1,000 · find 1,000 more or less than a given number · count backwards through 0 to include negative numbers · recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s) · order and compare numbers beyond 1,000 · identify, represent and estimate numbers using different representations · round any number to the nearest 10, 100 or 1,000 · 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 0 and place value
Pupils should be taught to: · 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
Pupils should be taught to: · 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 3 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 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects
Pupils should be taught to: · 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 100 and dividing tenths by 10 · 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 hundreds · recognise and write decimal equivalents to , , · 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 1 decimal place to the nearest whole number · compare numbers with the same number of decimal places up to 2 decimal places · solve simple measure and money problems involving fractions and decimals to 2 decimal places
Pupils should be taught to: · 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
Pupils should be taught to: · 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 2 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
Pupils should be taught to: · 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
Pupils should be taught to: · 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
Pupils should be taught to: · 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 0 · round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 · solve number problems and practical problems that involve all of the above · read Roman numerals to 1,000 (M) and recognise years written in Roman numerals
Pupils should be taught to: · 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
Pupils should be taught to: · 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
Pupils should be taught to: · 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, + = = 1 ] · 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 = ] · recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents · round decimals with 2 decimal places to the nearest whole number and to 1 decimal place · read, write, order and compare numbers with up to 3 decimal places · solve problems involving number up to 3 decimal places · recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fraction · solve problems which require knowing percentage and decimal equivalents of , , , , and those fractions with a denominator of a multiple of 10 or 25
Pupils should be taught to: · 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), 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
Pupils should be taught to: · 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 1 whole turn (total 360°) · angles at a point on a straight line and half 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
Pupils should be taught to: · 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
Pupils should be taught to: · solve comparison, sum and difference problems using information presented in a line graph · complete, read and interpret information in tables, including timetables
Pupils should be taught to: · 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 0 · solve number and practical problems that involve all of the above
Pupils should be taught to: · 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 4 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
Pupils should be taught to: · 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, × = ] · divide proper fractions by whole numbers [for example, ÷ 2 = ] · associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, ] · identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places · multiply one-digit numbers with up to 2 decimal places by whole numbers · use written division methods in cases where the answer has up to 2 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
Pupils should be taught to: · solve problems involving the relative sizes of 2 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
Pupils should be taught to: · use simple formulae · generate and describe linear number sequences · express missing number problems algebraically · find pairs of numbers that satisfy an equation with 2 unknowns · enumerate possibilities of combinations of 2 variables
Pupils should be taught to: · solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 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 3 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 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]
Pupils should be taught to: · 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 circles, 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
Pupils should be taught to: · describe positions on the full coordinate grid (all 4 quadrants) · draw and translate simple shapes on the coordinate plane, and reflect them in the axes
Pupils should be taught to: · interpret and construct pie charts and line graphs and use these to solve problems · calculate and interpret the mean as an average |