Compare and order numbers up to 1000 Count backwards through zero to include negative numbers Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers through zero * G * * I Use negative numbers in context, and calculate intervals across zero * G Identify, represent and estimate numbers using different representations Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens and ones) * G * G * * * G Round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000 Solve number and practical problems that involve all of the above * I ** Read and write numbers up to 1000 in numerals and in words Order and compare numbers beyond 1000 Ordering Journeys ** Solve number problems and practical problems that involve all of the above
Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction * * * G * G * * G * I ** ** ** G ** ** I *** I *** Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why ** ** ** I ** *** *
Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables * G * I Recall multiplication and division facts for multiplication tables up to 12x12 * G * * * * G * I * * G ** I * * G ** Identify multiples and factors, including all factor pairs of a number, and common factors of two numbers * I * * I * * I * G ** I * ** G Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication 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 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 Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers ** I 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 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 Multiply and divide numbers mentally drawing upon known facts Identify common factors, common multiples and prime numbers * ** I ** I ** ** I ** Divide numbers up to 4 digits by a number using the formal written method of short division and interpret remainders appropriately for the context * I Use their knowledge of the order of operations to carry out calculations involving the four operations Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 * * * Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates 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 and show, using diagrams, families of common equivalent fractions * * * Compare and order fractions whose denominators are all multiples of the same number Use common factors to simplify fractions; use common multiples to express fractions in the same denomination Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators * G Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths * Compare and order fractions, including fractions >1 ** ** Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators 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 ** ** ** I Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number (e.g. 2/5 + 4/5 = 6/5 = 1 1/5) * Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions **
** * * I * I Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and and 24-hour clocks * * ** ** *** I G Estimate, compare and calculate different measures, including money in pounds and pence * 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 * I * I * I ** ** I *** *** Recognise that shapes with the same areas can have different perimeters and vice versa * G 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 ** *** Read, write and convert time between analogue and digital 12- and 24-hour clocks Estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water] ** Recognise when it is possible to use formulae for area and volume of shapes
** I *** I *** G *** 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 Recognise, describe and build simple 3-D shapes, including making nets ** ** I 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 * G Identify lines of symmetry in 2-D shapes presented in different orientations * ** * G Draw given angles, and measure them in degrees (°) * I * * *** Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons * * * *** I *** *
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 * * ** I Complete, read and interpret information in tables, including timetables Calculate and interpret the mean as an average * I