# Maths

 Expectation by theend of Year 1 Expectation by theend of Year 2 Expectation by theend of Year 3 Expectation by theend of Year 4 Expectation by theend of Year 5 Expectation by theend of Year 6 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.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, most, least. Read and write numbers to at least 100 in numerals and in words.Recognise the place value of each digit in a two digit number (tens, ones)Identify, represent and estimate numbers using different representations including the number line.Compare and order numbers from 0 up to 100; use <, > and = signs.Use place value and number facts to solve problems.Count in steps of 2, 3 and 5 from 0, and in tens from any number, forward and backward. Identify, represent and estimate numbers using different representations.Find 10 or 100 more or less than a given numberRecognise the place value of each digit in a three-digit number (hundreds, tens, ones).Compare and order numbers up to 1000Read and write numbers up to 1000 in numerals and in words.Solve number problems and practical problems involving these ideas.Count from 0 in multiples of 4, 8, 50 and 100 Count in multiples of 6, 7, 9. 25 and 1000.Find 1000 more or less than a given number.Recognise the place value of each digit in a four digit number (ths, hs, ts and ones)Order and compare numbers beyond 1000Identify, represent and estimate numbers using different representations.Round any number to the nearest 10, 100 or 1000Solve number and practical problems involving all of the above and with increasingly large positive numbers.Count backwards through zero to include negative numbers.Read Roman numerals to 100 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 1000000 and determine the value of each digit.Count forwards or backwards in steps of powers of 10 for any given number up to 1000000.Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers including through zero.Round any number up to 1000000 to the nearest 10, 100, 1000, 10000 and 100000Solve number problems and practical problems that involve all of the above.Read Roman numerals to 1000 (M) and recognise years written in Roman numerals. 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 zero.Solve number and practical problems that involve all of the above. Addition, subtraction, multiplication and division 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 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 numbersShow that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot.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 two numbers can be done in any order (commutative) and division of one number by another cannot. Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtractionAdd and subtract numbers mentally, including:- a three-digit number and ones; a three-digit number and tens ; - a three-digit number   and hundredsWrite 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. Add and subtract numbers with up to four digits using the formal written methods of columnar addition and subtractionUse place value, known and derived facts to multiply and divide mentally, including:- multiplying by 0 and 1- dividing by 1- multiplying together three numbersMultiply two-digit and three-digit numbers by a one-digit number using formal written layout 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.Multiply and divide numbers mentally drawing upon known factsMultiply and divide whole numbers and those involving decimals by 10, 100 and 1000Multiply numbers up to 4 digits by a one or two digit number using a formal written method, including long multiplication for 2-digit numbersDivide 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. Perform mental calculations, including with mixed operations and large numbersMultiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplicationDivide 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 contextUse their knowledge of the order of operations to carry out calculations involving the four operations Derive and recall +-x÷ Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers.Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 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 Prime numbers and factors Recognise and use factor pairs and commutativity inmental calculations Identify multiples and factors, including finding all factor pairs of a number, and common factors of two 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). Identify common factors, common multiples and primenumbers Solving problems 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. Solve problems with addition and subtraction using concrete objects and pictorial representations, including those involving numbers, quantities and measures.Solve problems with addition and subtraction applying their increasing knowledge of mental and written methods.Solve problems with addition and subtraction recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100.Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.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 addition and subtraction two-step problems in contexts, deciding which operations and methods to use and whySolve 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 areconnected to m objects 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 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. Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and whySolve problems involving addition, subtraction, multiplication and division Checking 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 appropriatedegree of accuracy Fractions Recognise, find and name a half as one of two equal parts of an object, shape or quantity.Recognise, find and name a quarter as one of four 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)Compare, describe and solve practical problems for: 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] Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity. Write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2. 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 use fractions as numbers: unit fractions and non-unit fractions with small denominators. Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators.Recognise and show, using diagrams, equivalent fractions with small denominators.Compare and order unit fractions, and fractions with the same denominators.Add and subtract fractions with the same denominator within one whole [for example, 5/7 + 1/7 = 6/7 ]Solve problems that involve all of the above. 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. Compare and order fractions whose denominators are 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]Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates. Use common factors to simplify fractions; use common multiples to express fractions in the same denomination. Compare and order fractions, including fractions > 1 Generate and describe linear number sequences (with fractions) Add and subtract fractions with different denominations and mixed numbers, using the concept of equivalent fractions. Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example 1/4 x 1/2 = 1/8 ] Divide proper fractions by whole numbers [for example 1/3 ÷ 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] Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. Decimals Recognise and write decimal equivalents of any number of tenths or hundredths.Find the effect of dividing a one or two digit number by 10 or 100, identifying the value of the digits in the answer as ones, tenths and hundredthsSolve simple measure and money problems involving fractions and decimals to two decimal places.Convert between different units of measureCompare numbers with the same number of decimal places up to two decimal places.Round decimals with one decimal place to the nearest whole number.Recognise and write decimal equivalents to 1/4, 1/2 and ¾.Find the effect of dividing a one or two digit number by 10 or 100, identifying the value of the digits in the answer as ones, tenths and hundredths Read, write, order and compare numbers with up to three decimal places.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.Solve problems involving number up to three decimal places.Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000.Use all four operations to solve problems involving measure [ for example, length, mass, volume, money] using decimal notation, including scaling. Identify the value of each digit in numbers given to 3 decimal places and multiply 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. Percentages Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, 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, 4/5 and those fractions with a denominator of a multiple of 10 or 25. Solve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison.Recall and use equivalences between simple fractions, decimals and percentages including in different contexts. Algebra Use simple formulaeGenerate and describe linear number sequences.Express missing number problems algebraically.Find pairs of numbers that satisfy an equation with two unknowns.Enumerate possibilities of combinations of two variables. Ratio 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 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.