Fractions, decimals and percentages
COUNTING IN FRACTIONAL STEPS  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6 
 Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number line (Non Statutory Guidance)  count up and down in tenths  count up and down in hundredths 


RECOGNISING FRACTIONS  
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
 recognise, find and write fractions of a discrete set of objects: unit fractions and nonunit fractions with small denominators
 recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten
 recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents (appears also in Equivalence)


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 name a quarter as one of four equal parts of an object, shape or quantity  recognise and use fractions as numbers: unit fractions and nonunit fractions with small denominators  
COMPARING FRACTIONS  

 compare and order unit fractions, and fractions with the same denominators

 compare and order fractions whose denominators are all multiples of the same number  compare and order fractions, including fractions >1

COMPARING DECIMALS  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6  


 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  identify the value of each digit in numbers given to three decimal places  
ROUNDING INCLUDING DECIMALS  


 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  
EQUIVALENCE (INCLUDING FRACTIONS, DECIMALS AND PERCENTAGES)  
 write simple fractions e.g. ^{1}/_{2 }of 6 = 3 and 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 (e.g. 0.71 = ^{71}/_{100})  associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. ^{3}/_{8})  
recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents  


 recognise and write decimal equivalents to ^{1}/_{4}; ^{1}/_{2}; ^{3}/_{4 }
 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 as a decimal fraction  recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.  
ADDITION AND SUBTRACTION OF FRACTIONS  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6  

 add and subtract fractions with the same denominator within one whole (e.g. ^{5}/_{7 }+ ^{1}/_{7 }= ^{6}/_{7})
 add and subtract fractions with the same denominator
 add and subtract fractions with the same denominator and multiples of the same number  add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
 
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})  
MULTIPLICATION AND DIVISION OF FRACTIONS  



 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 (e.g. ^{1}/_{4 }× ^{1}/_{2 }= ^{1}/_{8})  
multiply onedigit numbers with up to two decimal places by whole numbers  




 divide proper fractions by whole numbers (e.g. ^{1}/_{3 }÷ 2 = ^{1}/_{6 })
 
MULTIPLICATION AND DIVISION OF DECIMALS  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6  




 multiply onedigit numbers with up to two decimal places by whole numbers  


 find the effect of dividing a one or twodigit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths 
 multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places  




 identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places  




 associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. ^{3}/_{8})  




 use written division methods in cases where the answer has up to two decimal places
 
PROBLEM SOLVING  
Year 1  Year 2  Year 3  Year 4  Year 5  Year 6  

 solve problems that involve all of the above
 solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including nonunit fractions where the answer is a whole number  solve problems involving numbers up to three decimal places

 


 solve simple measure and money problems involving fractions and decimals to two decimal places.
 solve problems which require knowing percentage and decimal equivalents of ^{1}/_{2}, ^{1}/_{4}, ^{1}/_{5}, ^{2}/_{5}, ^{4}/_{5 }and those with a denominator of a multiple of 10 or 25. 
