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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 non-unit 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 non-unit 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 = 11/5)

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 one-digit 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 one-digit numbers with up to two decimal places by whole numbers

 

 

 

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

 

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 non-unit 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.