Fractions, Decimals and Percentages

EYFS

By the end of EYFS children will be able to:

• Solve problems, including doubling, halving and sharing.

Year 1

By the end of Year 1 children will be able to:

• 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 two equal parts of an object, shape or quantity.

Year 2

By the end of Year 2 children will be able to:

• 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 the equivalence of 2/4 and 1/2.
• Write simple fractions e.g. ½ of 6 = 3

Year 3

By the end of Year 3 children will be able to:

• Count up and down in tenths; recognise that tenths arise from dividing and object into ten equal parts and in dividing one-digit numbers or quantities by ten.
• 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.
• Compare and order unit fractions, and fractions with the same denominators.
• Add and subtract fractions with the same denominator within one whole e.g. 5/7+1/7=6/7
• Solve problems that involve all of the above.

Year 4

By the end of Year 4 children will be able to:

• Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
• Recognise and show, using diagrams, families of common equivalent fractions.
• Add and subtract fractions with the same denominator.
• Solve problems involving increasingly difficult fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number.
• Recognise and write decimal equivalents of any number of tenths or hundredths.
• Recognise and write decimal equivalents to 1/4, 1/2 and 3/4.
• Round decimals with one decimal place to the nearest whole number.
• Compare numbers with the same number of decimal places up to two decimal places.
• Find the effect of dividing a one- or two-digit number by 10 and 100.
• Identify the value of the digits in the answer as ones, tenths and hundredths.
• Solve simple measure and money problems involving fractions and decimals to two decimal places.

Year 5

By the end of Year 5 children will be able to:

• 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 e.g.
• 2/5+4/5=6/5=1 1/5
• Compare and order fractions whose denominators are all multiples of the same number.
• 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 manipulatives and diagrams.
• Read and write decimal numbers as fractions
• e.g. 0.71 = 71/100
• 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.
• Read, write, order and compare numbers with up to three decimal places.
• Solve problems involving numbers with up to three decimal places.
• Recognise the per cent symbol (%) and understand that per cent related to ‘number of parts per hundred’, and write percentages as a fraction with a denominator of 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 multiples of 10 or 25.

Year 6

By the end of Year 6 children will be able 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 concepts of equivalent fractions.
• Multiply simple pairs of proper fractions, writing the answer in its simplest form e.g. 1/4 x 1/2 = 1/8
• Divide proper fractions by whole numbers e.g. 1/3 ÷ 2 = 1/6
• Identify the value of each digit in numbers given to three decimal places.
• Multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places.
• Multiply one-digit numbers with up to two decimal places by whole numbers.
• Use written division methods in cases where the answer has up to two decimal places.
• Solve problems which require answers to be rounded to specified degrees of accuracy.
• Associate a fraction with division and calculate decimal fraction equivalents.
• Recall and use equivalences between simple fractions, decimals and percentages including in different contexts.