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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

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Year 5 - Fractions (including decimals and percentages)

New Curriculum

  • compare and order fractions whose denominators are all 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= 11⁄5]
  • 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]
  • 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 number up to three decimal places
  • 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 and those fractions with a denominator of a multiple of 10 or 25.

Non-Statutory Guidance

Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions.

They extend their knowledge of fractions to thousandths and connect to decimals and measures.

Pupils connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions.

Pupils connect multiplication by a fraction to using fractions as operators (fractions of), and to division, building on work from previous years. This relates to scaling by simple fractions, including fractions > 1.

Pupils practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number.

Pupils continue to practise counting forwards and backwards in simple fractions.

Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities.

Pupils extend counting from year 4, using decimals and fractions including bridging zero, for example on a number line.

Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems.

They mentally add and subtract tenths, and one-digit whole numbers and tenths.

They practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 ( for example, 0.83 + 0.17 = 1).

Pupils should go beyond the measurement and money models of decimals, for example, by solving puzzles involving decimals.

Pupils should make connections between percentages, fractions and decimals(for example, 100% represents a whole quantity and 1% is 1⁄100, 50% is 50⁄100, 25% is 25⁄100) and relate this to finding ‘fractions of’.

Links and Resources

Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.
Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics.

– National Curriculum in England Framework Document, September 2013, p10

Connections within Mathematics

Fractions, decimals and percentages are used in many other areas of mathematics.

When converting units of measure, children need a good understanding of decimals, e.g. converting cm to m, g to kg etc.

Children should also be required to use fractions and percentages when interpreting and evaluating data.

Fractions may be used when describing turns.

Making connections to this topic in adjacent year groups

Year 4

Pupils should be taught to:

  • 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
  • recognise and write decimal equivalents of any number of tenths or hundredths
  • recognise and write decimal equivalents to ¼, ½, ¾
  • 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
  • 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
  • solve simple measure and money problems involving fractions and decimals to two decimal places

Year 6

  • 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 concept of equivalent fractions
  • multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, ½, × ¼, = ⅛,]
  • divide proper fractions by whole numbers [for example, ⅓ ÷ 2 = ⅙]
  • associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, ⅜ ]
  • identify the value of each digit in numbers given to three decimal places and 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
  • recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

Cross-curricular and real life connections

Learners will encounter fractions, decimals and percentages in:

Measurement – when calculating measures for recipes, calculating journey times and fuel consumption

Money – working out the result of sales offers, tips/gratuities on bills, comparing prices

Statistics – interpreting and evaluating data e.g. 19% of the world’s population lives in China

This article hosted by Nrich explores how children see fractions from an early age and the implications this can have for teaching practices. It includes ideas and images that can be used when presenting children with fractions work to build and extend their understanding of the part – whole relationship.

A fun article on the history of fractions that links well to the historical topic of Ancient Egypt.

A booklet that explains fractions, their uses and how they can be classified. There are some teaching and learning activities along with possible errors and misconceptions.

Maths4Life was written for those teaching adults but teachers of children will also find it very helpful.

An article exploring children’s intuitions about fractions and likely misconceptions that hinder progress through Key Stage 2 and beyond.

Programme of Study statements Activities
A B C D E F
compare and order fractions whose denominators are all multiples of the same number    
recognise mixed numbers and improper fractions and convert from one form to the other          
add and subtract fractions with the same denominator and related fractions        
multiply proper fractions and mixed numbers by whole numbers      
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          
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 relates to “number of parts per hundred” and write percentages as a fraction with denominator 100, and as a decimal        
write percentages as a fraction with denominator 100, and as a decimal      

Activity A - Fractions ITP

An interactive program that allows you to model part-whole relationships using a strip divided in to equal parts. Relationships can be shown as fractions, decimals (to three places) or percentages.

Fractions strip

Activity B - Fractions Jigsaw

A jigsaw-based activity that requires children to add and subtract fractions with the same and different denominators. Pieces must be matched to an answer that may be expressed in equivalent forms. It also includes multiplying fractions by a whole number.

Fractions jigsaw

Activity C - Peaches today, Peaches tomorrow…

A problem solving activity that requires children to find fractions of whole numbers. It provides plenty of practice and has many extension opportunities.

Peaches

Activity D - Metre sticks and metre strips

Use classroom metre sticks/rulers and I metre long strips of paper to model relationships between a whole, tenths, hundreds and thousandths. Children can explore the size of 1, 2 and 3 decimal places and how they link to units of measurement. Labelling points with decimal, fraction and percentage equivalents can help to reinforce links between all three.

Media stick

Activity E - Matching fractions, decimals and percentages

A pelmanism-style activity matching pairs of equivalent fractions, decimals and percentages. Points are awarded for correct answers and deducted for turning over cards without success.

Activity F - Using blank hundred squares

Use blank hundred squares to model and explore percentages, tenths and hundredths. Decimals, fractions and percentages can be represented by colouring in blank hundred squares which children can use to support addition and subtraction.

Squares

Useful Resources

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

compare and order fractions whose denominators are all multiples of the same number

Children should be able to circle the two fractions that have the same value, or choose which one is the odd one out and justify their decision.
6⁄10, 3⁄5, 18⁄20,9⁄15
 

recognise mixed numbers and improper fractions and convert from one form to the other. Write mathematical statements >1 as a mixed number

Put the correct symbol, < or >, in each box.

3.03 ☐ 3.3
0.37 ☐ 0.327
Order these numbers: 0.27 0.207 0.027 2.07 2.7

(e.g. ⅖ + ⅘ = 6⁄5 = 1⅕)

How many halves in: 1 ½ 3 ½ 9 ½ …?

How many quarters in 1 ¼ 2 ¼ 5 ¼ ….?

multiply proper fractions and mixed numbers by whole numbers

What is 3⁄10 of: 50, 20, 100…?

What is ⅘ of 50, 35, 100….?

read and write decimal numbers as fractions (e.g. 0.71 = 71⁄100)

What decimal is equal to 25 hundredths?

Write the total as a decimal:

4 + 6⁄10 + 2⁄100 =

Children partition decimals using both decimal and fraction notation, for example, recording 6.38 as 6 + 3⁄10 + 8⁄100 and as 6 + 0.3 + 0.08.

recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

Recognise that:
0.007 is equivalent to 7⁄1000
6.305 is equivalent to 6305⁄1000

read, write, order and compare numbers with up to three decimal places

Write these numbers in order of size, starting with the smallest. 1.01, 1.001, 1.101, 0.11

solve problems involving numbers with up to three decimal places

8 tenths add 6 tenths makes 14 tenths, or 1 whole and 4 tenths. The 1 whole is 'carried' into the units column and the 4 tenths is written in the tenths column

recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’

Write in the missing numbers.
30% of ☐ is 60

write percentages as a fraction with denominator 100, and as a decimal

Shade 10% of this grid.

Which is bigger: 65% or ¾? How do you know?

What percentage is the same as 7⁄10? Explain how you know?

What is 31⁄100 as a percentage?

Which is a better mark in a test: 61% , or 30 out of 50? How do you know?

Year 4 and 5 extending their fractions work (NCETM video on Youtube)

A video demonstrating how children can use rods to explore which fractions, decimals and percentages are represented when compared to one whole.