- National Curriculum Tool
- Year 5 - Fractions (including decimals and percentages)
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
| 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.
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.
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.
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.
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.
Useful Resources
- Moving digits ITP
- Maths rods
- Clock faces to model different fractions
- Area ITP
- Fractions ITP
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?
