Year 6 - Fractions (including decimals and percentages)
New Curriculum
- 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, ¼ × ½ = 1⁄8]
- divide proper fractions by whole numbers [for example, 1⁄3 ÷ 2 = 1⁄6]
- associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3⁄8]
- 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.
Non-Statutory Guidance
Pupils should practise, use and understand the addition and subtraction of fractions with different denominators by identifying equivalent fractions with the same denominator. They should start with fractions where the denominator of one fraction is a multiple of the other (for example,½ + ⅛ = ⅝ ) and progress to varied and increasingly complex problems.
Pupils should use a variety of images to support their understanding of multiplication with fractions. This follows earlier work about fractions as operators (fractions of), as numbers, and as equal parts of objects, for example as parts of a rectangle.
Pupils use their understanding of the relationship between unit fractions and division to work backwards by multiplying a quantity that represents a unit fraction to find the whole quantity (for example, if ¼ of a length is 36cm, then the whole length is 36 × 4 = 144cm).
They practise calculations with simple fractions and decimal fraction equivalents to aid fluency, including listing equivalent fractions to identify fractions with common denominators.
Pupils can explore and make conjectures about converting a simple fraction to a decimal fraction (for example, 3 ÷ 8 = 0.375). For simple fractions with recurring decimal equivalents, pupils learn about rounding the decimal to three decimal places, or other appropriate approximations depending on the context. Pupils multiply and divide numbers with up to two decimal places by one-digit and two-digit whole numbers. Pupils multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 × 2 = 0.8, and in practical contexts, such as measures and money.
Pupils are introduced to the division of decimal numbers by one-digit whole number, initially, in practical contexts involving measures and money. They recognise division calculations as the inverse of multiplication.
Pupils also develop their skills of rounding and estimating as a means of predicting and checking the order of magnitude of their answers to decimal calculations. This includes rounding answers to a specified degree of accuracy and checking the reasonableness of their answers.
Links and Resources
| Programme of Study statements | Activities | ||||||
|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | G | |
| Use common factors to simplify fractions; use common multiples to express fractions in the same denomination | |||||||
| Compare and order fractions, including fractions >1 | |||||||
| Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [ for example, 3⁄8 ] | |||||||
| 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, ¼ × ½ = 1⁄8 ] | |||||||
| Divide proper fractions by whole numbers [ for example, ⅓ ÷ 2 = 1⁄6 ] | |||||||
| 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 | |||||||
Activity A : Factors and Multiples Game
This game from Nrich could replace standard practice exercises on finding factors and multiples. In order to play strategically, pupils must start to think of numbers in terms of their factors
Activity B(i) : Rod Fractions
Compare a series of coloured rods and the relationships between them with this clearly presented Nrich activity
Activity B(ii) : Laundry Line
This activity features a laundry line with ‘fraction washing.’ The aim is to hang the fractions on the line in the right order between 0 and 1. Once a game has been completed, you can raise the level of difficulty.
Activity B(iii) : Chocolate
Using chocolate bars to compare fractions – a context guaranteed to keep them focused!
Activity C : Fraction strips
The ‘Fractions’ Interactive Teaching Programme, allows the user to divide a strip into equal parts and colour them as needed. Strips can be labelled as a fraction, decimal or percentage. The ratio of parts can also be displayed. Multiple strips can be created to demonstrate equivalence.
Activity D(i) : Clock Faces
Give children the chance to explore clock faces as a way of representing time. Talk about 5 minute sectors of the clock being equivalent to twelfths, ten minute sectors to sixths, fifteen minute chunks to quarters etc…
Use this to support them in adding 20 minutes plus 15 minutes as 1/3 + 1/4
Activity D(ii) : Andy’s Marbles
This challenging activity from Nrich requires children to use their conceptual understanding of fractions, and their sums, to determine the answer to Andy’s marble problem
Activity D(iii) – Soccer Shoot Out
Score and save goals by correctly answering fraction based calculations. A range of difficulty levels makes this game easy to adapt.
Activity E(i) : Folding ribbons
Show the children a lengths of ribbon (or string) measuring 3/4 metre in length. Fold it into three parts. What fraction of the ribbon have we found? ( 1/3 ). Measure the folded piece together. How long is it? ( 1/4 m). So, 1/3 of 3/4 or 1/3 x 3/4 = 1/4.
Try this with other fractions and starting lengths.
Activity E(ii) – ratio tables
Ask children to use their multiplication tables to scale recipe quantities up and down to complete the table below. Consider their multiplication of simple fractions for quantities of vanilla extract and chocolate chips.
| Ingredients | 3 cupcakes |
6 cupcakes |
12 cupcakes |
18 cupcakes |
24 cupcakes |
|---|---|---|---|---|---|
| Self- raising flour | 130 gm | 260 gm | |||
| Caster Sugar | 100 gm | ||||
| Butter | 125 gm | ||||
| Large Eggs | 2 | ||||
| Vanilla extract | ½ teaspoonful | 1 teaspoonful | |||
| Chocolate chips | ¾ cupful |
Activity F(i) - Pizzas
This pizza themed fraction resource from the TES can be used in many different ways, and includes several suggestions from the author.
Activity F(ii) – Planetary Wars
Published by BEAM, and hosted within the National STEM Centre E-library, this two-player dice game requires children to find fractional quantities of numbers.
Activity G – Decimal Point Chair
When multiplying or dividing by powers of ten, the key issue to emphasise in many classrooms is that it is not the decimal point which moves, but the digits of the number. Prepare a range of cards to include several zeros, a decimal point and two whole numbers [e.g. 2 and 7]. Give a group of children one card each and ask the child with the decimal point to sit in the middle of a row of chairs, facing the class. Ask the 2 children with the cards with whole numbers to choose a chair to sit on, leaving no empty chairs between them and the decimal point. Explore ways to do this. Then introduce one zero in various places and talk about the numbers created. Add a second zero and do the same. Move on to asking the children to decide what happens to the number created if we multiply or divide by 10, then 100, then 1000 – emphasise that the decimal point must not move. Ask children to consider ways in which they might record this.
For a similar activity visit the National Stem Centre E-library, for the Interactive Teaching Programme ‘Moving Digits’
Please note that you will need to log in to this site in order to access the materials. This is free and simple to do.
Useful Resources
Activity B(i) - coloured rods
Activity B(iii) – several bars of chocolate
Activity D(i) – analogue clocks
Activity D(ii) – marbles
Activity E(i) – ribbon/string, tape measures, scissors
Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement
use common factors to simplify fractions; use common multiples to express fractions in the same denomination
Children should be able to recognise that a fraction such as 5⁄20 can be reduced to an equivalent fraction of ¼ by dividing both numerator and denominator by the same number [cancelling] They should also be familiar with identifying fractions in different units. E.g. what fraction is 20 pence of two pounds? Of four pounds etc…
compare and order fractions, including fractions >1
Children should be able to:
i] Position fractions on a number line; e.g. mark fractions such as 7⁄5 , 11⁄20 , 18⁄12 on a number line graduated in tenths
ii] Answer questions such as: What number is half way between 5 ¼ and 5 ½ ?
iii] Which is larger, ⅓ or ⅖? Explain how you know.
associate a fraction with division to calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. ⅜)
Children should be able to find fractions of numbers and quantities;
i] What fraction of £1 is 35p, … 170p ?
ii] Write 23⁄100 of 4 kilogrammes in grams
iii] What fraction of 1 litre is 413 ml?
Convert a fraction to a decimal using known equivalent fractions:
i] ¼ = 0.25
ii] ⅖ = 0.4
add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
Children should be able to solve practical problems such as;
Here is a chocolate bar.
William eats 3 pieces and Amber eats 2 pieces. What fraction of the chocolate bar remains?
Joe has some pocket money. He spends three-quarters of it. He has fifty pence left. How much pocket money did he have?
multiply simple pairs of proper fractions, writing the answer in its simplest form, (e.g. ¼ × ½ = ⅛)
Children should be able to:
i] Recognise that ¼ of 12, ¼ x 12 and 12 divided by 4 are equivalent
ii] Use cancellation to simplify the product of a fraction and an integer
eg ⅕ x 15 = 3
⅖ x 15 = 2 x ⅕ x 15 = 2x3 = 6
ii] Work out how many ½s in 15, how many ⅖s in 15, how many 2/5s in 1 etc.
divide proper fractions by whole numbers (e.g. ⅓ ÷ 2 = ⅙ )
Children should be able to:
Decide whether they would prefer to share ½ of a pizza with 2 people or ¾ of a pizza with 4 people and explain why.
associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3⁄8)
Children should be able to:
Explain how much pizza each person would get if they divided 4 pizzas between 5 people, as a fraction and a decimal
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
Children should be able to identify the value of each digit in the number 17.036 and multiply and divide this by 10.100 and 1000
multiply one-digit numbers with up to two decimal places by whole numbers
Children should be able to calculate the answer to questions such as;
What is 3.86 multiplied by nine?
use written division methods in cases where the answer has up to two decimal places
Children should be able to calculate 601 divided by 36, to two decimal places
solve problems which require answers to be rounded to specified degrees of accuracy
Children should be able to solve problems such as;
Four friends win £48,623. The money is to be shared equally between them – how much will each person receive?
107 pupils and teachers need to be taken to the theatre. How many 15-seater minibuses will be required?
How many boxes of 60 nails can be filled from 340 nails?
recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.
Children should be able to put a ring around the percentage that is equal to three-fifths;
20% 30% 40% 50% 60%
As well as circle the two fractions that are equivalent to 0.6.
6⁄10 1⁄60 60⁄100 1⁄6
