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Fractions seem to worry students. They are something a bit alien. A bit weird. Integers or counting numbers, they have met before going to school and have loads of concrete ways of representing them. Fractions… well there’s cutting pies, cakes and pizzas.
I find the first thing to remember about fractions is they represent a number and quantity.
They can be shown on a number line.
Just remember that fractions represent a quantity, a number. Nothing too clever or difficult. They are just a type of number.
Students by the time they reach year 3, should be comfortable talking about half a bag of sweets and know how to write some more “well-known” fractions such as 1/3, ½ and ¾
Year 2 national curriculum:
Pupils should be taught 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
* write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2.
Adding Fractions and the National Curriculum.
Adding fractions appears in years 3-6 of the national curriculum. This reflects the fact that students struggle with adding fractions conceptually (generally fractions are a concept a large number of students struggle to grasp). The need to cover the subject and recover it every year reinforces the concepts involved year after year. It means your students will have to show a Growth Mindset. To encourage this approach, tell them it’s difficult, but they can do it and you must maintain high expectations for all!
Year 3: add and subtract fractions with the same denominator within one whole
Year 4: add and subtract fractions with the same denominator
Year 5: add and subtract fractions with the same denominator and denominators that are multiples of the same number
Year 6: add and subtract fractions with different denominators and mixed numbers
The Parts of a Fraction
Students should be introduced to the correct terminology as early as possible and use of this terminology is massively important. Don’t give up! Scaffold! But keep going.
The top part of a fraction is called the numerator.
The bottom part of the fraction is called the denominator.
The denominator relates to the number of equal parts something is divided into. So this box is divided into 5 equal parts:
The numerator relates to how many equal parts you have. So this box we have 3 of 5 equal parts coloured yellow.
This fraction is expressed as:
Adding Fractions with the SAME Denominator
If the fractions have the same denominator (year 3, 4 & 5 content):
Having the “same denominator” means the two fractions being added together have the same number below the fraction line.
So the following fractions all have the same denominator “8”:
If the sum is to add two fractions with the same denominator, then all you have to do is add the two numerators (or numbers on the top). For example, in the sum below the two fractions have the same denominator – 5:
To work out the correct answer, all we have to do is add the numerators 1 and 2. 1 + 2 = 3
Pictorially, this looks like:
Adding Fractions with DIFFERENT Denominators
If the Fractions to be added have different denominators (year 6 content):
Having “different denominators” means they have different numbers below the fraction line.
So the following fractions all have different denominators:
If the sum is to add two fractions with different denominators, then we can’t just add the two top numbers. It doesn’t work:
To add two fractions with different denominators, you therefore have to do something to make the denominators the same without changing the value or size of each fraction.
The most formulaic way of doing this is to multiply each fraction by different numbers so that they end up with the same denominator. (This isn’t easy to explain in a sentence.)
So to make 2/5 have a different denominator (but represent the same number), we can times both the numerator and denominator by the same number. If we multiply both the numerator and denominator by 2, 2/5 becomes:
Pictorially this looks like:
Similarly, to make ½ have a different denominator (but represent the same number), we can times both the numerator and denominator by the same number. If we multiply both by “5”, ½ becomes 5/10.
By swapping these different representations of the fractions into the sum, we can see:
All of a sudden, we have ended up adding two fractions with the same denominator!
To work out the correct answer, all we have to do is add the numerators 4 and 5. 4 + 5 = 9
Pictorially, this looks like:
The one thing we have glossed over here is the choice of the number to times the fractions by.
“So to make 2/5 have a different denominator (but represent the same number), we can times both the numerator and denominator by the same number. If we multiply both the numerator and denominator by 2, 2/5 becomes . (This is called an “equivalent fraction”)”
Why and how did we choose 2?
We choose 2 because it was the denominator of the other fraction.
Summary - How to Add Fractions
So to add fractions (which are just numbers) we need the denominator to be the same.
To make the denominator the same for both fractions, multiply the fractions by the denominator of the other fraction.
Then add the numerators together.
We’ll deal with improper fractions under “mixed fractions” in another blog.
Practise or Learn By Questions
We’re huge fans of practise with live/immediate feedback.
The more questions encountered with immediate correction, the more the approach is embedded and numeracy confidence improves.
Obviously, we suggest using Fractions with Emile. It assesses students and delivers games and activities at an appropriate level. What’s more it allows students to compete against each other in league tables and competitive games.