Teaching Issy fractions has been one of my success stories. At the age of 8, she’d learnt pretty much all she will need to know to take her up to GCSE. She went from not understanding what a fraction was to multiplying and dividing them in less than a month.
When looking at what to teach I took my lead with what to teach from the English National Curriculum.
What does the National Curriculum say you need to know?
The key areas are:
- What is a fraction?
- What type of fractions are there?
- Key fractions e.g. halves, quarters, thirds etc
- Equivalent fractions and simplifying fractions
- Ordering and comparing fractions
- Adding, subtracting, multiplying and dividing fractions
So what do you actually need to know?
Well, there are many that would say none of it!
However, having a knowledge of fractions is useful in catering, statistics and playing card games or board games such as scrabble and rumikub
A basic knowledge of fractions has helped Issy learn to tell the time, analyse statistics and understand probability and percentages.
So how did we tackle fractions?
We made it fun!
I started at the beginning and we used lots of hand-on props. This post is limited to the basics but part 2 will look at operations and converting fractions to percentages and decimals.
Issy’s tools of choice were dominoes, UNO cards and counters. There wasn’t a pizza, chocolate bar or a cake in sight. Food was a no go; a hangry Issy is not a learning Issy.
I made it relevant to her. Having hit a bit of stumbling block over the no cake or pizza, I asked her what she wanted use and she said chapters in a book (the numerator being the chapters she’d read and the denominator being the number of chapters in the whole book). That one switch made such a difference, it was literally like a light turned on.
So let’s begin with a starter for 10…
What is a fraction?
A fraction is a way of expressing how may equal parts of a whole we have. It can either be
- A number less than one e.g. ¾
- In a mixed number that part of a number that is less than 1 e.g. 3 ¾
- The number of items in a group with certain attribute or characteristic e.g. 17 out of 43 smarties are green
How do we write fractions?
A fraction is made up of 2 parts
NUMERATOR – The top part of the fraction which tells us what part of the whole we are referring to or the number of items in a set with a particular characteristic
DENOMINATOR – The bottom part of the fraction which tells us how many parts make up a whole or the total number of items in a set
Top tip – We get DOWN with the DENOMINATOR so it goes as the bottom
How do we say fractions?
The general rule is that we say the numerator followed by the denominator in it’s ordinal form e.g 3/8 is three eighths.
There are a few exceptions so 1/2 is a half and 1/4 is a quarter.
The table below shows the main fractions you are expected to know.
Fraction in words
What are the different types of fraction?
If I asked you to write down a fraction most people would write down a proper fraction. They are less than one
Top Tip – Numerator is SMALLER than the denominator
These are numbers bigger than one that are expressed in fraction format
Top Tip – Numerator is BIGGER than the denominator
An alternative way of expressing fractions bigger that one which include both a whole number and fraction e.g. 3 3/4
A quick word about whole numbers
All whole numbers have a denominator of 1 e.g. 4/1
they can also be written as a the number of parts making a whole e.g. 3/3
Top Tip – Numerator EQUALS the denominator
Converting Improper Fractions to Mixed Numbers and back again
To be able to do this well, you need to understand how improper fraction and mixed numbers are made up.
We went back to partitioning fractions in to their whole numbers and their part numbers. If you look at the example below you can see that 11/4 is the same as 2 3/4
4/4 + 4/4
4/4 + 4/4
Once you become more confident you will be able to use your times table to convert between the two
Express 15/4 as a mixed number
15/4 = 3 remainder 3
So we know that the mixed number will be 3 3/4
Express 3 and 4/25 as an improper fraction
Denominator =25 (we know this from the 4/25 part of the number)
Numerator = (whole number x denominator) + part number
Numerator = (3 x 25) + 4
Numerator = 79
Improper Fraction = 79/25
Equivalent fractions and simplifying fractions
These are fractions with different numerators and denominators which represent the same value or proportion of the whole.
We use our multiplication and division knowledge to find equivalent fractions.
The key with this is whatever you do to the numerator you MUST also do to the denominator.
Find an equivalent fraction to 3/5
We can’t make this fraction any smaller.
This tells us we need to multiply the numbers to get an equivalent fraction
So if we decide to multiply the numerator by 5, we MUST also multiply the denominator by 5
Numerator = 3 x 5 = 15
Denominator = 25
Fraction becomes 15/25
To simplify a fraction you find the smallest equivalent fraction.
This occurs when
- The numerator is 1; or
- There is no common multiple between numerator and the denominator
We know that both 72 and 81 are in the 9 times table so we can divide each number by 9
Numerator = 72/9 = 8
Denominator = 81/9 = 9
Simplest Fraction = 8/9
Fractions bars are a really good and visual way of showing equivalent fractions and explaining how to simplify fractions
Comparing and Ordering Fractions
There are few basic rules to remember when ordering and comparing fractions
- If the DENOMINATOR is the SAME, then the BIGGER the NUMERATOR the bigger the fraction
- If the NUMERATOR is the SAME, then the BIGGER the DENOMINATOR the smaller the fraction
- If the numerator AND the denominator are DIFFERENT, you need to ensure all the fractions have the SAME DENOMINATOR
Ensuring all the fractions have the same denominator
The simplest way is to see if you can find equivalent fractions which gives you the same denominator.
But what do you do if you can’t? Well that’s where the butterfly method comes in.
The Butterfly Method
Used when you need to find the same denominator but you can’t find an equivalent fractions
Compare 1/6 and 3/4
Step 1: Multiply 6 x 4 to give you the new denominator
Step 2: Work out the numerator of Fraction A
Numerator A x Denominator B
1 x 4 = 4
Fraction A= 4/24
Step 3: Work out the numerator of Fraction B
Numerator B x Denominator A
3 x 6 = 18
Fraction B = 18/24
Step 4: 18/24 is greater than 4/56
That’s all for now but keep an eye out for Fractions Unwrapped Part 2
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