Fractions Unwrapped – The Basics

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.

Denominator

Fraction

Fraction in words

2

1/2

One half

3

1/3

One third

4

1/4

One quarter

5

1/5

One fifth

8

1/8

One eighth

10

1/10

One tenth

25

1/25

One twenty-fifth

100

1/100

One hundredth

Click on the link below for Activity 1 – Write the fraction

Fractions – Activity 1

 

What are the different types of fraction?
Proper Fractions

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

Improper Fractions

These are numbers bigger than one that are expressed in  fraction format

Top Tip – Numerator is BIGGER than the denominator

Mixed Numbers

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 

but…

they can also be written as a the number of parts making a whole e.g. 3/3

Top Tip – Numerator EQUALS the denominator

Clink on the link below for Activity 2: Identifying types of fractions

Fraction – Activity 2

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 

 

Whole Number

Part Number

11/4

4/4 + 4/4

3/4

2 3/4

4/4 + 4/4

3/4

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

Click on the link below Activity 3: Converting mixed numbers to improper fractions

Fractions – Activity 3

Click on the link below for Activity 4: Converting improper fractions to mixed numbers

Fractions – Activity 4

Equivalent fractions and simplifying fractions
Equivalent 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

Simplifying fractions

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

Simplify 72/81 

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

Fraction Bars

Fractions bars are a really good and visual way of showing equivalent fractions and explaining how to simplify fractions

Click on the link below for Activity 5: Equivalent and Simplifying fractions

Fractions – Activity 5

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

Click on the link below for Activity 6: Comparing fractions

Fractions – Activity 6

That’s all for now but keep an eye out for Fractions Unwrapped Part 2

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Times Tables; Fun ways to teach them

Contrary to popular thinking, I think times tables are one of the cornerstones of basic maths.

I’ll say at this point, it’s taken Issy 18 months to 2 years but she now knows her times tables inside out, upside down and back to front.

What are times tables?

Times tables are just a shorthand way of writing the repeated addition of a particular number. 

So how did we go about teaching them?

Issy is a visual and kinaesthetic learner; she needs to see it and feel it to understand it.

The key is little and often. We practise every day for no more than 5 or 10 minutes. It’s fun, practical, usually involves physical activity and is reinforced with real life scenarios. Issy uses her times tables when converting currencies, working out whether it’s better to accept a 3 for 2 deal or buy items individually or scaling up a recipe according to the number of portions she needs.

General Strategies
Workbooks/Worksheets

When we first set out about learning our times tables, I used a lot of the twinkl resources and in particular the times table booklets. She tackled a booklet every 7-14 days and we would reinforce it with the other strategies listed below.

Step Counting...literally

This is the starting point for most people and it involves reciting the multiples in a particular times tables eg. 2, 4, 6…22, 24.

More recently we’ve been combining this with walking or running up the stairs (obviously this is a bit difficult in the motorhome!)

Drawing the multiples in a big number

Draw a big number and write all the multiples in it and stick it up somewhere.

Songs

There are various song and dance based apps and resources available.  I know a lot of people use Times Table Rockstars. We didn’t, mainly because I found it quite expensive as a private individual.

When it comes to free resources, You Tube is your friend and we did use the Laugh Along and Learn channel which uses popular songs to learn times tables eg. the 6 times table is Taylor Swift’s Shake It Off  and 8 times table is Adele’s Rolling in the Deep (https://www.youtube.com/watch?v=z_BJjR9rdwA)

Issy also liked the song that she used at school

CHS good as gold, this is how our fingers roll, the *[threes] 3,6,9…30, we’re no finished yet 33, 36, this is how roll our *[threes].

*substitute any times table

Physical Activity

Issy enjoyed the BBC Sport Supermovers videos and these are particular good for the football mad amongst you as they are supported by football club mascots.

We often practise whilst out walking, on a swing at the park or throwing a ball (apparently this develops the same neural pathways as learning maths).

Learn and Recite them in groups

We’d already learnt our times tables by the time I learnt this hack but we now recite our times tables in groups of 2/4/8, 3/6/12, 5/10/11 and 7/9.

This helps to solidify the relationship between the multiples and provides a strategy to work out any that you are unsure of using information you already know.

Strategies for Specific Times Tables
Counting Coins

We collected 2p,5p, 10p, 20p and 50p coins and counted the number of pennies in each pile.

As we advanced we’d roll two dice to decide how many would be in the pile and Issy would give me the answer.

Using your 2 times table knowledge to work out your 4 times table (double, double)

The 4 times table is double the 2 times table. If you know what 2 times a number is, you just need to double it to get 4 times a number.

Using a clock to learn the 5 times table

A clock is a ready-made tool for learning the 5 times table. Point to a number and ask how many minutes past the hour it is.

Using your 3 times table knowledge to work out your 6 times table (double threes)

The 6 times table is double the 3 times table. If you know what 3 times a number is, you just need to double it to get 6 times a number.

Using your 4 times table knowledge to work out your 8 times table (double fours)

The 8 times table is double the 4 times table. If you know what 4 times a number is, you just need to double it to get 8 times a number.

The Finger Method for 9 times table

This is a great one for all you visual learners out there.

Number patterns for 9 times table

As the tens digit goes up, the units digit goes down

Number patterns for 10 times table

You add a zero to the number you are multiplying ten by

Using your 6 times table knowledge to work out your 12 times table (double sixes)

The 12 times table is double the 6 times table. If you know what 6 times a number is, you just need to double it to get 12 times a number.

I know them...now what?

Even though I’m confident Issy knows them, we still practise every day and once a month she has a times tables test. She’s seeing the benefit now she’s tackling long division and more complicated multiplication.

In all seriousness, I do credit my times table knowledge to my maths teacher Mr Moore who gave us a times table test every Tuesday morning when I was in Year 7! It really is a case of practise makes perfect.