How do you compare fractions with different denominators? Comparing fractions is a nightmare for pupils and teachers.
This is a very difficult subject to teach and probably an even worse topic to
learn. Put this on an examination paper and you will separate the wheat from
the chaff, and mostly it will be chaff. How can we be more successful and not
have to teach it year after year to the same pupils.

Who has not had problems teaching or learning fractions? It is a painful experience for educator and learner. Despite our best intentions we do not always succeed. How can we make it easier? (if you have not done so have a look at my previous post Fractions - is that pizza for me (slice 1)?

How do you compare fractions? Who has not struggled with learning or teaching comparing
fractions? Ask a child (or even an adult) which is bigger 3/4 or 5/7 and you’ll
be met with a blank stare and a shrug of the shoulders, lets be honest it is
difficult.

Why do people have such difficulty with fractions and even more so comparing them? Perhaps they do not comprehend that a fraction is just part of a whole and have not had enough practical experience beyond 1/2, 1/4, etc. They need to involve themselves in dealing uncommon fractions such as 5/7, 4/9 and so on.

Below is how I tackle this problem, there is no rushing this
activity and it could take several lessons to achieve good results but it is
worth it. Once established it will provide a firm foundation for further work.

Have you ever wanted to improve the pupils learning and your
teaching of fractions? I have and I have probably taught fractions the same way
as everyone else, but I still had children who did not fully understand what a
fraction is, just like everyone else. How many metaphorical pizzas have been used each day during Maths lessons up and down the land? Yet our pupils have the same misconceptions year after year, despite using their favourite food. What is the
problem? What was I doing wrong? What is to be done?

The problem

If you give a diagram like the one below and ask the
question what fraction is shaded? What fraction is unshaded? How many children
would give the answers 2/8 and 6/8, probably most, but can they make the leap
to ¼ and ¾? They find this really difficult and need lot of questioning and
prompting to see the equivalence.

Another issue is when you ask a student to share 4 chocolate
bars between say 5 friends and ask how much do they each get. It takes some
time before a 12 year old for example realises it is 4/5. (Perhaps I am being a
bit optimistic there.)

As the pupil get older they are introduced to ratio. Do they
ever see the link between a ratio of 2:3 and the fractions 2/5 and 3/5?

Maths games, try putting this into Google
and the chances are that you will get a list of computer-based activities.
Worthy though they are how about the other type of game where the children play
with and interact each other? Finding these has proved a difficult task for me
over the years but I have collected a stock of them, the best of which are in
the books below. I have used them all and can highly recommend them.

The
advantages of these games are:

- The children work
collaboratively, rather than against a machine, learning from each other.

- They enjoy the challenge of
games, which is why computer gaming is such big business

- They are learning,
consolidating, revising knowledge in a fun way.

- It gives variety and interest
to the teaching and learning experience.

- It encourages positive
attitudes to Mathematics

During a conversation with a girl in my
class, at the end of a long school day, I was shocked to discover this was the
first lesson that she was not sitting in front of a computer. Although the lesson was a traditional ‘chalk
and talk’ before they attempted an exercise she was pleased that she didn’t
have to stare at a screen again. So Maths games does not necessarily mean log
on to the computer

1. Games, ideas and activities for the primary classroom by John Darbell

This gives ideas
for all areas of Maths that can be used for individuals, groups and classes. It
is clearly broken down into small clear sections. The activities can be easily adapted to suit different classes or topics. There are over 150 games and
activities, a real resource bank and time saver for any teacher.

One reader said 'I wish I'd bought this book last year while I was an NQT, but at least I have it
in my cupboard for this year.'

'Designed with busy teachers in mind, the Classroom Gems series draws
together an extensive selection of practical, tried-and-tested, off-the-shelf
ideas, games and activities, guaranteed to transform any lesson or classroom in
an instant.

Easily navigable, allowing you to choose the right activity quickly and
easily, these invaluable resources are guaranteed to save you time and are a
must-have tool to plan, prepare and deliver first-rate lessons.'

2. 25 super cool Math board games by Lorrine Hopping Egan

The games are reproducible fun and are linked to concepts that we teach very year. They are applicable to any classroom organisation even home schooling. The rules are not complicated, how often do games look good but when you try to play them with group they've lost interest and enthusiasm because they don't understand what they have go to do. Not so here.

'How does a hungry raccoon clean up behind a human picnic? If it's "Remainder
Raccoon," simple division and practice with remainders will do the trick. Each
game in this book presents math concepts (computation, fractions, decimals,
geometry, logical thinking) in a fun, imaginative context. You'll find both
competitive and cooperative games; individual, small group, and large group
games to accommodate home schoolers to entire classrooms; multi-level play so
that kids can achieve success and then advance to a more challenging level; and
complete reproducibles with spinners, boards, pieces, markers, and more.'

4 reviewers gave this 4 stars out of 5 on Amazon

3. Key stage 2/3 Numeracy games by John Taylor

This covers pupils from ages 5 to 14. Slightly differnt from my other recommendations as it has puzzles quizzes, investigations, games and ICT activities. One reviewer particulaly liked the preponderance of kinesthetic games, what a pleasure to find some.Plenty of ideas to pep up your teaching, or leaning.

'This book is fantastic! Just what I needed to make me want to teach
maths again. After being given many boring recommendations for maths teaching,
it has reminded me that creativity in maths makes it fun. Lots of kinaesthetic
games, and plenty of cool tricks using the interactive whiteboard for me to show
off with next time I am observed teaching maths.' - customer
review, amazon

11 reviewers gave this 4.2 stars out of 5 on Amazon

4. Mathematical team games by Vivian Lucas

I could have chosen any Vivian Lucas book to include here. Most re geared to an older age group but as always any competent teacher can use a good ide to their advantage. Once you've used this you'll use it again and again and again. I bought my own copies because prising them out of others hands was always difficult.

'Team Games are special mathematical puzzles and problems which produce real
cooperation between the members of a team. The mathematical content is that of
the normal curriculum. Each player only gets some of the information and so all
must play a part in arriving at a solution. Sixteen tried and tested team games
are provided in photocopiable form.'