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.'
Here is an idea that will get you plaudits
from those that like to see Maths in a context or ‘real life’ Maths. It will
give a different pace to your lessons and engage those who prefer a kinesthetic
learning style or experience. Yet again what you do depends upon your imagination and
perhaps appetite.
Preparation
Eat lots of cereal. Ban toast for breakfast
and force, if you have to, your family to eat packets and packets of cereal.
Keep the boxes. No recycling. You have to supervise the opening of the boxes as
you want them to be in as good a condition as possible.
The Lesson
Organise the class into groups around
tables, 4 to a table seems to work. As the proud owner of numerous cereal
packets distribute one or more to each group. Ask the class what they could
find out about the boxes, give them a minute or two to jot down some ideas then
collect one from each table and record them on the board. It is now up you how
you progress. Sometimes I have collected the ideas from the class, recorded them on the board, and then discussed what we have to find. Alternatively I have collected the ideas but also handed out a worksheet to some classes listing what needs
to be found or what tasks they have to do. Here are some suggestions of what they have to do and record as a group.
Find the height, width and length of the
box.
Find the volume of the box.
Draw a net of the box to scale.
Make an isometric drawing of the box.
Find the surface area.
How much does the it cost per gram? per
100g?
How many boxes could fill the classroom?
What is the ratio of sugar to salt? Does it fit in with Government guidelines?
If it takes 10 days to eat a box how much
salt would I consume in a year?
Further ideas
There are always new and exciting ways to tackle topics. Buy this books and you will be generating even more ideas for yourself 100+ Ideas for Teaching Mathematics (Continuum One Hundreds)
.
As one reviewer says 'I was looking for a book which would inspire me when planning sessions for
teaching mathematics. I browsed a number of books but this one was definitely
the best as far as I could see on-line. When it arrived it was even better than
I expected. I would certainly recommend this book to anyone who teaches maths! '
Extension ideas
Alternatively you could work on the suggestions gathered from the class. The outcome could be report produced by each group or answers in their books from prepared worksheet by you.
You could provide them with boxes of the
same product but in different sizes which is the best value? I am sure you can
think of other ideas. Happy eating. (By the way you have noticed a picture of porridge, I don't eat any other cereal these days, can't think why.)
Ratio
can be a difficult concept to understand. Like
fractions you can teach it year after year, think you’ve succeeded but year
after year it has to be retaught. The idea has not sunk in, the long term memory
has not been troubled, it seems as if you are presenting the pupils with a
totally new subject. What is to be done? How can we make our teaching more
efficient, reduce the frustration felt by our kids and us? This is how to teach
finding the ratio of a quantity.
The
solution
Using this method I have had a great
success, although we as teachers nothing is ever 100%, that’s the problem with
teaching humans! First I explain that the head teacher (principal for my
readers in the States) has given me £120 for the class as a reward for
outstanding progress in Mathematics. I tell them the money is in easy to carry bags;
in fact there are 6 bags in all. At this point I draw the 6 bags on the board.
The question is now posed ‘How much is in
each bag?’ Back comes the reply £20. I
fill in £20 in each bag, this is a vital step.
This step is a huge reminder to the kids
and really helps them to find an answer to the question posed, I am always
amazed that even some very bright pupils persist with this method long after
they have progressed beyond this level of Mathematics so it must have a lot of
value.
I now drop the bombshell on the class, I am
going to give them one bag, and I’ll keep the other five. On the drawing I put
in the colon. As you can imagine this is not always greeted with total
approval.
At no point have I mentioned ratio. I now
introduce the word and write on the board the numbers
1:5
You have now laid the groundwork for
explaining ratio. Introduce the word ratio and say when you share out any
quantity the colon is used to show who gets what. I always emphasize that ratio
is really sharing. I do several other examples on the board, always drawing the
bags, always writing the amounts in each bag. I then give the pupils an
exercise on ratio, encouraging them to do the drawing of bags putting the
amount in each bag and hence finding the answer.
.
