Fractions – is that pizza for me (slice 2)?

What fraction of the pizza am I getting?

 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)?

  

Comparing fractions (part 1)

Comparing fractions (part 1)

Comparing fractions

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.

Fractions – is that pizza for me (slice 1)?



Another fraction of a pizza

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 - the way granny used to play

Maths games – my top four resource picks

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.'

12 reviewers on Amazon gave it 4.1 stars out of 5

 

Games, Ideas and Activities for Primary Mathematics (Classroom Gems)

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.

25 Super Cool Math Board Games: Easy-To-Play Reproducible Games That Teach Essential Math Skills

 

'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.

Key Stage 2/3 Numeracy Games: Maths Activities and Games for Ages 5-14: Jumpstart!

 

'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.

Mathematical Team Games: Enjoyable Activities to Enhance the Curriculum

'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.'

 

5 out of 5 stars from 5 reviewers on Amazon

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Breakfast Maths or the cereal that never ends

A cereal lesson 

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.)

100+ Ideas for Teaching Mathematics (Continuum One Hundreds)