Where would we ever use this? What is the point of this? Undoubtedly, you have heard these questions from students. Yet mathematics surrounds us daily, in the everyday things around us, and in our cultural heritage and who we are as thinking individuals. There are countless ways to explore mathematics and have students experience some of the fun mathematics has to offer. With a bit of creativity you will be on your way to developing ideas to make mathematics learning more challenging, meaningful, and relevant to students of all ages.

 

Introduction

The extent to which mathematics pervades our daily lives tends to be rather invisible. Maths has a sort of silent presence in that although it has been a foundation for so many human accomplishments, its contributions have become embedded in those accomplishments. In fact, this embedding, or becoming implicit, is part of what makes mathematics so powerful. What are some of the reasons we devote so much school time to mathematics studies? Sure, there are important numeracy needs that must be addressed, and the mathematical knowledge and skills that are essential for various professions. But let's not lose sight of the fact that mathematics is in essence "... a creative activity, involving invention, intuition and exploration" (Education Department of Western Australia, 1994; p.4).

If we look around us with questioning, curious eyes, then we will find endless ideas for exploring mathematics in ways that make if fun and motivational for students of all ages. As a mathematics educator I find myself daily noticing things in my environment that I can use in my teaching, whether it be at a primary, secondary or tertiary level. All it takes is a little imagination! I will share with you here a small sample of the ideas I have collected or developed over the years.

 

KitKat Capers

One of my favourite activities is to examine the way KitKat chocolate bars are packaged. If you have never noticed, the standard sized bar is wrapped so that it is placed on an angle in the foil wrapping. The angle is not an obvious angle such as 45 or 30 or 60 degrees. Why might it be that it is wrapped this way?

Materials needed

KitKat chocolate bars (various sizes) and an assortment of other candy bars.

Outline of the activity

Unwrap a standard sized KitKat bar and examine the way it has been wrapped. Why might it be packaged this way? How does this packaging compare to that of a KitKat from Canada or the United States? (Each year when I am back in Canada visiting family I bring back to Australia samples of KitKats from overseas because they are wrapped in a more 'expected' way). Examine the packaging of other chocolate bars and form hypotheses about why they are packaged in certain ways.

Related activities

Investigate the packaging or crating of a range of other food products, including canned goods, cereals, biscuits, or fruit. For example, note that different cereals use different paper or plastic wrappings inside the cardboard outer box, and form these inside wrappings in different ways. Think about why it might be that different products are packaged in different sizes of cans, or why it is that different manufacturers use different sizes of cans. A particularly interesting investigation of food packaging is that of cardboard milk cartons (see the next activity, Milk Carton Mania). If you start considering the packaging of items other than food, you have a whole world of possibilities to explore.

 

Milk Carton Mania

I first encountered this idea for a mini-investigation in Pottage (1992). I have used this activity with adults as well as primary school children, even though the quotation below is in the context of high school. It has always generated much curiosity and bewilderment, as well as many smiles and laughs. The idea goes like this:

The most careful measurements of the milk carton yield a volume estimate, according to the formula V = lbh, of not more than about 960 cm3, or 0.96 litre. Students in Year 9 or 10 are quite impressed and are ready to accuse the suppliers of giving short measure, or else they suspect that their measurements have been inaccurate, or they struggle with pseudo explanations involving the densities of different liquids. What they don't catch on to without considerable urging is that the prism to which the formula V = lbh applies is an ideal one, very imperfectly instantiated by a filled carton with its bulging sides. This modest example might serve to protect them from placing too much faith in the applicability of abstract formulae (Pottage, 1992; p.13).

Materials needed

Empty and washed 1 litre milk cartons, calculators, and a variety of measuring equipment (including tape measures, string, rulers, MAB shorts and longs). It is advisable not to make liquid measuring materials available until after the students have calculated the capacity using measurements of the dimensions. Scissors should also be available since often students will want to cut the carton open to do more accurate measurements on the 'inside' of the carton.

Outline of the activity

Have students measure the dimensions of a milk carton in a variety of ways, each time calculating its capacity.

Related activities

Repeat the activity using milk cartons of other sizes (for example, the small drink containers and larger 1.5 litre cartons). Some plastic milk and juice containers are also 'soft' sided so it is worth also examining them also.

 

Friendly Giant

This is another activity that can be used with students from a wide range of ages, including adults. It is only one of numerous ways to use our own bodies in acting as a sort of mathematics detective. The original idea comes from the AIMS Education Foundation (1995), and there are several ways one can go about obtaining answers to the questions outlined below.

Materials needed

Calculators, a variety of measuring equipment, (eg, rulers, measuring tapes, etc.), and an overhead transparency of a hand (or a large sheet of paper with the outline of a hand).

Outline of the activity

Before the class begins, either prepare an overhead transparency of a hand that is on the overhead projector, or put up on the wall a large outline of a hand. Tell the students that during the night a giant entered the classroom and while groping around in the dark for the light switch left a large smudged hand print on the wall. From this print determine how tall the giant must have been. That is, what would be the approximate height of the giant? How many different ways can you find to determine how tall the giant must have been? Could this giant have stood up in the classroom? Would its head fit through the door? If the giant were to lie down on the floor, where would his/her feet be and how far away would the head be? What assumptions did you make in solving these problems?

Related activities

How does your height compare with your arm span, so are you a square, a tall rectangle or a far-reaching rectangle? What do you predict others in your class would be? Would the class results be different if everyone were five years younger, or five years older, or ten years older? Estimate the circumference of your head. How does it relate to your arm span? How does it relate to your height?

 

Impossible Peas and the Wonderful World of Mathemagination

If you have read the book Counting on Frank (Clement, 1990), then you are aware already of how a vivid imagination can bring to life a wide array of mathematics related to estimation, number, space, measurement, and chance and data ideas. If you have not read this book, then you should endeavour to do so!

Materials needed

Can of peas or bag of peas, calculators and a wild imagination!

Outline of the activity

Estimate the number of peas in a standard size can of peas (or a bag of frozen peas or dried peas). Count the number of peas, then estimate the number of peas it would take to fill a bucket. To fill the classroom? To fill your house? If you dumped 15 peas on the floor each evening at dinner, how many peas would that be in a year? How many after 5 years? How much space would they take up after 5 years? What other similar questions about peas can you generate and then answer?

Related activities

If your school were to collect one million plastic bread bag ties, how much space would they take up? How many times does your heart beat in a year? How many times will it beat in your lifetime? What assumptions did you make answering these questions?

 

Summary

These are just a small sample of ideas for fun and motivational maths activities. Just look around you for more ideas. I often carry a camera and capture my ideas so I can share them with students. For example, I recently went to a quilting exhibition and took photos of the patterns and designs of modern day as well as traditional quilts. When I have been on holidays I have taken photos of the crafts, weaving, floor tiles, wall decorations, decorative fencing, and other culturally related patterns. I have photos of the symmetries of seashells and other ocean creatures, of the designs of various musical instruments, of the architecture of buildings from around the world and from many different historical eras, of objects in the natural world such as gardens, trees and flowers, and of everyday items such as suncream bottles, cars and keys. They are all full of mathematical ideas. The possibilities are endless!

References

AIMS Education Foundation (1995) Jaw breakers and heart thumpers (pp.1-4) Fresno, California: AIMS Education Foundation.

Clement, R. (1990) Counting on Frank. Sydney: Williams Collins.

Education Department of Western Australia (1994) Mathematics Student Outcome Statements with pointers and work samples, Working edition. Perth: EDWA.

Pottage, J. (1992) Contextual mathematics and actualizing creative potential. Vinculum, 29 (2), 10-13.

©TalentEd is located at the School of Curriculum Studies, University of New England, Armidale, Australia.

This page updated: 23 January 2006 Webmaker: Howard Smith. hsmith4@une.edu.au