# Small Number and the Old Canoe

### Small Number and the Old Canoe

Written by Veselin Jungic & Mark MacLean
Illustrated by Simon Roy

In Small Number and the Old Canoe, mathematics is present throughout the story with the hope that this experience will make at least some members of our young audience, with the moderator’s help, recognize more mathematics around them in their everyday lives. Using terms like smooth, shape, oval, and surface, and mathematical phraseology like It must be at least a hundred years old, the artist skillfully presents reflection (symmetry) of trees in water, and so on. The idea behind this approach is to give the moderator a few openings to introduce or emphasize various mathematical objects, concepts and terminology. The short film is a little math suspense story and our question is related only to one part of it. The aim of the question is to lead to an introduction at an intuitive level of the concept of a function and the essence of the principle of inclusion-exclusion as a counting technique. The authors would also like to give their audience an opportunity to appreciate that in order to understand a math question, one often needs to read (or in this case, watch) a problem more than once.

## Story Transcript

Small Number is a five year-old boy who gets into a lot of mischief. He lives with his Grandma and Grandpa, who patiently put up with his antics most of the time. Today, Grandpa needs to finish carving a feast dish and decides that Small Number should go out and play with his friends

It is a beautiful, sunny, spring day, and the boys run down to play near the water.

Everything there sparks a new game, and Small Number’s friend Big Circle suggests they see who can make a stone skip the farthest on the surface of the water. The boys quickly learn that for a stone to go far it needs to be smooth, flat, and oval shaped.

Small Number wanders far along the shore looking for a winning stone. He scrambles through tall grass and trips over something, falling headfirst into an old canoe hidden in the grass. Small Number stands up, rubbing his forehead as he looks around at the canoe. Even though his head hurts, he is very excited at his discovery and he calls out to his friends, who come running.

The boys stand around the canoe, running their hands along its smooth shape. It looks very old and very big to them. Small Number asks, “How many people do you think it could hold?” Big Circle asks, “How many generations ago was it built?” The boys forget their previous game and spend a long time talking about the canoe and who might have used it.

As they are talking, Big Circle’s tummy starts to growl. “I’m hungry. Let’s go eat,” he says to his friends. The other boys realize they are hungry too, and they all run back to the village.

Small Number races home, where Grandpa is carving the surface of a huge wooden dish. Small Number is shouting excitedly and Grandpa looks up. He sees the bruise on Small Number’s forehead. “What happened?!” Grandpa asks. Small Number has forgotten that he bumped his head and starts to tell Grandpa about finding the canoe: “I found an old canoe down on the beach! It must be at least a hundred years old!

Grandpa smiles. “I know that canoe. It was once the fastest canoe in our village. It was built by my father and two of his brothers.” Grandpa proudly continues, “All the sons of my grandfather were known as great wood carvers."

"You know those three old totem poles in front of the longhouse? Each of them was built by one of my uncles.

That evening, just before falling a sleep, Small Number thought, "I'd like to build canoes and totem poles just like my ancestors. I have to ask Grandpa tomorrow how many brothers his father had. Two, three, four, five or more..."

Question: Why did Small Number think that his great-grandpa might have two, three, four, five or more brothers?

## Credits and Acknowledgements

• Written by: Veselin Jungic, SFU and Mark MacLean, UBC
• Illustrator: Simon Roy, Victoria, B.C.
• Director: Andy Gavel, Simon Fraser University

#### Special thanks to:

• Tom Archibald, Simon Fraser University
• Peter Jacobs, Squamish Nation
• Ozren Jungic, University of Oxford
• Kwosel, Seabird Island First Nation
• Kwelaxtelot, Seabird Island First Nation
• Susan Russell, Simon Fraser University
• Erin Tait, Nisga'a Nation
• Department of Mathematics, Simon Fraser University
• Faculty of Science, Simon Fraser University
• The IRMACS Centre, Simon Fraser University
• Office for Aboriginal Peoples, Simon Fraser University
• Pacific Institute For Mathematical Sciences

This story is part of the NSERC PromoScience project "Math Catcher: Mathematics Through Aboriginal Storytelling"

Financial support provided by NSERC, PIMS, UBC, the IRMACS Centre, and SFU