Small Number and the Old Canoe-Squamish
Small Number and the Old Canoe – Squamish
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.
EtsĂm Skw’eshĂmĚ“ iy ta eskwekwĂnĚ“ snexwĂlh
(Squamish Translation)
Written by Veselin Jungic & Mark MacLean
Illustrated by Simon Roy
Squamish Translation by T'naxwtn, Peter Jacobs of the Squamish Nation
Translations
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Story Transcript
Na na7 kwetsi s7Ăxwalh, EtsĂm Skw’eshĂmĚ“ kwi snas. Nekw tsĂyachisawánexw. Lhiḵ’ na wa ḵw’eshĂ©tsut. haw ḵ’as ya ḵ’esĂwsnitas Ta selsĂ7ls ta sḵw’eshĂ©tsuts.
Na wa ch’exwtĂmĚ“ ta si7ls ta x̱epiy̓éwelh. Stl’i7s kwis hĂşynexwas ti stsi7s. Na melh tsuntem ta Ămats namĚ“ as ḵw’eshĂ©tas ta sĂiyayĚ“s, nilh kwis ans ha7lh ta skwayl. Ta EtsĂm Skw’eshĂmĚ“ iy ta sĂiyayĚ“s na namĚ“ ḵw’eshĂ©tsut ch’it ta staḵw. An ḵex̱ ta ha7lh sḵw’eshĂ©tsutswit.
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 they see 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.
Na na7 kwetsi siyáyĚ“s, HiyĂ Shishi7ch kwi snas. Na hey̓ḵwtas namĚ“ aswit tsexwĂmĚ“ ta smant kwis xwĂxwitims na7 ta staḵw smen tĂ©lĚ“nexwaswit wa swa7s smant namĚ“ as an x̱éta. Na melh yĂ©lx̱tas i7x̱w ta s7Ăxwalh kwi smant, stl’i7s ta smants kwis ans ts’els, an tsewás, tim̓á tkwi ḵelĂşmĚ“.
Everything they see 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.
Ta EtsĂm Skw’eshĂmĚ“ na wa Ă7imĚ“esh ch’it ta staḵw ses men wa yĂ©lx̱tas ta yew̓ánĚ“ ha7lh smant. Na x̱wiyaḵw’ántsut ta an tl’aḵt sáx̱wi7 ses men lhĂkw’shen kwi stam as ses men txwnewĚ“ ta eskwekwĂnĚ“ snexwĂlh. Ta snexwĂlh ta kwáyantem na7 ta sáx̱wi7. Na melh lhx̱ilsh ta EtsĂm Skw’eshĂmĚ“ ses wa xwĂkwinĚ“tas ta st’uḵw’chus. Ses men kw’acháyĚ“s ta snexwĂlh. Yamen kwis ans aaḵw, na7xw wa x̱wi7elwas. Iy kwis ans ha7lh ta na yĂ©lx̱nexwas, na melh ḵ’áytentas ta sĂiyayĚ“s. Na melh mĚ“i tskw’átsutwit.
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.
Na wa lhilhx̱Ă7lsh wa shich’ántsutwit ta snexwĂlh, ses men tatsanĚ“taswit kwis ans tsewás. tim̓á ḵ’as an eskwekwĂnĚ“ iy an hiyĂ. Na melh welḵw’áls ta EtsĂm Skw’eshĂmĚ“, “Na7 way kw’in stĂ©lmexw wa em̓út wa iy̓áyĚ“ulh?”
Ses men welḵw’áls ta Hiyà Shichi7ch, “Na7 way txwnch7am̓ kwi ses hin̓ kwi ses chá7twilh?”
Na melh máynexwas iytsi swi7ḵa7Ăşl-lh ta sḵw’shĂ©tsut. Na melh xwi txwtĂ©ta7nitaswit ta snexwĂlh, wa ḵwelḵwálwenwit swat as kwi na ta7s.
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.
Yalh ses mĚ“i t’eykw’ ta kw’elĚ“s ta EtsĂm Skw’eshĂmĚ“. “An chen kw’ákw’ayĚ“. Wi7ski namĚ“ chet t’ukw’ kwis ilhen,” na tsuntas ta sĂiyayĚ“s. Ses men telĚ“nĂşmut iytsi nach’ swi7ḵa7Ăşl-lh kwis ans kw’ákw’ayĚ“ imen.
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.
Na melh tskw’átsut t’ukw’ ta EtsĂm Skw’eshĂmĚ“. Ta si7ls, na wa ch’etxwántas ta lha7lhchs ta x̱epiyĂ©welh. Ses men ḵ’ayt ta EtsĂm Skw’eshĂmĚ“ ses men ta7Ăşsem ta si7ls ses men kw’áchnexwas kwi ses x̱wuts’us, ses men welḵw’áls, “Chexw eshánĚ“?” Na máynexwas ta EtsĂm Skw’eshĂm kwi ses x̱wuts’us. Na tsuntas ta si7ls kwi ses mekw’em ta snexwĂlh na7 ta áyalhḵw, na tsut, “Chen mĂ©kw’em ta eskwekwĂnĚ“ snexwĂlh na7 ta áyalhḵw. Na7 lhkwun nách’awĚ“ich syel̓ánem!”
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!”
Na nsx̱iyá7ms ta si7ls. “Chen tĂ©lĚ“nexw kwetsi snexwĂlh. Na yexwt yew̓ánĚ“ awĚ“Ăts txwnamĚ“ ta i7x̱w ta snexwĂlh-chet. Na tá7stem kwen man iy ta anĚ“us eḵw’Ă7tels.” HiyĂ sḵwalwens ta si7ls, na men wá7ew, “An nexwschá7twilh i7x̱w ta em7Ămats kwen si7l. Kw’éna ta chánat snexwĂlh na7 ta s7átsus ta tl’aḵtax̱an lamĚ“! I7x̱w ta na ta7stem kwi tiná7 tkwen sĂsi7.”
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. “
Iy kwi ses wa namĚ“ Ătut, sḵwálwen ta EtsĂm Skw’eshĂmĚ“, “En-stl’i7 kwins ch’etxwĂmĚ“ ta snexwĂlh iy ta sch’etxw tim̓á ten swa7ámĚ“. Kwayl as iy wilḵw’t chen kwen si7l kw’in as ta kwĂşpits iy ta sḵa7ḵs. Wayti ánĚ“us, chánat, x̱a7Ăştsen, wayti ḵex̱.”
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..."
ł§·É±đ±ôḵw’ál˛ő:&˛Ô˛ú˛ő±č;
EshánĚ“ melh es ḵwelḵwálwen ta EtsĂm Skw’eshĂmĚ“ wayti ánĚ“us s7eḵw’Ă7tels, wayti chanat ta s7eḵw’Ă7tels iy ḵ’as wayti ḵex̱ ta s7eḵw’Ă7tels kwa si7ls?
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, ÓČÎďĘÓƵ
Special thanks to:
- Tom Archibald, ÓČÎďĘÓƵ
- Peter Jacobs, Squamish Nation
- Ozren Jungic, University of Oxford
- Kwosel, Seabird Island First Nation
- Kwelaxtelot, Seabird Island First Nation
- Susan Russell, ÓČÎďĘÓƵ
- Erin Tait, Nisga'a Nation
- Department of Mathematics, ÓČÎďĘÓƵ
- Faculty of Science, ÓČÎďĘÓƵ
- The IRMACS Centre, ÓČÎďĘÓƵ
- Office for Aboriginal Peoples, ÓČÎďĘÓƵ
- 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