Small Number and the Old Canoe-Squamish
Small Number and the Old Canoe 鈥 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鈥檚 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.
Ets铆m Skw鈥檈sh铆m虛 iy ta eskwekw铆n虛 snexw铆lh
(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 s7铆xwalh, Ets铆m Skw鈥檈sh铆m虛 kwi snas. Nekw ts铆yachisaw谩nexw. Lhi岣碘 na wa 岣祑鈥檈sh茅tsut. haw 岣碘檃s ya 岣碘檈s铆wsnitas Ta sels铆7ls ta s岣祑鈥檈sh茅tsuts.
Na wa ch鈥檈xwt铆m虛 ta si7ls ta x瘫epiy虛茅welh. Stl鈥檌7s kwis h煤ynexwas ti stsi7s. Na melh tsuntem ta 铆mats nam虛 as 岣祑鈥檈sh茅tas ta s铆iyay虛s, nilh kwis ans ha7lh ta skwayl. Ta Ets铆m Skw鈥檈sh铆m虛 iy ta s铆iyay虛s na nam虛 岣祑鈥檈sh茅tsut ch鈥檌t ta sta岣祑. An 岣礶x瘫 ta ha7lh s岣祑鈥檈sh茅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鈥檚 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 siy谩y虛s, Hiy铆 Shishi7ch kwi snas. Na hey虛岣祑tas nam虛 aswit tsexw铆m虛 ta smant kwis xw铆xwitims na7 ta sta岣祑 smen t茅l虛nexwaswit wa swa7s smant nam虛 as an x瘫茅ta. Na melh y茅lx瘫tas i7x瘫w ta s7铆xwalh kwi smant, stl鈥檌7s ta smants kwis ans ts鈥檈ls, an tsew谩s, tim虛谩 tkwi 岣礶l煤m虛.
Everything they see sparks a new game, and Small Number鈥檚 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 Ets铆m Skw鈥檈sh铆m虛 na wa 铆7im虛esh ch鈥檌t ta sta岣祑 ses men wa y茅lx瘫tas ta yew虛谩n虛 ha7lh smant. Na x瘫wiya岣祑鈥櫭tsut ta an tl鈥檃岣祎 s谩x瘫wi7 ses men lh铆kw鈥檚hen kwi stam as ses men txwnew虛 ta eskwekw铆n虛 snexw铆lh. Ta snexw铆lh ta kw谩yantem na7 ta s谩x瘫wi7. Na melh lhx瘫ilsh ta Ets铆m Skw鈥檈sh铆m虛 ses wa xw铆kwin虛tas ta st鈥檜岣祑鈥檆hus. Ses men kw鈥檃ch谩y虛s ta snexw铆lh. Yamen kwis ans aa岣祑, na7xw wa x瘫wi7elwas. Iy kwis ans ha7lh ta na y茅lx瘫nexwas, na melh 岣碘櫭tentas ta s铆iyay虛s. Na melh m虛i tskw鈥櫭sutwit.
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 lhilhx瘫铆7lsh wa shich鈥櫭tsutwit ta snexw铆lh, ses men tatsan虛taswit kwis ans tsew谩s. tim虛谩 岣碘檃s an eskwekw铆n虛 iy an hiy铆. Na melh wel岣祑鈥櫭s ta Ets铆m Skw鈥檈sh铆m虛, 鈥淣a7 way kw鈥檌n st茅lmexw wa em虛煤t wa iy虛谩y虛ulh?鈥
Ses men wel岣祑鈥櫭s ta Hiy铆 Shichi7ch, 鈥淣a7 way txwnch7am虛 kwi ses hin虛 kwi ses ch谩7twilh?鈥
Na melh m谩ynexwas iytsi swi7岣礱7煤l-lh ta s岣祑鈥檚h茅tsut. Na melh xwi txwt茅ta7nitaswit ta snexw铆lh, wa 岣祑el岣祑谩lwenwit 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, 鈥淗ow many people do you think it could hold?鈥 Big Circle asks, 鈥淗ow many generations ago was it built?鈥 The boys forget their previous game and spend a long time talking about the canoe and who might have used it.
Yalh ses m虛i t鈥檈ykw鈥 ta kw鈥檈l虛s ta Ets铆m Skw鈥檈sh铆m虛. 鈥淎n chen kw鈥櫭w鈥檃y虛. Wi7ski nam虛 chet t鈥檜kw鈥 kwis ilhen,鈥 na tsuntas ta s铆iyay虛s. Ses men tel虛n煤mut iytsi nach鈥 swi7岣礱7煤l-lh kwis ans kw鈥櫭w鈥檃y虛 imen.
As they are talking, Big Circle鈥檚 tummy starts to growl. 鈥淚鈥檓 hungry. Let鈥檚 go eat,鈥 he says to his friends. The other boys realize they are hungry too, and they all run back to the village.
Na melh tskw鈥櫭sut t鈥檜kw鈥 ta Ets铆m Skw鈥檈sh铆m虛. Ta si7ls, na wa ch鈥檈txw谩ntas ta lha7lhchs ta x瘫epiy茅welh. Ses men 岣碘檃yt ta Ets铆m Skw鈥檈sh铆m虛 ses men ta7煤sem ta si7ls ses men kw鈥櫭hnexwas kwi ses x瘫wuts鈥檜s, ses men wel岣祑鈥櫭s, 鈥淐hexw esh谩n虛?鈥 Na m谩ynexwas ta Ets铆m Skw鈥檈sh铆m kwi ses x瘫wuts鈥檜s. Na tsuntas ta si7ls kwi ses mekw鈥檈m ta snexw铆lh na7 ta 谩yalh岣祑, na tsut, 鈥淐hen m茅kw鈥檈m ta eskwekw铆n虛 snexw铆lh na7 ta 谩yalh岣祑. Na7 lhkwun n谩ch鈥檃w虛ich syel虛谩nem!鈥
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鈥檚 forehead. 鈥淲hat happened?!鈥 Grandpa asks. Small Number has forgotten that he bumped his head and starts to tell Grandpa about finding the canoe: 鈥淚 found an old canoe down on the beach! It must be at least a hundred years old!鈥
Na nsx瘫iy谩7ms ta si7ls. 鈥淐hen t茅l虛nexw kwetsi snexw铆lh. Na yexwt yew虛谩n虛 aw虛铆ts txwnam虛 ta i7x瘫w ta snexw铆lh-chet. Na t谩7stem kwen man iy ta an虛us e岣祑鈥櫭7tels.鈥 Hiy铆 s岣祑alwens ta si7ls, na men w谩7ew, 鈥淎n nexwsch谩7twilh i7x瘫w ta em7铆mats kwen si7l. Kw鈥櫭﹏a ta ch谩nat snexw铆lh na7 ta s7谩tsus ta tl鈥檃岣祎ax瘫an lam虛! I7x瘫w ta na ta7stem kwi tin谩7 tkwen s铆si7.鈥
Grandpa smiles. 鈥淚 know that canoe. It was once the fastest canoe in our village. It was built by my father and two of his brothers.鈥 Grandpa proudly continues, 鈥淎ll 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. 鈥
Iy kwi ses wa nam虛 铆tut, s岣祑谩lwen ta Ets铆m Skw鈥檈sh铆m虛, 鈥淓n-stl鈥檌7 kwins ch鈥檈txw铆m虛 ta snexw铆lh iy ta sch鈥檈txw tim虛谩 ten swa7谩m虛. Kwayl as iy wil岣祑鈥檛 chen kwen si7l kw鈥檌n as ta kw煤pits iy ta s岣礱7岣祍. Wayti 谩n虛us, ch谩nat, x瘫a7煤tsen, wayti 岣礶x瘫.鈥
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..."
厂飞别濒岣祑鈥櫭蝉:&苍产蝉辫;
Esh谩n虛 melh es 岣祑el岣祑谩lwen ta Ets铆m Skw鈥檈sh铆m虛 wayti 谩n虛us s7e岣祑鈥櫭7tels, wayti chanat ta s7e岣祑鈥櫭7tels iy 岣碘檃s wayti 岣礶x瘫 ta s7e岣祑鈥櫭7tels 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, 大象传媒 and Mark MacLean, UBC
- Illustrator: Simon Roy, Victoria, B.C.
- Director: Andy Gavel, 大象传媒
Special thanks to:
- Tom Archibald, 大象传媒
- Peter Jacobs, Squamish Nation
- Ozren Jungic, University of Oxford
- Kwosel, Seabird Island First Nation
- Kwelaxtelot, Seabird Island First Nation
- Susan Russell, 大象传媒
- Erin Tait, Nisga'a Nation
- Department of Mathematics, 大象传媒
- Faculty of Science, 大象传媒
- The IRMACS Centre, 大象传媒
- Office for Aboriginal Peoples, 大象传媒
- 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 大象传媒