間眅埶AV

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 moderators 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穩m Skwesh穩m iy ta eskwekw穩n snexw穩lh
(Squamish Translation)

Written by Veselin Jungic & Mark MacLean 
Illustrated by Simon Roy 
Squamish Translation by T'naxwtn, Peter Jacobs of the Squamish Nation

Story Transcript

Na na7 kwetsi s7穩xwalh, Ets穩m Skwesh穩m kwi snas.  Nekw ts穩yachisaw獺nexw.  Lhi廎菊 na wa 廎硬esh矇tsut.  haw 廎菊as ya 廎菊es穩wsnitas Ta sels穩7ls ta s廎硬esh矇tsuts.

Na wa chexwt穩m ta si7ls ta x戔epiy矇welh.  Stli7s kwis h繳ynexwas ti stsi7s.  Na melh tsuntem ta 穩mats nam as 廎硬esh矇tas ta s穩iyays, nilh kwis ans ha7lh ta skwayl.  Ta Ets穩m Skwesh穩m iy ta s穩iyays na nam 廎硬esh矇tsut chit ta sta廎硬.  An 廎畫x戔 ta ha7lh s廎硬esh矇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 Numbers 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獺ys, Hiy穩 Shishi7ch kwi snas.  Na hey廎硬tas nam aswit tsexw穩m ta smant kwis xw穩xwitims na7 ta sta廎硬 smen t矇lnexwaswit wa swa7s smant nam as an x戔矇ta. Na melh y矇lx戔tas i7x戔w ta s7穩xwalh kwi smant, stli7s ta smants kwis ans tsels, an tsew獺s, tim獺 tkwi 廎畫l繳m.

Everything they see sparks a new game, and Small Numbers 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穩m Skwesh穩m na wa 穩7imesh chit ta sta廎硬 ses men wa y矇lx戔tas ta yew獺n ha7lh smant.  Na x戔wiya廎硬獺ntsut ta an tla廎睏 s獺x戔wi7 ses men lh穩kwshen kwi stam as ses men txwnew ta eskwekw穩n snexw穩lh.  Ta snexw穩lh ta kw獺yantem na7 ta s獺x戔wi7.  Na melh lhx戔ilsh ta Ets穩m Skwesh穩m ses wa xw穩kwintas ta stu廎硬chus.  Ses men kwach獺ys ta snexw穩lh.  Yamen kwis ans aa廎硬, na7xw wa x戔wi7elwas. Iy kwis ans ha7lh ta na y矇lx戔nexwas, na melh 廎菊獺ytentas ta s穩iyays.  Na melh mi tskw獺tsutwit.

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戔穩7lsh wa shich獺ntsutwit ta snexw穩lh, ses men tatsantaswit kwis ans tsew獺s.  tim獺 廎菊as an eskwekw穩n iy an hiy穩.  Na melh wel廎硬獺ls ta Ets穩m Skwesh穩m, Na7 way kwin st矇lmexw wa em繳t wa iy獺yulh?  

Ses men wel廎硬獺ls ta Hiy穩 Shichi7ch, Na7 way txwnch7am kwi ses hin kwi ses ch獺7twilh?

Na melh m獺ynexwas iytsi swi7廎琦7繳l-lh ta s廎硬sh矇tsut.  Na melh xwi txwt矇ta7nitaswit ta snexw穩lh, wa 廎硬el廎硬獺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,  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 mi teykw ta kwels ta Ets穩m Skwesh穩m.  An chen kw獺kway.  Wi7ski nam chet tukw kwis ilhen, na tsuntas ta s穩iyays.  Ses men teln繳mut iytsi nach swi7廎琦7繳l-lh kwis ans kw獺kway imen.

As they are talking, Big Circles tummy starts to growl.  Im hungry.  Lets 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獺tsut tukw ta Ets穩m Skwesh穩m.  Ta si7ls, na wa chetxw獺ntas ta lha7lhchs ta x戔epiy矇welh.  Ses men 廎菊ayt ta Ets穩m Skwesh穩m ses men ta7繳sem ta si7ls ses men kw獺chnexwas kwi ses x戔wutsus, ses men wel廎硬獺ls, Chexw esh獺n?  Na m獺ynexwas ta Ets穩m Skwesh穩m kwi ses x戔wutsus.  Na tsuntas ta si7ls kwi ses mekwem ta snexw穩lh na7 ta 獺yalh廎硬, na tsut, Chen m矇kwem ta eskwekw穩n snexw穩lh na7 ta 獺yalh廎硬.  Na7 lhkwun n獺chawich syel獺nem!

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 Numbers 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 nsx戔iy獺7ms ta si7ls.  Chen t矇lnexw kwetsi snexw穩lh.  Na yexwt yew獺n aw穩ts txwnam ta i7x戔w ta snexw穩lh-chet.  Na t獺7stem kwen man iy ta anus e廎硬穩7tels.  Hiy穩 s廎硬alwens ta si7ls, na men w獺7ew, An nexwsch獺7twilh i7x戔w ta em7穩mats kwen si7l.  Kw矇na ta ch獺nat snexw穩lh na7 ta s7獺tsus ta tla廎睏ax戔an lam!  I7x戔w ta na ta7stem kwi tin獺7 tkwen s穩si7.

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 nam 穩tut, s廎硬獺lwen ta Ets穩m Skwesh穩m, En-stli7 kwins chetxw穩m ta snexw穩lh iy ta schetxw tim獺 ten swa7獺m.  Kwayl as iy wil廎硬t chen kwen si7l kwin as ta kw繳pits iy ta s廎琦7廎盜.  Wayti 獺nus, ch獺nat, x戔a7繳tsen,  wayti 廎畫x戔.

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..."

釦滄梗梭廎硬獺l莽:&紳莉莽梯;
Esh獺n melh es 廎硬el廎硬獺lwen ta Ets穩m Skwesh穩m wayti 獺nus s7e廎硬穩7tels, wayti chanat ta s7e廎硬穩7tels iy 廎菊as wayti 廎畫x戔 ta s7e廎硬穩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, 間眅埶AV and Mark MacLean, UBC
  • Illustrator: Simon Roy, Victoria, B.C.
  • Director: Andy Gavel, 間眅埶AV

Special thanks to:

  • Tom Archibald, 間眅埶AV
  • Peter Jacobs, Squamish Nation
  • Ozren Jungic, University of Oxford
  • Kwosel, Seabird Island First Nation
  • Kwelaxtelot, Seabird Island First Nation
  • Susan Russell, 間眅埶AV
  • Erin Tait, Nisga'a Nation
  • Department of Mathematics, 間眅埶AV
  • Faculty of Science, 間眅埶AV
  • The IRMACS Centre, 間眅埶AV
  • Office for Aboriginal Peoples, 間眅埶AV
  • 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 間眅埶AV