51社区黑料

Small Number and the Old Canoe-Halqemeylem

Small Number and the Old Canoe 鈥 贬补濒辩'别尘茅测濒别尘

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.

Skwi鈥檌kwexam Qes te Wet鈥檕t鈥檈 Slexwelh
(贬补濒辩'别尘茅测濒别尘 Translation)

Written by Veselin Jungic & Mark MacLean 
Illustrated by Simon Roy 
贬补濒辩'别尘茅测濒别尘 Translation by Siyamiyateliyot, Kwelaxtelot, and Kwosel, Seabird Island First Nation

Story Transcript: English and 贬补濒辩'别尘茅测濒别尘

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

Lheq鈥櫭ses m谩qe swiq贸llh te Skw鈥櫭璳w鈥檈x脿m, wey贸:th kw鈥檈s 贸lsu qw茅lqwel. Sta: sq鈥檕 te s铆sles qaste s铆las, kwa wey贸th 茅wes ts鈥檌w茅lmetem te l谩ts鈥檈 skw贸yxthets t煤tl鈥櫭.

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.

Loy kw鈥檈su hih贸ytes tl鈥檈 s铆la te sxet鈥檏w鈥櫭s stl鈥檈tl鈥櫭el l贸thel tlow谩yel. Iy贸lem kw鈥檈s las kw鈥檈 satl鈥檘 ew贸lemstexwes ye si:y谩:yes te Skw鈥櫭璳w鈥檈x脿m. Yu:w te sw铆wel, temqw鈥櫭璴es sw谩yel, qesu xwalx谩lems ye swowiqe鈥櫭砽lh stet铆s te qo, kw鈥檈s ew贸lems.

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. 

Me:kw鈥 stam kw鈥櫭﹖slexwes t煤tl鈥櫭瞝em qesu thet铆wel l谩 kw鈥檈 xaws sew贸lem qe kwa te siy谩yes te Skw鈥櫭璳w鈥檈x谩m, Stitl谩kw鈥檈, thet: 鈥淭ew谩t iy贸lem lem茅lstexw kw鈥檈 seml谩t ts鈥櫭﹖s鈥檈l chokw sts鈥檈ts鈥檛l鈥櫭璵lexw schelh贸lwelh te qo?鈥 Kw鈥檈 xwem t茅lexwes ye swowiqe鈥櫭砽lh kw鈥檈s las xwa chokws te seml谩t lo::y kw鈥檈su yelxws, sp鈥櫭璸e鈥檈lhs qesu tu st铆tel谩kw鈥檈鈥櫭瞞exs.

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.

La shxwh茅lems la xwa chokw lhe鈥櫭 te 铆yelth te Skw鈥櫭璳w鈥檈x脿m sawq鈥 kw鈥檈 stl鈥檈xw茅leq seml谩t. S鈥檕wth lhe鈥櫭 te tl鈥櫭eqt s贸xwel qesu lh茅kw鈥檟el tselh贸lwelh kw鈥檈 stam, kw鈥檈ts鈥檒铆qwem la te wet鈥櫭硉鈥 sl茅xwelh skw贸kwelt li te s贸xwel.

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.

Xw铆lex te Skw'铆kw鈥檈x脿m, y贸yetl鈥檈tes te sqw鈥櫭﹎els kw鈥檈ses kw鈥櫭砶w鈥檈tstes selts鈥 te sl茅xwelh. Lu s谩:yemstexwes te sx贸yes t煤tl鈥櫭, qe lu ts鈥櫭硑exw猫m xwel谩 te thexl谩xwes qesu t谩metes ye si:y谩yes, emi ye xw贸mxelem t煤tl鈥櫭瞝em.

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.

Lhexlhex茅ylex ye swowiq贸llh selts鈥 te sl茅xwelh q谩txtes te shxwe鈥櫭砽es貌mexs. Ste鈥櫭:mex kwes olu wet鈥櫭硉 qesu hi::kw xwel谩 t煤tl鈥櫭瞝em. Pet谩m te Skw鈥櫭璳w鈥檈x脿m 鈥淜w鈥檈l谩la mest铆yexw kw鈥檈s xet鈥檈 iy贸lem el鈥檈l贸lh?鈥 Pet谩m te Stitel谩kw鈥 鈥淜w鈥檌l yexw sq鈥檈q鈥櫭硉el te lulh la yel谩w kw茅selh h脿:y kw鈥檈w谩tes?鈥 M茅lqlexwes ye swowiq贸llh te ilh siw贸lems qesu hi:th kwes qwoqw茅leses xwel谩 te sl茅xwelh qas tew谩t yexw kw鈥檈 ilh hekwh贸kwex te sl茅xwelh.

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.

Kw茅selh ye qw贸qwel y煤tl鈥櫭瞝em, iy贸thet qw鈥櫭硑exwem te kw鈥櫭﹍es te Stitel谩kw鈥 鈥淭sel qw鈥檃y, xwemtl鈥 la 茅lhtel鈥 th茅tstexwes ye si:y谩:yes t煤tl鈥櫭. Ye ew swowiqe鈥櫭砽lh t茅lexw kweses ew kw鈥櫭砽ekw鈥檌 qesu me:kw鈥 la xwalx谩lem la te st鈥檈lt鈥檈l谩wtexw.

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

?茅w茅ltil xwe t鈥櫭硉鈥檈kw鈥 te Skw鈥櫭璳w鈥檈x脿m shxwel铆s kw鈥檈s x谩t鈥檏w鈥檈ls te s铆la stslh铆tsels te t谩鈥檃l kw鈥檈s hikws syolh l贸thel. Lexw sth铆qel te Skw鈥櫭璳w鈥檈x脿m sts鈥櫭硑xwemqel qesu xwep贸sem te s铆la. Kw鈥櫭﹖slexwes te st鈥櫭璽鈥檈qel lite sqw鈥櫭﹎els te Skw鈥櫭璳w鈥檈x脿m. Pet谩:m te s铆la 鈥淐hexw xwe鈥櫭璽?鈥 M茅lqlexwes te Skw鈥櫭璳w鈥檈x脿m kwes qw鈥檈qw鈥櫭﹍eqw t煤tl鈥櫭 qesu iy贸thet y茅thestes te s铆la xwel谩 te thexl谩xwes te sl茅xwelh. 鈥淭sel thexl谩xw te wet鈥櫭硉鈥 sl茅xwelh lite 铆yelth. Tsel铆l qe ulh l茅ts鈥檈 l谩ts鈥檞ets syil贸lem.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 carved by one of my uncles. 鈥

Xwel铆yemes te s铆la. 鈥淭sel lheq鈥櫭﹍exw tetha sl茅xwelh. Lets鈥櫭w kw茅selh tl鈥檕 贸lu xwemxw茅m tetha sl茅xwelh ite s鈥櫭砽h st鈥檈lt鈥檈l谩wtexw. Ilh tl鈥檕 tel m谩lelh qas te y谩ysela 谩lexs e鈥 h脿:y te sl茅xwelh.鈥 E鈥 ye鈥櫭﹜ te s铆la sqwelw茅lmethets, 鈥淢e:kw鈥 te m谩meles tel s铆la鈥檈lh lheq鈥櫭﹍em kw鈥檈s schew茅tmetes kw鈥檈s x茅t鈥檏w鈥檃ls kw鈥檈 syolh. Chexw lheq鈥櫭﹍exw te lhexlhex茅yelex sl贸qwleqw sxw铆thi exel茅smels te Sm矛lhe鈥櫭texw? Sl茅ts鈥檒ets鈥檈 tl鈥檕 sx茅t鈥檏w鈥檃ls yel shxweml谩lekw.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..."

Tetha xwel谩lt xwel xwew谩 lis 铆tet e鈥 thet铆wel te Skw鈥櫭璳w鈥檈x脿m, 鈥渆l stl鈥檌 kw鈥檈ls h脿:y kw鈥檈 sl茅xwelh q鈥檈lsu xet鈥檏w鈥櫭s kw鈥檈 sl贸leqw ste鈥櫭 yel siw谩lelh. Tsel cha pet谩met te s铆la lis kw鈥檈l谩la el谩lexs te ma:ls: y谩ysela, lhexw谩le, xeth铆le, lheq鈥櫭ses脿le, qew lis ew qel谩t 貌鈥.

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

Speta:m Selch铆m kwes ste鈥櫭el te Skw鈥櫭璳w鈥檈x脿m kwes la kw鈥檈l谩la te el谩lexs te sth鈥櫭砿eqws.

Credits and Acknowledgements
 

  • Written by: Veselin Jungic, 51社区黑料and Mark MacLean, UBC
  • Illustrator: Simon Roy, Victoria, B.C.
  • Director: Andy Gavel, 51社区黑料

Special thanks to:

  • Tom Archibald, 51社区黑料
  • Peter Jacobs, Squamish Nation
  • Ozren Jungic, University of Oxford
  • Kwosel, Seabird Island First Nation
  • Kwelaxtelot, Seabird Island First Nation
  • Susan Russell, 51社区黑料
  • Erin Tait, Nisga'a Nation
  • Department of Mathematics, 51社区黑料
  • Faculty of Science, 51社区黑料
  • The IRMACS Centre, 51社区黑料
  • Office for Aboriginal Peoples, 51社区黑料
  • 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