間眅埶AV

Small Number and the Old Canoe-Halqemeylem

Small Number and the Old Canoe 晨硃梭梁'梗鳥矇聆梭梗鳥

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.

Skwiikwexam Qes te Wetote Slexwelh
(晨硃梭梁'梗鳥矇聆梭梗鳥 Translation)

Written by Veselin Jungic & Mark MacLean 
Illustrated by Simon Roy 
晨硃梭梁'梗鳥矇聆梭梗鳥 Translation by Siyamiyateliyot, Kwelaxtelot, and Kwosel, Seabird Island First Nation

Story Transcript: English and 晨硃梭梁'梗鳥矇聆梭梗鳥

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獺tses m獺qe swiq籀llh te Skw穩kwexm, wey籀:th kwes 籀lsu qw矇lqwel. Sta: sqo te s穩sles qaste s穩las, kwa wey籀th 矇wes tsiw矇lmetem te l獺tse skw籀yxthets t繳tl簷.

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 kwesu hih籀ytes tle s穩la te sxetkw獺ls stletl獺xel l籀thel tlow獺yel. Iy籀lem kwes las kwe satlq ew籀lemstexwes ye si:y獺:yes te Skw穩kwexm. Yu:w te sw穩wel, temqw穩les sw獺yel, qesu xwalx獺lems ye swowiqe籀llh stet穩s te qo, kwes ew籀lems.

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. 

Me:kw stam kw矇tslexwes t繳tl簷lem qesu thet穩wel l獺 kwe xaws sew籀lem qe kwa te siy獺yes te Skw穩kwex獺m, Stitl獺kwe, thet: Tew獺t iy籀lem lem矇lstexw kwe seml獺t ts矇tsel chokw stsetstl穩mlexw schelh籀lwelh te qo? Kwe xwem t矇lexwes ye swowiqe籀llh kwes las xwa chokws te seml獺t lo::y kwesu yelxws, sp穩peelhs qesu tu st穩tel獺kwe簷mexs.

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矇lems la xwa chokw lhe獺 te 穩yelth te Skw穩kwexm sawq kwe stlexw矇leq seml獺t. Sowth lhe獺 te tl獺leqt s籀xwel qesu lh矇kwxel tselh籀lwelh kwe stam, kwetsl穩qwem la te wet籀t sl矇xwelh skw籀kwelt li te s籀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穩lex te Skw'穩kwexm, y籀yetletes te sqw矇mels kweses kw籀kwetstes selts te sl矇xwelh. Lu s獺:yemstexwes te sx籀yes t繳tl簷, qe lu ts籀yexw癡m xwel獺 te thexl獺xwes qesu t獺metes ye si:y獺yes, emi ye xw籀mxelem t繳tl簷lem.

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.

Lhexlhex矇ylex ye swowiq籀llh selts te sl矇xwelh q獺txtes te shxwe籀les簷mexs. Ste籀:mex kwes olu wet籀t qesu hi::kw xwel獺 t繳tl簷lem. Pet獺m te Skw穩kwexm Kwel獺la mest穩yexw kwes xete iy籀lem elel籀lh? Pet獺m te Stitel獺kw Kwil yexw sqeq籀tel te lulh la yel獺w kw矇selh h:y kwew獺tes? M矇lqlexwes ye swowiq籀llh te ilh siw籀lems qesu hi:th kwes qwoqw矇leses xwel獺 te sl矇xwelh qas tew獺t yexw kwe ilh hekwh籀kwex te sl矇xwelh.

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.

Kw矇selh ye qw籀qwel y繳tl簷lem, iy籀thet qw籀yexwem te kw矇les te Stitel獺kw Tsel qway, xwemtl la 矇lhtel th矇tstexwes ye si:y獺:yes t繳tl簷. Ye ew swowiqe籀llh t矇lexw kweses ew kw籀lekwi qesu me:kw la xwalx獺lem la te steltel獺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 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!

?矇w矇ltil xwe t籀tekw te Skw穩kwexm shxwel穩s kwes x獺tkwels te s穩la stslh穩tsels te t獺al kwes hikws syolh l籀thel. Lexw sth穩qel te Skw穩kwexm sts籀yxwemqel qesu xwep籀sem te s穩la. Kw矇tslexwes te st穩teqel lite sqw矇mels te Skw穩kwexm. Pet獺:m te s穩la Chexw xwe穩t? M矇lqlexwes te Skw穩kwexm kwes qweqw矇leqw t繳tl簷 qesu iy籀thet y矇thestes te s穩la xwel獺 te thexl獺xwes te sl矇xwelh. Tsel thexl獺xw te wet籀t sl矇xwelh lite 穩yelth. Tsel穩l qe ulh l矇tse l獺tswets syil籀lem.

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 carved by one of my uncles.

Xwel穩yemes te s穩la. Tsel lheq矇lexw tetha sl矇xwelh. Lets獺xw kw矇selh tlo 籀lu xwemxw矇m tetha sl矇xwelh ite s籀lh steltel獺wtexw. Ilh tlo tel m獺lelh qas te y獺ysela 獺lexs e h:y te sl矇xwelh. E ye矇y te s穩la sqwelw矇lmethets, Me:kw te m獺meles tel s穩laelh lheq矇lem kwes schew矇tmetes kwes x矇tkwals kwe syolh. Chexw lheq矇lexw te lhexlhex矇yelex sl籀qwleqw sxw穩thi exel矇smels te Sm穫lhe獺wtexw? Sl矇tsletse tlo sx矇tkwals yel shxweml獺lekw.

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獺lt xwel xwew獺 lis 穩tet e thet穩wel te Skw穩kwexm, el stli kwels h:y kwe sl矇xwelh qelsu xetkw獺ls kwe sl籀leqw ste獺 yel siw獺lelh. Tsel cha pet獺met te s穩la lis kwel獺la el獺lexs te ma:ls: y獺ysela, lhexw獺le, xeth穩le, lheq獺tsesle, qew lis ew qel獺t 簷.

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

Speta:m Selch穩m kwes ste獺wel te Skw穩kwexm kwes la kwel獺la te el獺lexs te sth籀meqws.

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