大象传媒

Small Number and the Old Canoe-Nisgaa

Small Number and the Old Canoe 鈥 Nisga'a

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.

Gadim G瘫an g瘫anhl W虛ii Mm虛aal
(Nisga'a Translation)

Written by Veselin Jungic & Mark MacLean 
Illustrated by Simon Roy 
Nisga'a Translation by Hlguwilksihlgum Maaksgum Hlbin (Emma Nyce), Ksim Git Wil Aksnakw (Edna Nyce-Tait), and Wilp Sim鈥檕ogit Hlee岣 (Allison Nyce)

Story Transcript: English and Nisga'a

Kwsdins x瘫k鈥檜uhlkwhl hlgutk鈥檌hlgum gat tgun tx瘫aan虛itkws aguxw-anbilwilt g瘫anhl nidii, nidii amukwst k鈥檌l虛hl wilt iit 岣碘檃p g瘫an wilaa siip鈥檌ndiit.

Gadim G瘫an is a five year old boy who gets into a lot of mischief.

Sil jog瘫at dip Nits鈥檌its鈥檛 g虛ans Niye鈥檈t iit anoo岣祍t dip gun k鈥檌l虛hl wilt, wil nigii aamhl wilt, nigidiit w虛ii kw鈥檌hl wilaakwdiit hluut鈥檜xwdiit n虛ig瘫an wilt.

He lives with his Grandma and Grandpa, who patiently put up with his antics most of the time.

Sa tgun ii dim hlisa鈥檃ns Niye鈥檈thl ts鈥檃k鈥 hooksit ahl lil虛git.

Today, Grandpa needs to finish carving a feast bowl.

Ii n虛ihl sagihl anhis Niye鈥檈t dim k鈥檃x瘫 ksaxw n虛iin, k鈥檃x瘫 kwsda岣祍diit ado鈥檕 ahl g瘫alaa岣碘檃n silg瘫awils, silg瘫al dip dihitgwin diya Niye鈥檈t loot.

And Grandpa decided that Gadim G瘫an should go out and play with his friends.

Amg瘫oogidim sa, sa ahl gwooyim, gyamgim sa,w虛ay n虛ihl dim g瘫o鈥檕diit dim wil g瘫alaa岣礵iit g瘫anhl ansipsiip鈥檌nskwt.

It is a beautiful, sunny, spring day and the boys run down to play near the water.

Tx瘫aan虛itkws aguhl dim wilaa g瘫alaa岣礵iit ii n虛ihl wildiit g瘫ans Wa岣礹l Ts鈥檌milx, aniip鈥檌nskwt tgun, silg瘫awilit, silg瘫asg瘫ootgwit iit sag瘫ootkwdiit dim guutdiithl lo鈥檕p, tx瘫a鈥檃m lo鈥檕p siwadim虛 bax瘫 lo鈥檕p tgun ahl lax瘫 aks, hlaa ma鈥檜xwdiit bax瘫t.

Everything there sparks a new game, and Gadim G瘫an鈥檚 friend, Wa岣礹l Ts鈥檌milx, suggests they see who can make a stone skip the farthest on the surface of the water.

Wilaaxdiit wil n虛akwhl dim wil bax瘫hl lo鈥檕p tgun lax瘫 aks iit guutdiit sim t k鈥檜bax瘫a鈥檃tdiit ahl g瘫a鈥檃t n虛i wilaa jabihl game dip siwadis gun huxwdii wilim虛 yukw sisuusin.

The boys quickly learn that for a stone to go far it needs to be smooth, black and oval shaped.

Yukwhl wilt gigil虛hl lo鈥檕p dim ang瘫alaa岣祎 iit n虛ihitkwhl ligii agu sbayt, ligii agu, um, haas, g瘫an haas t鈥欌檃hlihl lax瘫ts鈥檈ehl aks n虛i wil t鈥檃hlihl g瘫an haas n虛ihl nii bax瘫at, nidiit wilaax aguhl wat nigit t鈥檌l虛t wilaaxt.

As Gadim G瘫an wanders far along the shore looking for a good stone he scrambles through the tall grass, tripping over something.

Iit n虛ihl hitkwhl aguyama鈥檃hl watchit log瘫am tgwantkw, log瘫am ksg瘫oo岣 t鈥檌mg瘫est ahl agu tgun, log瘫a mm虛aal an win n虛ii bax瘫at ii nidiit t鈥檌l虛thl wilaaxt.

He falls headfirst into an old canoe hidden in the grass.

Hlaa haldim bax瘫t iit dashl t鈥檌mg瘫est kw鈥檌hl hlibal虛hlt hupxwt, yee wil log瘫am t鈥檌gwantkw ahl ts鈥檌m log瘫am mm虛aal tgun.

Gadim G瘫an stands up, rubbing his forehead as he looks around at the canoe.

Ji n虛ithl sg瘫etkwt wilt t鈥檌mg瘫est hupxwt wil yeet simgit yeet sg瘫e岣祍kwdima鈥檃 ii nigii an guut loot gigil虛thl wilaa wilhl ansiip鈥檌nskwt sil g瘫asg瘫ootgwit dim x瘫biyukwdim虛 ahl aguhl w虛aayit.

Even though his head hurts, he is very excited at his discovery and he calls to his friends who come running.

Ii hagwin a岣祂whl ansiiip鈥檌nskws sa silg瘫asg瘫oot ii yukw ga鈥檃diit iit dasdiit, ndayima鈥檃hl x瘫nagwit hlgis agu t tgun ahl lax瘫 ts鈥檈ets鈥檌ks tgunsa, nigit wilaaxdiit.

Yukwhl alalgax瘫diit ii n虛i wil hit ahl silg瘫awilt si鈥檃nsiip鈥檌nskwt, 鈥淣dahl g瘫abiidima鈥檃hl gathl batsdihl luuwandit g瘫an mm虛aal dip gunsa?鈥 Nidiit wilaaxdiit.

Gadim G瘫an asks, 鈥淗ow many people do you think it could hold?鈥 They didn鈥檛 know.

鈥淣dayima鈥檃 hlaa g瘫an虛agwihl hlidaa japkw鈥, diyahl friendtt Wa岣礹l Ts鈥檌milx yukwhl liseexwkwdiit sim git agu tgunsa.

Wa岣礹l Ts鈥檌milx asks, 鈥淗ow many generations ago was it built?鈥

Ii wandiit yukw liseexwdiit wilaa wilhl mm虛aal tgunsa, naayima鈥檃 anjap dihiida, ndayima鈥檃hl ahl g瘫an虛agwihl w虛aayit wil hookst.

The boys forget their previous game and spend a long time talking about the canoe and who might have built it.

Yukwhl wildiit si鈥檌i n虛ii wil algax瘫hl Wa岣礹l Ts鈥檌milx silg瘫a wilsihl, 鈥淗laa xwdayiy虛. Hlaa n虛uw虛hl xwdayiy虛hl aamhl dim k鈥檃x瘫 haw虛um虛 ii dim ii tx瘫oox瘫gum虛鈥, diya.

As they are talking, Wa岣礹l Ts鈥檌milx鈥檚 tummy starts to growl, 鈥淚鈥檓 hungry. Let鈥檚 go eat,鈥 he says to his friends.

Ii n虛ihl hihl ansiip鈥檌nskwt ji loot huxwdii wiliy虛, hlaa huxwdii n虛uw虛iy虛 xwdayiy虛, way di, dim luuwiiyalt n虛uum虛 ahl dim g瘫alts鈥檃p dim ii tx瘫oox瘫gum虛 Gitwinksihlkw.

The other boys realize they are hungry too, and they all run back to Gitwinksihlkw.

Hlaa bakwdiit wil jo岣礵iit iit ga鈥檃diit hlaa wil yukskw Niye鈥檈tdiit way laay虛um ts鈥檃k鈥檌m g瘫anhl jabit dim hookst ahl dim wil lil虛gitdiit.

Gadim G瘫an races home where Grandpa is carving the surface of a huge wooden dish.

Yukwhl wildiit kw鈥檌hl luu-amaamhl g瘫ag瘫ootdiit luu-si鈥檃maakwdiit aguhl ga鈥檃diit jabis Niye鈥檈diit iit ga鈥檃s Niye鈥檈t wil mukwhl hupxt iit gidax虛at, 鈥淣dahl wilhl hupxt g瘫ang瘫an mukwt?鈥 diya.

Gadim G瘫an shouting very excitedly and Grandpa looks up. He sees the bruise on Gadim G瘫an鈥檚 forehead. 鈥淲hat happened?鈥 Grandpa asks.

Iit t鈥檃岣祍t Gadim G瘫an siwil wilaa wilhl t鈥檌mg瘫est wil bruised, wil sg瘫e岣祍kwt wil mukwt iit mahlit as Niye鈥檈t aguhl w虛adiit, aguhl w虛ay虛t.

Gadim G瘫an has forgotten that he bumped his head and starts to tell Grandpa about finding the canoe.

鈥淲虛ay虛ihl mm虛aal lo岣 hlaa gi-one hundred years dim ahl sgit n虛ihl w虛ay虛it鈥 diya.

鈥淚 found an old canoe down the beach! It must be at least one hundred years old!鈥

Iit n虛i wil algax瘫s Niye鈥檈t. 鈥淲ilaayiy虛 anheenis,鈥 diya, 鈥淣虛ihl mm虛aal tgus k鈥檃 aluubax瘫at w虛itgwit dim g瘫alts鈥檃bim虛鈥, diya.

Grandpa smiles, 鈥淚 know that canoe, it was once the fastest canoe in our village.鈥

鈥淚i yukwt mahlis niye鈥檈t wil n虛idiit g瘫anhl wakkwt anjaphl agu tgun n虛ihl w虛ayisim虛,鈥 diya.

鈥淚t was carved by my father and two of his brothers,鈥 Grandpa proudly continues.

鈥淭x瘫aan虛itkwshl n虛uum虛 n虛iwagiit iit wilaaxt, wilaaxt gat wil dip wilaaxhl hlixhlalbihl g瘫an siwadiit ahl carve.鈥

鈥淎ll the sons of my grandfather were known as great wood carvers.鈥

鈥淕a鈥檃sim虛hl gwilal虛hl g瘫abiihl g瘫an m虛a岣祍gwit alihl gigalg瘫ahl wilp?鈥

鈥淵ou know those three totem poles in front of the Longhouse?鈥

鈥淢ahlik鈥檌l虛hl g瘫an tgun ahl jabihl nibibim虛, nibibiy虛,鈥 diya, 鈥淢ahlik鈥檡ooldiit gwilal虛hl g瘫abiit g瘫an japdiit niwa岣祎 dip gun.鈥

鈥淓ach of them was built by one of my uncles.鈥

Ji t鈥檃ayihl g瘫oott hlaa yukwdim wo岣祎 iit 岣碘檕om虛ax瘫kw g瘫oot dim hugax瘫 wils dip nibipt g瘫ans dip niye鈥檈t dim dii jabithl agu dim hlalbithl g瘫an, totem pole, ts鈥檃k鈥, lip agu n虛ihl hasak虛thl dim jabit.

That evening just before falling asleep, Gadim G瘫an thought, 鈥淚鈥檇 like to carve canoes and totem poles just like my ancestors.鈥

K鈥檌it gidax瘫at, 鈥淒im misoolhl wakgwin,鈥 diya, 鈥淪ilg瘫a tx瘫alpx瘫dool, kwsdinsool n虛ihl gidax瘫at as Niye鈥檈t.鈥

I have to ask Grandpa tomorrow how many brothers his father had, four, five or more?

Aguhl g瘫ant han虛iig瘫oodihl huxw wans wakkwt txalpxdool, kwsdinsool, gidax瘫as tgusda?

Why did Gadim Gan think that his grandpa had two, three, four or five more brothers? 

Hliskw, aam.

Finished, good.

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