間眅埶AV

Small Number and the Old Canoe-Nisgaa

Small Number and the Old Canoe 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 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.

Gadim G戔an g戔anhl Wii Mmaal
(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 Simoogit Hlee廎 (Allison Nyce)

Story Transcript: English and Nisga'a

Kwsdins x戔kuuhlkwhl hlgutkihlgum gat tgun tx戔aanitkws aguxw-anbilwilt g戔anhl nidii, nidii amukwst kilhl wilt iit 廎菊ap g戔an wilaa siipindiit.

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

Sil jog戔at dip Nitsiitst gans Niyeet iit anoo廎盜t dip gun kilhl wilt, wil nigii aamhl wilt, nigidiit wii kwihl wilaakwdiit hluutuxwdiit nig戔an wilt.

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

Sa tgun ii dim hlisaans Niyeethl tsak hooksit ahl lilgit.

Today, Grandpa needs to finish carving a feast bowl.

Ii nihl sagihl anhis Niyeet dim kax戔 ksaxw niin, kax戔 kwsda廎盜diit adoo ahl g戔alaa廎菊an silg戔awils, silg戔al dip dihitgwin diya Niyeet loot.

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

Amg戔oogidim sa, sa ahl gwooyim, gyamgim sa,way nihl dim g戔oodiit dim wil g戔alaa廎甦iit g戔anhl ansipsiipinskwt.

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

Tx戔aanitkws aguhl dim wilaa g戔alaa廎甦iit ii nihl wildiit g戔ans Wa廎痛l Tsimilx, aniipinskwt tgun, silg戔awilit, silg戔asg戔ootgwit iit sag戔ootkwdiit dim guutdiithl loop, tx戔aam loop siwadim bax戔 loop tgun ahl lax戔 aks, hlaa mauxwdiit bax戔t.

Everything there sparks a new game, and Gadim G戔ans friend, Wa廎痛l Tsimilx, suggests they see who can make a stone skip the farthest on the surface of the water.

Wilaaxdiit wil nakwhl dim wil bax戔hl loop tgun lax戔 aks iit guutdiit sim t kubax戔aatdiit ahl g戔aat ni wilaa jabihl game dip siwadis gun huxwdii wilim yukw sisuusin.

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

Yukwhl wilt gigilhl loop dim ang戔alaa廎睏 iit nihitkwhl ligii agu sbayt, ligii agu, um, haas, g戔an haas tahlihl lax戔tseehl aks ni wil tahlihl g戔an haas nihl nii bax戔at, nidiit wilaax aguhl wat nigit tilt wilaaxt.

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

Iit nihl hitkwhl aguyamaahl watchit log戔am tgwantkw, log戔am ksg戔oo廎 timg戔est ahl agu tgun, log戔a mmaal an win nii bax戔at ii nidiit tilthl wilaaxt.

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

Hlaa haldim bax戔t iit dashl timg戔est kwihl hlibalhlt hupxwt, yee wil log戔am tigwantkw ahl tsim log戔am mmaal tgun.

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

Ji nithl sg戔etkwt wilt timg戔est hupxwt wil yeet simgit yeet sg戔e廎盜kwdimaa ii nigii an guut loot gigilthl wilaa wilhl ansiipinskwt sil g戔asg戔ootgwit dim x戔biyukwdim ahl aguhl waayit.

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

Ii hagwin a廎痘whl ansiiipinskws sa silg戔asg戔oot ii yukw gaadiit iit dasdiit, ndayimaahl x戔nagwit hlgis agu t tgun ahl lax戔 tseetsiks tgunsa, nigit wilaaxdiit.

Yukwhl alalgax戔diit ii ni wil hit ahl silg戔awilt siansiipinskwt, Ndahl g戔abiidimaahl gathl batsdihl luuwandit g戔an mmaal dip gunsa? Nidiit wilaaxdiit.

Gadim G戔an asks, How many people do you think it could hold? They didnt know.

Ndayimaa hlaa g戔anagwihl hlidaa japkw, diyahl friendtt Wa廎痛l Tsimilx yukwhl liseexwkwdiit sim git agu tgunsa.

Wa廎痛l Tsimilx asks, How many generations ago was it built?

Ii wandiit yukw liseexwdiit wilaa wilhl mmaal tgunsa, naayimaa anjap dihiida, ndayimaahl ahl g戔anagwihl waayit 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 siii nii wil algax戔hl Wa廎痛l Tsimilx silg戔a wilsihl, Hlaa xwdayiy. Hlaa nuwhl xwdayiyhl aamhl dim kax戔 hawum ii dim ii tx戔oox戔gum, diya.

As they are talking, Wa廎痛l Tsimilxs tummy starts to growl, Im hungry. Lets go eat, he says to his friends.

Ii nihl hihl ansiipinskwt ji loot huxwdii wiliy, hlaa huxwdii nuwiy xwdayiy, way di, dim luuwiiyalt nuum ahl dim g戔altsap dim ii tx戔oox戔gum Gitwinksihlkw.

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

Hlaa bakwdiit wil jo廎甦iit iit gaadiit hlaa wil yukskw Niyeetdiit way laayum tsakim g戔anhl jabit dim hookst ahl dim wil lilgitdiit.

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

Yukwhl wildiit kwihl luu-amaamhl g戔ag戔ootdiit luu-siamaakwdiit aguhl gaadiit jabis Niyeediit iit gaas Niyeet wil mukwhl hupxt iit gidaxat, Ndahl wilhl hupxt g戔ang戔an mukwt? diya.

Gadim G戔an shouting very excitedly and Grandpa looks up. He sees the bruise on Gadim G戔ans forehead. What happened? Grandpa asks.

Iit ta廎盜t Gadim G戔an siwil wilaa wilhl timg戔est wil bruised, wil sg戔e廎盜kwt wil mukwt iit mahlit as Niyeet aguhl wadiit, aguhl wayt.

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

Wayihl mmaal lo廎 hlaa gi-one hundred years dim ahl sgit nihl wayit diya.

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

Iit ni wil algax戔s Niyeet. Wilaayiy anheenis, diya, Nihl mmaal tgus ka aluubax戔at witgwit dim g戔altsabim, diya.

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

Ii yukwt mahlis niyeet wil nidiit g戔anhl wakkwt anjaphl agu tgun nihl wayisim, diya.

It was carved by my father and two of his brothers, Grandpa proudly continues.

Tx戔aanitkwshl nuum niwagiit iit wilaaxt, wilaaxt gat wil dip wilaaxhl hlixhlalbihl g戔an siwadiit ahl carve.

All the sons of my grandfather were known as great wood carvers.

Gaasimhl gwilalhl g戔abiihl g戔an ma廎盜gwit alihl gigalg戔ahl wilp?

You know those three totem poles in front of the Longhouse?

Mahlikilhl g戔an tgun ahl jabihl nibibim, nibibiy, diya, Mahlikyooldiit gwilalhl g戔abiit g戔an japdiit niwa廎睏 dip gun.

Each of them was built by one of my uncles.

Ji taayihl g戔oott hlaa yukwdim wo廎睏 iit 廎菊oomax戔kw g戔oot dim hugax戔 wils dip nibipt g戔ans dip niyeet dim dii jabithl agu dim hlalbithl g戔an, totem pole, tsak, lip agu nihl hasakthl dim jabit.

That evening just before falling asleep, Gadim G戔an thought, Id like to carve canoes and totem poles just like my ancestors.

Kiit gidax戔at, Dim misoolhl wakgwin, diya, Silg戔a tx戔alpx戔dool, kwsdinsool nihl gidax戔at as Niyeet.

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

Aguhl g戔ant haniig戔oodihl huxw wans wakkwt txalpxdool, kwsdinsool, gidax戔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, 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