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 moderator’s 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 G̱an g̱anhl W̓ii Mm̓aal
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’oogit Hleeḵ (Allison Nyce)
Story Transcript: English and Nisga'a
Kwsdins x̱k’uuhlkwhl hlgutk’ihlgum gat tgun tx̱aan̓itkws aguxw-anbilwilt g̱anhl nidii, nidii amukwst k’il̓hl wilt iit ḵ’ap g̱an wilaa siip’indiit.
Gadim G̱an is a five year old boy who gets into a lot of mischief.
Sil jog̱at dip Nits’iits’t g̓ans Niye’et iit anooḵst dip gun k’il̓hl wilt, wil nigii aamhl wilt, nigidiit w̓ii kw’ihl wilaakwdiit hluut’uxwdiit n̓ig̱an wilt.
He lives with his Grandma and Grandpa, who patiently put up with his antics most of the time.
Sa tgun ii dim hlisa’ans Niye’ethl ts’ak’ hooksit ahl lil̓git.
Today, Grandpa needs to finish carving a feast bowl.
Ii n̓ihl sagihl anhis Niye’et dim k’ax̱ ksaxw n̓iin, k’ax̱ kwsdaḵsdiit ado’o ahl g̱alaaḵ’an silg̱awils, silg̱al dip dihitgwin diya Niye’et loot.
And Grandpa decided that Gadim G̱an should go out and play with his friends.
Amg̱oogidim sa, sa ahl gwooyim, gyamgim sa,w̓ay n̓ihl dim g̱o’odiit dim wil g̱alaaḵdiit g̱anhl ansipsiip’inskwt.
It is a beautiful, sunny, spring day and the boys run down to play near the water.
Tx̱aan̓itkws aguhl dim wilaa g̱alaaḵdiit ii n̓ihl wildiit g̱ans Waḵhl Ts’imilx, aniip’inskwt tgun, silg̱awilit, silg̱asg̱ootgwit iit sag̱ootkwdiit dim guutdiithl lo’op, tx̱a’am lo’op siwadim̓ bax̱ lo’op tgun ahl lax̱ aks, hlaa ma’uxwdiit bax̱t.
Everything there sparks a new game, and Gadim G̱an’s friend, Waḵhl Ts’imilx, suggests they see who can make a stone skip the farthest on the surface of the water.
Wilaaxdiit wil n̓akwhl dim wil bax̱hl lo’op tgun lax̱ aks iit guutdiit sim t k’ubax̱a’atdiit ahl g̱a’at n̓i wilaa jabihl game dip siwadis gun huxwdii wilim̓ yukw sisuusin.
The boys quickly learn that for a stone to go far it needs to be smooth, black and oval shaped.
Yukwhl wilt gigil̓hl lo’op dim ang̱alaaḵt iit n̓ihitkwhl ligii agu sbayt, ligii agu, um, haas, g̱an haas t’’ahlihl lax̱ts’eehl aks n̓i wil t’ahlihl g̱an haas n̓ihl nii bax̱at, nidiit wilaax aguhl wat nigit t’il̓t wilaaxt.
As Gadim G̱an wanders far along the shore looking for a good stone he scrambles through the tall grass, tripping over something.
Iit n̓ihl hitkwhl aguyama’ahl watchit log̱am tgwantkw, log̱am ksg̱ooḵ t’img̱est ahl agu tgun, log̱a mm̓aal an win n̓ii bax̱at ii nidiit t’il̓thl wilaaxt.
He falls headfirst into an old canoe hidden in the grass.
Hlaa haldim bax̱t iit dashl t’img̱est kw’ihl hlibal̓hlt hupxwt, yee wil log̱am t’igwantkw ahl ts’im log̱am mm̓aal tgun.
Gadim G̱an stands up, rubbing his forehead as he looks around at the canoe.
Ji n̓ithl sg̱etkwt wilt t’img̱est hupxwt wil yeet simgit yeet sg̱eḵskwdima’a ii nigii an guut loot gigil̓thl wilaa wilhl ansiip’inskwt sil g̱asg̱ootgwit dim x̱biyukwdim̓ ahl aguhl w̓aayit.
Even though his head hurts, he is very excited at his discovery and he calls to his friends who come running.
Ii hagwin aḵkwhl ansiiip’inskws sa silg̱asg̱oot ii yukw ga’adiit iit dasdiit, ndayima’ahl x̱nagwit hlgis agu t tgun ahl lax̱ ts’eets’iks tgunsa, nigit wilaaxdiit.
Yukwhl alalgax̱diit ii n̓i wil hit ahl silg̱awilt si’ansiip’inskwt, “Ndahl g̱abiidima’ahl gathl batsdihl luuwandit g̱an mm̓aal dip gunsa?” Nidiit wilaaxdiit.
Gadim G̱an asks, “How many people do you think it could hold?” They didn’t know.
“Ndayima’a hlaa g̱an̓agwihl hlidaa japkw”, diyahl friendtt Waḵhl Ts’imilx yukwhl liseexwkwdiit sim git agu tgunsa.
Waḵhl Ts’imilx asks, “How many generations ago was it built?”
Ii wandiit yukw liseexwdiit wilaa wilhl mm̓aal tgunsa, naayima’a anjap dihiida, ndayima’ahl ahl g̱an̓agwihl w̓aayit 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’ii n̓ii wil algax̱hl Waḵhl Ts’imilx silg̱a wilsihl, “Hlaa xwdayiy̓. Hlaa n̓uw̓hl xwdayiy̓hl aamhl dim k’ax̱ haw̓um̓ ii dim ii tx̱oox̱gum̓”, diya.
As they are talking, Waḵhl Ts’imilx’s tummy starts to growl, “I’m hungry. Let’s go eat,” he says to his friends.
Ii n̓ihl hihl ansiip’inskwt ji loot huxwdii wiliy̓, hlaa huxwdii n̓uw̓iy̓ xwdayiy̓, way di, dim luuwiiyalt n̓uum̓ ahl dim g̱alts’ap dim ii tx̱oox̱gum̓ Gitwinksihlkw.
The other boys realize they are hungry too, and they all run back to Gitwinksihlkw.
Hlaa bakwdiit wil joḵdiit iit ga’adiit hlaa wil yukskw Niye’etdiit way laay̓um ts’ak’im g̱anhl jabit dim hookst ahl dim wil lil̓gitdiit.
Gadim G̱an races home where Grandpa is carving the surface of a huge wooden dish.
Yukwhl wildiit kw’ihl luu-amaamhl g̱ag̱ootdiit luu-si’amaakwdiit aguhl ga’adiit jabis Niye’ediit iit ga’as Niye’et wil mukwhl hupxt iit gidax̓at, “Ndahl wilhl hupxt g̱ang̱an mukwt?” diya.
Gadim G̱an shouting very excitedly and Grandpa looks up. He sees the bruise on Gadim G̱an’s forehead. “What happened?” Grandpa asks.
Iit t’aḵst Gadim G̱an siwil wilaa wilhl t’img̱est wil bruised, wil sg̱eḵskwt wil mukwt iit mahlit as Niye’et aguhl w̓adiit, aguhl w̓ay̓t.
Gadim G̱an has forgotten that he bumped his head and starts to tell Grandpa about finding the canoe.
“W̓ay̓ihl mm̓aal loḵ hlaa gi-one hundred years dim ahl sgit n̓ihl w̓ay̓it” diya.
“I found an old canoe down the beach! It must be at least one hundred years old!”
Iit n̓i wil algax̱s Niye’et. “Wilaayiy̓ anheenis,” diya, “N̓ihl mm̓aal tgus k’a aluubax̱at w̓itgwit dim g̱alts’abim̓”, diya.
Grandpa smiles, “I know that canoe, it was once the fastest canoe in our village.”
“Ii yukwt mahlis niye’et wil n̓idiit g̱anhl wakkwt anjaphl agu tgun n̓ihl w̓ayisim̓,” diya.
“It was carved by my father and two of his brothers,” Grandpa proudly continues.
“Tx̱aan̓itkwshl n̓uum̓ n̓iwagiit iit wilaaxt, wilaaxt gat wil dip wilaaxhl hlixhlalbihl g̱an siwadiit ahl carve.”
“All the sons of my grandfather were known as great wood carvers.”
“Ga’asim̓hl gwilal̓hl g̱abiihl g̱an m̓aḵsgwit alihl gigalg̱ahl wilp?”
“You know those three totem poles in front of the Longhouse?”
“Mahlik’il̓hl g̱an tgun ahl jabihl nibibim̓, nibibiy̓,” diya, “Mahlik’yooldiit gwilal̓hl g̱abiit g̱an japdiit niwaḵt dip gun.”
“Each of them was built by one of my uncles.”
Ji t’aayihl g̱oott hlaa yukwdim woḵt iit ḵ’oom̓ax̱kw g̱oot dim hugax̱ wils dip nibipt g̱ans dip niye’et dim dii jabithl agu dim hlalbithl g̱an, totem pole, ts’ak’, lip agu n̓ihl hasak̓thl dim jabit.
That evening just before falling asleep, Gadim G̱an thought, “I’d like to carve canoes and totem poles just like my ancestors.”
K’iit gidax̱at, “Dim misoolhl wakgwin,” diya, “Silg̱a tx̱alpx̱dool, kwsdinsool n̓ihl gidax̱at as Niye’et.”
I have to ask Grandpa tomorrow how many brothers his father had, four, five or more?
Aguhl g̱ant han̓iig̱oodihl huxw wans wakkwt txalpxdool, kwsdinsool, gidax̱as tgusda?
Why did Gadim Gan think that his grandpa had two, three, four or five more brothers?
- Written by: Veselin Jungic, SFU and Mark MacLean, UBC
- Illustrator: Simon Roy, Victoria, B.C.
- Director: Andy Gavel, Simon Fraser University
Special thanks to:
- Tom Archibald, Simon Fraser University
- Peter Jacobs, Squamish Nation
- Ozren Jungic, University of Oxford
- Kwosel, Seabird Island First Nation
- Kwelaxtelot, Seabird Island First Nation
- Susan Russell, Simon Fraser University
- Erin Tait, Nisga'a Nation
- Department of Mathematics, Simon Fraser University
- Faculty of Science, Simon Fraser University
- The IRMACS Centre, Simon Fraser University
- Office for Aboriginal Peoples, Simon Fraser University
- 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