Small Number and the Old Canoe-Heiltsuk
Small Number and the Old Canoe – Heiltsuk
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.
Háusayáyu'u du glwa
Written by Veselin Jungic & Mark MacLean
Illustrated by Simon Roy
Heiltsuk Translation by Constance Tallio and Evelyn Windsor
Story Transcript: English and Heiltsuk
Small Number and the Old Canoe – Haulaɫas - Háusa du glw̓a
Small Number is a little boy,
Haulaɫa’uis wísm háusláya,
And he is always getting into mischief.
Gi hiálaq̓am nánúɫtuba la.
He is in the care of his grandparents,
For they put up with the way he plays.
’Ksay̓asi wán̓iqas hialama h̓áml̓ínisi.
Grandpa has to carve a feast dish,
’Kiágilaxv ǧaǧmpasi ɫúq̓va λiálac̓iƛ,
Go out and play with the other children.
Gi h̓auá yápa háusḷá’ qn láisi, h̓ámɫuls du w̓áukvas x̌ix̌apxv.
It’s a nice spring sunny day,
Háixƛalapsis hay̓ṇ́x̌s pxlas k̓vqḷá,
And they ran down to play in the water.
gi h̓auá k̓ík̓x̌vnc̓s lá h̓ámɫa la w̓a’ámpax̌i.
Everything they see sparks a new game,
’Hákq̓aṃ̓ás duqvlasusi wáli q̓áyax̌’aidailas h̓áluɫts h̓áml̓íní,
and Small Number’s friend Big Circle suggests they see who can make a stone skip the farthest on the surface of the water.
Gi h̓auá q̓ay̓ax̌’ait ’Qaikasas klxsm qn h̓ágvaƛiay̓alanás t̓ísm gila c̓x̌’áitsi la w̓a’ampax̌i.
The boys learned if they want their stones to go far, they had to use a flat oval shape stone.
Hál̓akaiq̓a’ áuɫ’aƛḷa wi’ísmáx̌i n̓ax̌vi msḷá qn x̌vísgílís t̓ísm hiáǧlmsi yíáqɫgiláy̓asi paɫtus glɫtúxst̓uxvs tism.
Small Number walked far looking for the rock that will win.
Yiálaglis Háuláɫas Háusḷá x̌víx̌vsgílá líta t̓ísmáts h̓áikuáy̓u.
He was walking in the grassy area and he kicked into something, and fell head first into an old canoe hidden in the grass.
Tuá laglisi la k̓ítṃ́isax̌i gi h̓auá q̓áq̓nx̌ṇála m̓núxvs m̓ás. Kíx̌c̓u xvák̓vná guɫdia t̓áy̓álá la k̓ít̓ṃáx̌i.
Even if he hit his head he was very happy over his find.
Waxv’ṃi ƛ̓uxválá háixt̓iási gi w̓alas h̓áik̓qḷas q̓ákanx̌vasi.
He called out to his friends, they went running to him.
Yáux̌vḷi w̓áukvasi gi h̓aua k̓ík̓vḷá lákáqi.
The boys were standing around the canoe.
λaxλuis wi’íṃáx̌i la w̓uistayas xvákvṇáyax̌i.
They were touching the sides of the canoe.
’Pakaxdax̌vu wuwakiax̌six̌s xvákvṇáyax̌v.
It looks old and look big to them.
Small Number asks
Gi h̓auá haúmá Háuláɫas Háusḷá
How many people do you think will fit in there, asked Big Circle.
Gṇ́caukvi dítgváṇm xvutiy̓aus qn haiɫx̌v láx̌v ’quik n̓ix kl̓xsm.
How many generations ago was it built?
Gṇ́acáukvix̌ndilic ’ƛíƛuw̓lstuá lay̓acx̌v x̌sílásu?
The boys forgot the game they had been playing.
’ƛ̓lístaq̓am wi’ísmáx̌v h̓áml̓ínáy̓asi.
They were talking about the canoe wondering who could have used it.
Gi h̓auá pk̓váláq̓ams glw̓áyáx̌i q̓a’áuƛ̓ix̌sda yiaqɫats glw̓aka’auax̌i.
As they were talking Big Circle’s tummy began to growl.
La bípk̓váláy̓asi ’Qvúml̓áláx’it tk̓iás ’Qáikas Kl̓xsm.
“I’m hungry. Let’s go eat”, he says to his friends,
Puw̓ísṃṇúgva ’waixsints hmsa, niki w̓áukvasi,
And they all ran home.
Gi hauá k̓íkx̌v’it lái n̓akv.
Small number ran home,
’Kíx̌vla Haulaɫas háusḷá láin̓akv,
At the place where grandpa was carving the surface of a huge (wooden) dish.
La la’asas ǧaǧṃpasi k̓iálagiɫ wusǧmiy̓as q̓áikaska’áuás ɫúq̓va.
And he shouted,
Gi h̓auá h̓átḷá,
And he looked up.
Gi h̓auá t̓ix̌sísta dúx̌v’it.
He saw the bruise on Small Number’s forehead.
Dúqvḷái h̓áxváyá la w̓úgvíwáyas háuláɫas háusḷá.
What happened asked grandpa.
’Wíx’ítxdas nix ǧáǧmá háum.
Small Number had forgotten that he bumped his head and started to tell Grandpa about finding the canoe.
’ƛlísta háulaɫas háuslá-ya lay̓asi t̓s’ála háixt̓iási, gi niɫas qakay̓si gḷ́w̓a.
I found an old canoe down on the beach. It must be at least a hundred years old.
’Qákánúgva glw̓a gvauɫ la wil̓iax̌i laganmits w̓úp̓nxstáis’ila w̓ása̓lásasi.
Grandpa smiled, it was one of the fastest canoes of our village.
Mḷ́xvlá ǧáǧámpa q̓a’áuƛṇugva gḷ́w̓áyáx̌i Mnúkvis yixálágvuts gḷ́w̓as qnts gvúkviásax̌.
It was built by my father and two of his brothers.
’Háƛ̓asugvauɫis qs h̓aumpa du má’álukvas w̓aq̓vásí.
Grandpa proudly continued, all the sons of my grandfather were known as the great carvers.
Níɫtu ǧáǧmpa gi níɫas ’hágám sásmás qs ǧáǧmá q̓a’áuƛ̓nx̌vs yis w̓alas h̓áikímás k̓iá.
You know those three (old) totem poles in front of the bighouse?
’Ga’áuɫ’msu qi yúdúkvas c̓uw̓áx̌si la w̓uw̓áx̌siás λiác̓iax̌i?
Each of them was built by one of my uncles.
’Hágámi k̓iásus qs m̓núkvas xvɫmp.
One evening before going to sleep, Small Number thought, I’d like to build a canoe and totem poles just like my ancestors.
Mnúkvis ǧánúɫ h̓ábas laxstasaiɫay̓asi qn k̓aɫ’it x̌sílíx̌sdnugva du ’cuw̓áx̌sigila ǧviála qs h̓áiámbiɫgvaiɫdia.
I will ask my grandfather tomorrow how many brothers his father had, two, three, four, five or more.
Háumáƛṇugva ǧáǧmá ɫansƛats gncaukv w̓íw̓aq̓váyaci h̓aumpasi, ma’alukv, yúdúkv, múkv, sk̓aukv, dun̓ax̌vi q̓áinám.
Question: Why did Small Number think his great grandpa had two, three, four, five great grandparents?
’Mási xvútagiɫts háuláɫ’uas háusḷá qits ma’áluxv, yúdúxv, múxv, sk̓a̓úxv ǧáǧasl̓ayats ǧáǧmpasi.
- 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