’uhwiin’ kw’ushnuts ’i’ tthu s’eluhw q’xhuw’lh
(Hul'q'umi'num' Translation)

Written by Veselin Jungic & Mark MacLean 
Illustrated by Simon Roy 
Hul'q'umi'num' Translation by Ruby Peter (Sti’tum’at)

Small Number and the Old Canoe – Hul'q'umi'num'

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.

Story Transcript: English and Hul'q'umi'num'

stl’i’tl’qulh tthu kw’i’kw’ushnuts, ’i’ yath ’uw’ ni’ ’u tthu ti’ya’xween.
Small Number is a five year-old boy who gets into a lot of mischief.

nilh tthu sul’si’lus ni’ shni’s ’i ya-a-ath ’uw’ mukw’ stem tuw’ suluthut’s kwus ni’ ’u tthu ti’ya’xween.
He visiting his grandparents’ place, and they are always busy doing stuff.

tus ’u tthu nuts’a’ lhqelts’ ’i’ wulh ti’ya’xwuthut nem’ heew’u nem’ ’utl’ yuqwulhte’ lemutus tthu siiye’yus.
This month they are hunting up north in Yuqwulhte’ territory at the home of their relatives.

ni’ tse’ ni’ kw’u tl’unuq ni’ ’u kwthu nem’ shnem’s.
And there’s going to be a potlatch at the place they are going.

they’tus tthu susule’ tthu la’thun, nilh tse’ ni’ hakw ’uw’ nem’us tus ’u kwthu yu shhwunum’s.
Granddad is making a dish, that will be used at that place they arrived to.

stl’i’s tthu susule’ kws shuqnehws tthu ni’ they’tus ni’ xt’ekw’tus tthu hwstl’up la’thun, thi-i-i hwstl’up la’thun.
Grandpa needs to finish carving a feast dish

wulh yukw’akw’usthut ’i’ hay ’ul’ ’uw’ ’uy’ skweyul.
It is a beautiful, sunny, spring day.

kwuyxthut thuw’ne’ullh stl’ul’iqulh swaaw’lusallh nem’ xwchenum huw’a’lum’.
The group of young boys go running off to play.

nem’ t’ahw nem’ ’u tthu qa’, t’ahw ’u tthu tsetsuw’ hiiw’a’lum’.
They go down to the water to the beach to play.

nilh tthu sye’yu ’utl’ kw’i’kw’ushnuts, thi syal’kw thut-stum ’eelhtun, “’ilhe’ kwunut kws smeent ’i’ qw’uyulushstuxhw ’u tthu qa’.
Small Number has a friend Big Circle who says, “Let’s take some rocks and dance them on the water.

nilh tse’ lhwet kw’u hay ’ul’ tsakw kws nem’s wenshus kw’ smeent nem’ yulhtsitsulh ’u tthu qa’.”
Let’s see who can make a stone skip the farthest on the surface of the water.”

xwum kwsus tul’nuhwus tthuw’ne’ullh stl’ul’iqulh kws nilhs tthu ’uy’ sthuthekw’ smeent.
The boys quickly learn that for a stone to go far it needs to be smooth, flat rock.

nilh ’uy’ ni’ hakwushuhw kwun’s wensh ’u tthu xwte’stuhw tthu qa’ kwsuw’ yulhtsituslh ’ul’.

huye’ kw’i’kw’ushnuts nem’ yulhun’e ’u tthu tsuwmun yusew’q’ ’ukw’ smeent, sthuthekw smeent, ’uy’ nem’ we’wun’shus.
Small Number wanders far along the shore looking for a smooth stone that will be good to throw.

ni’ nem’ ’imush kw’i’kw’ushnuts wulh nem’ shits’uthut ’u tthu tl’e’luqt saxwul, sus hwi’ lukw’shun.
He scrambles through tall grass and trips over something.

sus ’uw’ wutl’uts’, yuw’en’ tthu sxuy’usth kwus yu shhwi’a’luqw kwus nem’ wutl’uts’ hwtiqw’us.
And then he fell, headfirst, bumping his head.

’i’ nilh tthu s’eluhw q’xhuw’lh ni’ s-hwuhwets’ ’u tthey’ tl’eluqt saxwul nilh ni’ shni’s kwus wutl’uts’.
It’s an old canoe wedged into the tall grass that made him fall.

lhxilush kw’i’kw’ushnuts sus ’uw’ yuya-a-aytl’utus tthu sqw’umusth ni’ sme’kwulhs suw’ le-e-emutus tthu ni’ shlhukw’shuns ’i’ q’xhuw’lh.
Small Number stands up, rubbing his forehead as he looks around at the canoe.

hay ’ul’ ’uw’ xulh tthu ni’ sme’kwulhs ’u tthu sxuy’usth ’i’ nilh kwus lumnuxwus tthu ni’ kwunnuhwus.
His head really hurts, but he starts looking at what he’s found.

sis ’uw’ temutus tthu sq’uq’a’s.
He calls out to his friends.

sus muw’ xwulunchenum tthuw’ne’ullh stl’ul’iqulh, m’i lemutum tthu ni’ kwunnuhwus.
They come running to look at what he’s found.

hwu lhuxluxi’lush tthuw’ne’ullh stl’ul’iqulh, ni-i-i yay’tl’utus, ni’ kwukwoun’s, xetstus ’eelhtun tthu ni’ sht’es tthu ni’ kwunnuhwus.
The boys were standing around the canoe, running their hands along its shape, trying to figure out how it had got that way.

sht’eewun’ ’eelhtun kws hays ’ul’ ’uw’ s’eluhw ’i’ hay ’ul’ thi.
They think the canoe they found looks very old and big.

suw’ putum’s ’uhwiin kw’ushnuts, “nihw ’a’lu kw’iinu kw’u xwum ’aalh ’u tun’a q’xhuw’lh.”
Small Number asks, “How many people do you think could get aboard this canoe?”

putum’ tthu thi syal’kw, “ni’ ts’twa’ wulh kw’in sil’anum kwus thuytum tun’a q’xhuw’lh?”
Big Circle asks, “How many years ago was it built?”

mel’qtus tthuw’ne’ullh stl’ul’iqulh kwthu suw’a’lum’s.
The boys forget all about their game.

hith kwus qwuliil’qwul’tul’, pi’pta’mutul’ ’u tthey’ q’xhuw’lh ni’ kwunnuhws, ’uw’ niilhus lhwet kwu niilh ha’kwush ts’twa’.
They spend a long time talking, asking each other about the canoe that they found, about who perhaps could have used it.

’uw’ hwun’ qwuliil’qwul’tul’ ’eelhtun ’i’ ni’ wulh qw’ayuxwum tthu kw’ul’u ’utl’ thi syal’kw.
They are still talking and Big Circle’s tummy starts to growl.

“’i tsun wulh kw’ey,” thut thi syal’kw.
“I’m hungry,” Big Cirle says.

“’ilhe nem’ ’e’ ’ulhtun.”
“Let’s go eat!”

ni’ tl’uw’ulh tul’nuhwus tthu sq’uq’a’s kwus tl’uw’ulh kw’ey’.
The other boys realize they are hungry too.

suw’ xwulunchenum ’eelhtun nem’ t’akw’ nem’ ’u tthu shtun’ni’s lelum’.
And so they all run back to the village.

huye’ xwchenum kw’i’kw’ushnuts nem’ nem’ ’u tthu si’lus, ni’ xut’ukw’ ’u tthu hay’ ’ul’ thi hwstl’up la’thun.
Small Number races home, where Grandpa is carving the surface of a huge wooden dish.

wulh m’i yu xwan’chunum’ kw’i’kw’ushnuts hay ’ul’ hwthiqun kwus yututeem’ yuqwaqwul’.
He runs over to his Grandpa and Small Number is shouting excitedly.

sus ’uw’ lemutum ’u tthu si’lus, wulh lumnuhwus tthu susule’ kwus me’kwulh tthu ’imuths, ni’ ’u tthu sqw’umusth.
And Grandpa looks up, and he sees the bruise on Small Number’s forehead.

ptem’s tthu susule’, “ni’ ch ’a’lu tstamut, ’imuth?”
Grandpa asks,“What happened, Grandson?”

ni’ wulh mel’q tthu kw’i’kw’ushnuts kwus sum’e’kwulh ’u tthu sxuy’usth.
Small Number has forgotten that he bumped his head.

’uw’ nilh ’ul’ kwus titiya’xw kwus huy’thustus tthu si’lus kwus kwunnuhwus tthu q’xhuw’lh.
He excitedly tells Grandpa about finding the canoe.

suw’ thut-st-hwus tthu si’lus, “ni’ tsun kwunnuhw kwthu q’xhuw’lh ni’ ’u tthu tsetsuw’.
And he told his grandfather, “I found an old canoe down on the beach!

tl’lim’ ts’twa’ wulh hay ’ul’ s’eluhw, si’lu.
It seem really old, Grandfather.

ni’ ts’twa’ wulh nets’uw’uts sil’anum.”
It must be at least a hundred years old!”

suw’ hwyunumus tthu susule’, “ni’ tsun ’uw’ shtatul’tuhw kwthey’ q’xhuw’lh.
Grandpa smiles. “I know that canoe.

nilhulh hay ’ul’ xwum ’i’ ’u tun’a.
It was very fast.

nilh mens lhun’ si’lu ’i’ kwthu yey’sul’u shhw’a’luqw’a’s nilh ni’ thuyt kwthey’ snuhwulh.”
It was your grandmother’s father and his two male relatives who built that canoe.”

suw’ yuqwiil’qwul’s tthu susule’, “mukw’ kwthu shhwum’ne’lukwsulh lhun’ si’lu nan ’ul’ ’uw’ stsuw’et kws xt’ekw’s ’u tthuw’ stem ’ul’.
Grandpa continues telling him, “All the uncles of your grandmother were known as great wood carvers.

hayulh ’ul’ ’uw’ stsuw’et.
They were very talented.

niich le’lum’ut kwthu sxt’ekw’ ni’ ni’ ’u kwthu ’athusmuns kwthu thi lelum’, kwthu lhihw sxt’ekw’?
You know those three old totem poles in front of the longhouse?

shhum’nikws lhun’ si’lu niilh thuyt xt’ekw’t kwthey’.
Those were built by your grandmother’s uncles.”

nuts’a’ kwthu ni’ swe’s kwthu na’nuts’a’ ’i’ ni’ tl’uw’ st’e kwthu yuse’lu, ni’ tl’uw’ swe’s kwthu yey’sul’u shhwum’ne’lukws.”
One by one and the other two were but by two of her uncles.”

kwthey’ hwune’unt kwus wulh ’i’tut tthu kw’i’kw’ushnuts.
That evening, Small Number was just falling asleep.

’i’ sht’eewun’, sht’eewun’, “nus tl’i’ kw’unus tl’uw’ xt’ekw’ ’u kw’ q’xhuw’lh snuhwulh.
And he thought, “I’d like to build a canoe.

nu stl’i kw’unus tl’uw’ xt’ekw’ st’e ’u kwthu ni’ ni’ ’u kwthu ’athusmuns kwthu thi lelum’ st’e ’u kwthu nu shtun’naalhtunulh.
I would like to also carve a totem to put in front of a house, just like my ancestors.

st’e ’u kwthu nu shtun’naalhtunulh.

pte’mut tsun tse’ kwthu si’lu ’uw’ kw’iinu’es kwthu shhwumne’lukwsulh—yey’sul’u, lhhwelu, xuthiinu, lhq’utsse’lu, ’uw’ niis sts’uts’ihw.”
I have to ask Grandpa how many uncles he had—two, three, four, five or more…”

suw’ ptem’: nutsim’ shus sht’eewun’ tthu kw’i’kw’ushnuts kwus qux tthu ’ul’elushth tthu sts’a’muqwsulh—sht’eewun’s kws yey’sul’u, lhhwelu, xuthiinu, lhq’utsse’lu ’uw’ niis sts’uts’ihw?
Question: Why did Small Number think that his great-grandparent had a lot of brothers—two, three, four, five or more?

 

Credits: 

Hul’q’umi’num’ translation, and Editing by Ruby Peter (Sti’tum’at) and Donna Gerdts (Sp’aqw’um’ultunaat)
Sound recording and editing: Thomas Jones (Sewit) & Donna Gerdts

Credits and Acknowledgements
 

  • 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