大象传媒

Small Number and the Old Canoe-Hul-Q-Umi-Num

Small Number and the Old Canoe 鈥 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.

鈥檜hwiin鈥 kw鈥檜shnuts 鈥檌鈥 tthu s鈥檈luhw q鈥檟huw鈥檒h
(Hul'q'umi'num' Translation)

Written by Veselin Jungic & Mark MacLean 
Illustrated by Simon Roy 
Hul'q'umi'num' Translation by Ruby Peter (Sti鈥檛um鈥檃t)

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

stl鈥檌鈥檛l鈥檘ulh tthu kw鈥檌鈥檏w鈥檜shnuts, 鈥檌鈥 yath 鈥檜w鈥 ni鈥 鈥檜 tthu ti鈥檡a鈥檟ween.
Small Number is a five year-old boy who gets into a lot of mischief.

nilh tthu sul鈥檚i鈥檒us ni鈥 shni鈥檚 鈥檌 ya-a-ath 鈥檜w鈥 mukw鈥 stem tuw鈥 suluthut鈥檚 kwus ni鈥 鈥檜 tthu ti鈥檡a鈥檟ween.
He visiting his grandparents鈥 place, and they are always busy doing stuff.

tus 鈥檜 tthu nuts鈥檃鈥 lhqelts鈥 鈥檌鈥 wulh ti鈥檡a鈥檟wuthut nem鈥 heew鈥檜 nem鈥 鈥檜tl鈥 yuqwulhte鈥 lemutus tthu siiye鈥檡us.
This month they are hunting up north in Yuqwulhte鈥 territory at the home of their relatives.

ni鈥 tse鈥 ni鈥 kw鈥檜 tl鈥檜nuq ni鈥 鈥檜 kwthu nem鈥 shnem鈥檚.
And there鈥檚 going to be a potlatch at the place they are going.

they鈥檛us tthu susule鈥 tthu la鈥檛hun, nilh tse鈥 ni鈥 hakw 鈥檜w鈥 nem鈥檜s tus 鈥檜 kwthu yu shhwunum鈥檚.
Granddad is making a dish, that will be used at that place they arrived to.

stl鈥檌鈥檚 tthu susule鈥 kws shuqnehws tthu ni鈥 they鈥檛us ni鈥 xt鈥檈kw鈥檛us tthu hwstl鈥檜p la鈥檛hun, thi-i-i hwstl鈥檜p la鈥檛hun.
Grandpa needs to finish carving a feast dish

wulh yukw鈥檃kw鈥檜sthut 鈥檌鈥 hay 鈥檜l鈥 鈥檜w鈥 鈥檜y鈥 skweyul.
It is a beautiful, sunny, spring day.

kwuyxthut thuw鈥檔e鈥檜llh stl鈥檜l鈥檌qulh swaaw鈥檒usallh nem鈥 xwchenum huw鈥檃鈥檒um鈥.
The group of young boys go running off to play.

nem鈥 t鈥檃hw nem鈥 鈥檜 tthu qa鈥, t鈥檃hw 鈥檜 tthu tsetsuw鈥 hiiw鈥檃鈥檒um鈥.
They go down to the water to the beach to play.

nilh tthu sye鈥檡u 鈥檜tl鈥 kw鈥檌鈥檏w鈥檜shnuts, thi syal鈥檏w thut-stum 鈥檈elhtun, 鈥溾檌lhe鈥 kwunut kws smeent 鈥檌鈥 qw鈥檜yulushstuxhw 鈥檜 tthu qa鈥.
Small Number has a friend Big Circle who says, 鈥淟et鈥檚 take some rocks and dance them on the water.

nilh tse鈥 lhwet kw鈥檜 hay 鈥檜l鈥 tsakw kws nem鈥檚 wenshus kw鈥 smeent nem鈥 yulhtsitsulh 鈥檜 tthu qa鈥.鈥
Let鈥檚 see who can make a stone skip the farthest on the surface of the water.鈥

xwum kwsus tul鈥檔uhwus tthuw鈥檔e鈥檜llh stl鈥檜l鈥檌qulh kws nilhs tthu 鈥檜y鈥 sthuthekw鈥 smeent.
The boys quickly learn that for a stone to go far it needs to be smooth, flat rock.

nilh 鈥檜y鈥 ni鈥 hakwushuhw kwun鈥檚 wensh 鈥檜 tthu xwte鈥檚tuhw tthu qa鈥 kwsuw鈥 yulhtsituslh 鈥檜l鈥.

huye鈥 kw鈥檌鈥檏w鈥檜shnuts nem鈥 yulhun鈥檈 鈥檜 tthu tsuwmun yusew鈥檘鈥 鈥檜kw鈥 smeent, sthuthekw smeent, 鈥檜y鈥 nem鈥 we鈥檞un鈥檚hus.
Small Number wanders far along the shore looking for a smooth stone that will be good to throw.

ni鈥 nem鈥 鈥檌mush kw鈥檌鈥檏w鈥檜shnuts wulh nem鈥 shits鈥檜thut 鈥檜 tthu tl鈥檈鈥檒uqt saxwul, sus hwi鈥 lukw鈥檚hun.
He scrambles through tall grass and trips over something.

sus 鈥檜w鈥 wutl鈥檜ts鈥, yuw鈥檈n鈥 tthu sxuy鈥檜sth kwus yu shhwi鈥檃鈥檒uqw kwus nem鈥 wutl鈥檜ts鈥 hwtiqw鈥檜s.
And then he fell, headfirst, bumping his head.

鈥檌鈥 nilh tthu s鈥檈luhw q鈥檟huw鈥檒h ni鈥 s-hwuhwets鈥 鈥檜 tthey鈥 tl鈥檈luqt saxwul nilh ni鈥 shni鈥檚 kwus wutl鈥檜ts鈥.
It鈥檚 an old canoe wedged into the tall grass that made him fall.

lhxilush kw鈥檌鈥檏w鈥檜shnuts sus 鈥檜w鈥 yuya-a-aytl鈥檜tus tthu sqw鈥檜musth ni鈥 sme鈥檏wulhs suw鈥 le-e-emutus tthu ni鈥 shlhukw鈥檚huns 鈥檌鈥 q鈥檟huw鈥檒h.
Small Number stands up, rubbing his forehead as he looks around at the canoe.

hay 鈥檜l鈥 鈥檜w鈥 xulh tthu ni鈥 sme鈥檏wulhs 鈥檜 tthu sxuy鈥檜sth 鈥檌鈥 nilh kwus lumnuxwus tthu ni鈥 kwunnuhwus.
His head really hurts, but he starts looking at what he鈥檚 found.

sis 鈥檜w鈥 temutus tthu sq鈥檜q鈥檃鈥檚.
He calls out to his friends.

sus muw鈥 xwulunchenum tthuw鈥檔e鈥檜llh stl鈥檜l鈥檌qulh, m鈥檌 lemutum tthu ni鈥 kwunnuhwus.
They come running to look at what he鈥檚 found.

hwu lhuxluxi鈥檒ush tthuw鈥檔e鈥檜llh stl鈥檜l鈥檌qulh, ni-i-i yay鈥檛l鈥檜tus, ni鈥 kwukwoun鈥檚, xetstus 鈥檈elhtun tthu ni鈥 sht鈥檈s tthu ni鈥 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鈥檈ewun鈥 鈥檈elhtun kws hays 鈥檜l鈥 鈥檜w鈥 s鈥檈luhw 鈥檌鈥 hay 鈥檜l鈥 thi.
They think the canoe they found looks very old and big.

suw鈥 putum鈥檚 鈥檜hwiin kw鈥檜shnuts, 鈥渘ihw 鈥檃鈥檒u kw鈥檌inu kw鈥檜 xwum 鈥檃alh 鈥檜 tun鈥檃 q鈥檟huw鈥檒h.鈥
Small Number asks, 鈥淗ow many people do you think could get aboard this canoe?鈥

putum鈥 tthu thi syal鈥檏w, 鈥渘i鈥 ts鈥檛wa鈥 wulh kw鈥檌n sil鈥檃num kwus thuytum tun鈥檃 q鈥檟huw鈥檒h?鈥
Big Circle asks, 鈥淗ow many years ago was it built?鈥

mel鈥檘tus tthuw鈥檔e鈥檜llh stl鈥檜l鈥檌qulh kwthu suw鈥檃鈥檒um鈥檚.
The boys forget all about their game.

hith kwus qwuliil鈥檘wul鈥檛ul鈥, pi鈥檖ta鈥檓utul鈥 鈥檜 tthey鈥 q鈥檟huw鈥檒h ni鈥 kwunnuhws, 鈥檜w鈥 niilhus lhwet kwu niilh ha鈥檏wush ts鈥檛wa鈥.
They spend a long time talking, asking each other about the canoe that they found, about who perhaps could have used it.

鈥檜w鈥 hwun鈥 qwuliil鈥檘wul鈥檛ul鈥 鈥檈elhtun 鈥檌鈥 ni鈥 wulh qw鈥檃yuxwum tthu kw鈥檜l鈥檜 鈥檜tl鈥 thi syal鈥檏w.
They are still talking and Big Circle鈥檚 tummy starts to growl.

鈥溾檌 tsun wulh kw鈥檈y,鈥 thut thi syal鈥檏w.
鈥淚鈥檓 hungry,鈥 Big Cirle says.

鈥溾檌lhe nem鈥 鈥檈鈥 鈥檜lhtun.鈥
鈥淟et鈥檚 go eat!鈥

ni鈥 tl鈥檜w鈥檜lh tul鈥檔uhwus tthu sq鈥檜q鈥檃鈥檚 kwus tl鈥檜w鈥檜lh kw鈥檈y鈥.
The other boys realize they are hungry too.

suw鈥 xwulunchenum 鈥檈elhtun nem鈥 t鈥檃kw鈥 nem鈥 鈥檜 tthu shtun鈥檔i鈥檚 lelum鈥.
And so they all run back to the village.

huye鈥 xwchenum kw鈥檌鈥檏w鈥檜shnuts nem鈥 nem鈥 鈥檜 tthu si鈥檒us, ni鈥 xut鈥檜kw鈥 鈥檜 tthu hay鈥 鈥檜l鈥 thi hwstl鈥檜p la鈥檛hun.
Small Number races home, where Grandpa is carving the surface of a huge wooden dish.

wulh m鈥檌 yu xwan鈥檆hunum鈥 kw鈥檌鈥檏w鈥檜shnuts hay 鈥檜l鈥 hwthiqun kwus yututeem鈥 yuqwaqwul鈥.
He runs over to his Grandpa and Small Number is shouting excitedly.

sus 鈥檜w鈥 lemutum 鈥檜 tthu si鈥檒us, wulh lumnuhwus tthu susule鈥 kwus me鈥檏wulh tthu 鈥檌muths, ni鈥 鈥檜 tthu sqw鈥檜musth.
And Grandpa looks up, and he sees the bruise on Small Number鈥檚 forehead.

ptem鈥檚 tthu susule鈥, 鈥渘i鈥 ch 鈥檃鈥檒u tstamut, 鈥檌muth?鈥
Grandpa asks,鈥淲hat happened, Grandson?鈥

ni鈥 wulh mel鈥檘 tthu kw鈥檌鈥檏w鈥檜shnuts kwus sum鈥檈鈥檏wulh 鈥檜 tthu sxuy鈥檜sth.
Small Number has forgotten that he bumped his head.

鈥檜w鈥 nilh 鈥檜l鈥 kwus titiya鈥檟w kwus huy鈥檛hustus tthu si鈥檒us kwus kwunnuhwus tthu q鈥檟huw鈥檒h.
He excitedly tells Grandpa about finding the canoe.

suw鈥 thut-st-hwus tthu si鈥檒us, 鈥渘i鈥 tsun kwunnuhw kwthu q鈥檟huw鈥檒h ni鈥 鈥檜 tthu tsetsuw鈥.
And he told his grandfather, 鈥淚 found an old canoe down on the beach!

tl鈥檒im鈥 ts鈥檛wa鈥 wulh hay 鈥檜l鈥 s鈥檈luhw, si鈥檒u.
It seem really old, Grandfather.

ni鈥 ts鈥檛wa鈥 wulh nets鈥檜w鈥檜ts sil鈥檃num.鈥
It must be at least a hundred years old!鈥

suw鈥 hwyunumus tthu susule鈥, 鈥渘i鈥 tsun 鈥檜w鈥 shtatul鈥檛uhw kwthey鈥 q鈥檟huw鈥檒h.
Grandpa smiles. 鈥淚 know that canoe.

nilhulh hay 鈥檜l鈥 xwum 鈥檌鈥 鈥檜 tun鈥檃.
It was very fast.

nilh mens lhun鈥 si鈥檒u 鈥檌鈥 kwthu yey鈥檚ul鈥檜 shhw鈥檃鈥檒uqw鈥檃鈥檚 nilh ni鈥 thuyt kwthey鈥 snuhwulh.鈥
It was your grandmother鈥檚 father and his two male relatives who built that canoe.鈥

suw鈥 yuqwiil鈥檘wul鈥檚 tthu susule鈥, 鈥渕ukw鈥 kwthu shhwum鈥檔e鈥檒ukwsulh lhun鈥 si鈥檒u nan 鈥檜l鈥 鈥檜w鈥 stsuw鈥檈t kws xt鈥檈kw鈥檚 鈥檜 tthuw鈥 stem 鈥檜l鈥.
Grandpa continues telling him, 鈥淎ll the uncles of your grandmother were known as great wood carvers.

hayulh 鈥檜l鈥 鈥檜w鈥 stsuw鈥檈t.
They were very talented.

niich le鈥檒um鈥檜t kwthu sxt鈥檈kw鈥 ni鈥 ni鈥 鈥檜 kwthu 鈥檃thusmuns kwthu thi lelum鈥, kwthu lhihw sxt鈥檈kw鈥?
You know those three old totem poles in front of the longhouse?

shhum鈥檔ikws lhun鈥 si鈥檒u niilh thuyt xt鈥檈kw鈥檛 kwthey鈥.
Those were built by your grandmother鈥檚 uncles.鈥

nuts鈥檃鈥 kwthu ni鈥 swe鈥檚 kwthu na鈥檔uts鈥檃鈥 鈥檌鈥 ni鈥 tl鈥檜w鈥 st鈥檈 kwthu yuse鈥檒u, ni鈥 tl鈥檜w鈥 swe鈥檚 kwthu yey鈥檚ul鈥檜 shhwum鈥檔e鈥檒ukws.鈥
One by one and the other two were but by two of her uncles.鈥

kwthey鈥 hwune鈥檜nt kwus wulh 鈥檌鈥檛ut tthu kw鈥檌鈥檏w鈥檜shnuts.
That evening, Small Number was just falling asleep.

鈥檌鈥 sht鈥檈ewun鈥, sht鈥檈ewun鈥, 鈥渘us tl鈥檌鈥 kw鈥檜nus tl鈥檜w鈥 xt鈥檈kw鈥 鈥檜 kw鈥 q鈥檟huw鈥檒h snuhwulh.
And he thought, 鈥淚鈥檇 like to build a canoe.

nu stl鈥檌 kw鈥檜nus tl鈥檜w鈥 xt鈥檈kw鈥 st鈥檈 鈥檜 kwthu ni鈥 ni鈥 鈥檜 kwthu 鈥檃thusmuns kwthu thi lelum鈥 st鈥檈 鈥檜 kwthu nu shtun鈥檔aalhtunulh.
I would like to also carve a totem to put in front of a house, just like my ancestors.

st鈥檈 鈥檜 kwthu nu shtun鈥檔aalhtunulh.

pte鈥檓ut tsun tse鈥 kwthu si鈥檒u 鈥檜w鈥 kw鈥檌inu鈥檈s kwthu shhwumne鈥檒ukwsulh鈥攜ey鈥檚ul鈥檜, lhhwelu, xuthiinu, lhq鈥檜tsse鈥檒u, 鈥檜w鈥 niis sts鈥檜ts鈥檌hw.鈥
I have to ask Grandpa how many uncles he had鈥攖wo, three, four, five or more鈥︹

suw鈥 ptem鈥: nutsim鈥 shus sht鈥檈ewun鈥 tthu kw鈥檌鈥檏w鈥檜shnuts kwus qux tthu 鈥檜l鈥檈lushth tthu sts鈥檃鈥檓uqwsulh鈥攕ht鈥檈ewun鈥檚 kws yey鈥檚ul鈥檜, lhhwelu, xuthiinu, lhq鈥檜tsse鈥檒u 鈥檜w鈥 niis sts鈥檜ts鈥檌hw?
Question: Why did Small Number think that his great-grandparent had a lot of brothers鈥攖wo, three, four, five or more?

Credits: 

Hul鈥檘鈥檜mi鈥檔um鈥 translation, and Editing by Ruby Peter (Sti鈥檛um鈥檃t) and Donna Gerdts (Sp鈥檃qw鈥檜m鈥檜ltunaat)
Sound recording and editing: Thomas Jones (Sewit) & Donna Gerdts

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