Outcome: N6.9
Research and present how First Nations and Métis peoples, past and present, envision, represent, and use
quantity in their lifestyles and worldviews.
a. Gather and document information regarding the significance and use of quantity for at least one First
Nation or Métis peoples from a variety of sources such as Elders and traditional knowledge keepers.
b. Compare the significance, representation, and use of quantity for different First Nations, Métis peoples,
and other cultures.
c. Communicate to others concretely, pictorially, orally, visually, physically, and/or in writing, what has
been learned about the envisioning, representing, and use of quantity by First Nations and Métis peoples
and how these understandings parallel, differ from, and enhance one’s own mathematical
understandings about numbers.
Sources of information:
CULTURALLY NEGOTIATED SCHOOLING: TOWARD A YUP'IK MATHEMATICS
http://jaie.asu.edu/v33/V33S3CUL.htm
What Is Yup'ik Mathematics?
Numbers are an obvious place to investigate linguistic and cultural ways of representing mathematical
ideas. Yup'ik cardinal numbers are presented to illustrate basic Yup'ik number patterns in the base 20
sub-base 5 counting system, and to note the literal meaning of some numbers. The numbers are
ordered in a manner linguistically indicated and as shown by elders counting: four sets of five. The literal
meanings are noted next to some numbers. Table 1 was adapted from Jacobsen (1984) and from
interviews with the Ciulistet and elders.
Table 1 - Yup'ik Numbers and Literal Meanings
Cardinal Numbers Counting on
one hand
Counting on the other hand
1 atauciq
6 arvinlegen
(cross over)
2 malruk
7 malrunlegen
(not quite
10)
3 pingayun
8 pingayunlegen
4 cetaman
9 qulmgunritaraan
5 talliman (one arm)
10 qula, qulen
Counting below on one side
(see Note 3)
Counting below on the other side
(above)
11 qula atauciq
16 akimiaq atuaciq
12 quIa malruk
17 akimiaq malruk
13 quIa pingayun
18 akimiaq pingayun
14 akmiarunritaraan
19 yuinaunritaraan
15 akimiaq
20 yuinaq
Examples of counting beyond
20
30 yuinaq quala
(not quite
20)
(the whole
person)
(20 plus 10)
(two times
20
40 yuinaak malruk
Yup'ik counting from 1 through 5 begins on the left hand from the smallest end finger, to the thumb,
and then crosses over to the other hand repeating this process. To count from 11 to 20, one starts over
with the left end finger, and repeats the process. The Yup'ik system is base 20; yuniaq represents 20
(literally translated as a whole person). Also, elders at the workshop represented counting materials
such as sticks in bundles of 20s. This knowledge of numbers is readily accessible to all Yup'ik speakers.
For Yup'ik non-Yup'ik speakers it is cultural heritage. Further, the literal meaning behind the numbers is
still accessible to Yup'ik speakers--arvinlegen (six) means "cross over," qula means "above," and yuinaq
derives from yuk the "whole person," which adds meaning to numbers and counting.
QUIPU
http://aboriginalperspectives.uregina.ca/workshops/workshop2011/quipu1.shtml
The Inca are an indigenous people who controlled a region in South America prior to European contact.
The Inca built a sophisticated road system to connect the various regions of their empire to move goods
and information. The roads were paved with flat stones and goods and information were carried along
the roads by messengers travelling on foot. Information was carried either by word of mouth or using
knots on cords called quipu.
ALASKA NATIVE KNOWLEDGE NETWORK
Non-Standard Measurements - http://ankn.uaf.edu/publications/VillageMath/nonstandard.html
1906 Native Allotments - http://ankn.uaf.edu/publications/VillageMath/1906_native_allotments.html
TREATY MATH
What benefits did First Nations believe they were to receive in signing Treaty Six?
First Nations understood they would receive assistance to the transition of a new
lifestyle, maintenance of their cultural and spiritual rights, right to hunt, trap, and fish,
education, medical assistance, reserve land, agricultural tools and support, and
peaceful co-existence with the newcomers. The text of the Treaty states:
 Reserve land in the amount of one square mile per family of five;
 An annual cash payment at a rate of $25 per Chief, $15 per headman and $5 for
all other band members, and a one time present of $12 for each member of the
band who agreed to the Treaty;
 Twine and ammunition at a value of $1500 per year;
 For each band and family certain agricultural implements such as hoes, spades,
livestock, horse, and wagon;
 A school once the people settled on a reserve;
 The right to pursue hunting, trapping, and fishing;
 A medicine chest to be kept at the house of the Indian agent on each reserve;
 Rations were to be given in times of pestilence and famine;
 During the first three years after Treaty was taken, First nations who had settled
on reserves and were farming were to receive $1000 in agricultural provisions.
(Dodson21)
http://treaty6education.lskysd.ca/treaty6basics
ARMAND McARTHUR – Elder, Pheasant Rump First Nation
Calendars:
New Year began in June
June – Thick leaves moon
July – Red berry moon
August – black chokecherry moon
September – Yellow leaves moon
October – Stripey gopher looks for his place, looks back over everything before he goes in for the winter
November – Frost moon
December – Popping trees moon
January – Centre sons little brothers moon (sundogs and moondogs)
February – Long days moon
March – Sore eyes moon
April – Frog moon
May – Budding moon
Learning Activities:
KWL CHART
What do I KNOW about…
VENN DIAGRAM
What do I WANT to know about…
What have I LEARNED about…
Use of Numbers: Then and Now
HOW WOULD I…



If my family was given 1 m2 of land, how would I mark it out?
o Using current technologies
If I had to determine the height of a tree, I would…
What natural signals tell me when it is time to go home for supper? Get out of bed?