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?