Lesson Plan 2: To-pe-di Historical/Cultural Perspective: To-pe-di is a Native American counting game played at the turn of the 20th century by the Shoshoni-Bannock Native American nation of Fort Hall, Idaho. This game involves chance mixed with strategy. The object of the game is to win by acquiring all of the opponent’s dice sticks or to win enough objects to reach a previously agreed upon amount. To keep score, players collect counters like sticks, pebbles, or they tally points on a square representing four rows of ten.
Objective: SWBAT accurately measure sticks and to measure and mark the lines and “x’s.” Students will accurately count, sum and keep score. SW play to-pe-di cooperatively. SW then modifies game and creates their own rules.
Materials: Students can gather sticks, counting twigs or pebbles from the playground or their own homes. Traditionally, 4 – 8-1/2 inch long dice sticks traditionally made from painted and carved willow branches (one can substitute wooden dowels cut in half lengthwise). These sticks have been split in half, with the flat side painted red. Two of the sticks have parallel lines carved about two inches apart across the center of each stick. One of these sticks has an “x” drawn between the two lines. This stick is called Pi-au (female), the other stick with only the two lines is called A-ku-a (male). The other two sticks have plain tops. Additional materials include ruler, red paint, sandpaper, and marking pens for lines.
Procedure: Have students collect their sticks and counters. Discuss measurement with students. How can we measure our sticks? Different cultures used different standard units of measurement. The Shoshoni traditionally considered the distance across their outstretched hand from thumb to little finger to be a standard unit of measurement. Have students compare and contrast their outstretched hands and observe differences in length. Is this a problem when different people want to make the same thing in the same size?
SW measure and cut 4 – 8-1/2” long sticks, sand them, paint the flat bottom red, and make the appropriate lines on the tops of 2 sticks. TW model how to play the game, how to earn points, how to keep score. Students can be encouraged to cooperate by combining individual scores to foster cooperation and non-competition. Students may agree upon a predetermined accumulated team score, for instance 20 points. Then have students play, recording their cumulative scores using their counters. SW throw their to-pe-di sticks, record scores. TW observe methods used by students to count their counters (some may just pile them up, others may stack them by 5’s or ten’s, etc.). When initial games are played and completed, TW have students create new rules of play and explain them to class. SW vote on new rules they like best, then play using new rules.
Traditional scoring is as follows:
1) All top sides up = 1 point OR All red bottom sides up = 1 point.
2) A-ku-a (male) and Pi-au (female) top side up, the other two sticks with red bottom side up = 2 points OR The two plain top sides up with two red bottom sides up = 2 points.
3) Three sides the same = 1 point.
Modification: Instead of just using addition facts, the game can be extended by using subtraction, multiplication, and division. Students at other levels can use fractions, decimals, and integers to increase the type and number of applied mathematical concepts.
Assessment:Observation sheet based on level of participation on a 0-2 scale: 0-non-particpation 1-some participation 2- full participation in activity, and an anecdotal record based on behavior during activity.