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“Gesture Counting” Worksheet #1

Part A

  1. Choose a partner. You give the gesture counting for the even numbers from 1 to 10, your partner should give the odds. Do this activity both giving each discrete set of signs as individuals, then alternating with one another.

SOLUTION: Each partner needs to be familiar with all of the gestures for 1-10, as presented in the NA Materials Lesson No.3 PPT, Slide #9.

  1. Have someone give any five Plains Indian numbers from 1 to 10. Verify the gesturing of the presenter. Now switch roles.

SOLUTION: All students need to be familiar with all of the gestures for 1-10, as presented in the NA Materials Lesson No. 3 PPT, Slide #9.

  1. While gesturing the following numbers have a partner convert them to written Roman numerals: 1, 4, 5, 6, 8, 10.

SOLUTION: Respectively, the Roman numerals corresponding to 1, 4, 5, 6, 8, and 10 are I, IV, V, VI, VIII, and X.

  1. Using what you have learned in your regular textbook and this lesson, convert any three Plains Indian Gestures to Babylonian Numerals.

SOLUTION: Use the following conversion table to obtain the corresponding Babylonian numerals:

  1. Based on what you have learned about Plains Indian Gesture Counting in this lesson and the readings, how do you think you would sign 21? 37? 101?

SOLUTION: None of these numbers could be gestured in one step. Just as they require multiple individual numerals to be written to comprise the whole number, multiple gestures would be required to sign 21, 37, and 101. While not all tribes agree precisely on how to proceed, it makes sense to sign from left to right.

To sign 21, the first step is to sign 20 (achieved by signing for 10 – both hands completely open and touching at the thumbs – followed by right index finger touching the left index finger), and then signing the number 1.

To sign 37, the first step is to sign 30 (achieved by signing for 10 – both hands completely open and touching at the thumbs – followed by right index finger touching the left middle finger), and then signing the number 7.

Finally, to sign 101, the first step is to sign 100 (achieved by having both hands completely open, touching at the thumbs, and performing a waving motion), and then signing the number 1.

  1. Plains Indians also worked with other mathematical concepts such as equality and fractions. Research how this was done and discuss how consistent these methods are with Gesture Counting (Fronval and DuBois may be especially useful here, but many other resources may be just as informative).

SOLUTION:

Part B

1.Restate the Hindu-Arabic numeral 157 in each of the following number systems that were described in this lesson or your textbook:

Plains Indian

Babylonian

Mayan

Roman.

SOLUTION: The gesture for 157 in the Plains Indian number system involves first signing 100 (open both hands with all fingers extended, palms outward, and thumbs touching, and then perform a waving motion), following by 50 (first sign 10 by opening both hands with all fingers extended, palms outward, and thumbs touching, and then using the right index finger to touch the left little finger), and followed by signing the numeral 7.

The strategy is the same for the Babylonian system – first draw 100, then 50, and then 7. Here is the answer:

For the Mayan numerical system, we recall that

For the Roman numerical system, we have 157 = CLVII.

2.Compare and contrast Plains Indian Gesture Counting as given in this lesson with Roman Numerals from 1 to 10. What similarities or differences do you see? (Note: Tomkins may be especially useful here.) In this consideration, be sure to note the geographical and time differences in the development of each. What does this consideration tell you about the universality of mathematics?

SOLUTION: The Plains Indian Gesture Counting involves increasing the amount of displayed objects as the numerals increase in size. This is not always the case for Roman numerals. For instance, the number 8 converts to VIII in Roman numerals, but the larger number 9 converts to a smaller Roman numeral expression, IX.

3.How is the idea of greater than, less than or equal two clearly demonstrated by Gesture Counting? Is it more or less effective, than say, Roman Numerals or the Hindu-Arabic system in demonstrating the Trisotomy Property of numbers?

SOLUTION:

4. The Plains Indians also did addition and subtraction using gesturing. Build on your knowledge of Gesture Counting and investigate how signing was used to add and subtract.

SOLUTION:

5. Some people go through reversals of digits when they see them; that is, they confuse 13 and 31 or 27 and 72. How might this be a problem (or not) with Gesture Counting, and how would you try to help a person avoid such confusion?

SOLUTION: It is important to recognize whether the gestures are being presented for the numerals from left to right or from right to left. Most people read from left to right, so it makes sense to gesture the numerals from left to right, but there is not total agreement about this facet of gesture counting. Another complicating factor that can lead to confusion is that while people read from left to right, they often perform arithmetic operations from right to left. For instance, to add, subtract, or multiply two numbers, one begins perform operations with the ones digit, then moves left to the tens digit, hundreds digit, and so on. Therefore, it is important for communicating parties to agree ahead of time about whether the numerals will be gestured from left to right or from right to left. One way to avoid confusion would be to begin by gesturing a well-known numerical value ahead of time. For instance, if we gesture that the year date is 2012, then since 2012 is not the same as 2102, we can clarify which direction the numerals are being signed.