CA Handout 1 - M326K Class Activities Handout 1 A Finite...

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Unformatted text preview: M326K Class Activities Handout 1 A Finite Number System Spring 08 0.1 Previous Terms Used Number system 0.2 Introduction and Objectives You have become so accustomed to the usual number systems (integers, rational num- ber, real numbers) that most of their properties probably seem obvious to you by now. However, when you are a teacher, these obvious things will be part of what you need to teach. To help you focus on these properties, we will examine a different number system and compare and contrast it with the familiar number systems. The different number system will also have the advantage of being finite, which makes it easier to study completely. 0.3 Vocabulary to be learned or reviewed Associative Closure Commutative Digit Distributive Identity Inverse Units digit 1 Special instructions for students who have worked mod n You will recognize this system as arithmetic mod 10. However, you may not use any prior knowledge or terminology from prior experience working mod n in doing this activity . Instead, you have the additional assignment of acting as guide on the side in your group in any problem below where you could use that knowledge. In particular, this means: You should refrain from giving the answer away to other group members. If other group members are having difficulty figuring out something you know, you should try to provide small hints or ask questions that help steer them in a productive direction. 1 A Finite Number System with Addition In this number system, we use only the numbers 0 , 1 , 2 ,..., 9. To add, we first add as usual in the integers, but then keep only the units digit. For example, in our usual addition, 9 + 4 = 13, so in our finite system, 9 4 = 3. (We will write for addition in the finite system and write + for addition in the usual system.) Problem 1: Finish filling in the addition table below, using this new addition. Warning: No doubt youll see some patterns, but resist the urge to use the patterns to fill out the table. Use only the meaning of to fill out the table. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 2 2 3 4 5 6 7 8 9 1 3 3 4 5 6 7 8 9 1 2 4 4 5 6 7 8 9 1 2 3 5 5 6 7 6 6 7 8 7 7 8 9 8 8 9 9 9 1 Problem 2: a. What patterns do you see in this addition table? Discuss with your group. b. There are some diagonal patterns. Explain why they occur. Give both verbal and algebraic (that is, using symbols and equations) explanations. 2 1.1 Number System Properties 1.1.1 Additive identity Vocabulary: A number in a number system with an addition is called an additive identity (or identity for addition ) if adding that number to any other number never changes the value of the other number....
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This note was uploaded on 03/19/2008 for the course M 326K taught by Professor Harper during the Spring '08 term at University of Texas at Austin.

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CA Handout 1 - M326K Class Activities Handout 1 A Finite...

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