 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 1:
Homework

Think back to the finite system of units digits that you explored in Part A and answer the following questions about that system.  Problem H1 a. The commutative law for multiplication states that (a • b) = (b • a). Does this law hold for the finite number system in your table? Why or why not? b. The associative law for multiplication states that (a • b) • c = a • (b • c). Does this law hold for the finite number system in your table? Why or why not? Problem H2 a. How could you use the multiplication table you created to divide?  Think of division as a way of undoing multiplication. For example, to find y divided by x, think, "x times what number equals y?"    Close Tip Think of division as a way of undoing multiplication. For example, to find y divided by x, think, "x times what number equals y?"

 b. Does this finite system allow you to divide any two numbers in the system, or are there limits? Problem H3 Is this finite set closed under the operation of multiplication? Problem H4 The distributive law of multiplication over addition says that a • (b + c) = (a • b) + (a • c). Does the distributive law work for the finite system? Why or why not? Problem H5 Is it possible to categorize numbers as even or odd in the finite system? Why or why not? Problem H6 In the finite system, which numbers are multiples of 3? Which are multiples of 4? Of 5? How do you know? Problem H7 Which numbers are perfect squares (i.e., a product of a number multiplied by itself) in the finite system? How do you know? Problem H8 In the real number system, if you multiply two numbers and you get 0, what can you conclude about these two numbers? Does the same apply in the finite number system?  Think about a • b = 0, with, for example, a = 5.   Close Tip Think about a • b = 0, with, for example, a = 5.      Problem H9 You have determined the length of on the number line. Can you determine the length of on the number line?      Read these excerpts from the following book:
Seife, Charles (2000). Zero: The Biography of a Dangerous Idea (pp. 6, 12-21).
Reproduced with permission from Viking Penguin. © 2000 by Charles Seife. All rights reserved.

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