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L13_filled - Day 15 Coordinating Things 2 Lets Review Some...

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1 Day 15 Coordinating Things 2 Let’s Review Some stuff from Friday… Bob, Bob Jr., Bob 3 , Bob 4 , Bob 5 , Bob 6 , … All died The Monkey was evil. We learned about independent directions . And the notion of a point , line , plane , and space . Now… Suppose we drew a horizontal line and arbitrarily marked off two locations.
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2 3 Creating the Number Line Let the space between represent the amount of distance traveled in one physical step. So… Question! What if we just stood still on the first tick mark and didn’t move. How many steps have we taken? So we label this tick mark ________ and we label the other tick mark ________ for ________ step. 4 Creating the Number Line II If we wanted to, we could take two steps to the right and mark this new position as tick mark ______. In fact… we could repeat this process and step as far right as we wanted. But what if you’re a lefty… Keeping with convention, we’ll label one step to the left as ______.
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3 5 Geometric Integers And if we wanted, we could repeat this forever too. In this way can represent any ____________ on a single line. There is no good reason why the line has to be horizontal other than its easer to ________. We can actually model everything about the integers on this line. ___________________ rules come natural because the _______ of the integers on the line is consistent with their formal definition. 6 Geometric Integers II -- Addition To model addition via the number line we define the addition of a number “a” to mean Take “a” steps to the right if “a” is positive Take “a” steps to the left if “a” is negative To model Subtraction we define the subtraction by “a” to mean Take “a” steps to the left if “a” is positive Take “a” steps to the right if “a” is negative
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4 7 Geometric Integers III – Addition/Mult. Observe “Adding Negatives” is the same as “Subtracting Positives” And “Subtracting Negatives” is the same as “Adding Positives” To model multiplication we use a ____________ metaphor.
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