3.3+Exploring+Patterns

PM 4/27/09 Block C  Problem 3.3 and Follow Up  Big Idea Negative numbers help us to model many real world situations.
 * Essential Question #3: How do I find the difference between integers? **


 * Studying and describing patterns is important in math. Study the patterns in the equations below, and then work on the problem.**

15-5=10 15-4=11 15-3=12 15-2=13 15-1=14 15-0=15 One pattern is that the more you subtract from 15 the difference will get more and more less, and if your subtract 0 then the difference will be 15 because your aren’t taking anything away. || Subtract -1=16 || ||            I think that 15- -1 is 16. Black= +1 and Red= -1
 * A. **** Describe any patterns you see in the way differences change as the integers subtracted from 15 get smaller. **
 * B. **** Use the patterns you observed to predict the answer to 15- -1. Check your prediction using a number line or a chip board. **



15- -4=19, because subtracting a negative number from a positive is like adding a positive. -10-5=-15 -10-4=-14 -10-3=-13 -10-2=-12 -10-1=-11 -10-0=-10 The pattern is that the bigger the number that is subtracted from -10 the smaller the difference will be.
 * C. **** Predict the answer to 15- -4. Explain your reasoning. **
 * FOLLOW UP **
 * 1. **** Study the equations below. **
 * A. **** Describe any patterns you see in the way the differences change as the integers subtracted for -10 get smaller. **
 * B. **** Use the patterns you observed to predict the answer to -10- -1. Check your answer with a chip board or number line. **

|| Subtract -1 and get -9 ||  ||      <span style="position: absolute; z-index: 30; left: 0px; margin-left: 386px; margin-top: 73px; width: 27px; height: 28px;"> <span style="position: absolute; z-index: 28; left: 0px; margin-left: 316px; margin-top: 67px; width: 27px; height: 28px;"> <span style="position: absolute; z-index: 26; left: 0px; margin-left: 423px; margin-top: 35px; width: 27px; height: 28px;"> <span style="position: absolute; z-index: 25; left: 0px; margin-left: 386px; margin-top: 35px; width: 27px; height: 28px;"> <span style="position: absolute; z-index: 23; left: 0px; margin-left: 311px; margin-top: 30px; width: 27px; height: 28px;"> <span style="position: absolute; z-index: 22; left: 0px; margin-left: 279px; margin-top: 30px; width: 27px; height: 28px;"> -10- -1=-9 Black= +1 Red= -1



-10- -6= -4, because if you subtract a negative from a negative the number increases. No, because subtracting a negative integer is like adding a positive integer.
 * C. **** Predict the answer to -10- -6. Explain your reasoning. **
 * 2. **** When you add 2 negative integers, you get a negative sum. When you subtract 2 negative integers, do you always get a negative difference? Explain. **