3.3+Exploring+Patterns+0910

April 18 2010 NA Block: E
 * // Big Idea: Negative //** **//Numbers Help Us To Model Many Real World Situations//**
 * // Essential Question: How Do I Find the Difference Between Integers? //**
 * __Problem 3.3 Exploring Patterns

Studying and describing patterns are an important part of mathematics. 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 As the integers subtracted from 15 get smaller, the answer gets bigger. 15 – -1= 16 Answer: 15 – -1 = 15 + 1, it became into an addition problem since the “-“ in the negative number, and the subtraction sign are the same, they cross each other out, making it turn into a addition problem. Therefore 15 – -4 is same as 15 + 4= 19
 * A. Describe any patterns you observe in the way the 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 by using a chipboard or number line. **
 * B. Predict the answer to 15 – -4. Explain your reasoning **


 * __ Follow Up __**
 * 1. Study the equations below **
 * -10 - 5 =-15 **
 * -10 - 4 =-14 **
 * -10 - 3 =-13 **
 * -10 - 2 =-12 **
 * -10 - 1 =-11 **
 * -10 - 0 =-10 **

The answer gets bigger -9 19, because 15 – -1, is same as 15 + 1, so 15 – -4 =19
 * a. Describe any patterns in the way the differences change as the integers subtracted from -10 get smaller **
 * b. Use the patterns you observed to predict the answer -10 – -1 check your answer with a number line, or chip board. **
 * c. Predict the answer to 15- -4 **

No, if the negative integer on the right has a higher value than the one on the left, the answer is positive but if the negative integer on the right is smaller than the one on the left, the answer is negative.
 * 2. When you add two negative integers, you get a negative sum. When you subtract two negative integers, do you get a negative difference? Explain **