2.2+Inventing+a+New+Model+0910

04/18/10  SH 7E Big Idea: Negative numbers help us to model many real world situations.  Essential Question: How can I add integers? Notes from class: Fractions and decimals are Integers, but whole numbers and 0 are. __2.2 Inventing a New Model: __ RED-¤ = -1 BLACK-° = 1  ¤¤¤¤¤¤¤¤ ||  || ¤¤¤¤¤¤¤ || ¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤ ||   **2. -8+7=** -1 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">¤¤¤¤¤¤¤¤ || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">°°°°°°° || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">¤ || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> **3. 8+-7=**1 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">°°°°°°°° || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">¤¤¤¤¤¤¤ || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">° || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> **4. 8+7=**15 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">°°°°°°°° || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">°°°°°°° || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">°°°°°°°°°°°°°°° || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> **1. -3** <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> || <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">A. Use a chip board and Black and Red chips to find each sum. Draw a series of chip boards to illustrate your work. **
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> 1. -8+-7= **<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">-15
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">B. Find two combinations of black and red chips that will simplify to represent the given integer. Draw a series of chip boards to prove that each combination works. **
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">¤¤¤¤¤ ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">- ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">¤¤ ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">= ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">¤¤¤ ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">¤¤¤ ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">¤¤¤¤¤¤¤ **
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">¤¤¤¤¤¤¤ **
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">¤¤¤¤ ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">¤¤¤ ** ||

<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">1. -3+-4=-5 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">-3+-4=-7 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">2. 3+2=5 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">4+1=5 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">+4 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">-<span style="font-family: arial,helvetica,sans-serif; font-size: 17px; font-weight: normal; line-height: 24px;"> <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">2 - -2 = 0
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">°°°°° ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">°°°°° ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">°° ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">2. 5 **
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">°°° ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">°°° ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">°°° ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">°°°° ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">° ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">°°°°° ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">°°°°° ** ||
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">C. Write each combination you found in part B as an addition sentence **
 * __<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">2.2 Follow Up: __**
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">1. What integer added to -8 gives a sum of -4 **
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">2. Give two integers with a sum of that is less than either of the two integers. **

<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =(9+9)+2 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =0+2 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =2 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =(-80+80)+30 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =0+30 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =30 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =(35+-35+62) <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =0+62 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =62 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =(-8+8)+3 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =0+3 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> =3 <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">4. Use Conrad’s method to compare the following sums in your head. **
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">A. 9+-7= **<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">9+-9+2
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">B. -80+50= **<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">-80+80+30
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">C. 35+-27= **<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> 35+-35+62
 * <span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;">D. -8+-5= **<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 115%;"> -8+8+3