3.2+Pouring+Water+0910

PM 9/7/09 Block F  Problem 3.2 and Follow Up

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**BIG IDEA** : Many real world situations can be modeled and predicted using mathematics. ======

INV 3 Essential Question: How can I model a non-linear relationship?

 * A. ****If you started the experiment with 32 ounces of water in glass 1, how much water would be in each glass when you were done pouring? Arrange these data into a table. Describe the relationship between the glass number and the amount of water in the glass. **

As the glass number increases the amount of water decreases, every time you pour water from one glass to the next it’s like dividing the previous amount of water by 2 
 * B. ****Make a graph of the data, and draw a straight line or curve to model the trend. **

  <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">As the x value increases the y value decreases and the data points are connected by a curve. <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Every time you would pour water into a new glass it would keep getting split in half and it would start to approach 0, but won’t quite get there. <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Yes, it makes sense because the data perfectly fits into the curve made on my graph earlier. <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">It’s similar to the graphs from investigation 2, because they were also showing non-linear relationships and had curves, but the ones in investigation 1 were showing linear relationships and had straight lines. <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Eventually it would get really hard to split the water in half and would almost get to 0 ounces, but it won’t exactly reach 0.
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">C.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Describe the pattern you see in the graph. **
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">D.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">If you continued to add glasses and pour half the water from the last glass into the new glass, how much water would be in glass 20? **
 * __<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">FOLLOW UP __**
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">1.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Does it make sense to connect the data points on you graph? Why or why not? **
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">2.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Compare the graph you made in this problem with the other graphs you made in this unit. Describe how it is similar to and different from the other graphs. **
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">3.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> ****<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">If you continued to add glasses and pour half the water from the last glass into the next one, would you ever run out of water? **

<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">