The solution of the Frank and Doris race problem looked to be simple at first. Although Doris speed began faster, Frank gained speed and passed her and thus seemed to be the winner of the race. After looking more closely at the problem I discovered this was not quite the case. I first sketched Frank and Doris given values onto the one Velocity-Time graph. Originally looking at this graph, it looks as if Frank passes Doris at 10 seconds, because that is when his speed becomes greater than Doris’s speed. This was not true. Sure, Frank’s speed was now faster than Doris, but it did not tell me anything about the previous distances they had traveled, so I could not assume that Frank passed Doris at ten seconds. Then I realized it might be beneficial
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I divided the whole time interval into smaller intervals in order to find the area at each five-second interval. I had to separate them in order to find the total distance traveled. The speeds were not constant throughout the race so it made it difficult to complete only one calculation. In order to find out who won the ¼ mile race, I had to add the first interval area to the second intervals area to create different sub-intervals to see who reached 1320 feet first. I needed to know the previous area to compute the distance for a new sub-interval. I used covariation in this sense. AnaMaria and Kevin also used covariation. They reached a point where they knew if there were 23 cans of each flavor, and then they would have a total of 138 cans. From there, if they added one more of each flavor, or six cans to the total they would have 144 cans. If they added six cans two more times they had 156 cans. AnaMaria and Kevin were able to use the previous step to compute their answer. Additionally they knew that if there were six different flavors they could use the function f(x)=6x to calculate how many total cans there were if there were x amount of each flavor. This was beneficial to them because they understood multiplication. AnaMaria and Kevin’s area model they constructed showed how 156 cans could be divided into six different flavors. They did not have to know that the
I divided the whole time interval into smaller intervals in order to find the area at each five-second interval. I had to separate them in order to find the total distance traveled. The speeds were not constant throughout the race so it made it difficult to complete only one calculation. In order to find out who won the ¼ mile race, I had to add the first interval area to the second intervals area to create different sub-intervals to see who reached 1320 feet first. I needed to know the previous area to compute the distance for a new sub-interval. I used covariation in this sense. AnaMaria and Kevin also used covariation. They reached a point where they knew if there were 23 cans of each flavor, and then they would have a total of 138 cans. From there, if they added one more of each flavor, or six cans to the total they would have 144 cans. If they added six cans two more times they had 156 cans. AnaMaria and Kevin were able to use the previous step to compute their answer. Additionally they knew that if there were six different flavors they could use the function f(x)=6x to calculate how many total cans there were if there were x amount of each flavor. This was beneficial to them because they understood multiplication. AnaMaria and Kevin’s area model they constructed showed how 156 cans could be divided into six different flavors. They did not have to know that the