Average Rate of Change
Over the past few weeks the main concept we have been going over is rate. Here is a general definition for reate: A quantity measured with respect to another measured quantity. Whether that's rate in the form of speed or whether the rate of population growth. We have broken this concept down to speed and population growth.
For population growth, looked at the rate at which the world and California was growing during different times in history. We had graphs to look at and make observations around. For some activities dealing with population growth, we saw populations between two different years for example the years 1650 and 1900. We had to figure out if each year grew the same amount what was the average rate. The general equation for rate is the change in distance over the change in time. The same equation applies here except that our variables are different. In stead of distance and time we have population and year. Replace distance for population and time for year. This would give us the rate between the two years 1650 and 1900.
In other similar activities with population growth, we had two graphs to observe. It showed the rate of growth of a town during different times over the course of a few years. One had a higher curve than the other, so naturally we assumed that it grew faster. That was not the case when we found the rate. The axis of the graphs showing the integers for the year and population we not the same as each other. For one graph, it showed the population growth in consecutive years and the other graph grows evenly consecutive. We used the general equation for rate: change in population/ change in year. Once we found this for each graph, we compared the rate. The graph we the "lower" curve had the higher rate, opposite of our assumptions.
Another rate we went over was the rate for speed. The problem we went over was at a height of 400 feet, what is the speed at each second? There were other question involved, but that was the main idea that we were looking at. We used a different equation from before. The problem gave us a different equation: h(t) = 400 - 16t2. In this we were using functions where the h was height and t was time. I tried many different approaches to figuring out the rate at each second. I tried plugging in a variable to h, but that didn't worked. I tried working with my group members but we didn't do it correctly. When I worked on an equation with my table mate, we plugged in variables for t, not h which worked. We got that it would reach the ground at 25 seconds which wasn't true. I figured out that it dropped at a constant speed of 16 ft/sec which also wasn't true. When we went over it as a class, we worked out a chart for height per second and that it took 5 seconds to fall. We found that the rate increases as it falls and gets closer to the ground.
Reflection:
I feel that I used a habit of a Mathematician that I don't actually use too often, in one of these recent activities. THat is the habit of Collaborate and Listen. I usually go my own way and try to figure things out myself. I am very stubborn. For one of the activities I started going my own way but realized that it wasn't going to work. I was then more open to hearing from one of my a table mate of mine. We worked together and still got wrong answers and didn't approach the problems correctly. Then some of my classmates explained their methods to the whole class and got the correct answers. Here to I was open to answers, right answers. I honestly think that I had to let my pride down, at least some and be willing to be wrong and hear from others.
I think that I have participated very well. Sometimes I feel that I am one of the few who do. I not only am diligent in my own work, but I help others too. I also ask questions which is also a part of participating. Many times my table mates or others will come to me for questions and I willingly help them with what they need. I don;t get easily distracted and stay focused on my work and the task ahead of me. I believe that I could improve though. I think that I ma doing very well in class, grade wise and participation wise, so for me I think I can work on attitude. A lot of times I don't enjoy math, it can be a struggle or I just don't like it. I still need to be respectful towards it though and I'm not saying that I'm not. However, many times I find math somewhat boring and not that engaging and can have a negative out look or attitude on it. I need to be considerate and respectful as well as positive about it. For me math can be boring because I may not be challenged, but others might be challenged and I should respect that.
For population growth, looked at the rate at which the world and California was growing during different times in history. We had graphs to look at and make observations around. For some activities dealing with population growth, we saw populations between two different years for example the years 1650 and 1900. We had to figure out if each year grew the same amount what was the average rate. The general equation for rate is the change in distance over the change in time. The same equation applies here except that our variables are different. In stead of distance and time we have population and year. Replace distance for population and time for year. This would give us the rate between the two years 1650 and 1900.
In other similar activities with population growth, we had two graphs to observe. It showed the rate of growth of a town during different times over the course of a few years. One had a higher curve than the other, so naturally we assumed that it grew faster. That was not the case when we found the rate. The axis of the graphs showing the integers for the year and population we not the same as each other. For one graph, it showed the population growth in consecutive years and the other graph grows evenly consecutive. We used the general equation for rate: change in population/ change in year. Once we found this for each graph, we compared the rate. The graph we the "lower" curve had the higher rate, opposite of our assumptions.
Another rate we went over was the rate for speed. The problem we went over was at a height of 400 feet, what is the speed at each second? There were other question involved, but that was the main idea that we were looking at. We used a different equation from before. The problem gave us a different equation: h(t) = 400 - 16t2. In this we were using functions where the h was height and t was time. I tried many different approaches to figuring out the rate at each second. I tried plugging in a variable to h, but that didn't worked. I tried working with my group members but we didn't do it correctly. When I worked on an equation with my table mate, we plugged in variables for t, not h which worked. We got that it would reach the ground at 25 seconds which wasn't true. I figured out that it dropped at a constant speed of 16 ft/sec which also wasn't true. When we went over it as a class, we worked out a chart for height per second and that it took 5 seconds to fall. We found that the rate increases as it falls and gets closer to the ground.
Reflection:
I feel that I used a habit of a Mathematician that I don't actually use too often, in one of these recent activities. THat is the habit of Collaborate and Listen. I usually go my own way and try to figure things out myself. I am very stubborn. For one of the activities I started going my own way but realized that it wasn't going to work. I was then more open to hearing from one of my a table mate of mine. We worked together and still got wrong answers and didn't approach the problems correctly. Then some of my classmates explained their methods to the whole class and got the correct answers. Here to I was open to answers, right answers. I honestly think that I had to let my pride down, at least some and be willing to be wrong and hear from others.
I think that I have participated very well. Sometimes I feel that I am one of the few who do. I not only am diligent in my own work, but I help others too. I also ask questions which is also a part of participating. Many times my table mates or others will come to me for questions and I willingly help them with what they need. I don;t get easily distracted and stay focused on my work and the task ahead of me. I believe that I could improve though. I think that I ma doing very well in class, grade wise and participation wise, so for me I think I can work on attitude. A lot of times I don't enjoy math, it can be a struggle or I just don't like it. I still need to be respectful towards it though and I'm not saying that I'm not. However, many times I find math somewhat boring and not that engaging and can have a negative out look or attitude on it. I need to be considerate and respectful as well as positive about it. For me math can be boring because I may not be challenged, but others might be challenged and I should respect that.