course Phy121
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12:10:49 `q001. It will be very important in this course for your instructor to see and understand the process of visualization and reasoning you use when you solve problems. This exercise is designed to give you a first experience with these ideas, and your instructor a first look at your work. Answer the following questions and explain in commonsense terms why your answer makes sense.
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RESPONSE --> okay
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12:12:26 For each question draw a picture to make sense out of the situation, and include a description of the picture. Samples Sample question and response Question: If a bundle of shingles covers 30 square feet, how many bundles are required to cover a 600 square foot roof? Response: We might draw a picture of a rectangle representing the area, dividing the rectangle into a number of smaller rectangles each representing the area covered by a single bundle. This makes it clear that we are dividing the roof area into 1-bundle areas, and makes it clear why we are going to have to divide. Reasoning this problem out in words, we can say that a single bundle would cover 30 square feet. Two bundles would cover 60 square feet. Three bundles would cover 90 square feet. We could continue in this manner until we reach 600 square feet. However, this would be cumbersome. It is more efficient to use the ideas of multiplication and division. We imagine grouping the 600 square feet into 30 square foot patches. There will be 600 / 30 patches and each will require exactly one bundle. We therefore require 600 / 30 bundles = 20 bundles. {}Your responses might not be as clear as the above, though they might be even more clear. I won't be looking for perfection, though I wouldn't object to it, but for a first effort at visualizing a situation and communicating a reasoning process. This is not something you are used to doing and it might take a few attempts before you can achieve good results, but you will get better every time you try. {}You might be unsure of what to do on a specific question. In such a case specific questions and expressions of confusion are also acceptable responses. Such a response must include your attempts to come up with a picture and reason out an explanation. For example your response might be Sample expression of confusion: I've drawn a picture of a pile of bundles and a roof but I'm not sure how to connect the two. I tried multiplying the number of bundles by the square feet of the roof but I got 18,000, and I know it won't take 18,000 bundles to cover the roof. How do you put the area covered by a bundle together with the roof area to get the number of bundles required? A poor response would be something like 'I don't know how to do #17'. This response reveals nothing of your attempt to understand the question and the situation. Nor does it ask a specific question. Incidentally, you might be tempted to quote rules or formulas about rates and velocities in answering these questions. Don't. This exercise isn't about being able to memorize rules and quote them. It is about expanding your ability to visualize, reason and communicate.
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RESPONSE --> okay
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12:13:30 In your own words briefly summarize the instructions and the intent of this exercise.
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RESPONSE --> This is intended to demonstrate my ability to effectively communicate thought processes associated with problem solving.
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12:14:59 `q001. If you earn 50 dollars in 5 hours, at what average rate are you earning money, in dollars per hour?
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RESPONSE --> I earned 50 total dollars by working 5 hours. 50 dollars divided by 5 hours will give me the dollars per hour which is $10.
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12:16:14 If you travel 300 miles in 6 hours, at what average rate are you traveling, in miles per hour?
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RESPONSE --> I will divide 300 miles by 6 hours to get my average rate I am traveling in miles per hour which would be 50 mph.
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12:17:52 `q002. If a ball rolling down a grooved track travels 40 centimeters in 5 seconds, at what average rate is the ball moving, in centimeters per second?
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RESPONSE --> I would take 40 cm and divide it by 5 sec to get the cm per sec the ball is traveling. It will be 8 cm per second.
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12:18:55 The preceding three questions illustrate the concept of a rate. In each case, to find the rate we divided the change in some quantity (the number of dollars or the distance, in these examples) by the time required for the change (the number of hours or seconds, in these examples). Explain in your own words what is meant by the idea of a rate.
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RESPONSE --> Rate is an expression of a relationship between two variables.
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12:20:54 `q003. If you are earning money at the average rate of 15 dollars per hour, how much do you earn in 6 hours?
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RESPONSE --> I would simply multiply the dollars per hour by the number of hours I was working to get the amount of money I earned in the time given. $15 per hour * 6 hours worked = $90 earned
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12:22:24 If you are traveling at an average rate of 60 miles per hour, how far do you travel in 9 hours?
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RESPONSE --> You take your average rate of 60 mph and multiply that by the number of hours traveled, which is 9. 60 mph * 9 hours = 540 total miles traveled
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12:23:46 `q004. If a ball travels at and average rate of 13 centimeters per second, how far does it travel in 3 seconds?
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RESPONSE --> You take your average rate of 13 cm/sec and multiply that by the total time of 3 seconds to get the total distance traveled. 13 cm/sec * 3 seconds = 39 centimeters traveled.
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12:27:29 In the preceding three exercises you turned the concept of a rate around. You were given the rate and the change in the clock time, and you calculated the change in the quantity. Explain in your own words how this increases your understanding of the concept of a rate.
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RESPONSE --> It allows me to practice and use the steps for finding rates. By allowing me to calculate a number by using a rate, it increases my understanding of how rates are used.
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12:29:29 `q005. How long does it take to earn 100 dollars at an average rate of 4 dollars per hour?
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RESPONSE --> You take the $100 (which is your total income goal) and divide that by your rate of earning of 4 dollars per hour. By doing this, you get $100/$4 per hour to give you 25 hours needed to reach your $100 mark.
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12:31:15 How long does it take to travel 500 miles at an average rate of 25 miles per hour?
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RESPONSE --> You take 500 miles (which is your total travel distance) and divide that by your rate of travel of 25 mph to give you 20 hours of travel time.
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12:32:43 `q006. How long does it take a rolling ball to travel 80 centimeters at an average rate of 16 centimeters per second?
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RESPONSE --> You take your total distance of 80 cm and divide that by your average rate of travel of 16 cm per second to give you 5 seconds of roll time.
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12:34:26 In the preceding three exercises you again expanded your concept of the idea of a rate. Explain how these problems illustrate the concept of a rate.
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RESPONSE --> They give me practice at using rates and how to calculate various rates.
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