course Mth 163
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14:32:16 `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 --> ok
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14:32:26 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 --> ok
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14:32:51 In your own words briefly summarize the instructions and the intent of this exercise.
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RESPONSE --> The intentions of this exercise is to help yourself describe your visualization and reasoning of the problem.
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14:33:06 `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 --> To get the average rate of dollars per hour of work we need to divide the dollars earned by the hours worked. 50 dollars / 5 hours of work = 10 dollars per hour of work.
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14:33:19 If you travel 300 miles in 6 hours, at what average rate are you traveling, in miles per hour?
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RESPONSE --> Point A to Point B is 300 miles. it takes 6 hours to travel from point a to point b. The average rate of travel is 300 miles / 6 hours of travel time = 50 mile per hour.
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14:33:30 `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 --> From start to end of the track is 40 centimeters. We start rolling the ball at the beginning of the track, it takes 5 seconds to reach the end of the track. The average rate of ball travel is 40 cm / 5 seconds = 8cm/s So for every second the ball travels it travels a distance of 8 cm.
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14:34:28 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 -->
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14:34:43 `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 --> Joe starts a job making 15 dollars per hour. The first day of work he works 6 hours. What Joe makes for that day of work is 15 dollars per hour multiplied by 6 dollars per hour is 90 dollars. Joe made $90 for the 6 hours of work performed.
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14:34:54 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 --> i start traveling in my car at 60 miles per hour. I drive for 9 hours straight. My total distance traveled is 60 mph multiplied by 9 hours of travel is 540 miles traveled.
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14:35:06 `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 --> A ball travels for a total of 3 seconds. Its average rate of speed is 13 cm/s. For the total length it travels is 13cm/s multiplied by 3 seconds is 39 cm.
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14:35:09 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 -->
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14:35:24 `q005. How long does it take to earn 100 dollars at an average rate of 4 dollars per hour?
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RESPONSE --> Joe works for an average rate of 4 dollars per hour. He earned 100 dollars for his work. The total hours work by Joe is 100 dollars divided by 4 dollars per hour is 25 hours. So Joe worked 25 hours and earned 100 dollars.
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14:35:34 How long does it take to travel 500 miles at an average rate of 25 miles per hour?
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RESPONSE --> A car travels 500 miles at a rate of 25 miles per hour. The total time it takes to travel 500 miles is 500 miles divided by 25 miles per hour = 20 hours.
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14:35:44 `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 --> A ball travels a total of 80 cm. It average rate of travel is 16 cm/s. The total time of travel for the ball is 80cm divided by 16cm/s = 5 seconds.
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14:35:46 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 -->
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