You will need to copy and paste the actual problems into your word processor. Just drag the mouse across the problems to highlight them, right-click on the highlighted text, then move into your word processor and create a new document. Right-click in the document and select Paste.
You will insert your responses into this document, as indicated below. Then you can send the final document either saving it as a Rich Text file and attaching it to your email, or by just cutting and pasting it into your email.
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.
Don't let this exercises prevent you from starting the pulse experiment. However
Answer the following questions and explain in commonsense terms why your answer makes sense.
For each question describe a picture you might draw to make sense out of the situation.
Here is a sample question and the general type of response we are looking for:
Sample question and response
If a bundle of shingles covers 30 square feet, how many bundles are required to cover a 600 square foot roof?
<Response cms00>
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.
<End response>
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 and you will eventually get the 'hang' of it.
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 bad 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.
Here are the questions. Insert your answers between the <Response cms**> and <End response> tags and E-mail questions and answers to me for critique. If you have not already done so copy and paste the text of the questions into your email or word processor, and after reading the directions below give your answers in this file as instructed.
Instructions for answering questions:
Start your answers on the line after the vs. response tag and end them on the line before the 'end response' tag. Don't put anything on a line which contains a tag.
Be sure to E-mail your response as text.
If you insert your response in an E-mail document it will be in text format.
If you attach your response as a file be sure you have saved it as a text file.
Questions 1-9
1. If you earn 52.85493 dollars in 7 hours, at what average rate are you earning money, in dollars per hour?
<Response cms01>
<End response>
2. If you are earning money at the average rate of 54 dollars per hour, how much do you earn in 8 hours?
<Response cms04>
<End response>
3. How long does it take to earn 91.7513 dollars at an average rate of 16 dollars per hour?
<Response cms07>
<End response>
4. If you travel 40.86813 miles in 8 hours, at what average rate are you traveling, in miles per hour?
<Response cms02>
<End response>
5. If you are traveling at an average rate of 48 miles per hour, how far do you travel in 7 hours?
<Response cms05>
<End response>
6. How long does it take to travel 110.2556 miles at an average rate of 16 miles per hour?
<Response cms08>
<End response>
7. If a ball rolling down a grooved track travels 144.1136 centimeters in 10 seconds, at what average rate is the ball moving, in centimeters per second?
<Response cms03>
<End response>
8. If a ball travels at an average rate of 59 centimeters per second, how far does it travel in 8 seconds?
<Response cms06>
<End response>
9. How long does it take a rolling ball to travel 102.5251 centimeters at an average rate of 22 centimeters per second?
<Response cms09>
<End response>