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Describe a section of your String Art Project

Questions to use for DESCRIBING your math.
 

Pretend that you are answering these questions for a friend who is as smart as you are, but who hasn't had as many math classes as you have had yet.  Also pretend that this person is looking at your drawings, your Geometer's Sketchpad files, and your String Art Project.

You want to DESCRIBE this work. Be sure to WRITE A LOT OF DETAILS! Do not just answer the questions listed below one by one. Read through all of the questions first, then just start writing. Write several paragraphs for each question.

1. Why did you choose the particular section of your String Art Project that you chose?
Where else on your String Art Project is this design repeated?
How is each repeated section the same? How is the same pattern different in each quadrant or area on your board?

2. Describe the series of straight line segments that make up the section that you chose to copy.
What do you notice about the lengths of the lines?
What patterns do you notice about the lengths of the different segments?
Which segments are shorter? Which are longer?
Explain why you ended up with this pattern.

3. What is slope? Write a definition and say what the formula is for slope.
What do you notice about the slopes of the lines?
How does this concept help you to describe the differences you see between the line segments in the section you chose?

4. What is the y-intercept?
How does this concept help you to describe WHERE the lines are on your board?

5. Explain each term (number, letter, symbols for operation...) of the equation for each line.
What is "m"? What is "b"? Where did you get these numbers on your chart?
Use an example to prove that your equation is correct. Choose any number for x and put that number in the equation. Solve for y, then go back to your "section.gsp" drawing in Sketchpad. Is the coordinate (x,y) that you found in your calculations on the line for that equation?
Explain each step to a reader (e.g. "First you take the opposite of... because.... Then you... The fifth step is to...").
At the end of describing every step, explain how this proves that you have the correct equation for this line.

6. Explain how you put equations into Excel for slope and the y-intercept.

7. Finish by saying what you have been learning. What is new to you? What questions do you have now?

Later you will be asked to describe how you calculated the Standard Form of the equation for a line, and how you used substitution and systems of equations to find the intersections between lines.
 

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