1. A description of the Measure Your World Project, including an overview of all the mathematical content it covered. The content started with the Pythagorean Theorem and then went into the distance formula, the equation of a circle, the unit circle, the definition of sine, cosine and tangent, right-triangle trigonometry, area of polygons, area of a circle, and then volumes of many different shapes. For each topic, give the relevant formulas/equations. Be sure to explain how the formulas or equations were derived or proven. For example, don't just mention the equation of a circle with radius r centered at the origin is x^2 + y^2 = r^2, explain how the equation relates to the distance formula.
Pythagorean Theorem:
Distance Formula:
Equation Of A Circle:
Unit Circle:
Definition of sine, cosine, tangent:
Right-triangle trigonometry:
Area Of Polygons:
Area Of A Circle:
Volume Of Different Shapes:
2. Your "Design Your Own Project" Write-Up. This should closely mirror your presentation and have three sections:
A. Project Description: What did you measure and why? - For this project I had a hard time trying to figure out what to measure. At first I was planning on doing something challenging like measuring a baby grand piano or my washing machine but because I was doing this project alone, I knew that I wasn't going to have a lot of time and even though I had all the measurements, it was going to be difficult trying to find the volume. So I ended up not going with none of those and settled with finding the volume of a softball since I have easy access to a softball. Finding the measurements weren't so hard but it wasn't too easy.
B. The Math (show calculations: be very, very neat!). - The pictures are down below. - I used measuring tape to wrap around the ball and then I went online trying to find a softball with the same circumference and I mostly used scratch paper.
C. Brief reflection. - Success: For this project I didn't make a lot of mistakes and had found the correct measurements. I was also able to find another way to find out the Volume since I got stuck trying to do so the first time. -Challenges: Trying decide what to do in a certain amount of time by myself and making sure that I didn't give up. I mean, this was kind of easy compared to everybody else's but this was something that I felt comfortable with. -Changes: I think that I would probably want to do something a little more challenging if I had the chance because finding the measurements of a softball wasn't really my goal but because of how busy our year has been, I've had a hard time trying to come up with something. I would also try and work with people that I don't normally work with.
3. Overall "Measure Your World" Reflection. Be sure to place a heavy emphasis on The Habits of a Mathematician and your learning.