In this project, we explored measurement by starting with one dimension shapes. We started with the pythagorean theorem and this led us to the distance formula. From there we moved into two dimensions. We worked on right triangle trigonometry and the area of polygons and circles. In the end we started learning about volume in all 3 dimensions. A habit of a mathematician I used in this project is looking for patterns because he had to use what we knew to help us with the next topic. For example, we learned how to find distance using the distance formula which we got from the pythagorean theorem. We solved for different sides of triangles using the pythagorean theorem equation: a^2+b^2=C^2. We practiced this equation in the “Working with the Pythagorean Theorem” worksheet.
Using the pythagorean theorem we were able to complete the distance formula worksheet. After we worked with the distance formula, we started working with circles. The equation for circles is x^2+y^2=r^2 Once we practiced the equation for circles, we explored the connection between the points on the x and y axis, the angles and the radial lines. We used the equation of a circle to find points in the x and y axis of a triangle using right triangles. This led us to right angle trigonometry. We learned about sine, cosine and tangent. Sine is the “function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse.” Cosine is a “function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.” The four trigonometry equations we used were opposite/hypotenuse= sine, opposite/adjacent=sin/cos=tan, adjacent/hypotenuse= cosine. When he had this background information, we solved for the area of polygons. We took apart the polygons into triangles and made formulas for the area of these shapes. Using this information we found an equation for the area of a circle. Then we moved onto volume equations. We found the equation for the volume of a cylinder which is area of the base x height. We created yangmas which are three triangles cut from a cube. We knew they were ⅓ of the volume of the cube, we used Cavalieri’s principle to put together the pyramid in the center to find the equation for the volume of the cones and pyramids, which is the area of the base x height x ⅓ .
Design Your Own Project For this project, Monique Luci and I decided to find the area of Disneyland. Not only did we find the area of both parks, we found the area for the hotel, casting center and parking structures. We used the measure distance tool on google maps to find our lengths. We decided to find the area of Disneyland because we wanted to use a place that we have all been to. Finding the area of a place we all love made this project easier to relate to and connect with.
Our success was learning how to use google maps to help us measure the distance. We obviously weren’t able to measure that by ourselves, by using google maps that really helped us with this project. A challenge we faced was figuring out how to push ourselves even further and challenge ourselves. We wanted to find the volume of Luci’s cat but that was too easy. Overall, I liked that we got to use a real life location to practice our skills with area.
Measure Your World Reflection The habit of a mathematician I used the most throughout this project was take apart and put together. I used this in almost all of the topics we learned especially when we were practicing trigonometry. Another habit I used was looking for patterns. Looking for patterns was a good way to connect all of the worksheets together. We needed to relate all of them in order to move on to the next topic. I’ve always struggled with the topics we learned in this project, so I really enjoyed being able to practice all of them. I personally think I grew a lot as a mathematician because I felt challenged throughout this whole project. There was never a moment where I thought what we were working on was “easy”. I think the portfolios helped me stay organized, which is another habit of a mathematician I used. We had a lot of worksheets in this project, and staying organized was important for me in order to keep track of all of the portfolios. In closing, this project made me realize how it takes multiple worksheets of practice for me to be able to understand the topics.