We started this unit with the HTHCV Flagpole problem. Our goal was to find out the measurement of our flagpole by using different methods. We started off by simply guessing how tall we thought it would be, before taking any measurements. We then tried estimating using the shadow method. After that, we made another estimation using the mirror method. The last method we tried was the isosceles method.
Process & Solution:
The Isosceles Method
My initial guess was 45 feet for the flagpole. We launched off this problem by simply going outside and taking a look at the flagpole as a whole class. Similarity means two shapes have the same shape or equal angles but do not share the same length sides.
The Shadow Method:
To start this method, we needed to collect some data like our average group members height and our average group member shadow length. To get the average we needed to add the collected data and divide it by the number of people we collected it from. We also needed to get the shadow length of the flagpole which was 29 ft. Now all we have to do is draw it out!
An Isosceles triangle has two equal sides and angles and all the interior angle must always have to add up to 180. For this method we needed to go outside, with a partner. One of us was the "pointer" and the other person is the measurer. The pointer had to stand on point C and had to point up towards the top of the flagpole. The measurer had a protractor and used it to make sure there partner was doing a 45 degree angle. Then we measured the flagpole to the pointer. My group got 460 inches, and since an isosceles triangle has two equal sides, the height of the flagpole is 460 inches or 38 feet. To get 38 feet all we did is divide 460 with 12 and rounded up.
The Mirror Method:
For the mirror method we needed a partner to stand in front of the flagpole, in between the flagpole and the person the other partner is going to place a mirror. The person standing needs to make sure they can see the top of the flagpole reflecting on the mirror. Their partner would measure the distance between the person and the mirror, as well as the distance between the mirror and the flagpole. Some of the data my group got shows the height of my classmate (64"), distance between the person and the mirror (14"), and the distance between the mirror and the object (95"). Now all we have to do is draw it out with the data we got. We also placed the numbers that correspond across from each other, and solved for x.
Problem Evaluation:
This problem was fun and interesting because it was more interactive than our usual math problems. I think within one problem we were able to learn multiple math skills like similarity and algebra. Something that furthered my thinking was understanding when to bring in and apply certain formulas that weren't always present in other problems. One of those formulas being the quadratic formula (x=−b±√b2−4ac/2a). With the help of my teachers and peers I was then able to understand more clearly how and when to apply this formula when working with similarity.
Self-Evaluation
I would give myself an A because although I missed a couple of days of school, I was able to get back on track and finish my work on time. I was not as productive as I could've been on a couple of days which is why I would take off a few points. I would also reduce my grade because I did not get an amazing test score. I did ,though, finish all my star problems and was able to understand all of them clearly. I definitely understand this subject way more than I did at the beginning, but like anything else, I also know that there are things I can work on to develop my understanding even more.