Mathematical Reflection #1

1. What are the common properties of all polygons?

All polygons must be a closed figure. A closed figure is when all the sides are connected, or there is no gap between the edges. The next property is that there are no curved edges, the edges have to be straight lines. If a figure does have curved edges, like a circle, then it is not considered a polygon. The next rule is that there can be no overlap of lines as demonstrated in the pictures below.

2) What does the measures in degrees tell you about an angle?

The measures of degrees tell me how far the angle is from 0 degrees. It also tells me the degrees of rotation an angle. This can be helpful not just when solving a math problem, but also in real life situations. For example, a skateboarder might say that he did a “720.” This means that he jumped and completed two rotations in the air before landing.

3) What are some common benchmark angles?

Some of the common benchmark angles include, 90 degrees (right angle), 180 degrees (straight line), 30 degrees, 60 degrees, and 45 degrees. These angles can help you when you are estimating angles. If the angle is close to one of the benchmark angles, then you can make an reasonable estimate about the angle’s size.

4) What are some strategies used to estimate angle measures?

When I estimate angles, I use the benchmark angles. When I get a clear idea of where 90 degrees is, and the angle is slightly less that 90 degrees, then I might estimate the angle is 85 degrees as shown in the picture below. When you have a clear idea of the benchmark angles, they are very useful and vital to get precise estimates.

5) What strategies can you use to deduce the angle measures from given information?

The first step to solve for angles is to know whether it is a straight, obtuse, acute, or right angle. You will know if an angle is acute because it is less that 90 degrees (right angle), however it is greater than 0 degrees. A right angle is usually indicated with a small square, instead of a curve for indicating the angle. This means that this angle is exactly 90 degrees. An obtuse angle is more than 90 degrees, but less that 180 degrees. I have drawn some examples in the picture below. After you have identified the type of angle, you know what degree range the angle is going to be in. For example, if the angle is acute, then you know the angle is between 0 degrees or 90 degrees.

6) What strategies can you use to find accurate measurements using tools?

Link for Video #1      

Link For Video #2
To prove my estimates right, I use a tool called a protractor. First, you draw your vertex. Form your vertex, draw a straight line. Place the protractor on the line so that you can see the vertex from the hole in the center, your line is lined up with the lines on your protractor. If we were to draw a 20 degree angle, then I would place by pencil/pen under the 20 degree mark and make a tiny mark. Then I can draw the angle by using a ruler and connecting the vertex with the other point which I drew with my protractor. I have attached two video's demonstrating how to use a protractor.

Google Science Fair

Deepika Kurup - Photocatalic approach to purify water

A world changing invention crafted by a mere teenager has the potential to trigger a drastic change in the amount of people affected by drinking impure water. 

Deepika Kurup was inspired to solve the water crisis during her visits to India. She saw some students drinking impure water from a nearby creek. She was troubled and set ambition to change this situation. Her research proves that currently, many countries are using the SODIS process. Clear plastic bottles are filled with contaminated water, and are exposed to the sun for about 8 hours. This disrupts the DNA of any harmful bacteria or germs. This is a very useful, and cost effective method, however consumes a large amount of time.

Recently, photocatalyst, such as titanium dioxide has been used to accelerate the cleaning process. A film of titanium dioxide is added on the inner side of these clear bottles. But even this process has a problem. When exposed to sunlight, this layer of titanium dioxide mixes into the water , thus making this process ineffective.

Deepika has invented a novel way to filter the toxins out of the water using a pervious composite mixture of titanium dioxide and silver. She created seven filters with different amounts of silver. (The last sample was her control sample with no titanium dioxide and silver. She then took these filters and placed methylene blue on top. She discovered that the combination of 3.85 % of titanium dioxide and 0.04 of silver (Ag) is the fastest in changing methylene blue to clear. (Her filter disrupts the harmful chemicals in methylene blue).

In her next experiment, she took sample number four and 7 (control) and passed impure water through both of them. She took the samples and set them in the sun. Her experiment proved that her filter is more effective and less time consuming than the simple photocatalytic and SODIS process.

I believe that Deepika can win the Google Science Fair because she has taken a worldwide crisis, and has come up with an effective, and less time consuming way to solve the problem. Water is a necessary element needed for human survival. For this reason, we need a pure source of it. This method can quench a large amount of people’s thirst and save thousands of lives. It can also prevent people catching diseases by consuming impure water.