## Unit 4- Desmos Drawing Project with Function Families

Link to Graph- https://www.desmos.com/calculator/yzkdb4ooir

Unit 3: Area, Volume, Measurement

Reflection:

Reflection:

- The skills and content that have been most interesting to me are visualization and volume. Visualization is interesting to me because it helps me apply math to the real world. I am a visual learner so when visualization is used in teaching I am able to grasp concepts better. Volume has been interesting to me because I was able to better understand this part of the content. It has had a great benefit when having to apply it to my work.
- This content has helped me grow mathematically by giving me more tools to apply to my work. When doing work it has really helped me when I know how to find volume and visualize the problem in a way that I can understand.

## Unit 2 Reflection

Q1: What has been the work you are most proud of in this unit?

Though I am proud of most of my work in geometry, my best work has been on the topic of similarity. Similarity has been a large part of the unit and is something I focused on. I felt that this was a topic I easily grasped and understood which helped me when applying it to my work.

Q2: What skills are you developing in geometry/math?

The skills that I am developing in geometry/math are working with fractions and finding area. I have had issues in the past with these topics, but am just now starting to better understand them. In fact, area is actually becoming a strength of mine.

Q3: Choose one topic: similarity (ratios) or trigonometry. Explain what it is. Provide an example of how it is used in mathematics to solve problems. State an application of the topic in the adult world that interests you.

The topic I choose is trigonometry and that is because it is similar to a ratio. A way we use this in math is finding the height of a triangle to then find the area of such triangle. The reason this interests me in the real world is how people can use this to find the area of a triangle on your house, probably your roof angles or something.

Though I am proud of most of my work in geometry, my best work has been on the topic of similarity. Similarity has been a large part of the unit and is something I focused on. I felt that this was a topic I easily grasped and understood which helped me when applying it to my work.

Q2: What skills are you developing in geometry/math?

The skills that I am developing in geometry/math are working with fractions and finding area. I have had issues in the past with these topics, but am just now starting to better understand them. In fact, area is actually becoming a strength of mine.

Q3: Choose one topic: similarity (ratios) or trigonometry. Explain what it is. Provide an example of how it is used in mathematics to solve problems. State an application of the topic in the adult world that interests you.

The topic I choose is trigonometry and that is because it is similar to a ratio. A way we use this in math is finding the height of a triangle to then find the area of such triangle. The reason this interests me in the real world is how people can use this to find the area of a triangle on your house, probably your roof angles or something.

Perrin Kileen

Geometry

C.Kneller 5

POW #4

Problem Statement: For this POW we are given a cube similar to a rubiks cube. The cube’s dimensions are 5 by 5 by 5 centimeters with the cubes that make up the larger cube measuring 1 by 1 by 1 centimeters. Someone painted six of the cubes faces or the six smaller cubes, determine how many of the smaller cubes have one face painted? Two faces painted? Three? All the way up to six faces and now how many of the cubes have zero faces painted? After finding the numerical answers, see if you can find a recurring N by N by N pattern.

Process:

For this POW I started with drawing a 5 by 5 by 5 cube. I then took this cube and broke the problem down. After drawing out the cube, I shaded the 1 by 1 by 1 cubes according to how many faces were painted. I left the small cubes with one face painted black, lightly shaded the cubes with two faces painted, and shaded the cubes with three faces painted dark. There was no cubes with 4, 5, or 6 faces painted. After shading the cubes I did some basic math: There were nine cubes with one face painted and I knew that there are six sides to a cube. I then multiplied six and nine finding that there was 54 cubes with one side painted. I repeated these steps for cubes with 2 and 3 sides painted. I found 36 cubes with two sides painted and 8 cubes with three sides painted. I was not able to find a recurring equation.

New Problem:

You are given a rectangular prism with the dimensions of 5 by 5 by 10 centimeters. Making up the prism are smaller cubes measuring 1 by 1 by 1 centimeters. Half of each side is painted. Find the number of smaller cubes with 1 side painted. Now how many have 2 sides painted? 3? 4? 5? 6? Is there a pattern or equation you can find to obtain the correct answers.

Evaluation:

This POW taught me some very important mathematical skills like basic problem solving and breaking how to break problems down. This skill is one that is used everyday, we constantly break situations down to better understand the possible outcomes, I found this to be a very valuable everyday connection. My only issue that I had was that my supposed partner (Corry) left me to do all the work, which pushed the time constraint I had. I do not believe we are partners anymore and he didn’t contribute to the work. Overall, I think that I deserve a decent grade. (23/25) This is because while I was not able to find the N by N by N equation, I did my best and gave this POW my best effort.

Geometry

C.Kneller 5

POW #4

Problem Statement: For this POW we are given a cube similar to a rubiks cube. The cube’s dimensions are 5 by 5 by 5 centimeters with the cubes that make up the larger cube measuring 1 by 1 by 1 centimeters. Someone painted six of the cubes faces or the six smaller cubes, determine how many of the smaller cubes have one face painted? Two faces painted? Three? All the way up to six faces and now how many of the cubes have zero faces painted? After finding the numerical answers, see if you can find a recurring N by N by N pattern.

Process:

For this POW I started with drawing a 5 by 5 by 5 cube. I then took this cube and broke the problem down. After drawing out the cube, I shaded the 1 by 1 by 1 cubes according to how many faces were painted. I left the small cubes with one face painted black, lightly shaded the cubes with two faces painted, and shaded the cubes with three faces painted dark. There was no cubes with 4, 5, or 6 faces painted. After shading the cubes I did some basic math: There were nine cubes with one face painted and I knew that there are six sides to a cube. I then multiplied six and nine finding that there was 54 cubes with one side painted. I repeated these steps for cubes with 2 and 3 sides painted. I found 36 cubes with two sides painted and 8 cubes with three sides painted. I was not able to find a recurring equation.

New Problem:

You are given a rectangular prism with the dimensions of 5 by 5 by 10 centimeters. Making up the prism are smaller cubes measuring 1 by 1 by 1 centimeters. Half of each side is painted. Find the number of smaller cubes with 1 side painted. Now how many have 2 sides painted? 3? 4? 5? 6? Is there a pattern or equation you can find to obtain the correct answers.

Evaluation:

This POW taught me some very important mathematical skills like basic problem solving and breaking how to break problems down. This skill is one that is used everyday, we constantly break situations down to better understand the possible outcomes, I found this to be a very valuable everyday connection. My only issue that I had was that my supposed partner (Corry) left me to do all the work, which pushed the time constraint I had. I do not believe we are partners anymore and he didn’t contribute to the work. Overall, I think that I deserve a decent grade. (23/25) This is because while I was not able to find the N by N by N equation, I did my best and gave this POW my best effort.

Perrin Kileen

4/8/15

Geometry

POW #5

Problem Statement:

For this POW our objective was to find the radius and height of a soda can that holds 12 ounces of soda and has a volume of 355 milliliters. We need to do this by finding the soda can that uses the least amount of aluminum but still holds the same amount as a 12 ounce soda can.

Process:

The first thing that I did was that we made a table for all of our data. I then found out through help of another student that to find the SA we needed to find the radius and the height. I was then given the equation for finding the height and used it for a series of numbers in the table. After I had the different radiuses and heights, I used the equation to find the surface area. I did a number of different heights and found that it would be a number between 3 and 4. So I did more numbers in the table and found that the radius would be 3.9.

Solution:

Based on the table we found that the radius was 3.9 the height 7.825 and the SA of the can.

Questioning the result:

The answer that I found does not fit a soda can. I believe that this is because the makers need to make a can that is also aesthetically pleasing so that they make more money.

Evaluation:

This POW made me think how sometimes I make problems harder than they need to be and things like graphs can help me figure out solutions. Overall This POW was fairly simple, it just required some trial and error by finding the perfect radius and height of the soda can.

4/8/15

Geometry

POW #5

Problem Statement:

For this POW our objective was to find the radius and height of a soda can that holds 12 ounces of soda and has a volume of 355 milliliters. We need to do this by finding the soda can that uses the least amount of aluminum but still holds the same amount as a 12 ounce soda can.

Process:

The first thing that I did was that we made a table for all of our data. I then found out through help of another student that to find the SA we needed to find the radius and the height. I was then given the equation for finding the height and used it for a series of numbers in the table. After I had the different radiuses and heights, I used the equation to find the surface area. I did a number of different heights and found that it would be a number between 3 and 4. So I did more numbers in the table and found that the radius would be 3.9.

Solution:

Based on the table we found that the radius was 3.9 the height 7.825 and the SA of the can.

Questioning the result:

The answer that I found does not fit a soda can. I believe that this is because the makers need to make a can that is also aesthetically pleasing so that they make more money.

Evaluation:

This POW made me think how sometimes I make problems harder than they need to be and things like graphs can help me figure out solutions. Overall This POW was fairly simple, it just required some trial and error by finding the perfect radius and height of the soda can.

POW Reflection

I personally enjoyed the POWs, even though they could be difficult. Through doing these I learned how to problem solve on different levels and it has improved my critical thinking. It has also developed my skill of breaking problems down. POWs could be very overwhelming and sometimes it would be hard to find a starting place. I found that taking a small part of the problem and going from there was the best method to use. Although POWs don’t always directly relate to what we’re learning, they will serve me in the future when problem solving.

I personally enjoyed the POWs, even though they could be difficult. Through doing these I learned how to problem solve on different levels and it has improved my critical thinking. It has also developed my skill of breaking problems down. POWs could be very overwhelming and sometimes it would be hard to find a starting place. I found that taking a small part of the problem and going from there was the best method to use. Although POWs don’t always directly relate to what we’re learning, they will serve me in the future when problem solving.