## Desmos Drawing Project

## Unit 3: Area, Volume, MEASUREMENT

We learned a lot during this unit. Some of the content was finding area of shapes, finding surface area of solids, and much more but I feel these two things helped me out the most because I have always had trouble in the topic of finding areas. Although now I feel like a pro. During this project we also gained a lot of skills and most of those are visualization from the rubix cube Pow, I also learned how to use a calculator to more of an advanced level. Now I can find the max function of an equation. The last important skill I feel I learned was how to use a chart, table, and graph to find the smallest volume to hold a certain amount of something.

## Problem of the week

Problem of the week helped me grow mathematically by teaching me better skills of teaching myself.

POW Write up

Restated Problem

You are given four rods. The lengths of each rod is; 6 inches, 4 inches, 3 inches, and two inches long. In addition to this, you are given an unlimited amount of whole inch rods, with none exceeding the length of 20 inches (1-20 inches). The objective is to find as many PAIRS of similar triangles as you can, using all four of your original rods as well as two other extra rods. What is the maximum amount of similar pairs of triangles that you can make?

Process

We started by forming as many triangles as we could to form pairs to each of the triangles. We did not really know any formula to make it easier, so we mostly just guessed and checked until we found five pairs of triangles that worked for this problem. To understand this problem the key thing you need to know is when you start a new pair of triangles don’t start the same way you did last time, find new ways to go about the problem. The picture below is our work to find the three triangle above, the way this helped us was we wouldn't have to memorise each number, We never forgot a number because we had everything conveniently right in front of us. One thing we could have done better was organize our work a little more, as you can see it is kinda splattered across the page. Like we said before we tried and looked for a pattern but one never showed up. The biggest geometry principles you need to know for this project are the equation to form a triangle. I know the triangles are similar because they all follow the same equation: a2+b2=c2. If you use that equation and the number work together than the numbers will make a triangle.

Solution

These above are some of the triangles that work! We were able to create five pairs of triangles.

A New Problem

What is true about the sides of similar triangles?

What is the largest triangle you can make?

Do the sizes of the triangles affect the amount and variations of triangles that you can make?

Evaluation

Our reaction to the problem was immediately to partner up. This problem seems to be not worth the time, and doesn't seem to be necessarily educationally worthwhile. What we learned from this POW was how to use the given amount of sticks with the given amount of lengths and form as many similar triangles as possible. We also learned how to work with new people. I am new to the geometry class period 3, and Travis welcomed me with tremendous kindness and we worked well together and collaborated without trouble

POW Write up

Restated Problem

You are given four rods. The lengths of each rod is; 6 inches, 4 inches, 3 inches, and two inches long. In addition to this, you are given an unlimited amount of whole inch rods, with none exceeding the length of 20 inches (1-20 inches). The objective is to find as many PAIRS of similar triangles as you can, using all four of your original rods as well as two other extra rods. What is the maximum amount of similar pairs of triangles that you can make?

Process

We started by forming as many triangles as we could to form pairs to each of the triangles. We did not really know any formula to make it easier, so we mostly just guessed and checked until we found five pairs of triangles that worked for this problem. To understand this problem the key thing you need to know is when you start a new pair of triangles don’t start the same way you did last time, find new ways to go about the problem. The picture below is our work to find the three triangle above, the way this helped us was we wouldn't have to memorise each number, We never forgot a number because we had everything conveniently right in front of us. One thing we could have done better was organize our work a little more, as you can see it is kinda splattered across the page. Like we said before we tried and looked for a pattern but one never showed up. The biggest geometry principles you need to know for this project are the equation to form a triangle. I know the triangles are similar because they all follow the same equation: a2+b2=c2. If you use that equation and the number work together than the numbers will make a triangle.

Solution

These above are some of the triangles that work! We were able to create five pairs of triangles.

A New Problem

What is true about the sides of similar triangles?

What is the largest triangle you can make?

Do the sizes of the triangles affect the amount and variations of triangles that you can make?

Evaluation

Our reaction to the problem was immediately to partner up. This problem seems to be not worth the time, and doesn't seem to be necessarily educationally worthwhile. What we learned from this POW was how to use the given amount of sticks with the given amount of lengths and form as many similar triangles as possible. We also learned how to work with new people. I am new to the geometry class period 3, and Travis welcomed me with tremendous kindness and we worked well together and collaborated without trouble

## Pictures to pow above

## Problem of the week

POW #4

Travis VonTersch

3-13-15

For this Pow we had to first find out the amount of sides on a cubes painted in a certain circumstance, the first cube we had to research was a five centimeter by five centimeter by five centimeter cube. The questions that were asked about this cube was how many smaller cubes have one face painted, how many smaller cubes have two faces painted, how many smaller cubes have three faces painted, how many smaller cubes have four, five, or six faces painted, and the last question for this cube was how many smaller cubes have zero faces painted? Then we had to find a general formula for any size cube to answer these questions.

The process for me coming up with the 5x5x5 was very straightforward. For finding all the cubes with one small cube painted I counted all the inner cubed on one side than multiplied it by all the sides so nine times six equaled fifty four cubes with one small face painted. To find all the small cubes with two faces painted I found a edge and counted the cubes between the corners then multiplied that by the amount of edges on a cube so three times twelve equals thirty six. The way I found three cubes painted was the easiest one because only the corners have three sides painted and there are eight corners therefore there are eight small cubes with three sides painted. For finding the amount of small cubes with four, five, and six sides painted was a teaser because there are non. Although, finding the amount of small cubes with zero was very difficult, the way I did it was count inner amount of cubes on on surface area and multiplied it by three because there are three rows. Therefore there are twenty seven smaller cubes without any sides painted. I had a lot of trouble because I could not find a solid formula for a NxNxN. I mostly just counted and did it all the hard way. I would like to understand this more so I could find a formula for any size cube.

If I were to create a new problem I would use the same question but instead of using a cube I would a circular rubix cube such as the one below the text.

I feel compared to other Pow’s this one did not make me grow as much because we did work on it much in class so I missed a lot of things I could have understand if it was explained to me. I realized through this Pow that I am not a strong self learner, yet. I had a lot of friends help me and I still didn't understand a lot, especially how I found the amount of smaller cubes with zero faces painted.

Travis VonTersch

3-13-15

For this Pow we had to first find out the amount of sides on a cubes painted in a certain circumstance, the first cube we had to research was a five centimeter by five centimeter by five centimeter cube. The questions that were asked about this cube was how many smaller cubes have one face painted, how many smaller cubes have two faces painted, how many smaller cubes have three faces painted, how many smaller cubes have four, five, or six faces painted, and the last question for this cube was how many smaller cubes have zero faces painted? Then we had to find a general formula for any size cube to answer these questions.

The process for me coming up with the 5x5x5 was very straightforward. For finding all the cubes with one small cube painted I counted all the inner cubed on one side than multiplied it by all the sides so nine times six equaled fifty four cubes with one small face painted. To find all the small cubes with two faces painted I found a edge and counted the cubes between the corners then multiplied that by the amount of edges on a cube so three times twelve equals thirty six. The way I found three cubes painted was the easiest one because only the corners have three sides painted and there are eight corners therefore there are eight small cubes with three sides painted. For finding the amount of small cubes with four, five, and six sides painted was a teaser because there are non. Although, finding the amount of small cubes with zero was very difficult, the way I did it was count inner amount of cubes on on surface area and multiplied it by three because there are three rows. Therefore there are twenty seven smaller cubes without any sides painted. I had a lot of trouble because I could not find a solid formula for a NxNxN. I mostly just counted and did it all the hard way. I would like to understand this more so I could find a formula for any size cube.

If I were to create a new problem I would use the same question but instead of using a cube I would a circular rubix cube such as the one below the text.

I feel compared to other Pow’s this one did not make me grow as much because we did work on it much in class so I missed a lot of things I could have understand if it was explained to me. I realized through this Pow that I am not a strong self learner, yet. I had a lot of friends help me and I still didn't understand a lot, especially how I found the amount of smaller cubes with zero faces painted.

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

The work I have been proud of most during this unit is my worksheets. The reason my worksheets have been my most proud work is because they have been most challenging although I found a way to do good on them, finish them and have fun while doing them.

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 always struggled with these topics, I am not sure why but it just never sticks. I finally feel like I am starting to get it though.

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 will choose trigonometry and that is just basically 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 somthing.

The work I have been proud of most during this unit is my worksheets. The reason my worksheets have been my most proud work is because they have been most challenging although I found a way to do good on them, finish them and have fun while doing them.

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 always struggled with these topics, I am not sure why but it just never sticks. I finally feel like I am starting to get it though.

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 will choose trigonometry and that is just basically 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 somthing.

## Tessellation

**Tessellation write-up**

**Travis VonTersch**

There are a lot of ideas and themes my tessellation could mean but the one I wanted it to mean the most is to have peace and quiet alone. The airplane is alone in a field and nothing is around and I like just sitting and listening to music alone relaxing. The noise of the airplane represents music in this tessellation. The reason relaxing alone and listening to music means enough to me to make a art piece on it is because that is what I do most when I am not playing football im usually just listening to music. Also music is super important in my life because before a football game I need to listen to music so I can get pumped up

The polygon I started with was a square and the way I altered it was by cutting a shape out of each side and sliding it to the other. It just happened to turn out to be an airplane.The transformation I used was called Translation. The reason it was Translation was because it translated when I slid it over one space.

There are a lot of ways this could be thought of but I do not think that tessellations are math because it does not really seem like there is a formula and thats a big thing about math is it has a formula. The Reason I think it needs a formula is because for example when you make “art” from points on a graph it still it has math ways to find out where those points are.

## BURNING tent lab

## Burning tent questions:

1) They are the same angle

2) It is the shortest distance because the decimal is for shortest distance is at the smallest number possible.

3) That point river should be where alpha and Beta angles are the same

2) It is the shortest distance because the decimal is for shortest distance is at the smallest number possible.

3) That point river should be where alpha and Beta angles are the same

## Snail Trail Lab

## Snail trail Reflection

By following direction I was able to create “snails” and the reflective plain. What I noticed about the snails and the trails is that they move symmetrical to one another if one moves they all move. The type of symmetry my “Snail Trail” has is called reflective because each trail reflect the same pattern.