**Unit 4 - Desmos Drawing and Function Families**

**How did you go about drawing this image?**

I went into this project knowing exactly what I wanted to create. I started of by drawing my image with a pencil on graph paper then started experimenting with desmos. I knew by looking off my drawing that I needed lots of straight lines and circles so I went for help to learn how to create those. Then I experimented with the other equations that were required and got creative of where they should go.

**How did using Desmos and creating this drawing help you understand function families and their transformations?**

By being engaged in what I was doing I felt as though the equations stuck with me a lot more. Another way using desmos helped was I often needed to be repetitive with the equations so the repetition helped me remember how to create the lines I wanted. I understand Liner better now because I used those often and needed to know the correct equation to place the line exactly where I needed it. Before this I didn't know the equation of making a circle on a graph but after creating a couple I know the equation.

**DP UPDATE DUE 4/10/15**

**Unit 3 Reflection: Area, Volume, Measurement****Q1: What content/skills have been most interesting to you?***Surface area has bee most interesting to me. I find this interesting because I also find it the most beneficial. Surface area is something I thought I knew prior to this unit but was proven wrong when I learned different ways of approaching it. I learned about lateral surface area and the base. I also learned the equation for SA which is SA=2(pi)rh... which is for lateral surface area and +2(pi)r(squared) which is for area of both bases.*

**Q2: How have you grown mathematically?**I definitely feel more confident when faced with shapes. Before I would just count and guess things such as areas. Now I know equations which will be great help in the future.

**Unit 2 Reflection: Shadows, Similarity and Right Triangle Trigonometry**

**Q1: What has been the work you are most proud of in this unit?**I am most proud of my "Pick up triangles" POW. I am most proud of this because I feel like it exhibit its my hard work. It shows my effort because the written portion is done well along with the evidence I provided of how I did my work. I am going to start to try to use this POW as exemplary work on how well I should do on upcoming problems.

**Q2: What skills are you developing in geometry/math?**A skill that I am developing is how to use my calculator. With this world becoming more and more relent on technology everyday I feel learning how to use an advanced calculator is an important skill. I am not very good at working with electronics, understanding the way the calculator works is a big step forward for me.

**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**

Ratios are an important mathematical skill to understand. Ratios are when two statics are compared to one another and see how they stand against each other. Websters defines it as: the quantitative relation between two amounts showing the number of times one value contains or is contained within the other. We often associate construction work with this skill but one job ratios are really important in is food. Being a Chef you will use ratios with every recipe you cook, if you put too much pepper in ratio to how much chicken you have your food will not taste good.

**Problem of the Week Reflection: How have problems of the week helped you grow mathematically? (**

Problems of the week, also known as POWs, have helped me a lot this year. They have helped me learn how to break down problems that I am struggling with. This is helpful not only with POWs but with daily problems as well. It has also helped me learn how to back up my answer and explain ho I got to the solution. This is important because if I get the problem right it helps me understand how to do those types of problems. If I get the problem wrong then I can look back at how I got the answer and see where I went wrong.

## Slices of Pie

## POW 5 Ideal Soda Can

## Tessellation Project

## Final Tessellation Write up

**What is the idea/theme behind your tessellation?**

Throughout the process of creating my tessellation, we had many different ideas of patterns that we wanted to use. We noticed it was fall, and we are both looking forward to winter. We decided because we love winter, to make our project snow based. I ended up coming up with the idea of the snowman. I decided to add the child creating the snowman because it added another challenge that took our thinking one step farther. We decided to color each snowman the same color to keep it visually pleasing. The shape of the snowman worked perfect!

**What polygon(s) did you start with and how did you alter it (what transformations did you use)?**

When we started this project, we started with a simple design. When we started to tessellate our simple design we started to realize the shape didn't fit into each other to create a accurate tessellation. We moved to a snowman. The snowman took three circles and the outline of a boy. We used a square, and transformed the original cut out shape to the other three sides on the square. We used translations to tesselate the shape onto the paper.

**What transformations describe how your pre-image tile moved to create your two image tiles (math overlay)?**

The transformations that described how my pre-image tile moved to create my two image tile was my transformations of my cut out shape to the adjacent side of my square. All four sides of my square were 90 degrees, and my shape was transformed onto all sides creating my final shape I was going to tesselate. When we added our shape onto each side it reflected the previous tessellation witch made our shape fit together. We didn't need to rotate our shape to tesselate it.

**Are tessellations math or art?**

I think tessellations are math. Tessellations have to be very structured and perfected for them to work. Tessellating takes skill and preciseness. There are many math techniques used in doing these pieces like shape and pattern. I think it's important to realize that art is free and un structured. Art is based on creativity. I can see how people think of a tessellation as art because it may include color and shape, but to have a art piece is to have no right or wrong way of doing it.

**Evidence:**

http://mathforum.org/library/drmath/view/52366.html

## Burning Tent Lab

**Snail Trail lab**

**Snail Trail reflection**

When I move point D, every other point I created stays perpendicular to each other and moves in the exact same way/pattern. All the points stay the same distance away from each other even when in motion. While every point moved, the points would reflect each other. To construct the "Snails," I used the "reflect object about line" tool, and this helped me reflect the colored point that I started with clockwise, creating and resulting in more snails. I than hid the points, so that the letters were gone. Only the snails remained. I had to make sure when I dragged Point D, that all the letters reflected each other. I had to select "Trace On" tab, and this helped me create the snail trails. When I dragged Point D, more points would emerge and that's what gave it the trail effect. I noticed at the end, every trail I created was a mirror image of all the other trails. My final and piece was a example of reflectional symmetry and line reflection.