## Unit Four- Desmos Drawing Project With Function Families

- How did you go about drawing this image? (Did you plan? Did you use patterns, reflections of lines? Did you experiment? Did you consult peers/teachers?)

I wanted to do something that I could relate to so that is why I choose to draw the Colorado flag. I tried different shaped until I could get the right one for it to look lie the flag itself. I did need some help from the teacher/s. because I had trouble getting this one shape to look the way it is. - How did using Desmos and creating this drawing help you understand function families and their transformations? (Be sure to touch on at least two specific function families.)

It was really easy to see the relationship between family functions and how they look one a graph, this program really helped me understand that better.

**Here is the link**https://www.desmos.com/calculator/kijz4okidy?create_account

## Unit 3: Area, Volume, Measurement

Reflection:

I found it very interesting to know the volume of the shapes, and how to break it down to why we use those equations for it.

At the beginning of the year I had little to no interest in math, I haven't had the best experiences in past math classes. This year it was a much more inviting environment, I was able to focus more on the lessons.

*Q1: What content/skills have been most interesting to you?*I found it very interesting to know the volume of the shapes, and how to break it down to why we use those equations for it.

*Q2: How have you grown mathematically?*At the beginning of the year I had little to no interest in math, I haven't had the best experiences in past math classes. This year it was a much more inviting environment, I was able to focus more on the lessons.

**Unit 2**

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

**Q1: What has been the work you are most proud of in this unit?**In this unit I am most excited about Toree and I's POW number two which is in the link below. We both put a lot of time into this assignment and I felt like it turned out really good. We were able to dissect this POW very well and we leaned a lot from it.

**Q2: What skills are you developing in geometry/math?**When I first started this class I had very no no little knowlage about how to use a graphing calculator, since the class I have learned a lot about the calculator that I didn't already know how to use. I also developed the ability to problem solve using different strategies for harder problem that I will be using in the future.

**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.**Trigonometry is when you are given the angle of a triangle and either using Cos, Sin, or Tan depending on what angles and sides you were given. It is important to know trigonometry when you are building a house and you need to find the missing side lengths or angle in order to build it.

**Problems of the Week**

**Problem of the Week Reflection:**I felt like all of the Problems of the week had made me grow academically personally because it showed me how how to look at math problems in a different way that would help me solve problems.I will use this skill in other problems like these in the future.

**POW 2 Pick Up Triangles**

Question 1: Once you have a minimal path, what appears to be true about the incoming angle and the outgoing angle?

Answer 1: The angles are approaching the same size.

Question 2: Why is the path from points Camper to TentFire' the shortest path? Briefly explain. (Think about the shortest distance between two points.)

Answer 2: The point Tent is reflected across the line AB to point Tent’, creating a straight line from point Camper to Tent’. When you have a straight line that makes the shortest distance you can have therefore the path from points Camper to Tent’ is the shortest path.

Question 3: Where should the point River be located in relation to segment Camper to TentFire' and line AB so that the sum of the distances is minimized?

Answer 3: Point river should be located on line AB and from where if you draw a line from Camper to Tentfire’.

Answer 1: The angles are approaching the same size.

Question 2: Why is the path from points Camper to TentFire' the shortest path? Briefly explain. (Think about the shortest distance between two points.)

Answer 2: The point Tent is reflected across the line AB to point Tent’, creating a straight line from point Camper to Tent’. When you have a straight line that makes the shortest distance you can have therefore the path from points Camper to Tent’ is the shortest path.

Question 3: Where should the point River be located in relation to segment Camper to TentFire' and line AB so that the sum of the distances is minimized?

Answer 3: Point river should be located on line AB and from where if you draw a line from Camper to Tentfire’.

My theme for my tessellation was cat faces. I chose this theme because I found a very similar idea on Shala Kerrigan’s website. For this tessellation I started with a perfect square, I cut out a triangle out of the bottom of the square and translated the shape up to the top of the square. The next thing I did to my project was measure exactly half way down from the top of the square to the bottom of the square, Then flipping and mirror that line, and turned 180 degrees and match it up with the bottom and middle beads that I marked. For translating the pre-image the image does not rotate so the image only moved up the y-axis by 3 points (or half the image height) and stayed in the same x-axis for the ones in the same row. In my opinion I believe tessellations are definitely math because if you break it down there's a lot of mathematical concepts and explanations. But M. C. Escher used tessellation as more of an art, that is what I did in this project. “Only those who attempt the absurd will achieve the impossible. I think it's in my basement... let me go upstairs and check.”-M. C. Escher

Cited sources

M. C. Escher Quotes (BrainyQuote)

How to graph tessellations in seed beads (- Beadwork)

Cited sources

M. C. Escher Quotes (BrainyQuote)

How to graph tessellations in seed beads (- Beadwork)

## Snail Trail Project

- -The points in the Picture mirrored off of each other creating symmetric design in the picture. I noticed each point in reflected off of an other point, there is three different sections and each one has two points located in each one. If I didn't choose to color the snail’s trails I would still be able to see the reflection in the design it would just be less clear than if it were to be color. The points in the Picture mirrored off of each other creating symmetric design in the picture. I noticed each point in reflected off of an other point, there is three different sections and each one has two points located in each one. If I didn't choose to color the snail’s trails I would still be able to see the reflection in the design it would just be less clear than if it were to be colored.