Desmos Drawing Project
- How did you go about drawing this image? (Did you plan? Did you use patterns, reflections of curves? Did you experiment? Did you consult with peers/teacher?) I went about drawing this image by looking for something that would be simple and easy to draw but also something that when it is finished that people would see what the drawing is. I wanted to draw a simple background and use the colors efficiently to make the drawing as accurate as possible. When I picked a background I thought of creating a meadow for cows right away. When I realized there was no white color and also that I couldn't figure out how to draw a cow my idea switched to a bear, then pig. I experimented with the shapes and sizes of the the animal. When I was creating my drawing I showed several of my friends my progress and laughed with them about the way my funny animal looked.
- How did using Desmos and creating this drawing help you understand function families and their transformations? (Be specific and discuss two types of functions and what you learned about them - for example, discuss how you understand linear and quadratic functions.) Understanding these functions while creating the desmos drawing was actually simple. Using these 6 equations helped me to understand how they all worked together and I learned how the entire line of shape will change based on the inputs of different numbers. I did have a little challenge when shapes or lines changed over any of the axises making the equation positive or negative. While working with linear functions I learned how to shift the curve up by increasing B in the y-intercept and to shift down by decreasing the y-intercept. With the cubic function I learned how to shift the equation left by making H negative and to shift the function right I made H positive.
Unit 3 Reflection: Area, Volume and Measurement
Q1: What content/skills have been the most interesting to you?
The content that has been the most interesting to me is learning more about volume. I have area and measurement down really well and this unit has helped me to practice my understanding of area and measurement. I got to expand my understanding and learn more about volume and I got the chance to understand volume as well and I understand area and I began to think about shapes in a different way. This has been the most interesting to me in this unit because it was hands on and fun and I really enjoyed practicing using different equations.
Q2: How have you grown mathematically?
I have grown mathematically in this unit by learning how to work with multiple equations at a time. It has also helped me to learn how to take apart shapes and piece them together to find a total volume. I have grown a lot in this unit and I have learned a lot of new skills to help me through the rest of the year and into further mathematic classes.
The content that has been the most interesting to me is learning more about volume. I have area and measurement down really well and this unit has helped me to practice my understanding of area and measurement. I got to expand my understanding and learn more about volume and I got the chance to understand volume as well and I understand area and I began to think about shapes in a different way. This has been the most interesting to me in this unit because it was hands on and fun and I really enjoyed practicing using different equations.
Q2: How have you grown mathematically?
I have grown mathematically in this unit by learning how to work with multiple equations at a time. It has also helped me to learn how to take apart shapes and piece them together to find a total volume. I have grown a lot in this unit and I have learned a lot of new skills to help me through the rest of the year and into further mathematic classes.
Unit 2 Reflection: Shadows, Similarity and Right Triangle Trigonometry
Q1: What has been the work you are most proud of in this unit?
The work that I am most proud of in this unit is my work on the POWs. I feel that POWs in math are my strong suit. I have gained so much knowledge throughout solving each individual POW and I think that this is one of the best ways that I express my work and knowledge. I am most proud of the Problem of the Week problems because it is the work in geometry that keeps me the most engaged and helps me to think outside the box and even work physically with objects that I wouldn’t be as engaged with or be able to use if it were just a worksheet.
Q2: What skills are you developing in geometry/math?
Some of the skills that I am developing in math is learning how to work through problems from start to finish like I am in the Problem of the Week. I am learning how to write out my work and explain what I did step by step to solve it in an incredibly detailed write up which could help some one who never worked with the POW to understand what it was and how I solved it. I also have developed the skill of solving trigonometry. 9th grade year I began an intro to trig and it was incredibly frustrating and confusing so we did not make much process throughout that. This year I expanded my knowledge with trig and I am now able to solve for tan, sin, and cos.
Q3: Explain what similarity 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.
Similarity is the correspondence or aspects of a shape. An example of this is when two triangles share all of the same angles making them corresponding this also works with sides. This is used in mathematics to solve problems when you are looking for missing angles and the two triangles share two identical sides or measures. In the adult world an application that I am interested in that relates to this topic is engineering. I am interested in this because it is such an incredible work force and it involves so much math.
The work that I am most proud of in this unit is my work on the POWs. I feel that POWs in math are my strong suit. I have gained so much knowledge throughout solving each individual POW and I think that this is one of the best ways that I express my work and knowledge. I am most proud of the Problem of the Week problems because it is the work in geometry that keeps me the most engaged and helps me to think outside the box and even work physically with objects that I wouldn’t be as engaged with or be able to use if it were just a worksheet.
Q2: What skills are you developing in geometry/math?
Some of the skills that I am developing in math is learning how to work through problems from start to finish like I am in the Problem of the Week. I am learning how to write out my work and explain what I did step by step to solve it in an incredibly detailed write up which could help some one who never worked with the POW to understand what it was and how I solved it. I also have developed the skill of solving trigonometry. 9th grade year I began an intro to trig and it was incredibly frustrating and confusing so we did not make much process throughout that. This year I expanded my knowledge with trig and I am now able to solve for tan, sin, and cos.
Q3: Explain what similarity 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.
Similarity is the correspondence or aspects of a shape. An example of this is when two triangles share all of the same angles making them corresponding this also works with sides. This is used in mathematics to solve problems when you are looking for missing angles and the two triangles share two identical sides or measures. In the adult world an application that I am interested in that relates to this topic is engineering. I am interested in this because it is such an incredible work force and it involves so much math.
Problems of the Week
POWs have helped me grow mathematically by teaching me to think outside of the box and test every scenario for a problem to get the most accurate answer possible. I have grown a lot in math by doing POWs weekly and learning about real life issues or problems that can be solved in our math class. POWs are also teaching me how to work together with other students and how to work independently and challenge myself with new math skills and techniques. I am being taught how to manage my time and put effort into my work. Overall I think that POWs have been very beneficial and taught me a lot this year.
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Tessellation Project
How I created my template:
The tessellation that I created is a seahorse that perfectly fits into every other seahorse. The theme that I came up with for my tessellation is under the sea. I wanted to create a tessellation showing off the underwater world. I didn't know how to come up with an underwater design and after several attempts that seemed to fail I decided to look up ideas for an underwater tessellation. I saw the idea of the seahorse and loved the idea. I followed an online template of how to create my underwater themed seahorse template.
To make my template I first made a rectangle where all the angles are all even and both pairs of reflective sides are equal in length. Then I finished following the guide on the internet by drawing a spiral for the tail making sure that the same spiral can be rotated and fit perfectly. The I drew the stomach caving into the neck then chin. I drew it so that the arch of the stomach can fit exactly where the head of the seahorse indents. The neck and snout were sketched to the same size, curves, and lines so that they could fit together and finish the other seahorses that were being formed around the original one. The backs fit perfectly together with the straight back the ridges and edges. Finally after making my tessellation fit perfectly in every way my tessellation was finished.
In my opinion I think that tessellations are both art and math. Although tessellations can be made simply by a random sketch that fits together and be called art there is always math incorporated into it. A tessellation has to have cemetery, angles and edges which are apart of math. Tessellations are also art because in tessellations there is drawing and coloring. Without coloring or just shading in black and which it is still considered being decorative and adding depth to the drawing. I think that tessellations are both art and math because of the elements that are included in making the tessellation to the outcome and final product.
To make my template I first made a rectangle where all the angles are all even and both pairs of reflective sides are equal in length. Then I finished following the guide on the internet by drawing a spiral for the tail making sure that the same spiral can be rotated and fit perfectly. The I drew the stomach caving into the neck then chin. I drew it so that the arch of the stomach can fit exactly where the head of the seahorse indents. The neck and snout were sketched to the same size, curves, and lines so that they could fit together and finish the other seahorses that were being formed around the original one. The backs fit perfectly together with the straight back the ridges and edges. Finally after making my tessellation fit perfectly in every way my tessellation was finished.
In my opinion I think that tessellations are both art and math. Although tessellations can be made simply by a random sketch that fits together and be called art there is always math incorporated into it. A tessellation has to have cemetery, angles and edges which are apart of math. Tessellations are also art because in tessellations there is drawing and coloring. Without coloring or just shading in black and which it is still considered being decorative and adding depth to the drawing. I think that tessellations are both art and math because of the elements that are included in making the tessellation to the outcome and final product.
GeoGebra!
The Burning Tent Problem
Question 1: What appears to be true about the incoming angle and the outgoing angle? Both the incoming angle and outgoing angle are very close in size. They both are 37Degrees then slightly differ in smaller decimals. Question 2: Why is the path from Camper to TentFire the shortest path? The path from the Camper to the TentFire is shortest because there is only one direction that the Camper has to travel instead of in two different directions to reach the river then Tent. Question 3: Where should the point River be located in relation to the segment Camper to TentFire and the line AB so that the sum of distance is minimized? The point river should be located in the middle of points Camper and TentFire on line AB. It should be located there to create the minimum distance the camper has to travel so that the camper can cover more distance by running at the angle of getting closer to the Tent and the River. |
GeoGebra Snail Trail
How I constructed this GeoGebra design was I first learned how to create the
individual points that all have the same angles and are connected with a circle.
The circle helps them to move together when the original point is dragged around
Each point was made as a reflection of the other so that the were connected to
the first point. The snails or points were mirrors of the others that made the exact
same mark as the other just as a reflection from the other side. The cemetery found
in this figure is rotational, symmetrical, and relational.
How I constructed this GeoGebra design was I first learned how to create the
individual points that all have the same angles and are connected with a circle.
The circle helps them to move together when the original point is dragged around
Each point was made as a reflection of the other so that the were connected to
the first point. The snails or points were mirrors of the others that made the exact
same mark as the other just as a reflection from the other side. The cemetery found
in this figure is rotational, symmetrical, and relational.