## BEES fINAL WRITE UP-

Portfolio-

Triangles: My understanding of geometry has grown this semester through learning about trigonometry, calculating units of triangles, and how much triangles apply to other shapes and prisms. Specific activities pushed us to use design thinking, creativeness, and harsh brainstorming. For example, the early activity of brainstorming our own formulas to find the area of right triangles made us come up with creative mathematical ideas and build off of those to design the correct formulas that made sense.

Trigonometry: Later in the unit, we applied those formulas to triangles in prims. We gained an understanding of trigonometry to find unknown side lengths of un-right triangles and also applied that understanding to the prisms. The pythagorean theorem and mnemonics are things we learned for deciding units of triangles separate from and part of prims. We used both of these in an assignment on page 266 of the text book where we had to find the area of a triangle to find the volume of a prism (pythagorean theorem), and then to find the base area and volume of a hexagon, decagon, and dodecagon shaped building (pythagorean/ mnemonics). This understanding of triangles applies to the central question about bees because it gave us the knowledge to observe and analyze characteristics of other shapes, prisms, and functions in geometry.

Motivation & Focus: Over the entirety of this unit, I became more motivated to put forth my best effort and to focus on what I was actually learning. When I turned 16 in January, I realized how frustrated I was with myself for not applying myself to my academics when they were being presented to me in ways that benefitted me as a learner. Being someone with a creative mind, I find it extremely rigorous to have the motivation I need to use my nature in things like math. Math hasn’t been an easy subject for me since about seventh grade. Seventh grade is when I really started to care about music and creative thinking, and I couldn’t find a way to apply that thinking to math. This is also why I struggle much more with the algebraic side of math.

Individual Growth: On my birthday, I ended up bummed out at the end of the night because the idea of my age and how close I actually am to my future (that I am extremely eager to pursue), all sort of hit me at once. Failing math last semester made me disappointed in myself. I felt failure, regret, and worst of all it gave me a ton of undesired, negative anxiety. However, I took it as a lesson; “a man lives a life full of mistakes.” I realized that the work we were doing was pretty hands on for a math class and that is how I learn best. Geometry and using it in a hands on fashion, showed me that I can apply my creative mind and style of thinking to math. Hands on mini projects like using marshmallows and toothpicks to create angles, shapes, and prisms allowed me to do so.

Problem Solving: Whether it was group work, or using critical thinking skills to solve a specific problem forced me to grow as a person, student, and mathematician. Working on the white boards and collaborating with our table groups is frustrating sometimes, as I am not a huge fan of group work. Group work teaches us all important collaborative and social skills, an essential for our careers and the industry I want to work in. Critical thinking skills also apply to my future. In the music industry, new ideas and alternative ways of doing things are a need. For example, if I am in the middle of a session (recording) and a client wants to do something different with their mix, I am the person that will have to find the right fx or change the eq.

Summary Paper-

Question: Why do bees tessellate hexagons to form their hives?

Introduction: This problem was proposed at the beginning of the unit, before we gained a basic understanding of needed things like volume, surface area, tessellations, and structural integrity.

Volume: An enclosed area of space that an object or substance occupies.

Surface Area: The area of such an exterior or uppermost layer.

Tessellation: An arrangement of shapes fitted closely together, polygons repeated without overlapping each other.

Structural Integrity: A structure or structural components ability to uphold a load.

This problem consisted of a course of assignments that introduced us to the areas of math that those 4 terms applied to in a few different ways. Sometimes those terms would apply at the same time.

Discussion-

Comparison:

1. Hexagonal Prism

V= 3897.1

LSA= 735

2. Triangular Prism

V= 3897.1

LSA= 900

3. Rectangular Prism

V= 3897.1

LSA= 789.6

4. Pentagonal Prism

V= 3897.1

LSA= 752.5

Triangles: My understanding of geometry has grown this semester through learning about trigonometry, calculating units of triangles, and how much triangles apply to other shapes and prisms. Specific activities pushed us to use design thinking, creativeness, and harsh brainstorming. For example, the early activity of brainstorming our own formulas to find the area of right triangles made us come up with creative mathematical ideas and build off of those to design the correct formulas that made sense.

Trigonometry: Later in the unit, we applied those formulas to triangles in prims. We gained an understanding of trigonometry to find unknown side lengths of un-right triangles and also applied that understanding to the prisms. The pythagorean theorem and mnemonics are things we learned for deciding units of triangles separate from and part of prims. We used both of these in an assignment on page 266 of the text book where we had to find the area of a triangle to find the volume of a prism (pythagorean theorem), and then to find the base area and volume of a hexagon, decagon, and dodecagon shaped building (pythagorean/ mnemonics). This understanding of triangles applies to the central question about bees because it gave us the knowledge to observe and analyze characteristics of other shapes, prisms, and functions in geometry.

Motivation & Focus: Over the entirety of this unit, I became more motivated to put forth my best effort and to focus on what I was actually learning. When I turned 16 in January, I realized how frustrated I was with myself for not applying myself to my academics when they were being presented to me in ways that benefitted me as a learner. Being someone with a creative mind, I find it extremely rigorous to have the motivation I need to use my nature in things like math. Math hasn’t been an easy subject for me since about seventh grade. Seventh grade is when I really started to care about music and creative thinking, and I couldn’t find a way to apply that thinking to math. This is also why I struggle much more with the algebraic side of math.

Individual Growth: On my birthday, I ended up bummed out at the end of the night because the idea of my age and how close I actually am to my future (that I am extremely eager to pursue), all sort of hit me at once. Failing math last semester made me disappointed in myself. I felt failure, regret, and worst of all it gave me a ton of undesired, negative anxiety. However, I took it as a lesson; “a man lives a life full of mistakes.” I realized that the work we were doing was pretty hands on for a math class and that is how I learn best. Geometry and using it in a hands on fashion, showed me that I can apply my creative mind and style of thinking to math. Hands on mini projects like using marshmallows and toothpicks to create angles, shapes, and prisms allowed me to do so.

Problem Solving: Whether it was group work, or using critical thinking skills to solve a specific problem forced me to grow as a person, student, and mathematician. Working on the white boards and collaborating with our table groups is frustrating sometimes, as I am not a huge fan of group work. Group work teaches us all important collaborative and social skills, an essential for our careers and the industry I want to work in. Critical thinking skills also apply to my future. In the music industry, new ideas and alternative ways of doing things are a need. For example, if I am in the middle of a session (recording) and a client wants to do something different with their mix, I am the person that will have to find the right fx or change the eq.

Summary Paper-

Question: Why do bees tessellate hexagons to form their hives?

Introduction: This problem was proposed at the beginning of the unit, before we gained a basic understanding of needed things like volume, surface area, tessellations, and structural integrity.

Volume: An enclosed area of space that an object or substance occupies.

Surface Area: The area of such an exterior or uppermost layer.

Tessellation: An arrangement of shapes fitted closely together, polygons repeated without overlapping each other.

Structural Integrity: A structure or structural components ability to uphold a load.

This problem consisted of a course of assignments that introduced us to the areas of math that those 4 terms applied to in a few different ways. Sometimes those terms would apply at the same time.

Discussion-

Comparison:

1. Hexagonal Prism

V= 3897.1

LSA= 735

2. Triangular Prism

V= 3897.1

LSA= 900

3. Rectangular Prism

V= 3897.1

LSA= 789.6

4. Pentagonal Prism

V= 3897.1

LSA= 752.5

## Driving Project-

I used the problem solving cycle in a variety of ways, asking many questions, analyzing plenty of research, and discovering many new things. I specifically went in the order of asking a question, then using design thinking to come up with a question on a smaller scale than my beginning question; after I came up with an answerable question I did rigorous research regarding the physics of maglev, then analyzed that research to answer my question. My initial question was "How could we transfer all on ground vehicles from fossil fuel powered to Magnetic Levitation (maglev) powered?" After researching maglev trains and maglev physics, I realized it would take me until I graduated to come up with an answer for that question. I then decided to ask communal based question regarding a maglev train. My question became "How much would it cost to build a maglev train to Purgatory Mountain Resort?" I created a mathematical framework for this question when I gathered info for a route, and the cost of each needed part of the train. My math was simple yet surprising. I then reflected while I put together my final product. I grew during the driving project in areas like design thinking, creativity, and focus.