Math 3 Unit 9 – Percentiles

Part 1

I think the most important thing i learned was what percentiles were and how to find/use them. I always heard about these, like the weight percentiles or height percentiles the doctor gives you at checkups, but never really understood what they meant. Now, I can understand what these stats mean in terms of the data.

Since percentiles are used so often to help explain data points and such, they will be important moving on. One thing that helped me understand were the notes we captured on what they were. They explained to me how a percentile was a measurement or indication of how many data points in a given set are lower than the specific data point you are looking at. This gives a sign of how extreme that data point is, and can be used to calculate whether that point is statistically significant, a very important skill that we will use a lot now and later.

Part 2 – Designing an Experiment Project

I specifically learned what statistically significant meant. Before, I would just look that the means of data and if one was higher, or higher enough, then I would conclude there was a significant difference. I understand now that you need to run a large amount of randomization tests and compare if the original mean is within the most extreme 5%.

For this project, we first had to come up with what we wanted to test. This was honestly the hardest part, because we really had to idea what to do. After quite a bit of consideration, and some inspiration from some classmates, we decided on the color influence experiment. Next, we decided how we wanted to test it. We choose to use a Google Form so it would be easy to distribute them to participants and collect data in one place.

One part of the project that did turn out very well was our data collection design. The idea of the Google form was very easy to use to get participants. We didn’t find people at lunch and use their time to do it, so we got a fairly large amount of respondents. We could post announcements on our messaging platforms and find quite a few people there.

One thing that didn’t go well was the presentation. My partner and I did not have communications over the weekend as she did not have internet, and she didn’t know what we had to present on Monday, so we barely had time to prepare. We had a bit of miscommunication during the presentation, but it wasn’t too bad. It just wasn’t very smooth. Next time, I would make sure we had reliable communication to avoid something like this from happening again.

Math 3 Unit 8 – Unit Circle

Part 1

The most important thing I learned in this unit was the unit circle. It will be important in the future as it provides a way to find sin, cos, and tan values without a calculator, along with their degrees and side lengths. When we go to NC State, where we cannot use calculators, we will need to rely on this to do our calculations. Even when we do have access to calculators, however, this tool will still be a very convenient tool to evaluate trigonometry.

To learn about the unit circle, we constructed one ourselves. Using our new knowledge about radians and trig rations, we put down all of the measurements, angles, and numbers. This showed us exactly how the unit circle worked. Now, we can construct one ourselves using the methods we learned without a calculator or notes.

Part 2 – Cycles in Nature Project

I learned that the hours of daylight throughout the year actually follow an exact cycle. Growing up, hours of daylight always affected my family, since my dad had vision issues and could not drive in the dark. Learning exactly when and how the time of day changed was a very educational experience. I never knew what the seasonal equinoxes were before.

To model the data for our project, we had to manually find each day of the year that were the 1/8th milestones of 365 days. Then, for those 8 dates plus the 4 equinoxes, we had to, again, manually search how many daylight hours each day had. It was a very tedious process and my partner and I very nearly messed some of our data. Then, we had to figure out how to write our model equation, which was difficult because we were confusing our radians and degrees. This whole process was the hardest part of the project. In the end, however, it mostly worked out; we just had to focus our effort, time, and concentration onto this part of the project. One thing that helped was having one teammate read off numbers and have the other put them in, so the latter would not have to keep switching around and risk entering incorrect data. It was also much easier and faster than having only one person do it at a time. Everything else, like the poster, was not really difficult compared to that.

One good thing about this project was our poster. This was the first time I ever developed a poster theme from scratch (though it was inspired by a infographic design and has similar elements). It has a very clean look, with effective use of background images. My grade level poster also used the same theme, and I worked on both posters alongside one another.

One thing I would do differently next time is to put all of our information on the poster. When we made the poster, we assumed that some of the rubric’s requirements could be left on our project documents, since it did not explicitly state that everything had to be on our poster. As a result, we missed many points.

Math 3 Unit 7 – Triangles

Part 1

The most important thing I learned this unit was the centers of triangles. There are 3 types that can easily be mistaken for each other; circumcenter, incenter, and centroid. The additional page that was included in our task helped visualize (I am a visual learner) just where each point was and how they were positioned in relation to the sides and vertices. The circumcenter is the point where all the perpendicular bisectors of the sides meet. The incenter is where all the angle bisectors of the vertices meet. The centroid is where all the lines connected between a vertex and the midpoint of the opposite side meet. This will be important in the future as we will need to find points that need to be equidistant from different sides or angles, and/or divide areas.

Part 2 – Castlerigg Stone Circle Project

I realized during this project that volume of non-standard 3D shapes is often very difficult to manage. Given a 10 oz. requirement, we first had to convert that into a cubic volume requirement, then guess and check several dimensions to finally find a size that was functional. All the heights, lengths, bases, slant lines, etc. that we had to manage all at the same time was very difficult.

One specific detail I learned was how to calculate the volume of a milk carton. The bottom part was easy; a simple rectangular prism, but the top triangle part was confusing. This led to a miscalculation in volume. At first, I calculated a volume with over 40 cubic centimeters over what we needed, which left us plenty of space. Then I realized that the triangle was not a triangular prism and could not be counted as one; after a bit of thinking, I then realized that it was actually a pyramid! the slanted faces of the carton and the slanted triangle on the sides formed a square-based pyramid with the height of the triangular prism. Even after that, I realized that the diagonal folds were reducing the height, and accounting for that I found the true volume to be exactly our initial goal, with 0.1 ounces to spare. I was very lucky that I made the design larger than I thought I needed, because in the end, it was exactly what we were required to make.

That was the greatest challenge of the project: handling all the numbers. I am prone to random mistakes, and in calculating the numerous volumes and areas I made several errors. In the end, I had to go back and fix them all last minute. Next time, I will have another team member double check all my numbers before I move forward, as to prevent another total do-over again.

But in the end, our project was a success in what it outputted. Our milk carton was very solid, functional, and good looking. Our presentation was effective in presenting all our information in a concise, non-overwhelming manner. I was able to use my design not just in a slideshow, but on a physical product.

Math 3 Unit 6 – Equations of Circles

Part 1

I believe the most important thing I learned in this unit is how to write the equation of a circle. This will be useful as I have never had a method to plot a circle onto a coordinate plane, allowing comparisons to lines and other equations on a physical space.

The activity that definitely explained how the equation of a circle worked is the circle we constructed using the right triangles. The moment I visualized how the paper would look like with all the triangles on it, I understood how the concept worked. This was a very creative way to show this idea.

Part 2 – Castlerigg Stone Circle Project

An interesting fact I learned about Castlerigg (and one of the reasons I choose this circle) is that this stone circle predates infamous Stonehenge by 2 centuries. As for mathematics, I learned how to convert degrees to physical distance. Once Mrs. Parker explained how the minutes and seconds worked, I finally understood why they were called minutes and seconds; they were on a 60 scale.

But the hardest part of this project was the video; it required dozens of videos and images to compile into a 6 minute video. Then after hours of work on putting the video together, I needed to cite all 38 links. But with planning and time management we were able to complete all we needed on schedule, having eliminated other tasks to allow time to finish it all. But next time I would start grabbing plenty of images and videos from the very beginning and make sure we had all the content first; otherwise, we will have to re-render the video again and again with all the changes we had to make.

One thing that did turn out very well though was our poster; with experience from both my partner and I we were able to create a very attractive and clean poster design that accurately captured the theme of the stone circle.

Math 3 Unit 5 – Irrational Functions

Part 1

I think the most important thing I learned this unit was how to sketch irrational graphs without a graphing calculator or Desmos. This is important because being able to do math without technology is an important skill. On some tests, sometimes calculators are not allowed and being able to still make a rough graph of a complicated irrational equation.

The table in the beginning of Task 4.3 was a very helpful way to help me understand how to find the features of an irrational graph could be found. Given an equation, I could look at the characteristics, compare it to the chart, and get instructions to easily find what features could help me graph it.

Part 2 – Technology Manufacturing Project

After researching the Tech Manufacturing industry, I found it interesting how there were so many companies developing different things, with different strategies. Some always did the same thing over and over again, like Dell which always sells PCs. Others were always trying new things in an attempt to always keep up with the latest developments, like IBM. Others do a mix of both, like my company, Intel, which both continuously does computer chips, improving them by doing the same thing over and over again in new ways, as well as joining the fray in new fields like drones.

About financial investments, I learned that math isn’t always a great way to predict things that have so many factors, including a lot of human influence. Using Desmos to create a graph using a couple of data points isn’t going to produce a result that will mathematically, and more importantly, accurately, predict the success of a company which is run by human CEOs and makes money from the work of human employees selling to human consumers. Math cannot predict the stock market. That’s why humans are the ones who are looking at data as well as numerous other factors in the real world that math cannot take in account for. For them, math is a tool, not the answer.

The hardest part of this project was spending so much time looking and manipulating data. We had to navigate databases and then manually copy numbers to our documents, then hand type them into Desmos, just to get ridiculously inaccurate graphs. I understand why accountants and people in the financial industry get paid so much now.

One part of this project that turned out well was we were able to make a solid conclusion on which company we should invest in. We didn’t have to struggle to decide, but that might be because we only had a few data sources.

Next time, I would allot more time to do the data work. It took an extremely long time, and if I did this again I would plan to spend longer on that part.

Math 3 Unit 4 – Polynomial Division

Part 1

I believe the most important thing we learned this unit was how to divide polynomials, either though long division or synthetic division. This is a very vital skill because there are many tasks that require using it, such as factoring. If you have one root, then you can find the next lowest degree factor and that may be enough to find all the roots.

Synthetic division will be especially helpful, as it is an absurdly quick and easy way to find quotients with 1 co-efficient divisors. That will allow for easier factoring of quadratic and cubic polynomials, as well as assist in higher degree functions.

Mrs. Parker assigned a day dedicated to explaining how synthetic division worked, as it was not in our workbook but she felt it was important anyways. It made us understand how it worked, and was a great way of teaching us that new concept.

Part 2 – Cartoon Project

This unit we had a Cartoon Project where we were tasked to explain some concepts about polynomials in a cartoon format. We already understood the material in this unit, but that was not the goal of this project; we now were supposed to present that knowledge in an easy-to-understand format. The hardest part of this project was actually focusing on it, as it was assigned during our grade level project. I found it very difficult to prioritize working on it while we had all the other work looming over us. While this project never really demanded much time, I know I could have done better given more effort. On most projects I go all in and cover as many points as possible but it felt impossible for this one.

Nonetheless, our final result did not look bad. Our presentation looked decent, and thanks to a teammate, we had nice little characters to base our cartoon around. Our slideshow’s theme was fairly simple but pleasant. I probably would have executed a makeover given more time but I didn’t.

Next time I need be able to focus more on this project. In an ideal situation I would be assigned one project at a time, but given that nobody ever gets it all their way, I will need to be able to multitask between multiple projects at once. While in this situation the Grade Level Project was definitely more important, I will need to learn how to prioritize certain elements of two, maybe even three tasks at the same time.

Math 3 Unit 3 – Logarithmic Functions

Part 1

The most important thing I believe I learned this unit is how to really use logarithmic functions. This will allow me to expand my knowledge on many other topics, such as the ones we also did this unit. We learned how to calculate interest as well as the real world applications of money and banking. That will be a great life skill to have. We learned what e is, what it does, and how to use it.

Task 2.6: Compounding the Problem was a great transition from the compound interest we had just learned into continuous compound interest. As we learned how to compound interest multiple times a year, we found that as we compounded it more and more, from quarterly to monthly to daily, we got closer and closer to the irrational number called e. That explained to concept to me perfectly, and I now fully understand it.

Part 2 – College Tuition Project

In this project, we learned about the process of college tuition: how much it was going to cost, what the costs include, what loans there are to pay them off, how loans work, and of course, how to calculate the loans. The procedure for this experiment was to research the tuition of a college of your interest and choice, find scholarships and loan programs to pay it off, then evaluate an equation to calculate monthly payments.

The hardest part of this project was figuring out how to convert the equation. I used a monthly payment formula I found and it worked; I had an exponential equation. The harder step was to find the inverse of that, or the logarithmic form. Using some self-defined variables, I was able to simplify the equation into a clean, easier-to-manage set of numbers and then solve.

That also turned out to be a success of my project; after this simplification the numbers were incredibly easy to deal with. I was also able to show a few of my classmates how to do the same thing for their equations.

The design of my project was also a success and pain in the back. The website I used to create the infographic was too unstable and buggy, and my technology-design oriented mind really hated using it. That was a lot of stress that could have been avoided if I had used a better option. I will definitely use something else next time. But nonetheless, I think my final product does look good.

Speak Visually. Create an infographic with Visme

Math 3 Unit 2 – Functions and their Inverses

The basic idea of inverse functions is mirroring equations by switching inputs and outputs.

I think this concept will be used later in math for changing the way functions are written and what purpose they are for. For example, a graph that has a price as the input and a number of cookies for it’s output is intended for finding out how many cookies you can get with x amount of dollars. But using inverses, we can change the equation so that its input is now cookies and its output is dollars. Now this function is for finding out how many dollars you must pay for x amount of cookies.

Additionally, this concept will be used to introduce logarithm functions thought the inverting of exponential functions.

Something I need to work on as I move on past this unit is having the patience to do some of the undemanding but very time consuming questions I encountered. They aren’t hard, but they are longer than the effortless questions I started to take for granted.

Math 3 Unit 1 – More Functions, More Features

Part 1

The most important thing I believe I learned this unit is how to graph a Piecewise Function. It was a totally new concept that I had never seen before. I think that this will be useful moving forward to create functions to visualize varied data.

The 4.1 Some of This, Some of That graph story was a great way to introduce the concept of a Piecewise Function.

The task was to label the graph as a story, then evaluate it. It was a sneak peek to the Piecewise Project (below) and the question underneath took the next step to pointing out that the graph could be dissected into a few different, simpler functions. After this, I understood the basics of this new concept, and all I needed to know was the details.

Part 2 – Piecewise Function Project

My favorite part of this project was being able to create any story I wanted with any functions. That ability to decide was very nice.

The hardest part of the project was all the evaluation. I had to find domains, ranges, 6 relative maximums and 6 relative minimums, catalog all the information, then put them all in my presentation. It was not hard in the terms of difficulty, but it was very time consuming. I made sure to do as much work as possible before the due date approached but it was still draining. I made it through though.

The part of the project that turned out the best was the design of the slides. I thought my presentation looked great; but I might be spending too much time on it. Next time I will try a minimalist design.

I would also plan out a day for me to just scrutinize the presentation and check every single point on the rubric. This time, I totally forgot to dress formally. I had too much going on my mind and I didn’t write it down. That is something I will not forget again. (I hope).