Desmos Holiday Card (Click Here!)

Initially, I was very excited to start this project as I love Christmas and I love the idea of using my mathematical skills in a creative way. I started thinking of what I could make from different Christmas  characters to family traditions; however, I wanted to keep things simple as I was sure this project would be difficult but hoped it wouldn’t be. So, I began with a tree, trying to think of a cool and interesting way to create this Christmas tree that didn’t use the expected idea of using triangles to build it. Instead, I used relations with reflections, transformations, and stretches. This was my mentality through the entire creative process of my card, the notion of using different and unexpected functions and relations to build the holiday themed card.

In the end, I used 278 equations some being functions and others being relations. Through the entire process I consistently tried using function notation from my knowledge of translations, reflections, and stretches. I tried keeping the equations simple, but at times I had to make some more complex to fit the picture. As I read the rubric, I used at least one equation of every needed function to shape the card and the self-portrait. The reason for certain equations over others were due to the fact that I used Desmos before to create an image in grade ten for my Math 10 Honours project; therefore, I had some previous knowledge with this site, but not much as I encountered quite a few challenges.

When I faced difficulties or roadblocks, I started placing random numbers into the equations in the spots that I knew transformed them, in our math books they are known as the a, b, h, and k spots. From here, I was able to translate and transform the functions and relations better as I then better understood them. Allowing me to overcome this challenge to make a prettier card that led me to review our first lessons in the curriculum. Later on, I started wanting to colour and shade the picture. I had to learn to use inequalities with domain and range restrictions to shade the Christmas tree ornaments and body parts. I had to discover how to use my made functions to colour, as they had curves and I couldn’t just use simple restrictions to not go over the lines; therefore, I needed to use function notation within restrictions to really colour the needed spots on the graph. When this came to my knowledge, the ability to create domain and range restrictions became a lot easier, I used simple and complex ones as shown in the side panel of Desmos within the equations. These where the biggest two challenges I faced, learning how to truly change my created functions and relations by using function notation and a, b, h, and k values. As well as, using domain and range restrictions initially, but also realizing how to use the simple and complex ones to shade and colour my card. When I overcame this, it was truly an aha moment as I was able to create more images through equations in a quicker manner. On the other hand, I realized that I wasn’t able to use simple function notation with relations and circles. For the relations I had to make the equal to x at times to be able to then use a, b, h, and k value changes; additionally, for circles, at times I solely copy and pasted the equations as I found it quite difficult and frustrating on how to create function notation for them.

With this being said, it wasn’t only through random changes, unexpected solutions, and realizations that I was able to surpass the roadblocks or work around them. I used some help from Google and YouTube to accomplish this. I learned from the Desmos site itself on how to shade circles and then also how to make folders on Google. This was a good strategy as I was able to get help, but also make the creative process a tad easier. As I was able to create a nicer self-portrait which included my unique features with my style, eye colour, and the way I wear my hair. From watching all the videos on the ins and outs of Desmos to reviewing some pages in my workbook, this was truly the best approach as I used this strategy to then create easier equations, in a faster manner, and understood colouring/shading, and function notation in greater depth.

In the end, I was able to review all the different functions we learned in class, domain and range restrictions, as well as function notation. All which will help on the final and really showed me how math is used in a different setting than just in the class, in the real world. I was truly able to better my math skills and better understand the functions we learned a couple of months ago and recently. I also was able to learn about new ways to transform some functions in diagonal or vertical ways when I have never encountered those methods before. This project caused me to genuinely enjoy all the ups and downs from challenges to the aha moments that made it easier to create a beautiful card that I’m proud of. It may have been quite difficult, but I learned a lot and am glad I chose to complete this optional project as it helps me to bring back the memory of these past functions and all the rules associated with them.