Just like my Algebra 1 class, my Algebra 2 class is looking at the end of the quarter, year, distance learning, and chapter 10. A test just doesn't feel right. So I have decided to have the students complete a project based on sequences. There are so many great things that they could do, I have found it difficult to pick just a couple. I have settled on 5 projects, the students will pick one to do that interests them. The projects are: Dragon Fractals Patterns on a Grid Serpinski's Triangle Spirolaterals Visual Patterns I had a sixth project, Artwork Copycat, but decided to not give it to the students. In the end, I didn't feel like it analyzed the sequences enough. Dragon Fractals: I first came across this idea looking at the wonderful math art challenge website by Annie Perkins. I was intrigued by the paper folding and how you could develop the fractal by drawing on the previous iteration. I played with it for days, even doing it in spare moments during my zoom lessons. I hope that some of my students will find it just as interesting. If we were in class, I would love to explore the connection between the paper folding and drawing the iterations. But, since this is more of an independent project and I don't have them captive in my classroom to interact with, I left that part out. Patterns on a Grid: I first came across this idea at an art museum in Wurzburg, Germany where they had an amazing math art exhibit. The picture above is a number grid that starts in the middle and spirals out. The colored blocks are prime numbers. It did not occur to me to do this with other patterns until I was thinking about doing these projects. I had a start to a project with this idea when I stumbled upon Megan's Sprials in Annie Perkin's math art challenge. The rest, as they say, is history. It is quite interesting how the layout of the number grid and the coloring of the pattern can give a design. I highly recommend playing around with this. Serpinski's Triangle: Who doesn't love a good session with Serpinki's Triangle. It is such a fun fractal and lends itself so well to sequences. I love the idea of doing the 3D version of it and I really hope I have a student or two that will do it. I am also excited to sneak in a little bit of Pascal's Triangle. I did a different version of the 3D card with a class on Valentines day a couple years ago. Instead of straight lines, we did the top part of hearts. (I am secretly hoping to receive a card or two from my students). Spirolaterals: Have I mentioned Annie Perkins' website with math art challenges? Well, this one comes from there too! I actually saw it first when Annie tweeted about it. Of course, it screamed sequences and I had to include it. It was fun to play around with the idea. I am hoping to play around with it more after school is out. Visual Patterns: It wasn't that long ago that I was visiting with some teachers and they said that every math teacher should know who Fawn Nguyen is. Well, I didn't. So I figured I should find out, and now here I am, a fan girl. One of the things Fawn has brought to all of us is her visual patterns website. When I first looked at it, I didn't do anything with it because I didn't now what to do. After attending Fawn's workshop, I have become an avid user of visual patterns. To start the sequence chapter, I had my students do many visual patterns and then used them to introduce notation and concepts of arithmetic and geometric. It also helped us with being able to find the expressions. It seems fitting that one of the projects is playing with visual patterns. I am especially excited for this project because of the fun I had with my daughters creating a tiktok. Between the quarantine and being 13 years old, it can be tough to find things that my oldest daughter and I can enjoy together. We had so many laughs creating the video, I am hoping my students will enjoy doing something similar. Artwork Copycat:
And then there is the one that didn't make the final cut. Which I am somewhat sad about. In 2016, I went on an amazing trip to Germany. It was a week-long school for math education researchers. My cup was filled from so many spouts: teaching math, traveling to Germany, exploring another culture, and visiting with math teachers from so many countries. One of our activities for the week was to visit a math art exhibit. Looking back on pictures, there were two art pieces that could be used to explore sequences. I am especially intrigued by the bright colored geometric design. Once you start exploring it, you see that it is a geometric sequence with a common ratio of 2. Trying to recreate it proved to be a fun, artistic challenge. I chose not to include it just because it wasn't quite as much sequence work as the rest and it didn't feel as rigorous as the others. I really want the projects to have the same amount of work and "value". That about covers it all. Please feel free to use any of these projects. I hope to save someone out there some work. Wishing everyone a good ending to the 2019-2020 school year.
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I am looking at the end of a quadratics chapter, the end of the year, the end of distance learning, and the end of 9th grade before summer. A normal assessment does not feel like the right thing to do. But I want to do something to culminate the end of the unit. Enter the end of chapter projects. I decided on 3 diverse projects that require knowledge about quadratics. Students get to pick which project they will do based on their interest. I am hoping I have given a diverse enough selection that all the students will be able to find interest in at least one of them. I am sharing them here for anyone that would like to use them with their students. String Art: I love the parabolic curve string art. The use of straight lines that create a curve is beautiful. But first I want them to understand what that design has to do with parabolas (it isn't completely obvious). In the 9th grade algebra class, I do not teach them about the focus and directrix of a parabola. So this project starts with a small lesson about that. I used a quick video from Khan Academy. I also used an idea from Sarah Carter's blog to have the students create a wax paper parabola. See here for her post. After that, it is a matter of teaching them the basics about creating a parabolic curve and then let them get creative. Below is my favorite recent creation and the link to the project I am giving my students. Catapult: When I have had time, I have had my students create a gummi bear catapult in class and then find the equation of the trajectory of the flight of the gummi bear. It has been a fun project in school, and I am hoping it is something students can do at home. The set up is pretty simple. First, they need to create a catapult with supplies they have or supplies I get to them through our delivery system during distance learning. In the google slides, I include a quick video to give them a couple ideas for creating their own catapult. Second, they need to collect data, with the help of another person or two. Third, they will use Desmos to create the quadratic regression. I include instructions for how to do this since they have done it for linear regressions, but not quadratic. Below is a link to the project I am giving my students. Desmos Words: Earlier this year, after our linear unit, I assigned an optional project where students did linear Desmos art. Some of my students really got into the project and gave me some great art! I wanted my third project to follow along those lines (pun intended). I struggled with what to have the students create in Desmos. I had a few students figure out that they could google Desmos art and get an already completed project to turn in as their own. Since they were working in class, I caught it pretty quickly. But now that I will not be able to observe them working on it, I am worried about the originality of their work. I decided to have the students create their name or a favorite phrase out of lines and parabolas. Hopefully this will be original enough that they won't be able to use someone else's work. We dabbled a little bit with transforming quadratics in the unit, but not enough to assess on it. So the beginning of the project is to have the students go back to the Desmos activity and reacquaint themselves with it. There are many activities out there, but I am particular to "Quadratics Graphing Lab" from Mrs. Turpin. I modeled the instructions after a Desmos Name Project I got from Dianna Hazelton. Each letter has to be constructed according to the alphabet chart. They also have to do a minimum of 8 letters. Below is a snap of the example I created for my students and the link of the project. I won't be giving this to my students for another week or two. I am hoping they will be a success and much more enjoyed than an assessment. Please feel free to use any of them in your classes.
My next task is to come up with projects for my juniors to do to finish their sequence unit. |
AuthorI teach mathematics for grades 7-12. Teaching mathematics is my passion. Archives
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