Week 5- Activity Reflection

Trying Out Extending the Activity:

I chose to primarily explore Sarah Chases illustration of moving 3 against 2. Initially needing a few attempts to start to get the hang of it, I appreciated her tip of assigning the different arms different non-numbers to make it a bit easier to follow the cyclic progression.

After feeling I got the hang of that I tried to think of what else could be represented through this type of movement, and wondered about using it for fraction multiplication (proper fractions multiplying by proper fractions). Where using your two arms can represent the multiplication of the two numerators and then your two legs could represent the two denominators. This idea felt more clear to think than do, I picked small numbers for both numerators and denominators 1/3 by 2/5 I also picked something that wouldn't simplify because I wanted to focus on using all my limbs first before considering what a simplifying fraction through this illustrated movement might look or feel like. Ultimately I found it challengeing using all four limbs to keep track of where my arms were in the count and my legs but manged to still try out movements connecting to proper fraction multiplication.

After more time with the movements I started to wonder about using numbers that were not prime, not to determine their product but to consider divisibility, so looking at something like 2 and 4, then 12 and 3, I found myself needing to use my fingers to track what cycle of the divsor I was on in my movement so I could focus on executing the correct movement for the count. I found it worked where if after one cycle of the divided your dividend and divisor were both going to start back at position 1 at the same time then the number was divisible. I wondered how this may look if divided among two people, one as the divisor and one as the dividend to make it a group activity, leading further to the thought of doing it with a class and having multiple students be different divisors and perhaps a student or the teacher be the dividend, and as a bigger group go through the movements and when the dividend is done and returning to the first position again to stop and see what divisor students are also at the first position. Challenges I would anticipate from that would be coordinating the pacing of the movements but feel a slow beat could help keep everyone at the same pace. 

I took some time to consider Ali and Colins work as well, as I loved learning more about the Bridges works last week and greatly enjoyed their video. I was thinking back to a few years ago when I had some advanced students who I was trying to create extension projects for, these students were also very engaged with artistic and alternative expression, and I was trying to find a way to create a project that they could make that would express the rules of simplifying polynomials through artistic expression. After multiple attempts to create an example, I sat with them and left it open for them to create anything that would visually communicate the simplification of polynomials without giving an example, partly because I wanted to see what they would do and partly because I was struggling to create an example that I felt represented it well. One of those students made a book, and all the key components of like terms, the degree of the terms, etc. were all communicated through such detail it took me multiple times going through it to notice the level of detail they attained and communicated. 

A video from 2024 when I received this book from the polynomial unit extension.

Edit: The video wasn't working when I looked back at this post, try this VIDEO LINK if you are interested.

The Start of the Curriculum Idea:

Sarah Chase's mathematical movements, reminded me of my first week reading by Gerofsky, Seeing the graph vs. being the graph. Currently my grade nine students are working through our Linear Relations Unit, there is an art integration project I have used before first with only extension students, and then the following year with the whole class. This is a unit that is current for myself in the moment and one I am more familiar with having taught. I used this as the focus for my curriculum idea.

I wrote my ideas out on paper for more of a flow (if parts are hard to read in the image let me know and I will type out a digital version).

From 2024, the first year I tried having extension students draw, determine equations, and digitally graph their drawings

From 2025, a student both completed the digital graph of their drawing and created restrictions for all of their equations.