Annaliesa Coupe

Equation 1:

Solution: x = -4

(A, C, D, F, G)

Equation 2:

Solution: no solution. (extraneous root: x = 4)

(B, E, H)

Note: screenshots of equations are provided as formatting did not compute with Edublog.

Reflection Questions

1: “Which constraints did you choose to complete first, and why? What strategies did you use to tackle the more difficult tasks on the menu?”

I chose “A: The equation has a radical expression on each side” to solve first because it was one of the most limiting, as well as “G: The solution is negative” because that is a significant determining factor of my answer. I started out by putting a radical on each side of my equation and went from there. When I factored in a couple of the easier constraints, I went back to solve it and tweaked a few things to ensure that my result was negative. A strategy I used for the more difficult tasks on the math menu was choosing them first in order to get them out of the way. By doing this, the easier prompts just fell into place with the limits of the harder ones. Another strategy I found effective was practicing trial and error; checking everything at least twice to make sure my equations fit the limits.

2: “Were there any constraints you struggled to pair together? How did you approach a problem that you initially found confusing or difficult?”

Constraints “H: The equation has no solution” and “B: The radicand contains a binomial” were not necessarily difficult to put together, but were challenging to incorporate in general. “H” was hard because I didn’t know how to structure an equation with an extraneous root as the solution. To work past this, I referenced my Pre-Calc workbook where I remembered having an answer that did not have an adequate solution. Taking inspiration from how the equation was written helped me make my own equation with no solution. “B” was initially tricky to include since having a binomial in one of my radicands didn’t fit with how I’d incorporated the “G” and “H” constraints, both of which determined my answers. To work around this, I went back to the technical definition of a binomial, which is that it is two terms separated by a + or – symbol. So, 4x + 0 is a binomial, even though it is equivalent to 4x, which is a monomial. This allowed for me to satisfy all restraints put on my equation, and also worked with my “H” constraint.

3: “Can you describe a moment when you had an “aha” moment while working on a task?”

When I was working on equation 1, trying to satisfy the “G: The solution is negative” limit, I kept finding that my solution was positive. This is because every time I put a negative symbol outside of a radicand, it kept canceling out when I squared the equation. However, I soon realized there were other ways to make my answer negative, and the way I used was by making the x value and the constant on the right side greater than the left. This way, my x value on the left side would end up being negative, and the constant on the right would be positive. The constant would end up being negative when I divide by a negative number to ensure that the variable is not negative. When I finally determined this after lots of trial and error, it felt very fulfilling because it was one of the bigger challenges of this assignment.

4: “Did you find it helpful to have the freedom to choose the order of activities? Why or why not?”

I think it was helpful, but slightly irrelevant because I could have found a solution either way to satisfy all of the restraints. There are a lot of different pairings that would work, so if which go together were decided for me, that would not be too limiting.

5: “How did working independently on the math menu activities help you develop your skills?”

In class, we do lots of partner/group work on the boards which I think is effective for building collaborative skills as well as critical thinking skills. However, for this assignment I worked independently because then I didn’t have to consult anyone else and I get to have my own thought process. This is beneficial because I had to figure out any complications independently, which contributed to my growth of my math skills.

Critical and Reflective Thinking Reflection

“I remain open minded as I explore viable options or alternative approaches, like when I…”

When creating and solving my equations, I demonstrated persistence and perseverance by trying different techniques when I was faced with a problem. For example, I used homework questions to give me inspiration for my equation’s structure when I wasn’t sure how to proceed with an equation. I also solved my equations several times each to explore alternate routes I could take, mainly to see how I could work towards one end solution (while tending to the constraints). Additionally, I asked questions and attended Flex times to make sure that I was on the right track. My openness to be flexible, my effort, and the time I have put into this assignment has contributed to my overall success.