Similarity in a Wrap!
For the past month or so, we have been learning about similarity, We defined similarity and congruence, dilations, similar figures, etc... through several open-ended problems and very much groupwork. To wrap it up, and end the unit, we did a final which we were allowed to work on in groups and with the use of whatever resources we could acquire. The following is a problem from the quiz that I found interesting and somewhat challenging! :)
This problem asks whether square ABCD (the smaller one in the left corner) is similar to square A'''B'''C'''D''' (the bigger, sideways square on the right). Then it asks us to prove it using a set of rigid motions and dilations that would map one onto another. When I first got the problem, I immediately thought about lining point A with point A''', B with B''', and so on. I knew that there would probably be many that made the mistake of not doing that (like my group members which I worked with to help solve that) and was going to make sure I wasn't one of them. That being said though, it did make the problem initially a lot more difficult than anticipated. After quite a lot of time, energy, thought, and mistake, I came up with a solution that would map the smaller square onto the bigger one in four steps involving translation. rotation, dilation, then reflection. Though I knew that I could make the transformation in a less amount of steps (A to A''' is three steps), I chose not to persist on that path due to time restraints. I also decided on this problem not to use technical math terms and numbers to describe each step of the transformation/ For example, instead of describing exactly what angle to rotate the smaller square on in the second step, I just told them to match side BC and B'''C'''.
Regularly, I kind of find myself using the pattern finding, different approaches, and persistence habits of a mathematician but, in this problem I found that I actually really collaborated with others very well and used pattern finding a lot less (because this is not much of an algebra problem where I usually use that habit)! This makes me happy because I believe that collaboration is the habit I use least and need to become comfortable with opening up to others' approaches/say about the problem rather than just sticking directly to mine. :)
(P.S. Looking at the problem now, I realize how to solve it in three steps. You would reflect the smaller square, rotate, then dilate it to the size.)
Regularly, I kind of find myself using the pattern finding, different approaches, and persistence habits of a mathematician but, in this problem I found that I actually really collaborated with others very well and used pattern finding a lot less (because this is not much of an algebra problem where I usually use that habit)! This makes me happy because I believe that collaboration is the habit I use least and need to become comfortable with opening up to others' approaches/say about the problem rather than just sticking directly to mine. :)
(P.S. Looking at the problem now, I realize how to solve it in three steps. You would reflect the smaller square, rotate, then dilate it to the size.)