7, 8 And A Little Bit of 2

Don't want to bore anyone to tears, AND, if you had some trials trying to differentiate some of the SMP's, here is how I see it:

SMP 7-Look for and make use of structure vs. SMP 8-Look for and express regularity in repeated reasoning. 

With some help from a very LOGICAL colleague, I have wrapped my head around "Look for and Make Use of Structure" as being about taking a big chunk and breaking it down into pieces. (This is one of my favorite SMPs--what a geek!) With Pre-Calc we are working with Polar Graphing. Looking at each piece of a polar equation and determining where to begin, what part drives the petals, the loop, and the dimple has been a lot more enjoyable and pragmatic.
We started with this hand-out: file here
after a some explores with this Desmos Activity Builder: Polar Equation Investigation
Notice and Wonder. Can you make sense of the structure of the equation? Can you break it down by family? Are you curious what wonderment it will draw and why? If you want to alter it, can you? How much do you need to see before you can fill in the rest by yourself?
In an earlier post, I commented on how I want my students to view equations as stories. They (the equations) have families and quirks, and regularities, and some stuff that isn't so regular. It is kind of like taking apart a machine and putting it back together so that you understand how it works. 

What story do these polar equations tell?

You may also like

No comments :

Like what you read? Want to contribute to the conversation? Leave a comment!