I wrote in detail last year about how our students practice I can look for and express regularity in repeated reasoning to make sense of the equation of a circle in the coordinate plane.
This year we took the time not only to notice what changes and what stays the same but also to note what changes and what stays the same.
Our ELA colleagues have been using Notice and Note as a strategy for close reading for a while now. How might we encourage our learners to Notice and Note across disciplines?
Students noticed and noted what stays the same and what changes as we moved point P.
They made a conjecture about the path P follows, and then we traced point P.
We connected their noticings about the Pythagorean Theorem to come up with the equation of the circle.
Students moved a circle around in the coordinate plane to notice and note what happens with the location of the circle, size of the circle, and equation of the circle.
And then most of them told me the equation of a circle with center (h,k) and radius r, along with giving us the opportunity to think about whether square of (x-h) is equivalent to the square of (h-x).
And so the journey continues … with an emphasis on noticing and noting.