RSS

Notice and Note: The Equation of a Circle

19 Mar

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.

1 03-19-2016 Image005

They made a conjecture about the path P follows, and then we traced point P.

2 03-19-2016 Image006

We connected their noticings about the Pythagorean Theorem to come up with the equation of the circle.

3 Screen Shot 2016-03-04 at 9.47.46 AM

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.

15 Screen Shot 2016-03-04 at 11.01.34 AM

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).

16 Screen Shot 2016-03-04 at 10.58.42 AM.png

And so the journey continues … with an emphasis on noticing and noting.

 

 

Advertisements
 
2 Comments

Posted by on March 19, 2016 in Circles, Geometry

 

Tags: , , , , , ,

2 responses to “Notice and Note: The Equation of a Circle

  1. Princeton University

    February 7, 2017 at 3:27 pm

    It’s surprising to find on wordpress.com a resource so precious about equations.

    We will note your page as a benchmark for Notice and Note:
    The Equation of a Circle .
    We also invite you to link and other web resources for equations like http://equation-solver.org/ or https://en.wikipedia.org/wiki/Equation.
    Thank you ang good luck!

     

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

 
%d bloggers like this: