Agenda for Thursday, May 14 (166)

Good Morning!

First, I mentioned yesterday that my daughter, Gwyneth, is taking her AP Chemistry Exam today and that I might need to be helping her negotiate how this is working out in our "distance learning" mode. It looks like we will be all done before our zoom starts. So, our normal meeting time of 12:30 to 1:30 looks good. I will post in the comments below if that changes.

Yesterday we started a new Desmos lesson which focuses us on the relationship between the radius and area of a circle. We began by sketching out what we thought the graph might look like and discussed our thinking. We saw students drawing straight lines and discussing the angle (slope) of those lines. Should the line be more towards the radius axis or the area axis? What does it mean if the line is more towards one? Students agreed that the graph needs to go through the origin, (0,0), and there was discussion about proportional relationships and if the relationship between the area and radius of a circle is yet another example. But the plot thickened as we started to collect and graph some data! Oh my, not even straight! What's going on here? Why not straight? What causes the graph to curve.

In today's class we will continue this work. We will examine more closely why the graph curves-- what is it about this situation that is causing it to curve. We will also work on developing a more compact equation for finding the area of a circle and will very possibly look at how some algebraic thinking can help us see where that equation comes from. I'm hearing really nice reasoning in the zoom. Students are asking great questions, sharing very nice insights and enthusiasm. I can't tell you how much I appreciate your enthusiasm for thinking!

Don't forget your DreamBox-- today is the last day to get it done.

See you in class.

Onward.