Teach 180: The Day Before Christmas Break (Day 75)

As part of the Desmos Fellow's weekly challenge, I made the following to celebrate the Christmas season.  When I shared it with my students, I told them that I created the graph and many wanted to know how the stars were "blinking".  Designing activities and lessons to make students wonder why something makes sense or how something works is what I strive to do on a daily basis. I look forward to continuing to reflect and blog on January 2.  Now for a much needed break!

Teach 180: Comenius Independent Study Projects (Day 74)

https://www.famousbirthdays.com/people/john-comenius.html

From 3:30 - 4:45 this afternoon students met with me and other members of our independent study committee to describe their progress on their Comenius Independent Study projects.  Although we only met with five students today, by the end of the week we will have met with all sixteen independent study scholars.  Comenius Independent Study projects have been an optional part of the curriculum for at least 20 years.  I have been a mentor for some scholars with math projects, but this year the projects students chose to do are more focused on English and history with a few science projects.  Many of the students spoke rapidly and were very animated in describing the work for their project.  Others had not made as much progress as anticipated.  The next round of check-in meetings is in March and presentations happen in April.  Each year I am impressed by the work and initiative of our Comenius scholars.

Teach 180: WODB (Day 73)

I love it when I reach into my folder from last year for a particular chapter and discover engaging activities that I had forgotten about. "Which One Doesn't Belong"? is a great way to open up discussion at the beginning of a class.  Or it can be used to help break up a long class.

This year, I used it as a class opener.  We had just finished a unit on polynomial functions.  Each table of students was asked to identify which one they thought didn't belong.  Usually students don't pick up on the line-type (dotted vs solid) or the color of the graph, but these students did.  So next, I asked for a mathematical reason for why a function wouldn't belong.

Here are some answers my students gave me.

Top Left: Has same end behavior on both left and right.  Others rise on one side and fall on the other for end behavior.
Top Right: It is the only function where the graph crosses at x = 0, instead of touching and turning.
Bottom Right: It is the only graph that is not in the fourth quadrant.

The bottom left was the most challenging.  What about the graph makes it different than the others?  One of my students said it was the only one to have a minimum in the 4th quadrant, but that wasn't true.  Someone else suggested that it was the only one to have a x-intercept of 3.  But that wasn't true, either.

We finally decided on the following.  The bottom left function doesn't belong, because is the only one that has both positive and negative y-values when x is positive.  Can you find any other reasons why the bottom left function doesn't belong?