# A Twist on Old Venn

How many of you went nuts over the Google Doodle for John Venn’s 180th Birthday?  I have no shame in admitting I spent more than a few minutes messing around with it.

These not-so-modern overlapping circles of wonder have fascinated mathematicians, scientists, and even linguists alike.  When searching for rich tasks for my college algebra classes, I came across this new twist on the traditional Venn diagram:

This activity can be applied to all kinds of topics with the main task being to find an equation to fit into all eight of the Venn diagram regions.  Since we are working with systems of equations, I offered this challenge to my classes:

Can you find three graphs that all intersect and also each intersect one another at unique points?  Also, is there a 4th graph that does not intersect the first three?

Out came the iPads and Desmos.  Here are a few highlights:

Some of my observations during their work time:

• A few of them assumed we were creating an actual Venn Diagram with Desmos. I made sure the expectation was more clear the next period.
• Attention to precision was important.  Some students assumed that if the three graphs appeared to cross one another, their task was complete.  They were mistaken when I zoomed in to examine the intersection points.
• Students assumed that if a graph did not intersect another in their viewing window, it didn’t intersect at all.  We had some good conversation about where graphs might cross as the x and y approached infinity.
• Using sliders in Desmos makes this task more doable in one class period.
• I wonder if they would be able to solve for their intersection points algebraically.

Side note:  these RISPs (Rich Starting Points created by Jonny Griffiths) are all available on this website, and are excellent starters for college level mathematics.

# A Desmosian Gem

I finally had a chance to do the Function Carnival with my classes.  Thank you to Desmos, Christopher Danielson, and Dan Meyer for their work on this project.

As David Cox captured in his blog previously, the real power of this activity is the immediate feedback.

When the graph looks like the one below and 8+ rocket men burst out of the cannon, the students see that right away and adjust for it.

Dan had mentioned in a blog post a while back that “this stuff is really difficult to do well.”  After seeing students work through this activity today, I can appreciate the difficulty in creating an online math activity that gives both students and teachers detailed feedback in real time.

Some observations:

• Students don’t realize at first that you can see their work live.  I allowed them to “play” for a minute, but some may need more encouragement.
• A tool to allow you to communicate digitally with the class would be nice.  Google chat, for example?
• Some students don’t realize that the bumper car SHOULD crash and make their graph to avoid it.
• A student or two misunderstood the graph misconception questions and went back and changed their graphs to look like the misconception graphs.
• It was interesting to see which students wanted their graphs to be perfect versus which ones said there’s was “good enough.”  It would be interesting to have a discussion about which is appropriate in the particular situation.

Bravo, Dan, Christopher and the Desmosians.  Thank you for creating an online math activity that gives me some faith in online math activities for the future.