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. *