# Friday Five for June 17

The Friday Five is getting excited for Twitter Math Camp and other summer holidays. Do you have big travel plans this summer? With whom will you play Polygraph? Important questions—hit us with your answers on Twitter!

## Polygraph: Rational Functions, Part 2

Last week, we offered you a follow-up activity for Polygraph: Lines. This week, we have the same thing for rational functions. Students can formalize important ideas about branches, asymptotes, and continuity by working through this activity after playing Polygraph: Rational Functions. If you search “Polygraph” at teacher.desmos.com, you’ll uncover a few other “Part 2” Polygraph activities.

## Near Miss

From the mind of Michael Fenton comes this distance-minimizing activity from outer space. We are proud of our modeling work here at Desmos, and this activity shows some of the important parts of that work—starting with a prediction in a situation that seems accessible but non-obvious. The formality and precision slowly increase, and pretty soon students are engaged in a challenging bit of algebra or calculus. Go check it out.

## Commuting Times

Do you remember Function Carnival, Part Deux from a while back? Go ahead and read about it. We’ll wait. Well, here’s a great follow-up activity which has students consider relationships between scatter plots and their models, using the language of functions. If you’re noticing a trend here—that Function Carnival got a follow up activity, and that this one has a follow-up, and that the Friday Five was writing about activity pairings recently, and second parts of Polygraphs are popping up everywhere—if you’re noticing such a trend, you may just be onto something. Stay tuned!

## Put the Point on the Line

How do you help students become more friendly with abstract ideas about slope? This activity is an example of how you can do that. Slope as a rate of change between contextual variables is a big and important piece of the puzzle for sure. But so is slope as a relationship between vertical and horizontal change in the coordinate plane. This activity works on that second idea. In Desmos house style, students begin with approximations and develop more precise techniques as they move along.

## Exploring Triangle Area with Geoboards

Areas of triangles on a Des-mofied geoboard is good times guaranteed. Starts simply, gets difficult. Totally worth your time playing with.

With that, the Friday Five is over and out. It’s Friday and it’s summer, after all. The beach is calling.