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Ask questions to guess which graph your classmate picked.
What we had in mind
  • Algebra 2, Advanced Algebra or Precalculus students
  • One 60-minute class period
  • Students who are developing vocabulary relevant to rational functions and graphing
Goals of this activity
Students will be able to...
  • Identify important features of rational functions
  • Precisely describe these features to their peers
  • Increase their relevant vocabulary
Supported Devices
About this activity

We have designed Polygraph to foster the pleasure and the power of words without the drudgery of the lists.

With Polygraph, Desmos provides tools for developing informal language into formal vocabulary. Because words should result from a need to describe our world—this is where they gain their power.

And we also know well the pleasure of having just the right word handy at just the right moment—what the French call le mot juste.

How the activity works:
1.
Each student plays a practice round against the computer to learn how the game works.
2.
Next, students are paired with a classmate to play polygraph with rational functions. One person chooses a rational function; their partner asks yes/no questions in order to narrow a field of suspects down to one.
3.
Between rounds, students answer questions that focus their attention on vocabulary and strategy.
The Student Experience

Before you put students on computers, make sure they understand the premise of the game. We do not recommend playing a sample round with the class, as the first round involves the computer asking questions of all of the students (a fact we do not reveal until they have finished the first round). You could easily, however, play a low-tech version—show the array, pick your graph, have students ask questions aloud, respond, et cetera.

Starting in the second round, we pair students with each other. One student picks the graph and answers questions, the other student asks the questions and tries to identify the chosen graph. Between rounds, students answer questions that focus their attention on vocabulary and strategy.

Students will play a practice round with faces to learn the game mechanics, then use graphs to play against their classmates.
Pro Tip!The easiest way to test out Polygraph is to find a friend to play with you. Create a class code, give your friend the class code, and each of you can enter that at student.desmos.com. Your friend may be in the same room, down the hall, or halfway around the world—so long as the two of you are playing at the same time.

If you want to play on your own, you’ll need two browser tabs, and you’ll need to play the roles of two different students. After you create a class code as a teacher, go to student.desmos.com in each tab and enter the class code. Be sure to sign out on each tab so you don’t appear to be the same person in both tabs. Then just toggle between the two tabs to play both sides of the game.
The Teacher Experience

Observe and talk with students as they play their rounds. Use those conversations, and what you glean from the teacher dashboard to keep track of which features students notice and discuss.

Keep an eye out for students who are waiting too long for a partner.
To what extent are students using formal vocabulary? What ways do they create to describe standard (and non-standard) features of the graphs?
Keep an eye out for students who pick the wrong suspect. Thinking about what went wrong, is a challenging bit of reflection. Some students may need encouragement and support to see it through.
You can click on a pair’s game in the teacher dash to view the entire game.

There are a couple of ways you can wrap up this lesson. You could end it by playing a round against the class. Invite discussion of the ideas and strategies behind the questions your students ask. (And then play a second round — if you can guess the class’s suspect in fewer questions than they guessed yours, you are the reigning Polygraph champion!)

As an alternative, you could use the teacher dashboard to identify some interesting questions that students asked as they played, and bring these questions to their attention. These might include use of vocabulary you want to introduce or examples of students noticing things about the suspects that most did not.

Tips from Teachers