In What’s My Rule, students move point Z and observe how W follows. Z is mapped to W according to some rule that the students are trying to determine.

There are all sorts of great questions to ask with an activity like this. After moving Z for a few seconds, I ask “Can Z and W ever coincide?” And then, of course, someone has to tell the class what coincide means in terms of points.

If I move Z to Quadrant I, then where will W go?

If I want W to be in Quadrant II, then where must I put Z?

I sent a Quick Poll to get student responses for the rule.

Students entered the mathematical practice of **attending to precision**. Students entered into the mathematical practice of **constructing viable arguments and critiquing the reasoning of others**. Students entered into the mathematical practice of **reasoning abstractly and quantitatively**.

We went back to the TNS document and showed why Z was not always the image of W reflected about the line y=-x.

We also showed what happens when we require Z to be on the function y=x^3 (I’ll eventually learn how to do LaTex…) and origin symmetry.

There are 7 transformations for students to explore in What’s My Rule. I could write an entry about each one. But instead, I’ll just share one more snippet.

In this problem, Z gets mapped to W through a translation with the rule (x,y)→(x,y-4). One question I asked was where Z would be if W was in Quadrant IV. Obviously, Z can be in Quadrant I. Can it be anywhere else? Someone suggested that Z could be in Quadrant IV. So Z can be in Quadrant I or Quadrant IV. Can it be anywhere else? After a while (a long while…I had to wait, **easing my hurry syndrome**), someone suggested that it could be on the positive side of the x-axis.

And so, the journey continues….

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What’s My Rule?”