The Roots of the Equation

I was reviewing solving equations for my SAT Math class. It’s a tricky thing to do because “equations” includes linear, systems, quadratic, and exponential equations. A lot of different skills to go over in a short amount of time.

After working through the requisite problems, I wanted a little more practice, so I came up with a game that they could play, based on the Bid-a-Note sections of the old “Name That Tune” game shows. I called it Name That Solution. Gameplay goes like this:

• Start over with a simple equation, like “x = 2.”
• Each turn, a team can change the equation in one way to make it more complex. (For example, make it “x + 3 = 2” or “5x = 2”.) Only one operation and one term can be added at most per turn. The team finished by saying “I can name the solution of that equation.”
• On a team’s turn, they may challenge the other team to, in fact, actually solve it. (“Go ahead! Prove it!”) If the challenged team can, in fact, solve the equation, they earn a point. If not, the challenging team gets a point.
• First team to 5 points wins.

They played on whiteboards so they can change the equations quickly. The students quickly learned to not overextend themselves when making the equations harder, lest they find themselves challenged. So it leads to a nice exercise of constantly mentally making sure you know the steps to solve something before you take your turn, getting a lot of practice.

At the end of one of the classes, I did a big class-wide version, half the class versus the other half. But they wound up being very conservative, with neither team challenging the other and only take moves they knew they could solve. Which I guess was the point.

That final round.