I gave my Advanced Algebra 2 students the following question today to open class:
Write a system of equations with two equations and two variables with a solution of (2,3). Be prepared to justify your answer in two ways.
We have done solving systems of equations by graphing and substitution. We started elimination yesterday. I had hoped that they would come up with equations by working backwards - for example, 2 + 3 = 5, so x + y = 5 is one equation they could use in the system. I had hoped that once they got the equations, they would use either substitution or elimination to check the solution was (2,3).
What I got was blank stares. They had no idea where to start. I ask them to give me one equation and we'll put together a system. Then the student I have from the ED (emotionally disturbed) unit - who is bright mathematically - raises his hand and gives me an equation. Then he gives me a second one. And, right or wrong, I take the time to show them that (2,3) is a solution to it, first by substituting the values in to check and secondly by using substitution since it made the most sense for the equations he had given me.
I asked them to give me two more equations, and after a few moments, I had two more equations, one each from two different students. Demonstrated that (2,3) was the solution again. I asked them for two more equations and got two more equations, this time a little quicker from my students.
After I was done checking the third system of equations, I did talk with them a little about how I wanted them to understand what the solution to the system meant.
I'm still behind on More Good Questions and I guess I need to read some more to have a better idea of how to handle open questions with my classes. I decided to try this with my Advanced Algebra 2 class since they are a little more willing to think and work at stuff than my regular kids. I'm not totally sure what I wanted to get out this, but I had hoped for better responses from them. Will have to read more and think more before bringing in the next open question.