This was the open question I posed to my Advanced Algebra 2 students today:
Write a system of inequalities that has (4, 3) as a part of its solution. It should have 2 or 3 inequalities. (I had thought about leaving the last sentence off, but I was trying not to overwhelm them.)
When I asked for their answers, I got crickets again. (Recall, I had tried this with them a couple of weeks ago and pretty much got no response from them.) So, I asked them for one inequality that would work. Crickets. More crickets. That, and a "I don't know how to work backward." After a few moments, someone gave me one inequality. So we graphed it and checked (4, 3) and it didn't work - (4, 3) was on the line. I asked him how to change it and he thought about it and came back with a different inequality. This time (4, 3) wasn't on the line, but he had the wrong inequality symbol. We flipped the inequality and had a working inequality. Yay! How about a second one? Crickets.... but for a shorter time. Same student, new inequality. Worked - success!
Can we come up with 2 different ones? Just try... Different student, new inequality. Got a working one and the student came up with a second one.
By the time we were done, we came up with 5 systems (look at the first 3 pages of the pdf below - first 5 slides). The first time we did an open question, I primarily had 3 students contributing. This time I had 6 or so contributing - 4 of them who had not last time. I'll take the improvement. Maybe next time, I'll have more.
Tomorrow I'm trying this question with Algebra 2 (similar to what I did with my Advanced Algebra 2's a couple of weeks ago):
I know that (2, 3) is the solution to a system of equations. Find two equations (in x and y) that have (2, 3) as their solution. How do you know that (2, 3) is the solution?
(I think that's how I phrased it.
Showing posts with label open questions. Show all posts
Showing posts with label open questions. Show all posts
Thursday, November 17, 2011
Wednesday, November 02, 2011
An attempt at an open question
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.
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.
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