So I am really looking over problems I have posted and am trying to see if I have fallen into the Teacher trap of being “too helpful” with directions. Looking at this problem:
Using the numbers 1 to 4, using each only once, create 2 points that lie on a line with the following conditions:
1) The line has a positive y-intercept
3) The line has a negative y-intercept
3) The line has the greatest slope possible
4) The line has the smallest positive slope possible
5) The line has the greatest negative slope possible
6) The line has the smallest negative slope possible
Looking at this, I know why I was so specific about the instructions. I was thinking of Open Middle Problems, where you present a problem that seems like a nutshell- but actually allow students multiple paths to find the answer. I like my overall thinking of the design, but I want to change it for class.
I’m thinking of starting like this…
Using the numbers 1 to 4, using each only once, create 2 ordered pair and graph them
Describe the characteristics of the line they create as accurately as you can.
Arrange the numbers to form ordered pairs that create a different line.
Compare the two lines.
My hope is to have students discussing characteristics of lines, and if they fall short of what I expect that I can ask a good guiding thought question to get it there. Once students get a different line down and we start comparing it, there should be variation on what types of lines they are, answering the original question set.
No better way than to test drive it.