In our introduction to systems, we reviewed some basic concepts about lines. We started with "I Notice, I Wonder "... with the graph of a single line that I snipped from Desmos. Here are my students' thoughts:
I notice …
...That it is a straight line
...It’s linear
...It has a positive slope
...It has points in 3 quadrants
...It’s y-intercept is (0,2)
...It’s the linear parent function translated
...It’s linear
...It has a positive slope
...It has points in 3 quadrants
...It’s y-intercept is (0,2)
...It’s the linear parent function translated
I wonder …
...What the equation is?
...If the line ends?
...What the slope is?
...What’s the point to this?
...Does it represent data? If so, what data?
...What does it mean?
...What’s the relationship to the parent function?
...Why doesn’t it go through the origin?
After just a few minutes of noticing and wondering we discussed intercepts, slope, and graphing linear equations by hand. Right before I was going to plunge into systems ... I put the slide on the board that asks, "What is the solution to 2x - 3 = y?" The slide included a graph of that line. There was a great pause. Only one student out of six classes could respond immediately. In all of the other classes I needed to coax them to the correct response.
I waited ... let the pause hang in the air. Then I suggested that we build a table of values for that equation. Students helped me build a short table. I asked, "Are these solutions to that equation? How do you know?" Only then could I see eyes widen, heads nod, thoughts churning ... the graphed line represented the infinite solutions to that equation!
It was a good day in Room 730!
