I used the Shapes of Algebra acivity with my Algebra 2 students and my Algebra 1 students. We took 4 days to do the whole activity in Algebra 2. We finished our 5th day in Algebra 1 today. We have a few more days to go. I have really enjoyed this activity. It has given me opportunity to touch on items that I wouldn't get to normally in my Algebra 1 class. The way I did the activity was to first put each exploration on a different page with a place for a table and graph for each equation (I attached the file). We took about a day or so on each exploration, where the students received some instruction, then did some work and then discussed their results. I took the "alien" equation and had the students do that at a different time than the other three explorations. So far the response has been good.
Wow. This took a lot of class time. I was under the impression that splitting the experiments up to groups and having them present would only take about 90 minutes of instructional time max.
But I really like the worksheet with the graphs and tables! It's a nice addition to the investigation. Thanks for sharing.
Our old book Discovering Algebra is function based. We have all done this to some extent. I have some exceptional students and we were able to inquire how to graph x=2 even though it is not really x=.
The slope is sooooooooooo steep it looks like even though it cannot be.
Setting up y=20x
then y= 20x + 2...
no joy
then y= 20(x+2)
then y= 200 (x+2)
then asking how to make it x=2
is possible
this also sets the stage for y=(x-h)^2 +k
later on.