Lesson Idea: Investigating Linear Function Graphs Lab

Last year, after weeks of working on linear equations, slope, and y-intercept, my students were still lost on the nuances of the concept. I thought that how changing the slope and y-intercept would effect the graph was obvious. Sure, you could graph equations to compare and contrast them on the graphing calculator, but the problems would be a hundred times easier if they could visualize these effects without the calculator. I also thought that I could connect these ideas to simple quadratic equations (in y = ax² + c form).

I did some research and found various permutations of lessons where students would graph various linear equations and observe the differences, but nothing fit the bill. So I put together a first version, which incorporated many different ideas into one lab. Long story short, it was far too complicated and served only to frustrate my students.

So I rewrote the directions and questions, eliminated the quadratic equations (important of course, but distracted students from the linear equations part) and anything else that took the focus off of what happens when the parameters of linear equations change.

The goal is to get them to start to predict and visualize what changes in the equation will do to the graph, and to be able to problem solve, make observations and plan

The lab follows the scientific method and the structure of the type of lab reports I used to write for science classes in middle and high school:

1. Pose a question: How can we predict the shapes of linear equations without a calculator?
2. Do research: Already done through our previous work.
3. Construct a hypothesis: In class, I define hypothesis and connect it to what they have done and will do in future science classes. Based on our work thus far, what do they think is the answer to the question we posed?
   
4. Test the hypothesis in an experiment: Graph groups of linear equations with one parameter changing (y-intercept only, increasing and decreasing slope, changing the sign of the slope) with calculators, in order to make observations about how we might figure out what will happen without calculators.
   
5. Make observations and analyze data: I keep the questions very focused on the observations I think should be obvious (for better or worse).
   
6. Draw a conclusion: Was the hypothesis correct? What did you learn from this experiment?
   

This year's lab still took two class days to complete, but unlike last year, they were two productive days. I have still not figured out how to word the observation questions to avoid all confusion, but again, perhaps that's my problem. I keep trying to drive the students toward the conclusions I want them to draw, towards seeing these equations the way I see them. Perhaps that's my fatal flaw: I can't expect all of my students to see things my way. Maybe they don't need to, if they can see the big picture themselves.

The TI-Navigator could obviously be integrated into this project, however, I think it's better that the students make the graphs and draw conclusions individually.

Math Lab: Investigating Linear Functions Graph (via Google Docs)

If you can improve upon this idea, please let me know so I can share it here (teachforever AT gmail DOT com).