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:
- Pose a question: How can we predict the shapes of linear equations without a calculator?
- Do research: Already done through our previous work.
- 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?
- 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.
- Make observations and analyze data: I keep the questions very focused on the observations I think should be obvious (for better or worse).
- Draw a conclusion: Was the hypothesis correct? What did you learn from this experiment?
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.
If you can improve upon this idea, please let me know so I can share it here (teachforever AT gmail DOT com).