We’re in the “World of Functions” unit in IMP4. This may be my favorite unit in the whole curriculum.
Instead of a separate sections on linear, quadratic, radical, rational, exponential, …, we’re studying functions. Delving deeper into the relationship between the table, the graph, and the equation. Working on translating from one form to another to another. We’re doing application problems too. Lots of them.
Of course, they’ve used to working from multiple representations. They’ve been doing it for almost four years now.
This week we began algebra of functions.
I gave my students the following graph and asked them to draw , , and .1
I didn’t tell them what to do. They didn’t need me to. They figured it out. They helped each other. They debated. They used numerical examples. They figured it out.2
Did they all do it perfectly on the first try? No. After working on it in their groups? Yep, most of them. Did they all try? Yep. Not one person sat there waiting for me to tell them what to do. No one said “I can’t.” A few are still working on solidifying their understanding of this. I’m okay with that. Not everyone gets it at the same time.
I’m blown away on a daily basis by my seniors in IMP4. Both by the mathematical understanding they’re demonstrating and they willingness with which they tackle new problems. I’m not sure which impresses me more.
1While not exactly a “What Can You Do with This” image, I still like it.
2We also discussed when f/g would be undefined and why f*g needs a scale. Any other ideas as to where we could have taken this?