I really, really like my new prep – IMP4. Our first unit is High Dive. It covers topics from trigonometry with some physics thrown in for fun. Students are given the following situation and are asked to determine when to release the person from the platform so they land in the cart of water.
We first consider the diver’s height as a function of time – which nicely develops the sine function. They were able to come up with rather painlessly. They have also developed a nice understanding of the relationship between the graph and the equation.
What would happen to the graph if the equation was ? The midline would be at 80 or It would be shifted up 15 units.
What would happen to the graph if the equation were Well, that would be a faster angular speed so the period would be shorter. The period would be 360/30= 12, which means it makes one rotation every 12 seconds.
I wasn’t sure if they really understood transformations, so I threw a few graphs on the screen (I love Grapher!) and told them they had 4 minutes to work in their groups to determine the equations that generated each function.
Transformations were tough for my seniors last year1. This year? They rocked.
What most impresses me though is they way in which they are working in class. Their ability (and willingness) to tackle the usually dreaded word problems is amazing. They volunteer alternate methods of solving problems. They ask questions when they’re stuck. Good questions. Not “I don’t get it” but “”How did you know that would work?” or “I didn’t understand that. Can you explain it again?” Then other students answer the questions. Really.
I owe their previous teachers a big round of thanks. They came to be with these traits on Day 1. It has inspired me to work even harder at instilling these habits of work in my freshmen.
1This is our first year of teaching IMP4.