## High Dive

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.

Image Source: Key Curriculum Press, High Dive Teacher's Guide

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 $h\left( t \right)=65+50\sin \left( 9t \right)$ 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 $h\left( t \right)=80+50\sin \left( 9t \right)$? The midline would be at 80 or It would be shifted up 15 units.

What would happen to the graph if the equation were $h\left( t \right)=65+50\sin \left( 30t \right)$ 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.

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### 9 Responses to High Dive

1. Richard says:

Great post, Jackie. IMP is a great curriculum, and perhaps the results are best shown in students that went through three or so years of properly taught IMP classes. Too bad programs like this aren’t more common.

Great job.

2. Really nice problem. I’m thinking of animating it with the guy flailing around before he hits the water- or ground! Actually, the real reason I’m writing is that I’ve been creating some hobby tutorials on the practical uses of the imaginary number, and hoping to get some input from the teaching community as far as effectiveness. I’m not selling anything, and don’t have any advertising – just a hobby for making fun and interactive tutorials. Would appreciate a review if you get a chance, at picomonster.com.

3. Jackie says:

Richard I can’t take credit for the great job in getting these students to this point – it was my wonderful coworkers. I too wish it were more common. I also wish there were more agreement on what it means to “do” mathematics. (and I feel like I’m opening a can of worms with that comment).

Bradley I’ve taken a quick look. Interesting idea. I’ll get back there this weekend to peruse in depth.

4. Thanks for checking it out.

5. Pingback: Yarr? « Continuities

6. rachel says:

Your blog showed up in my google reader. I really enjoyed reading yours posts. I just bought some of the IMP books (even though my school, sadly, uses a more traditional curriculum) and I have really enjoyed looking over them, so far. I am planning to use some of the problems, but it’s very intimidating when you’re faced with seniors who’ve never been asked to do that kind of problem solving before!

7. Jackie says:

That could be tough for seniors Rachel, but I think it’s worthwhile. I’d love to hear how this works for you! (and thank you!)

8. emily says:

hey how do u get the 7,85 when figuring out the VV and VH?

9. Jackie says:

Emily – it might help to think of the units on the 7.85 (or 2.5pi). Was it a distance? Acceleration? Velocity?

Looking at Homework 2 might also help.