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## Follow (and Use) The Bouncing Ball

Recently, I re-discovered a teaching idea suggested by Denise Miller via an early Math Forum discussion (1996). I do not know Denise or where she teaches math, but she deserves full credit for what follows.

Denise's suggestion for teaching Sequences and Series....

First: Involve students physically in gathering data. Drop a ball from a marked height, and record heights for each bounce. Analyze that data, describe patterns in data, and try to create a math model.

Second: As a class, discuss and develop traditional concepts of sequences and series, both formulas and recursive form.

Third: Show an application. Here Denise offers a surprise...show the 1946 B&W English movie Dam Busters. Why? Anyone ever heard of that movie?

As Denise writes: "The movie traces the history of a bomb run on German dams during WWII. A mathematician had an idea to get through the defenses of the dams supplying the power to munition factories in Germany by dropping a 5-ton bomb from just the right height so that it "bounced" across the water in a predictable way (ala sequences and series) through all the conventional defenses and landed right on the dam itself as it exploded!"

Denise continues: "The movie started with a physical model he built in his "cottage" while the kids are running around. next model is a water tank in some military installation. Then a larger model outdoors. They devise a simple way to know exactly when it's time to drop the bomb...fantastic development of problem solving in a realistic way."

Not having ready access to this 1946-era movie Dam Busters in 1996, I filed Denise's suggestion. Now, on my discovery, the key aspects of the movie and related events can be accessed via YouTube:

• Clip One is movie re-enachment of Professor Barnes Wallis' attempts to calculate precisely the "bounching bomb" patter (i.e. the sequence)
• Clip Two is actual footage of British bombers practicing the "bouncing" bomb, trying different release heights, distances, etc.
• Clip Three is a another segment from the movie Dam Busters, showing the multiple efforts to "bounce" the bomb successfully to breach the target dam...complete with the worried mathematician fretting silently that his mathematical plan may not work
• Clip Four is the full movie Dam Busters...two full hours worth!
• Clip Five is a one hour modern examination of the myths and realities of the movie Dam Busters...not specifc to any mathematics, but it proved to be a worthwhile viewing experience on many levels.
If you have gotten this far and reviewed the footage, I hope you enjoyed the varied learning experience as much as I did. Thanks, Denise....!