How to teach the division algorithm?

Question

What is the best way to introduce the division algorithm? Are there real life examples of an application of this algorithm. At present I state and prove the division algorithm and then do some numerical examples but most of the students find this approach pretty dry and boring. I would like to bring this topic to live but how?

Answer 1

[Cue sci-fi sequence.]

A number of clones in an underground cloning lab escape from their enclosure. Most of the clones are from the same batch, and they all weigh 150 pounds. There is also a clone from a later batch--not as fully developed, only weighing 50 pounds. They manage to reach the elevator out of the facility, and through [plot contrivance] are able to make it operational for one trip up, only. The elevator has a 2000 pound carrying capacity. How many of the grown clones will escape the facility (assuming that the volume of the elevator is not a restriction)? Will the elevator be able to carry the youngster?

Tune in next time, for Division Algorithm!

[Cut to black.]

Okay, that isn't a real life example, but it certainly isn't dull.

You have a pocket full of quarters (39 in all) and a serious gumball craving. The supermarket gumball machine charges a dollar per gumball. (The money-grubbers!) How many gumballs can you get, and how many quarters will you have left?

That isn't quite as exciting, but it's more "real."