# Math Teachers at Play #29

The last time I hosted Math Teachers at Play I attempted to start a tradition of including a math puzzle pertinent to the number of the carnival. Alas, it didn’t take, but now that I’m hosting again I can mention an old classic:

Three people check into a hotel. They pay \$30 to the manager and go to their room. The manager finds out that the room rate is \$25 and gives \$5 to the bellboy to return. On the way to the room the bellboy reasons that \$5 would be difficult to share among three people so he pockets \$2 and gives \$1 to each person.

Now each person paid \$10 and got back \$1. So they paid \$9 each, totaling \$27. The bellboy has \$2, totaling \$29.

Where is the remaining dollar?

If you’re a teacher, here’s a meta-question: can you generalize the errors made in the puzzle? Can you give a textbook, not-designed-as-a-puzzle example where this happens?

### Teaching

Ryan at Maths at SBHS ran a lesson using a segment from the show Community, and wants to know how to make it better.

Pat Ballew writes about The Marginal Economics of a Kindergarten Education — how much is an education really worth?

Research demonstrating misunderstanding of the equal sign has been in the news lately. Maria Miller takes up the case.

Meanwhile, David Wetzel wants to eliminate elementary student math misconceptions.

Should we be discouraging young students from finger counting? Caroline Mukisa examines the debate.

Mark Graybil ponders the choice between Java and Javascript in classes the require programming.

### Learning

Pat Ballew reaches to this category as well with an “Almost Pythaogrean” relationship.

Sue VanHattum posts a video from the Richmond math salon, which she describes as “A monthly math festival in my living room.”

Scott Palat also reminds students to get help when needed.

Guillermo Bautista has an excellent way of making sense of exponential growth.

Denise at Let’s Play Math has an equally excellent introduction to probability.

John Cook finds Three surprises with bc, which is as he describes “an arbitrary precision calculator with only five basic math functions. This post explains how to bootstrap these functions to do everything you’d expect from a calculator.”

Last but not least, Sol Lederman wants to share a “very interesting and simple trick to impress your friends” involving 12 pennies.

And that’s a wrap! Math Teachers at Play #30 comes next month to JD2718.