The Locker Problem: Factors, Multiples, Primes, Composites, Squares

October 3, 2014: Please note, this is now 87 fun filled pages, and includes everything below with additional activities:

Activity: Dude, Where's My Locker? These are 10 different "clue games" about multiples and factors to find a locker. Includes a Do It Yourself sheet so your students can make their own problems and share them.

Activity: Let's pick a number - my friend walks into the classroom with a jar of tiles labeled 1 - 100. She is blindfolded and makes the following offer: "If I pick out a square number, I'll pay you $1. If I don't pick out a square number, you have to pay me $1." Should you take the bet? There are 4 other scenarios like this, complete with an answer key.

This is my magnum opus: a fully documented version of the infamous "Locker Problem."

What is the locker problem, you ask?

It is a magnificent problem which asks the following: if you had 1,000 lockers and 1,000 students, and the students took turns reversing the position of the locker (that is, the first student opens all the lockers, the 2nd student closes every 2nd locker, while the third student reverses the position of every third locker, etc.), which lockers would be open after all 1,000 students have had their turn?

This is an incredibly rich problem for investigating starting with the nature of mathematical modeling (students plan and build models of the problem as well as use and critique them.) They then use the data they collect to investigate the nature of multiples and divisors, then extend their knowledge to include primes, composite and square numbers.

But wait, there's more: they then extend their thinking to classify numbers as "abundant," "deficient" or "perfect" and use them to play a factor game, both against an opponent, or against the computer (links to the computer program are included.) They make predictions about what moves are most optimal and then apply them to game play.

BUT THERE'S MORE!

• Locker Puzzles involving factors and multiple
• Extensions into Triangular Numbers, the Sieve of Eratosthenes and the application of prime numbers to securing data.
• Graphing square numbers

And much, much more, including full documentation, photos of students and their models, answer keys.... everything EXCEPT the kitchen sink.

This may be the most thorough documentation of the this problem you will ever see!

Great for enrichment classes, homeschoolers, and those who love, LOVE to putz around with math. Anybody who uses it will become an expert on elementary number theory. How about that!