Multiply Who, a math game

This past semester I got to teach a senior project class. Four preservice elementary teachers working on understanding math games, game design and making their own. Sam came into class with the idea for her game. All the games were tested with kids, and went through multiple revisions and I'm really proud of their work and the games they made.

GUEST POST by Sam Bosma.

Learning to Go Forwards to Go Backwards

Many of us remember ‘learning’ multiplication in second or third grade. I remember ‘learning’ multiplication in 3rd grade through the use of flashcards. It didn’t matter what was happening behind the scenes just as long as I got the right answer/ could memorize the answer.
Too often with multiplication, we see children simply memorizing that, for example, 3 x 8 is 24 and not really understanding the ‘why’ behind how it works. The problem with this memorization is that once students move on to division, we see them getting very quickly. This makes sense since how can we expect students to go backwards (the undoing of multiplication) if they can’t even move forwards (multiplication).
In the game I have invented, Multiply Who?, my attempt is to have student thinking more deeply about multiplication instead of simply memorizing. In this game, students will have to find patterns and think about the components of each number in order to ask the most strategic questions in order to guess an opponent’s number.

If you are interested in learning more about this game, watch the video down below or click here for the instructions and rules.

John's postscript: I got to see one of the playtests of this game with a class of 5th graders and was impressed. The format of the game works really well for 2 on 2 playing. And though Sam put the sheets in sleeves, you could play directly on a printup as well. And the game is highly adaptable to level, by modifying the sheet. But the best thing to me is that this could definitely lead to students making up a sheet for playing and really getting to do the math.

Handout: gdoc, pdf

Make It, Take It

In addition to making their own game, the teachers made a video for a game of their choice that they'd like to see in a classroom. Sam chose Make It, Take It, a money game I made up a long time ago for a teacher that wanted a money game for 2nd year.

Again, highly adaptable. It's nice how just the progression of play gets players to think of new combinations.

Handout: docx, pdf

Running Out of Options

This game was a favorite for Paul Rettinger, a brilliant grad school room-mate I had at Penn State. He went from a Master's of Fisheries and Wildlife to a law degree. Amazing guy. I was lucky to ever win.

Last Letter Loses

Players take turns adding a letter to a word. The first player to be forced to spell a word (at least three letters) loses. A player can challenge the previous turn if they think there is no such word. If there is such a word, the challenger is out. If there is not, the challenged player is out.

Example:
1- A
2- A-M (doesn't lose because less than 3 letters)
1- A-M-E (P would lose, even if you're thinking of 'amplify', since amp is already a word.)
2- A-M-E-R (thinking of america)
1- (thinking they're in trouble) A-M-E-R-I
2- (happily) A-M-E-R-I-C
1- (inspiration strikes) A-M-E-R-I-C-I
2-(thinking what? that's not a word!) Challenge
1-Americium! I still would have lost but thought you might not remember that word. (It's an element.)

In that example Paul would have been player 1, snatching victory from the jaws of defeat.

(From a repository of free educational clipart, click the image.)

That inspired the following game, which I use to introduce prime number decomposition.


Last One Loses

Players take turns breaking down a number by multiplication. The first player starts with a whole number. The next player makes a string of two numbers that multiply to give the first. The next player then can break down one of the two numbers, making a three number string. The last player who can break it down is the loser of the game. Numbers chosen must be able to be broken down more than twice. A player may challenge if they disagree with a breakdown, or if they say it's the end but it's not. Players may not reuse starting numbers. 1 may not be used in the breakdown. You can't use a number that's been used this session.

Example 1:
A- 24
B- 3x8
A- 3x4x2
B- 3x2x2x2 - augh! (loses)

Example 2:
A- 112
B- 2x56
A- 2x2x28
B- 2x2x4x7
A- 2x2x2x2x7 - curses! (loses)

Instructional uses:
Have students keep track of which numbers make first player lose, and which numbers made second player lose. When the data is collected, students will see that the same number almost always has the same effect. (Although there's usually a number that was mis-factored.)

Pose the questions: what if you break the number down in a different way? Is it always the same number of steps? Is the end result always the same?

Several important ideas about the prime decomposition will come out immediately, including the idea of prime numbers! Also why 1 is not a prime. (And 1 is NOT a prime.)

I allow calculators for numbers bigger than 144. Follow up investigations can be things like: find a number that takes 6 steps and is between 500 and 1000, or trying the Sieve of Eratosthenes.