Pick on Someone Your Own Size

A Math Mystery Game

A Math Mystery Game

Fourth grade students in Mrs. Bruckbauer’s class described this as a math mystery game, because you’re trying to find out what the other player’s hiding.

Materials: game sheet, calculator (if needed for checking), scrap paper for making your plays.

How to Play: Each player comes up with 3 numbers that add up to 1000. When both players are set, they fill in the fight boxes from largest to smallest. You get a point when you have the greater number.

For example, 800, 100, 100 and 500, 300, 200; player 1 gets 1 point and player 2 gets 2 points. It’s okay to have two of your numbers be the same. If your number is equal to an opponent's, no points.

Player1 Player 2

800 > 500

100 < 300

100 < 200

1 point 2 points

You play for five rounds, and the person with the most points wins.

Player 1 Score ....................................................................... Player 2 Score

PDF of the game.

Teaching with the game: I started with a guessing game. I picked a number between 0 and 1000, and they tried to guess it, using only my more or less answer as clues. I picked 673, and the students took turns guessing. I wrote down on the resulting comparison. using x for my number, like x>89. They guessed: 89, 587, 1000, 998, 823, 650, 657, 760, 700, 699, 689, 666, 680, 676 and 673. (I wrote 673, then x then filled in the =, to great rejoicing, x=673.) Just refreshing use of the comparison relation, and seeing how they were with ordering numbers in the hundreds. They really enjoyed this, and I think that could be turned into a lesson of its own.

Then I played me vs. the students, as I often like to teach games. It solidifies rules and shares some strategies. My triples were (900,99,1), (500, 250, 250), (501, 498, 1), (350, 350, 300), (501, 301, 198). As the students played later I saw them using several variations on these, and also the idea of modifying a previous guess.

The game was really engaging, and students took their guesses seriously. I watched at first, and a couple hadn't really gotten the adds to 1000 idea, and several had to be reminded to put their guesses in order. I went back and forth on that in design, but it really worked well for game play.

Rules they wanted to add were having 1/2 point or 1 point each for ties, and playing an extra set if it ends in a tie. The ties were nice for getting the students to modify their guesses up or down a few ticks.

The math involved encourages students to think about sums to nice numbers, as well as how to partition 1000. I shared with students how they could pick two numbers and do 1000-sum to find the third. We had calculators for them to quickly check their opponents picks, but mostly they did it in their head. Several students, not too familiar with the calculators, really enjoyed playing with them to try different numbers.

Game analysis: it's a little more interesting than you might think, kind of a nuanced Roshambo. (Rock-Paper-Scissors) The three basic strategies are big-small-small, medium-medium-small, and third-third-third. Of course, you can win by a point, and that's where some nuance and psychology comes in. Much like Rock-Paper-Scissors.

Let me know if you give this a try and what you think! Thanks to Denise at Let's Play Math! for catching the missing instruction.

You wrote, "several had to be reminded to put their guesses in order." So is that one of the rules, that the numbers should be listed in (checking the examples) descending order? If so, you should state it up above.

ReplyDeleteSounds like a fun game! I think I'll give it a try at our next elementary math club meeting.