Monday, May 23, 2016

Division Dice (math games class)

Who: grades 3 and 4
Where: in school

A dice division game

We created a simple dice game to practice division. Here's a description of the basic element of play:
  1. roll three dice: for example, 3, 4, 5
  2. group two of them into a two digit number: for example, 45
  3. Divide the two digit number by the remaining single digit: for example, 45 / 3 = 9
  4. This value is your score for the round
  5. First player to 200 or more points wins (we used 100 for the initial game)
Key constraints
  • You can only score points if the single digit is a factor of the two digit number (remainder must be 0)
  • Where there are multiple options, the player can choose the combination that gives them the maximum score
This pencilcode program (see code) analyzes this basic game structure, identifying how often there will be no legal scoring arrangement and showing a histogram of the largest scores.


I wasn't satisfied with three elements of this game: (a) any time a 1 occurs, the division calculation is too easy, (b) too many combinations don't allow a score (about 15%) and (c) there aren't many decisions for the students to make (just six combinations to investigate).

We addressed these by adding two extra rules:

  • 1 is a wild that must be replaced by a value from 2 to 6 (cannot be left as a 1)
  • On your turn, you can flip the over the dice in the two digit number. For example, a 6 can be flipped to a 1, 5 to 2, 4 to 3, etc.
The first point removes the division by 1 cases, the second one allows more choices and reduces the number of non-scoring cases.

Allowing the dice flip and wild 1s seems to make the game too loose. Instead we dropped the wild 1s rule and added these two:

  • Division by 1 is not allowed in the game
  • If you roll triple 1, re-roll

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