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Math OER
Dice Games Playground

So Einstein was wrong when he said, "God does not play dice." Consideration of black holes suggests, not only that God does play dice, but that he sometimes confuses us by throwing them where they can't be seen.

- Stephen Hawking

These games ask players to make decisions based on the numbers rolled with dice.

Many of these games involve mental arithmetic. Others ask players to place the number they roll on a game board, or pick which game board square they will claim with the number they roll.

Most of the games are fun for all ages. But a couple require careful arithmetic.


Addition and Subtraction

No Pigs! No Pigs!

Equipment: two six-sided dice, perhaps paper and pencil

The game always has five rounds.

five turns and total

For this game, the 1s on the dice are called pigs.

Each round begins with rolling both dice. If either die rolls 1, reroll how that round starts until neither die is 1. Now the players choose to either "play it safe" and keep the total of both die or "be risky" and go for a running total.

If any player chooses "be risky", the dice are rerolled. If either die is a 1, the players who chose "be risky" gain no points for that round. If neither die is a 1, the choice repeats. Those players who just picked "be risky" may "play it safe" and keep the running total so far for the round, or continue to "be risky" and attempt to gain a higher score for the round.

The round ends either when all players have "played it safe" or when either die rolls a 1.

The game ends after five rounds. Players add up their score for a grand total. The highest total wins.

Note: To practice other arithmetic use more complicated dice. How about rolling two ten-sided dice and a six-sided die, then finding the product of the ten-sided dice and subtracting the six-sided die? Similarly, younger children might need to start with only one six-sided die and then work their way up to using two dice per roll.

Note: This game is a variation of the old British game named Pig.

Cameron's Game

Equipment: a pencil, two six-sided dice (one of which is labeled 5 to 10), the game paper below

The game uses a blank five-by-five grid, like an empty bingo board. The center spot is a "wild" spot that both players can use to win.

Cameron's Game

The other twenty-four spots need a number. So before the game starts, the two players fill up those spots with numbers. They take turns writing numbers, counting from 1 up to 12 in any twelve of the empty spots. Then they do it again. Now every empty spot has a number.

The basic game is to play five-in-a-row. On your turn roll both dice. You may add or subtract, which provides a choice of two values. Hopefully one of those two values represents an unclaimed spot on the board, so you can claim a new spot. (If not, you lose your turn.)

If neither player can get five-in-a-row to win, the player that claims the most spots wins.

For a more advanced game, try four-in-a-row. Trickier!


Place Value

101 and Out

Equipment: a six-sided die, two types of objects to represent tens and ones (see below)

The game always has six rounds. In each round, the die is rolled and each player chooses to take that number of either tens or ones.

A running total is kept for each player. After six rounds, whomever is closest to 100 withut going over wins.

Note: There are many fun ways to represent ones and tens: pennies and dimes, Base Ten Block units and tens, Cuisenaire rod ones and tens, tiles and taped strips of ten tiles, beans and popsicle sticks on which ten beans are glued, sticks and bundles of ten sticks, etc.

Reject

Equipment: paper and pencil, one ten-sided die

Players each use a game board with empty place value spots for ones through ten-thousands, as well as an extra spot labeled "reject".

reject game board

The game always has six rounds. In each round, the die is rolled and each player picks where to put the rolled number: in a unused place value spot or in the reject box. After six rolls, the player with the largest number wo can read it aloud wins.

For a "beginner" version of the game that can help teach the concept of place value, use fewer digits.

Here is a version with three digits (and the reject box) that is useful to an average first-grader that somewhat understands the concept of hundreds but is still a bit foggy about thousands. A game would involve four rounds, since there are four spots to write a number.

reject beginner game board

This game works equally well with more than two players/teams.

The Caves of Wumpus and Grue

Equipment: paper and pencil, four six-sided dice

Play alone or cooperatively with friends! Roll dice to explore a cave system of 16 rooms. Hunt the wumpus! Don't get eaten by a grue.

wumpus game board

This game is, of course, a tribute to Hunt the Wumpus and Zork.


Fractions

Starship

Equipment: one game board per player

This is a fun version of battleship. Players can shoot "rays" instead of always targeting one board square at a time.

(In December 2013 I glanced over this WSJ article, which mentioned a game named Battleship Numberline. I misread the name as "Fraction Battleship" and was disappointed that the game was not about equivalent fractions on Battleship boards. So I invented the game I had in my mind. There is some subtlety involving the shapes of the ships and how to fit them in between the common "rays" made by equivalent fraction combinations.)

starship game board

This game works equally well with more than two players/teams.

Fraction Bingo Twenty

Equipment: one game board per player, one twenty-sided die (percentile dice may be used instead to teach about percentages)

Each players draws a five-by-five bingo board with five "free" squares as arranged below.

fraction bingo twenty game board

Each player arranges the following twenty fractions in any order in the remaining squares of his or her bingo board.

1/2

1/4, 3/4

1/5, 2/5, 3/5, 4/5

1/10, 7/10

1/25, 4/25, 7/25, 9/25, 11/25, 14/25, 16/25

34/40, 36/40, 38/40

124/125

Players take turn rolling a twenty-sided die. The die shows the numerator for a fraction whose denominator is always 20. With each die roll all players cross out the remaining fraction closest to the fraction produced by the die roll.

(The fractions are carefully chosen so that even different-looking pairs can be compared by "unreducing". Multiply the denominator by a number to change it to 100, then be fair by also multiplying the numerator by that number. Initially each fraction on the bingo board is within two-hundredths of a different die roll fraction. But as the game goes on the closest remaining game board fraction can grow farther in absolute value from the die roll fraction.)

One or more players win by being the first to score a five-in-a-row "bingo" using the current die roll.

The fourth and fifth grade students I work with love this game. It has just the right blend of cooperation (working together to determine which remaining fraction is closest in value to the die roll fraction) and competition (getting "bingo" first).

This game works equally well with more than two players/teams.


Multiplication and Division

Twenty-Four

Equipment: four ten-sided dice

The classic game Twenty Four involves four numbers supplied by a moderator, dice, or cards. Players or teams race to use these numbers along with any arithmetic operation, parenthesis, or fraction bars to get to 24.

Each of the four provided numbers must be used once and only once. Two answers are considered the same solution if they only differ by having terms rearranged.

Example of Twenty-Four Game

Consider these four provided numbers: 2, 3, 4, and 6

Possible answers include (2 × 4) × (6 − 3) and 6 × 4 × (3 − 2).

Can you find any of the other answers? There are at least seven more!

Note that (6 − 3) × (2 × 4) is not a new answer because that is merely the first of our answers with terms swapped.

This game works equally well with more than two players/teams.

In the classroom it works well to divide the class into three teams that earn points by finding correct answers. Most sets of four numbers provided will have many possible answers, so do not stop just because other teams have found some answers.

Here are more examples of four provided numbers, with each set having many answers.

Play the Twenty Four Game with these numbers: 1, 2, 3, and 5

Play the Twenty Four Game with these numbers: 1, 2, 4, and 12

Play the Twenty Four Game with these numbers: 2, 3, 5, and 11

Play the Twenty Four Game with these numbers: 3, 3, 6, and 9

The Invisible Fairy Race

Equipment: four six-sided dice are shared, each player needs one gameboard, a pawn or other marker, and book to hide those before

This game is my simpler way to make Twenty-Four more fun. Having multiple target numbers makes the game fun even when students have different amounts of arithmetic proficiency.

Each player moves a pawn along the path, racing to get to the end first. But the players do not know where each other's pawns are.

On your first turn, roll 1 die and move that many spaces forward.

On later turns, roll 4 dice and try to use all four numbers and basic arithmetic to make a certain number.

If you can, make the number of your pawn's space. That allows you to secretly roll 1 die and move that many spaces forward. If you cannot, make any other number. Then any players whose pawns are on the space with that number must (each separately) roll 1 die and move that many spaces backward.

Finally, you can always decide to skip rolling dice, and simply move forward 1 space on your turn. That can help you get past spaces whose numbers are difficult to make (such as 17 and 23).

fairy race game board

Contig

Equipment: three six-sided dice, pencil and paper, two sets of tokens (to claim squares)

Contig (and Contig Jr.) are nicely enhanced versions of Twenty-Four by MathWire. These games are available here.

As with The Invisible Fairy Race, multiple target numbers allow the game to be fun even when students have different amounts of arithmetic proficiency.

This game works equally well with more than two players/teams.


Geometry

The Kittens of Tindalos

Equipment: the game paper below, patterns blocks (triangles, rhombuses, trapezoids, and hexagons), one eight-sided die

Start the game with "Tindalos" having one pattern block of each shape.

Your turn has four parts.

The player that first finds six kittens wins.

The Kittens of Tindalos game board