Wholes: The Game

by Joseph Hartman

e-mail: tentwelveeight@yahoo.com

| Instructional Objective | Learners & Context | Object of Game | Game Materials |

| Time Required | Rules | Design Process | References |

Instructional Objective

Wholes: The Game is intended to reinforce in young players the understanding that fractions, percents, decimals conversions of fractions, and fraction graphics are all representations of values between zero and one whole on a number line. Additional concept reinforcements include the idea that fractions can be added together to create one whole. Wholes: The Game is intended for classroom use in grades as low as 4 and as high as 6. The specific curriculum area addressed by Wholes: The Game is under Number Sense "Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths." Read more of the Grade 4 Mathematics Standards for California here.

Learners & Context of Use

The game is designed for upper elementary students ages 9-11 or in grades 4-6. The strength of Wholes: The Game is that it reinforces already learned concepts. It is most effective with students who have studied fractions, percents, and decimals, but have not yet mastered the conversions between the three. While the game is intended for classroom use, it may be wise to provide a separate area for the students to play the game as it is likely the players will make noises during play that could distract others from learning. The game is designed to be played from beginning to end very quickly and is open to expansion packs of cards to reinforce fractions of different and more difficult denominators.

Who is the game designed for? Describe them in terms of their age, grade level, affinity towards the subject matter, and anything special about them that the reader should know.

Where would the game be used? If in a school, what accomodations would you need to make to do it in a typical classroom? Is it designed to be played more than once? What would happen prior to the game? What would happen after it?

Object of the Game

The object of Wholes: The Game is to be the first player to reach the last space on the game board.

What's the game goal? What's the end state that players are striving for (e.g., to be the first to reach the Finish square, or to be the first to reach 100 points.)

Game Materials

Materials included in the box:

  • one board to be used as a score keeping device. The board has 20 spaces, each space representing a fraction of 20. For example, the first space would be the fractions one-twentieth. The twentieth and final space is twenty-twentieths, or one whole.

  • three of each of the following types of card (36 total)

    • graphic representation of one-fourth, one-half, and three-fourths. These can be either in the form of a pie or a rectangle, so long as it is clear which fraction is being represented on each card.

    • the fraction one-fourth, one-half, and three-fourths. These cards should be written consistently with the numerator over a horizontal line and the denominator beneath the same horizontal line.
    • the decimals 0.25, 0.5, and 0.75
    • the percentages 25%, 50%, 75%
  • one REPLAY card allowing the holder to play two turns in a row if they choose.

  • two SWAP cards, allowing the holder to switch board positions with another player if they choose.

  • one BAIT card allowing a player to bluff without consequence if they are caught.

  • six game pieces of different color but similar shape.


List each of the physical objects one would find in the box. For example, the board, each type of card, each type of prize or token, etc.)

  • xxx
  • xxx
  • etc.

After listing the materials, describe each in as much detail as needed. Include illustrations of the board and each type of card.

Time Required

Game set-up takes only a few minutes to deal the cards and select game pieces. Depending upon how many players bluff and how often they are caught, the game length will vary between ten and twenty minutes. Play is not carried over from game to game.

The Rules

Starting the game

  • Cards should be shuffled and dealt to each player beginning with the player on the dealer's left.

  • Each player receives five cards to start the game.


  • Each player's turn begins by drawing a card.

  • A player may choose to play or not play cards during a turn.

  • If a player chooses not to play during a turn, they signal this by saying "pass," at which time their turn is over.

Playing cards and moving on the board

  • A player moves on the board by playing cards from their hand that , when added together, equal EXACTLY one whole.

  • A player moves the same number of spaces on the board as cards that they played during their turn. For example, if a player plays three cards that equal one whole during their turn,  they are allowed to move forward three spaces on the board.

  • A player must vocalize the addition of the cards they are playing when playing them. For example, a player might say, "one-half, plus one-fourth, plus twenty-five percent equals one whole."

  • Cards must be placed face down by the player when played from the hand.


  • During their turn, a player may elect to bluff about the cards they are playing.

  • Bluffing or not, a player is still responsible for vocalizing the cards they are playing or pretending to play.

Calling Bluffs

  • If at any time after a player has played, and before the next player has drawn, a player may elect to "call" the play.

  • To "call" another player, the "caller" picks up all of the cards that were used during the turn and verifies either the accuracy or inaccuracy of the play.

Calling Bluffs Correctly

  • If a player correctly calls another players bluff:

    • the caller is allowed to keep all of the cards used by the bluffer to bluff during that turn.

    • the bluffer is moved back to the space on the board where they started their turn, and also moves backwards on the board the number of spaces equal to the number of cards they attempted to bluff with.

Calling Bluffs Incorrectly

  • If a player incorrectly calls another player's bluff:

    • the caller moves backwards on the board the number of spaces equal to the number of cards played during that turn.

Special Cards

  • The SWAP cards allow the holders to switch positions on the board with any other player at any time during the game.

  • The BAIT card allows the holder to play the BAIT card during their turn and not be penalized if another player "calls" the play. Instead, the "caller" is penalized as if he/she has incorrectly called a bluff.

  • The REPLAY card allows the holder to play two turns in a row. The REPLAY card can only be played after the holder has already played their turn and before the next player has drawn.


  • The first player to reach the final space on the board is the winner.

  • A player may "overshoot," (does not have to land directly on) the final space to win.

Design Process

Being a 6th grade math teacher, the first subject that came to mind was a game dealing with math. Understanding the correlation between fractions, decimals and percents seems to be a perpetual issue for young students, and it quickly became a subject I knew I wanted to explore for the game. Thinking about card games had already got me started on the idea of poker hands and bluffing, and when I remembered one of my most favorite and simple games from childhood (B.S.), I knew I wanted to incorporate the aspect of bluffing into my board game.

B.S. is very similar to Wholes: The Game. It simply requires that a player play all four cards of a given number from a standard deck during a turn to get rid of cards in their hand. The first player to get rid of their cards is the winner. Yet I recalled a fatal flaw in B.S., that the strategy of simply collecting as many cards as possible would almost always result in success. This is because the other players would be left with very few cards to play, while the collector would never be caught bluffing because he/she always had all the cards. To combat this flaw, I at first played around with the idea that players could move only one space during a turn. Trial games soon exposed that rule as unnecessary and hindering to the pace of the game. The rule that was put instead of this rule was that players could play only hands that equaled exactly one whole, no more, no less. Unless of course they were bluffing.

Another aspect of the early game that I abandoned was the idea of having "Safe" places on the board on every third or fourth space. The idea was that these safe places would be where a player would be moved back to if they had been caught bluffing, or incorrectly called another player's bluff. Unfortunately, trial games revealed this idea as complicated and unnecessary as well. Instead of helping players if they were caught bluffing or incorrectly calling bluffs, it encouraged all the players to call bluffs while they were on the safe space. The idea of moving backwards or forwards the number of spaces equal to the cards played during a turn eventually seemed to make the most sense and keep the game moving at a more desirable pace.

The most helpful experience in designing the game was in having other people play it. The comments that were made both in play and afterward were infinitely helpful in refining the purpose and rules of the game, while also reinforcing my idea that it could indeed work. Playing other game prototypes was also very helpful, as it forced me to notice what it was about games that was fun and exciting, as well as what aspects of games were cumbersome and unnecessary. Ultimately, the lesson that I took away from playing prototypes and having my own prototype played, was that the pacing of games is infinitely important. If a player's turn takes too long, the other player's lose interest quickly. As fast as I was sure my game would move, it moved far too slowly to be fun, and this was the case with several other games I played.



  • http://edweb.sdsu.edu/Courses/EDTEC670/
  • http://www.neirtec.org/activities/math_portal.htm


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Last updated October 17, 2004