Decimals, Fractions & Percentages


by Wayland Lim


Wayland is an independent business analyst and graduate student in Educational Technology.

Instructional Objective The learners will be able to determine the relationship between different forms of numbers and their comparative values.

Learners/Context The learners are students in the 5th grade or above who have been exposed to the different forms of numbers: decimals, fractions and percentages.

The game is designed to be played during or after a mathematics exercise to reinforce the understanding of number values

Rationale A game is an appropriate format for this situation because it is a fun and visual way to learn comparative values of different forms of numbers.

Rules For one or multiple players: High-Low-Medium Game.

The game is played in the following manner:

  1. After the cards are shuffled, the first play begins on the dealer's left and continues clockwise around the table so that everyone plays. The dealer places two cards face up in the center of play.
  2. The first player then evaluates the cards and makes a guess as to whether the next card on the deck will be the highest, lowest or intermediate value compared with the two exposed cards. For example, if the first two cards are "10%" and "1/4", it is most likely that the next card will be the highest of the three.
  3. After the player declares his/her guess, the dealer shows the next card and if the player was correct, that player receives all three cards. If the player guesses wrong, the cards are discarded. If the third card is of equal value to one of the first two, the player loses three cards (if he/she has won any) and must discard them along with the three exposed cards.
  4. Play continues until all cards are played from the deck. Afterwards, the players count up the number of cards they have collected and the one with the most, wins the round.
  5. The game continues if all players agree. The first player now becomes the dealer, and play restarts in the same manner.

Rules For two players at the same time: Classic War variation.

The game is played in the following manner:

  1. Shuffle the cards, then deal all the cards face down so that each player has the same number of cards.
  2. Each player then turns one card over. The player who dealt the card with the higher value wins "the battle" and takes both cards and forms a pile.
  3. If the players show cards of the same value the battle continues. Both players then place two cards face down and then another card face up. As before, the player showing the higher value card wins the battle and takes all the cards.
  4. Play continues in the same manner until one player quits or loses all his/her cards. If both player agree to a time limit, the player with the most cards when time expires wins.
  5. Optional Rule: A player can also win a battle if he/she is the first to recognize that the value of the two exposed cards combined equals 1.0 exactly (example, 40% and 3/5). The player exclaiming "One!" first, gets the cards that were played, plus the next card in the opponent's hand. If the players exclaim "One!" simultaneously, the player with the higher value card wins the battle as normal. If a player claims "One!" incorrectly, that player loses the battle plus the next card in hand. This can make the game very exciting and very loud. It is not recommended if other children nearby are studying.

Card Design

Each card is of similar design and color. There are three different suits: fractions, decimals and percentages. A number appears prominently in the center of the face of the card with an equivalent value in decimal, fraction or percentage form in smaller print at each corner of the card. Fraction and percentage cards also have a graphic to aid the learner in recognizing the card's value.

All cards have identical backs and are made of a plastic-coated card stock with silk finish just like standard playing cards. The cards are designed for durability and ease of use, and to create familiarity with other card game formats.

Deck Design The deck has a total of 54 regulation size playing cards. There are three types of cards: decimal numbers, fractions, and percentages. Each type has 18 cards of different values. They are as follows:

Decimals

Fractions

Percentages

.10

1/10

10%

.125

1/8

12 1/2%

.20

1/5

20%

.25

1/4

25%

.30

3/10

30%

.333

1/3

33 1/3%

.375

3/8

37 1/2%

.40

2/5

40%

.50

1/2

50%

.60

3/5

60%

.625

5/8

62 1/2%

.666

2/3

66 2/3%

.70

7/10

70%

.75

3/4

75%

.80

4/5

80%

.875

7/8

87 1/2%

.90

9/10

90%

1.0

1

100%

Design Process I started my card game in an attempt to help children have fun in comparing the value of different fractions. Trying to determine which number is bigger 5/8 or 3/5, for most people is not immediately discernable. This led me to develop a poker or war type card format which focuses on the relationship between cards. I then selected Fractions, Decimals and Percentages as the three "suits" in my card deck.

I decided to limit the deck to more than 54 cards (the same number as in a new deck of playing cards), so that the deck did not become unwieldy for children with smaller hands. A prototype was created and field tested for game playability and educational value. Three teachers and two students participated in the test. The basic rules of the first card game developed were similar to the classic "War." Later the rules were modified to make the game more fun and educational. A second set of "poker" rules were used to allow single as well as multiple players. The finished rules appear above.

References Ellington, H., Addinall, E., & Percival, F. (1982) A Handbook of Game Design. London: Kogan Page.

Last updated by Wayland Lim on September 28, 1995.

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Educational Technology 670, Fall 1995.