# One

## by Elizabeth Hennesey

After teaching English in a middle school for many years, Elizabeth decided to head back to SDSU and immerse herself in the EdTech Master's degree program. With her daughter's acquisition of a driver's license, she finally surrendered her side job as taxi driver and now makes her second "home" at SDSU. Water skiing, snow skiing, and relaxing on the weekends have all been put on hold. Perhaps one day she'll look back and say, "It was all worth it!"

Instructional Objective The learners will be able to put together numerous combinations of fractions that add up to "one". In the process they must be able to recognize the values of various fractions (i.e., that 1/2 is larger than 1/4), know fraction equivalents (i.e., 1/4+1/4=1/2 and that 2/4=1/2, etc.), and know the various combinations of fractions that add up to ONE.

Learners/Context The learners are students in a seventh grade basic math class at Greenfield Middle School. This class encompasses basic math skills with much of the curriculum being remedial. The game would be used during a unit on fractions to reinforce new knowledge and provide additional practice in adding fractions.

Middle school students require variety, movement, and change of pace to remain motivated. Games allow students with different learning styles the opporturnity to learn in a different mode.

Rationale Any time a game can be constructed to support concepts that are usually learned through repetitious paper and pencil exercises, it is both relevant and welcome. Being highly social creatures, middle shcool students eagerly embrace any activity that involves interaction and fun. Card games are especially appropriate due to the fact that they are portable, easily stored, and require virtually no set-up time. Even reluctant learners will be able to experience some degree of success with this game as long as they know that 1/2 + 1/2 = 1.

Rules Two to four people may play with one deck of cards. The object of the game is to acquire the most points by collecting sets of fraction cards that add up to "one". The more cards used to add up to "one," the more the set is worth. A dealer is selected, and then play proceeds as follows:

1. The dealer deals out six cards to each player. S/he then places the remaining cards in a stack and flips the first card over face up next to the stack.

2. Players assess the cards in their hand. If they have one or more fraction cards that add up to (or equal) "one," they may lay the card(s) down as a set.

3. Play progresses in a circle starting with the person on the dealer's right. After laying down any combinations already in one's hand, the player picks one card selecting either the card that is face up or one from the face down stack. If the face up card is selected, another card is flipped over from the stack.

4. The game continues until there are no more cards in the center stacks. All combinations that add up to "one" are placed on the table in sequence so that the fraction with the highest value is first and the lowest value is last. Do the same for each set.

5. The sets are awarded points as follows: one card (such as 2/2) = 1 pt., two cards=5 pts., three cards=10 pts., four cards=15 pts., five or more cards=20 pts. Points for the sets are added up, and the player with the most points is declared the winner! (Left over cards are discarded without penalty.)

Card Design The cards will be a mirror design so that either end can be up, and they will be the size of regular playing cards. Each card will have a fraction written on it and a small graphic.

Deck Design The deck will contain a total of 52 cards consisting of the following types: 1/2 (4), 2/2 (1), 1/4 (4), 2/4 (4), 3/4 (2), 4/4 (1), 1/8 (6), 2/8 (4), 3/8 (2), 4/8 (4), 6/8 (4), 1/16 (6), 2/16 (4), 4/16 (4), 8/16 (2).

Sample Cards

face card, back of card

Design Process Most students enrolled in a basic math class have difficulty grasping and retaining basic fraction facts. My goal was to design a game that would help them to review what they had learned in class while allowing them to interact with their peers and have fun. This game will force students to practice adding simple fractions, realize which fractions are equal in value, and use some strategy in trying to use five or more cards to equal ONE and thereby gain the most points.

A great deal of time was spent pondering how many cards should be in the deck and how many of each kind should exist. I decided that the fractions with the least value (i.e., 1/8 and 1/16) should have the most cards. Fractions that equal one whole (2/2 and 4/4) would have only one card each. To add a little more interest and challenge, I decided to throw in a few cards that did not have "one" as their numerator. Students will need to practice their knowledge of reducing fractions to use these cards: 2/4, 2/8, 4/8, 6/8, 2/6, 4/16, and 8/16. For a more advanced group of students, this game could be revised using more challenging fractions.

I wanted the card to be clean and simple in appearance and at the same time attractive. I selected a simple border that would not interfere with the necessary information, and then searched for an appropriate graphic. I did consider using a different graphic for each card with the graphic actually representing the fraction. I decided that students might rely on the graphic to detemine the value of each fraction, so instead, each card will have the same graphic. My first choice was to use a picture of a pizza with a slice being lifted out of it (the #1 food choice in middle school); however, none of my sources provided such a graphic. The pie with the slice missing is clean and simple and clearly illustrates a fraction--I believe it works quite well. A suitable prize for winning the game might be a hot slice (fraction) of pizza!

References Ms. Dinah Groff and Mr. Pete Bishop, middle school math teachers.

Last updated by Elizabeth Hennessey on September 28, 1996.