.

As part of their instruction in the reading-writing process, the students learned to assume responsibility and control of their own learning by continually questioning and evaluating everything they read and write.  They were encouraged to develop critical judgment and made to feel their ideas and views were worthwhile.  In their mathematics instruction the students were taught published games for learning about fractions.*

An unexpected outcome was the spontaneous desire of many of the students to revise the given games or to create their own games.  By revising published games, and in most cases producing more sophisticated games, the students had a means of measuring their accomplishments.  The student became the author and inventor, teaching his or her own rules to other students and adults.  As owner of the game, the student became responsible for its improvement, playing and revising the game many times while sharing and exchanging strategies and knowledge of fractions.  At the beginning of the school year each student was issued a deck of fraction bars. 

After the games had been played a few times some students began to change the rules to improve the games or make them more challenging.  Here is one of the games which was taught by the teacher.  This game provides readiness for addition.

Gradually, this became unnecessary as the students became familiar with the bars.  Mike and Alex revised Fraction Bars Black Jack (see illustration) by requiring that three arbitrary fraction bars be placed face up at the beginning of each round.  The total shaded amount of these bars became the "target" for the round.  They called their game Super Black Jack.  In one round the following three bars were selected.

There have been several memorable stories about students learning with the fraction bars.  For example, shortly after the introduction of fraction numerals, one parent wanted to know if her son was learning about fractions by using the bars.  The teacher asked the boy to deal out five fraction bars and find the smallest common denominator of the fractions.  The boy gave both the smallest common denominator and the sum of the five fractions, while the parent was still trying to find the smallest common denominator.  Needless to say, the parent went away satisfied.

One game which helps to provide a transition between the concrete (Fraction Bars) and abstract (fraction numerals) is called Bars and Cards.

On a player's turn he or she may select a bar or card.  If a bar is chosen it may be used to replace any of the player's bars, as in the original game.  But if a card is chosen it may be placed to the left or right of any bar, and any one of the five bars may be removed.  For example, Abby had the five bars shown below and selected a playing card with 9/12. She put the 9/12 card between the 4/6 bar and the 10/12 bar to obtain three fractions in order, and removed the 4/4 bar.

The preceding games are only a few of those which were revised or created by the students.  Seth and Jason created Super Concentration when Seth was teaching Jason the Addition Game.  Heather and Tosca created Super Rummy in which a player tries to obtain runs of three or more "consecutive" fractions which increase by either twelfths, sixths, fourths, thirds, or halves.  Alie, Amy, Chikayo, and Jenny invented a game called Two Run.

The Fraction Bar games and workbook are appropriate for grades 3 through 8.  Many of the readiness games (before fraction numerals) have been used in grades 1 and 2.  Joyce Strong, a first grade teacher at Oyster River Elementary School, has used several of these games with her students.

The fraction games have been used with a wide range of students, from learning disabled to gifted.  One of the school's most severely handicapped learning disabled students had problems in processing and memory recall.  According to tests which were given in earlier grades, this student was incapable of learning about fractions.  However, the student eventually played most of the Fraction Bar games and successfully completed the workbook sections on basic concepts of a fraction and equality of fractions.  Even students who are capable of computing with fractions can gain an understanding of fractions from visual experiences with the bars.  These students not only have algorithms for using fractions, but they will be able to provide intuitive explanations.  As examples, a student might explain that 1/3 > 1/4 because when a bar is divided into 3 equal parts, the parts are bigger than when the bar is divided into 4 equal parts; or, that 1/2 = 2/4 because if both parts of a 1/2 bar are divided in half, there will be 4 parts and 2 shaded parts.

Graves, Donald H.  1983.  Writing:  Teachers and Children At Work.  Exeter, NH:  Heinemann Educational Books.

Shaw, Joan G.  May 1983.  "Mathematics Students Have a Right to Write."  The Arithmetic Teacher, 30:16-18.

^**FRIO was first described by Rowenda Drizigacker, Arithmetic Teacher, Vol. 6, No. 4, December 1966, 436-37.

"Fraction Games - Visions and Revisions" was published in Teaching Mathematics: Strategies That Work, edited by Mark Driscoll and Jere Confrey, 1985. It is printed here by permission of the Northeast Regional Exchange.