Go Reduce

by Brenda L. Kahler

Brenda is a Mathematics and Science teacher for San Diego Unified School District. She is a Language Development Specialist. The students she primarily works with are students whose first language is not English. She enjoys camping, fishing and that great Wisconsin air!

Instructional Objective Given a fraction, the learner will be able to reduce the fraction to its lowest terms. The learner will then multiply the reduced fraction by 2, 3, 4, 5, 6, 7, 8, or 9 to produce an equivalent fraction.

Learners/Context The learners are children, nine years old and older. The ideal placement for the game is a fifth grade math classroom where the children are learning fractions. My intent is to use this game in a remedial seventh grade math class.

Rationale Two of the many skills that children are to learn in the fifth grade are how to reduce fractions and to identify equivalent fractions. These skills are closely related because of their inverse relationship (i.e., multiplication and division). The card game is useful for developing both of these skills. The game itself will provide a structure for cooperative learning groups. The students will check each other's matches for accuracy thus, reinforcing their newly acquired skills. For extensions, each group can create a new deck of fractions to give to another team.

Process The game design is similar to that of the children's game, "Go Fish." The student's will be introduced to the game after the skills have been taught. This will reinforce the new concept and bring closure to the unit.

The students will be told there will be six different lowest term fraction existing in the deck, but, not necessarily told the actual six fractions. The 48 cards in the deck are equivalent fractions to these six fractions. The object of the game is to collect the most pairs of equivalent fractions.

Rules The game is played in the following manner:

1. The ideal number of players is between two and six students.

2. First choose a dealer. The dealer shuffles the deck of cards and then deals five cards to each player. The remaining cards are placed face down and spread in a small circle (the pond).

3. The player to the left of the dealer begins. If the player has pairs of equivalent fractions he/she can start their own "count" of pairs. If the player can find no matches he/she will ask any player by name, for an equivalent fraction. For example: "Adam, do you have an equivalent fraction to 1/2?"

If Adam does have the equivalent fraction, Adam must surrender his card. The player continues asking the others until one player has no match and will have to reply, "Go Reduce."

4. The player will then take a card from the face down pond. The next player is on his/her left.

5. The play continues until all cards are matched. If players run out of cards, the game has ended for them. They will have to wait until all players have played their hands.

6. The winner is the player with the most pairs of equivalent fractions.

Card Design The back of all cards will have the four parts shaded out of the total eight parts of the rectangle, thus a graphic representation of 4/8 = 1/2. The front of the cards will be the following fractions:

Lowest Term Fractions The Deck of Multiples

1/2 2/4, 3/6, 4/8, 5/10, 6/12, 7/14,

8/16, 9/18

1/4 2/8, 3/12, 4/16, 5/20, 6/24, 7/28,

8/32, 9/36

1/3 2/6, 3/9, 4/12, 5/15, 6/18, 7/21,

8/24, 9/27

2/3 4/6, 6/9, 8/12, 10/15, 12/18, 14/21, 16/24, 18/27

1/8 2/18, 3/24, 4/32, 5/40, 6/48, 7/56, 8/64, 9/72

3/4 6/8, 9/12, 12/16, 15/20, 18/24, 21/28, 24/32, 27/36

Back of Card Front of Card

Design Process This game was designed with limited English proficient students in mind who for one reason or another are having problems reducing and/or understanding equivalent fractions at the seventh grade level.

The idea of the game is for the student to realize what are equivalent fractions by reducing! For example, if the student had a 3/24 card and a 9/72 card the student hopefully could reduce 3/24 to 1/8 and reduce 9/72 to 1/8 and see they are equivalent. There are many entry points to solve this game, the student could possibly see that 3/24 could be enlarged by a factor of 3 to equal 9/72 and they are also equivalent this way.

This game was designed with specific learners in mind and can be modified and or adapted to other situations. It is hoped that this deck can be developed and used by other math teachers.