Ken Marushige is a graduate student in the Educational Technology Masters program at San Diego State University. In his spare time he a 6th grade math and computer teacher, parent of two, assistant soccer coach and a juggler with the Fern Street Circus.

**Instructional Objective** The learners will be able to
determine the least common multiple (LCM) of any two numbers between
two and fifteen.

**Learners/Context** The target audience is 4th-6th grade
students who are learning how to add and subtract fractions with
different denominators. The learners are already familiar with the
multiplication facts 1-10 and have already learned to add and
subtract fractions with the same denominator.

The game is designed to be played after a lesson on LCM's/common denominators and prior to the lesson on adding fractions with different denominators. This game lends itself well to a learning center for four to six students (2-3 decks) in which the the students could play a number of times.

**Rationale** One of the prerequisite skills for adding and
subtracting fractions with different denominators is finding the LCM
for the two denominators (a.k.a the common denominator). Finding the
LCM is a critical yet mundane skill. A game format can reinforce this
skill, keep the students motivated as well as encourage them to make
the determinations quickly.

**Rules**

- Number of players: 2
- Materials: (besides the cards) Pencil and paper to keep score
- Basic Game
- Remove cards numbered eleven through fifteen.
- Deal half of the deck to each player.
- Each player simultaneously throws down a card.
- Each player tries to be the first to state the least common
multiple of the two cards on the table. If the first player to
respond is correct they get two points. If that player gives an
answer that is a common multiple but not the least, they are
given one point. If the first player to respond is completely
wrong, the other player may get one point by answering
correctly. Otherwise no points are given.
- The players can check their answer by looking at both lists of multiples and finding the lowest number that appears on both lists.

- After points are awarded and the score is updated the two cards go into a discard pile.
- The game ends when both players run out of cards.
- The winner is the player with the most points

- Advanced Game: The rules are identical to the basic game except that the entire deck is used.

**Card Design** The cards are 2.5" x 3.25". In the upper left
corner of each card is a number from two to fifteen. Directly below
that number is a list of the first fifteen multiples of that number.
The same information appears upside-down starting in the lower right
corner so that the card is readable from both directions. During the
game the players may choose to refer to the list on each card to find
the least common multiple. In the center of the card is the "LCM"
logo.

**Sample Cards**

**Deck Design** The deck consists of cards numbered two to
fifteen. There are six of each kind of card for a total of
eighty-four cards. The cards numbered eleven through fifteen may be
removed for the basic game leaving a deck of 54. In this way the deck
size is manageable for both games but also large enough to provide a
meaningful amout of practice.

**Design Process** I want my students to be familiar enough
with the numbers two through ten so that they can quickly find, if
not memorize, the LCM's for any two numbers in that set. At the same
time I want them to know how to how to determine the LCM of two
numbers by looking at the multiples of each number and then finding
the smallest number on each list. I had considered giving each player
a copy of the multiplication table for the numbers two through
fifteen but I felt that it would be very difficult for the player to
quickly isolate two particular columns (or rows) to find the LCM and
would thus interfere with the the reinforcement of the skill
objective. For this reason, I decided to put a list of the first
fifteen multiples on each card directly under the card's number. I
chose to make the list of multiples big enough to read easily but
small enough so that a more savy player could choose to ignore them.
It is my hope that if students play the game a number of times, they
will wean themselves from the lists as they become more familiar with
the numbers. In the prototype shown above, the list of multiples is
in a larger font size to illustrate this feature. I would use a
slightly smaller font size in the production model.

*Last updated by Ken Marushige on September 30 , 1996. *

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Educational Technology 670, Fall 1996.