# PEMDAS Racer

## by Ken Marushige, Keely Kelman, Charles Elliot

Ken Marushige, Keely Kelman, and Charles Elliot are graduate students in Educational Technology at San Diego State University.

Ken In his spare time is a 6th grade math and computer teacher, parent of two, assistant soccer coach, and a juggler with the Fern Street Circus.

Keely is pursuing her career as a professional student and hopes to use her multiple subject credential when a career change is a parentally enforced necessity. In her minimal amount of spare time, she enjoys spending time with her roommate and friends.

Charles is CEO of MindStar, Inc., the nonprofit for mental health education. He is studying for a career as a writer/producer of multimedia materials for CD-ROM and Web-Based Education.

Instructional Objective Students will be able to evaluate mathematical expressions using order of operations. Students will be able to write expressions using order of operations.

Time Required Estimated time to play: 20-40 minutes.

Learners 4th to 6th graders who are already familiar with the order of operations, known by the acronym PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction.

Rules

• Number of players. Two to four people may play at the same time.
• Winner is the first person to cross the finish line, as described below.
• Game setup. Place game pieces (little cars) at the starting line. Place whiteboard (dry-erase board). Place Bonus cards in the Bonus card space. Place job aids with examples in the triangles at the corners. The 30-second timer can be placed anywhere. Each player spins to see who goes first -- highest goes first.
• Playing the game. Spin the spinner. Move piece that many spaces ahead. If the space is a numbered space, the player has to write an expression that equals the number on the space. The number that they spun is the number of numbers they must use in their expression. If their expression is correct, they stay in that spot. Otherwise they must move back to their old spot. Players that correctly use exponents get to move ahead 2 extra spaces.
• If the space is a bonus space (indicated by a "B"), the person to the right of the active player draws a card from the Bonus card pile and writes the problem on the card on the whiteboard. The active player writes their answer on the whiteboard. If the answer is correct, they get to spin the spinner and move that number of spaces ahead. At this point, their turn is over. (They do not have to write an expression for the number they land on). If their answer is incorrect, they must move back to their original space.
• To win, a player must land on or pass the finish line space and write an expression equaling the number 100.

Board Layout. The board looks like an auto racing track, with 50 numbered spaces. There is a place inside the track for the whiteboard. There are places outside the track for the spinner and the bonus cards. (see graphic)

Sample Cards

Front:
Back:

Design Process

At first, we had the concept of the order of operations in a racing metaphor. The students would write the problems. Later we modified the rules, such as going backwards for a wrong answer. Then we needed a shortcut, so we added the Bonus cards. We prototyped the card layouts. First, the cards looked like miniature game boards, then little cars as the border. We finally decided on having a car in the center.

It is a game of obstacles. If you are correct, you advance; if you are wrong, you go back. There is a time limit for each question. Each question is an obstacle.

The game was clever, a novelty. There was no game like it. We had chosen an exogenous fantasy (Lepper & Malone, 1987). The fantasy depended on a skill. The motivation was in a competitive format. PEMDAS content was put onto a racing setting.

The flow theory of Csikszentmihali (1990) was there, of "doing itself is reward". However, we hoped that there should also be future benefit from the game.

The ARCS model was in effect, too (Keller & Suzuki, 1988). The game gets the learners attention fast. It is relevant because most are familiar with racing, although not all are "into" it. Confidence is an important element. There is satisfaction because there is a lot of opportunity to practice skills and to be successful.

References

Csikszentmihali, M. (1990). Flow: The psychology of optimal experience. New York: Harper & Row.

Indy car racing magazine. Available Internet: http://www.icr.com/photogallery

Keller, J.M., & Suzuki, K. (1988). Use of the ARCS motivation model in courseware design. In D.H. Jonassen (Ed.). Instructional designs for microcomputer courseware. Hillsdale, NJ: Lawrence Erlbaum.

Lepper, M.R., & Malone, T.W. (1987). Intrinsic motivation and instructional effectiveness in computer-based education. In R.E. Snow & M.J. Farr (Eds.). Aptitude, learning and instruction. Volume 3: Conative and affective process analysis. Hillsdale, NJ: Lawrence Erlbaum.

Last updated by Charles Elliot on October 28, 1996.