Movement and Kisses for Beginning Algebra Students

Research & Teaching in Developmental Education, Fall 2003 by Hoy, Barbara

To solve for x, they need to get the kiss alone. The single kiss will weigh the same as the number of chips on the other side of the balance scale. They can remove the 2 chips from the left side. Then 2 chips also need to be removed from the right side to keep the scale in balance. The students physically remove 2 chips from both sides of their paper scales. They will understand that the fulcrum of the balance scale corresponds to the equal sign in the equation and that the same operation needs to be done to both sides of the scale and thus to both sides of the equation.

Problems can be presented with variables on both sides of the equation. For the problem of solving for x in 3x + 1 = 2x + 4, students put 3 kisses and 1 chip on the left side of their scale and put 2 kisses and 4 chips on the right side. They remove 2 kisses from both sides and remove 1 chip from both sides. They can then see that x = 3.

The concept of combining like terms can be readily understood. An example is to solve for x in the equation 2x + 3+x + 2 = x + 1 + x + 2 + 2x. When all the kisses and chips are put on their respective sides of the scale, students see that the equation is the same as 3x + 5 = 4x + 3. They remove 3 kisses from both sides and remove 2 chips from both sides. Then 2 = x.

If there is still time, if the students are still enjoying the activity, and if there are still enough uneaten kisses, multiplication/division may be attempted. Solve for x: 2x = 6. The students put 2 kisses on the left side and 6 chips on the right. They can remove half the weight from each side and keep the scale balanced (multiply each side by ½ or divide by 2). Then x = 3. Addition and multiplication properties can be combined as in solving the equation 4x + 1 = 2x + 5.

Similar to using game chips for demonstrating addition but not subtraction, using only positive constants in hands-on equations is advisable. Since I devote only one 50-minute class period to this exercise, it works best when kept uncomplicated. Many more varied examples are done algebraically during subsequent classes once the students have the concept of keeping equations balanced.

At the end of class, students comment on how much fun it was. They feel good about their abilities and about math. They can actually solve simple equations. They also can tell their friends that their math professor gave them kisses (Hershey's, that is!).

By Barbara Hoy, Onondaga Community College

Barbara Hoy is an Assistant Professor in the Mathematics Department at Onondaga Community College in Syracuse, New York.