Be the Equation - Algebra Activity

Looking for a way to help students gain a concrete understanding of the abstract idea of variables and how to solve for them? Try this quick and simple activity.

Activity: Be the Equation
Time: 5-10 minutes
Materials: an equals sign, an X (both can simply be written on typing paper), a dry-erase or smart board to write on, and students

Prior to starting this activity, I recommend a brief full-class discussion on variables and equations to get the neurons firing in your students' brains and to activate the prior knowledge they may already have in place.

Now it is time for your students to be an equation. Divide the class so that half of the students will go to one side of the room and the other half will go to the other side of the room. Explain that this is because equations must be balanced. Everything on one side is always equal to everything on the other side. Your equals sign can be posted in the middle of the room, or held by you in the middle of the room.

If you have an odd number of students, include yourself or another adult on one side of the equation to even things out.

Choose a few students to "be the X" on one side of the room. Tell the students that it is a great mystery how many students the X is worth, and that we will be using the magic of algebra to figure out what that value is. Have those students stand together - separate from the other students on their "side of the equation" - holding the X sign.

Of course, students will recognize immediately how many students are standing with the X sign and they will shout out the answer. This is not a problem. I find that this helps to drive home the concept to those students who have never quite understood how a letter could also be a number.

At this point, write on your dry-erase or smart board (or on a large piece of paper) the equation that the room represents. If you have twenty students and select four to be the X, for example, your equation would be x + 6 = 10. If you have eight students, and three are the X, you have x + 1 = 4. For the purpose of this explanation, I will use the example of x + 6 = 10.

Explain to the students how the equation you have written represents them standing in the room. Ask students to raise their hand if they are part of the group of 10, then the group of 6, then the "mystery" group of X.

Now we are ready to solve the problem. Ask students how we could solve for X with this type of problem. The solution, of course, is to subtract 6 from both sides. Take time to explain why to subtract 6 from both sides.

Then, have the group of 6 sit down. They have been subtracted from the equation.

Ask what needs to be done now that we have subtracted six people from one side of the equation. The answer is that we need to subtract the same number from the other side. Ask 6 people from the group of 10 to sit.

Ask students what information we now have. We have the answer! Since the two sides of the equation must be the same, and we know one of them is worth four, we know the other must also be worth four.

Work out the equation on the board and show how the paper and pencil process is tied to what they just did.

Post-activity: have students write a reflection on the activity, explaining why people stood where they did, why some people sat down, what variables are, and how equations can help to solve variables. This will help them to think through the experience and tie it to the process of solving equations.