Start Algebra with Expressions Instead of Equations

Many students’ first experience with algebra comes in the guise of arithmetic practice. For example, they are given problems such as 7 + [] = 22 and asked to fill in the boxes. At some point, a question like this morphs to 7 + x = 22. This switch in notation raises a number of issues. One, the unknown, x, no longer appears to be a container and students typically call it a “letter” rather than something they imagine is a placeholder for a value.  The next issue is that this new way of representing arithmetic does not typically connect to any new interesting use. Solving equations as a first algebraic experience teaches that algebra is about “finding the one right answer” – an answer the teacher and textbook already know. These one-variable, linear equations involve an unknown with a single solution. The unknown is not a variable that can usefully take on many values. Yes, we can plug in whatever we want, but only one value solves the equation.

Starting early algebra exposure with expressions makes it possible to introduce applications and engaging problems that highlight algebra’s power. Expressions represent an infinite number of possibilities all of which have meaning. They can represent and explain a whole set of problems all at once. That is the power of algebra we want to wow students with at the start! Check out our activities for beginning with this emphasis.