Picture Algebra

One of my absolutely favorite lessons in Carnegie’s Bridge to Algebra is Picture Algebra. This has not always been the case. It is the opening lesson to the solving equations unit. I have to admit that last year Melissa and I were totally baffled to why Carnegie would start a unit with a lesson like Picture Algebra, so “foreign and complicated.” The sequence of lessons did not seem logical. Why weren’t we starting the students with learning the skill of solving one-step equations, leading up to two-step equations, and finally ending with word problems? There were many nights of teeth gnashing and hair pulling from teachers, students, and parents!

I remember thinking and telling Melissa, “Carnegie must have a good reason. We must have faith and trust them. I am sure they know what they’re doing, I hope.”

Now it all makes sense! Thank goodness.

Apparently if you give students a hypothetical situation (aka word problems) to begin a unit, students can use prior knowledge and experiences to help themselves work through the problem. The new math skills and concepts make more sense if worked concurrently with a real-life application. Duh!

In Picture Algebra, students draw diagrams to represent the situation. They then use these diagrams to solve the problem and answer the question(s) as well as come up with an equation. In other words, application leads to algorithm, instead of the reverse practice that most of us experienced in a math classroom.

Give Picture Algebra a chance. Like anything new, different, or requires some thinking, Picture Algebra will receive resistance from many students. Repeated exposure will help the students feel more comfortable. I had half a dozen or so students show up this afternoon for tutorials to get help on Picture Algebra. It warmed my heart that these students cared enough to take the initiative to seek the extra help. In addition, they seemed to enjoy each other’s company as they worked through the problems together. “Frank,” who came in lost and clueless, caught on the quickest this afternoon and was given the charge of guiding the other students. He took on the responsibility with great pride. I couldn’t have asked for a better tutorials session.