Algebraic Thinking


One of the most exciting things for 5th grade students is learning about algebra. They have been anticipating this subject for some time. What’s interesting is that they have been working with abstract mathematics forever, but it just isn’t often called algebra.

When we ask: 5 x 5 = ?, this could be written 5 * 5 = X sometime early on in elementary school. This introduction to variables can be a huge stumbling block for many students. It’s really important to get comfortable with variables in mathematics early on. We can make this problem slightly more difficult by asking it another way.

5 * X = 25 or finally 5X = 25 – now we’re doing simple algebra.

This week we have been looking at systems of equations and solving for all of the variables. These are wonderful problems that help students get familiar with variables in equations.

Here is a sampling of some of the problems we have worked on. Feel free to create some on your own. As long as you have a unique equation for each variable, there will be one and only one answer.

A + B + C = 36

A + A + B = 26

B + B + B = 18

The next problem we tried was

2A + B + C = 48

A + B + C = 40

2B + A = 18

At least one class tried this one

2/5A + B = 17

A + B = 20

And most challengingly some attempted the following

2A + B + C = 30

A + 2B + C = 35

A + B + 2C = 37