Solving Equations - Simplified

In grade 5/6 math, students have been learning about patterning and algebra as well as the math processes of representing and connecting. We taught students to use three simple steps to solve any equation...

Step 1: Isolate the variable

Step 2:  Use opposite operations

Step 3: Do the same to both sides

To get students to the point where they are following the three steps to solving equations fluently, we started with some concrete math tools.  The algebra balance allows us to physically illustrate to students the idea of isolating the variable (Step 1),  using opposite operations (step 2), and do the same to both sides (step 3).  

The red trays represent negative numbers and the yellow represent positive.  The small canister on the right represents our variable.

Using playing cards and a plain envelope as our variable, we can represent the same question as on the algebra balance.  While using playing cards, we used red cards as negative numbers, and black cards as positive numbers.

 Mr. Richardson A.K.A. the Sagonaska Math Ninja came to help teach on Thursday!

We gradually want students to move from concrete thinking to symbolic thinking.  We start by introducing concepts with math tools like the algebra balance and playing cards (concrete models).  Then we move to algebra tiles which can be drawn (pictoral models). Finally students realize that math tools become cumbersome while trying to solve problems involving large numbers and begin to use numbers and symbols (symbolic models) to communicate their thinking and knowledge of math.

Mac uses algebra tiles as concrete model to solve his equation.

In the next few math classes, we will be helping students to start representing their thinking symbolically.  Stay tuned to see how our will become "symbolic representers" when communicating their thinking and knowledge around equations!