Substitution for Systems – Scaffolded

Solving systems of equations using the Substitution Method may be the most task intensive algorithm the students learn. It is easy to overlook concepts as the students attempt the numerous steps. This post provides details about a scaffolded handout that guides students through the mental and conceptual steps, as well as the traditional written steps.


The focus is on systems with a variable that has a coefficient of 1. The variable is not isolated. The entry point is typically with the variable already isolated with the written step being substitution. This handout works for both situations. For the variable already isolated, step 2 can be skipped.

The Scaffolded Handout

The scaffolding addresses the skills used the method but also reinforces vocabulary and concepts.

  • The first step is a mental step but the students are asked to circle as a means of focusing attention on this step. It is useful for a think aloud as the teacher talks through the process.
  • Substituting an algebraic expression in for a variable allows for focus on the terms variable, expression, equation and the idea that a variable is a simple expression being replaced by another one.
  • The solution is an ordered pair. Often, students may stop once they find the value for the first variable.

Scaffolded Steps

Page 2 of the handout is scaffolded to guide the students through the steps I found to be problematic. Replacing a variable with an algebraic expression is the central component of this method and is new to students at this point. previously, they would have substituted in only numeric values for variables.

The Handout

Here is a link to the handout. The image below shows page 3, a blank template.

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