System of Equations: Substitution

Every once in a while I get excited to have my students do a worksheet.  This is one of those worksheets.  I’ve been waiting to get to this in 8th grade this year to see if it would go as smoothly as it did last year.  So far, it has.  🙂

Last year, I dreaded the thought of teaching solving systems of equation by substitution.  I envisioned my students getting frustrated by the long process involved -solving for a variable, substituting that expression into the other equation, solving for the remaining variable, plugging that back into the other equation to solve for the other variable…  These were all things that students knew how to do already, but putting it all together can feel overwhelming to them.  I didn’t want them to see this as a process to memorize, but rather see this as something that made sense based on what they already knew.

The result of my brainstorming on how to teach/introduce this to students is one of my favorite worksheets.  This worksheet is also an example of one of my favorite parts of teaching/lesson planning -taking a concept I’m dreading teaching and finding a way to smoothly get my students from where they currently are to where they need to be.

I don’t know if this is considered best practice or not, but basically my goal when creating this worksheet was to go back to the basics when it comes to evaluating an expression for a given value of a variable and simplifying expressions and slowly add one more step to the process until students unknowingly solve your typical system of equations by substitution type problem.

Should I help students make the connection to the graphs and the equations earlier than I do?  I don’t know.

The worksheet essentially goes from substitute and simplify to substitute and solve an equation.  Students start by substitution a numerical value and it moves to an algebraic expression.

After students complete the worksheet, I have them graph one of the last problems in Desmos and ask what they notice.  They are amazed when they realize that their answer is the intersection of the two lines.  The first time I had a student do this she thanked me for “tricking” her into doing this type of problem.  No joke.