Solving for y is necessary for 8th grade math and Algebra 1. It is often a pain point for students and teachers. Let’s talk about how solving for y is important and tips for teaching it.
Why Students Need to Solve for Y
While “solving for y” is not mentioned in any specific standard, it is necessary for so many other standards:
- A.2(B) write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1), given one point and the slope and given two points
- A.5(C) solve systems of two linear equations with two variables for mathematical and real‐world problems.
First off, slope-intercept form (y=mx+b) makes graphing possible. Slope-intercept form makes identifying your slope and y-intercept instantaneous. This question was pulled from a previous STAAR test:
This problem requires a student to convert standard form 8x+3y=15 to slope-intercept form which means they must solve for y. (They could also use -A/B which supports the steps needed to isolate y anyway!) This problem also requires point-slope form and then converting back to standard form – jeez!
Slope-intercept form also supports solving systems of equations by graphing. Solving for y will support students using substitution to find a solution too.
Essentially, students must be flexible in converting between the various types of equations: standard form and slope-intercept form.
Furthermore, in Quadratics, converting standard form to vertex form requires solving for y too. Similar to slope-intercept form, vertex form gives information about the function (like the vertex and the direction it opens) that cannot be determined in standard form.
Teach Literal Equations First
Literal equations are equations with only letters. Typically, students are solving for an assigned variable. It can be extremely tricky for students to wrap their heads around this which is why I love how our Algebra 1 Solving Equations Unit covers it.
Maneuvering the Middle’s student handouts set students up to solve various step equations with numbers and then follow the same steps with variables only. (Need more ideas for solving equations?)
Start From Scratch
When students see something foreign, they assume that it is all brand new information, so start at the beginning:
- Review order of operations backwards
- Review what the inverse operations are
- Review what makes something “like terms”
- Review that if there is not a sign before a number, it is positive
- Review integer operations rules
- Review solving for a single variable when there are numbers present
Once this is ingrained in their head, then make the jump to solving for y when the variable x is present. Students get stuck usually because teachers assume that students know and understand more than they do.
Try the X-citing Move + the Great Divide
If you are teaching converting from standard form to slope-intercept form, the steps will often be the exact same to isolate y. This mnemonic device is a way to help your students remember the steps required. Mrs. Newell’s math blog has other great ideas, so be sure to check it out. “X-citing move” reminds students to move x to the other side of the equal sign using inverse operations. “The great divide” reminds students to divide by y’s coefficient. Sometimes it is the simplest methods that make the biggest impact!
Substitution, Graphing, and Elimination
With so many ways to solve systems of equations or inequalities, it is important to teach when you apply different methods. Or better yet, have students make observations for what method works best and why. Solving for y supports solving systems by graphing or substituting.
- Substitution – an equation is already solved for a single variable
- Elimination – both equations are already in standard form and don’t require lots of manipulation to eliminate both of the x’s or y’s
- Graphing – one or both of the equations are already in slope-intercept form
What would you teach students regarding this problem?
- Students may want to graph – the answer choices have graphs, the numbers are friendly, but the equations are in standard form requiring the extra step of converting to slope-intercept form.
- You could substitute the answer choices’ solutions into the standard form equations to see whether the solution provides true statements.
- You could use elimination, but all of these require multiple steps.
I think that is what makes this a good problem – students will have to weigh the pros and cons of each method with their confidence in solving.
How do you teach solving for y?