A.5A Solving 1-Variable Linear Equations

Hooray! The language in standard A.5A is pretty clear. For me, the critical information needed to design instruction comes from the vertical alignment. 

When I began teaching Algebra 1 (several years before the 2012 TEKS revision), we would spend a day solving one-step linear equations, a second day solving two-step equations, a third day solving with variables on both sides, finally working our way up to multi-step equations.

Well, you can imagine how overwhelming adding distributing, combining like terms, decimals, fractions, and variables on both sides was when students had only solved equations for a few days!

And as a beginning teacher, it was challenging to find the time to create the vertical alignment for a standard - or even to read, process, clearly understand the implications of one that was handed to me.

Lucky for you, the vertical alignment for A.5A, the solving linear equations SE is below!

Vertical Alignment

Students are expected to master solving linear equations in Algebra 1. 

"solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides" TAC §111.39 

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    In future courses - even in Geometry - students will be expected to demonstrate fluency in solving linear equations. By the time students take Algebra 2, they will be solving equations of many types - including absolute value linear equations and rational equations - for which solving linear equations fluently is critical.

    Fortunately for Texas Algebra 1 teachers, students will have solved simple linear equations multiple times throughout middle school mathematics. They should be bringing with them a familiarity with balancing equations using the properties of equality - addition, subtraction, multiplication, and division.

    Don't forget the Knowledge and Skills statement!

    Don't forget to take a quick look at the Knowledge and Skills statement. I know, its like the last thing you want to spend time doing, so here it is - no excuses now!

    The K&S statement reminds us to provide students with the opportunity to solve linear equations both with and without technology. 

    Evaluating the reasonableness of the solutions is also important. 

    So what should I teach?

    Solving linear equations

    • with distributive property
    • combining like terms
    • variables on both sides
    • include decimal and fraction real number coefficients
    Looking for this handout? Find it here.

    Solve equations with special solutions

    • No solution
    • All real numbers
    • x = 0 (I know it isn't "special" but students DO confuse it with no solution and all real numbers)

    Looking for this handout? Find it here.

    Solve algebraically

    Solve using technology

    • Graphing
    • Tables
    • Possibility: nSolve on TI-Nspire (I suggest waiting until the end of the unit/year, or showing learners in need of more support on a case-by-case basis as it fails to be a successful method when solving more complex equations of different types)
    Looking for this handout? Find it here.

    Verify equations by substituting the solution back into the original equation for mathematical problems

    Verify the reasonableness of solutions from applied problems - Did Johnny reallllly eat -5.2 apples??

    So what shouldn't I teach?

    • Solving one-step and two-step equations in isolation as a first-time introduction to equations 
      • Exception: Review for remediation, RTI, closing gaps, etc. as needed
      • Why? Students solved with variables on both sides in 8th grade math
    • Solving absolute value linear equations
      • Why? Students will solve them in Algebra 2.

    Extension Opportunity

    Formulating and solving one-variable linear equations is not explicitly stated in the Texas Algebra 1 TEKS, nor is it tested on the Algebra 1 STAAR EOC test. However, students wrote and solve linear equations with variables on both sides in 8th grade math, so this application is a great way to incorporate many of the process standards. Consider including problems that require the use of the distributive property to adequately address the Algebra 1 standard when solving. 

    Short on time?

    If you need a little help getting started this year and are interested in a complete unit, I sell a TEKS-aligned unit that covers solving 1-variable linear equations and inequalities. I developed it from the ground up with the TEKS at the forefront of the development process. Find it here.


    Hi! I'm Allison, a curriculum writer and Texas native. I have extensively studied the secondary math TEKS throughout my career as an educator. While attending Texas A&M University-Corpus Christi to earn my M.S. in Curriculum and Instruction, I focused on learning as much as I could about interpreting the standards and developing standards-aligned resources grounded in research-based strategies.

    Many teachers have excellent resources from their campus or district at their disposal. That is a wonderful thing! My goal is to deliver complementary information to help ease the burden on teachers. 

    The Math Beach TEKS guides are subject to my interpretation of the standards. As always, please continue to use your professional judgment and consult with your colleagues for clarification when needed.