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Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

Author: Mika Fox

Addresses a variety of solution methods for the following standard:


Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.


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Welcome to our solving equations with variables on both sides tutorial. This page includes access to resources and guided practice for 3 of the 4 stations that you will visit during this exploration. Videos may be assigned to complete in class with your small groups, or may be assigned to view in a flipped classroom scenario.

While working though each station, you will be completing a graphic organizer. Your options for a graphic organizer include:

  • Creating your own
  • Printing off the template of a mind map below and use low-tech enhancements (markers, Post-Its, highlighters, etc) to make it meaningful.
  • Downloading the template and typing into it. You may include images and videos. Consider taking pictures of your own work and integrating it. Enhance your mind map with color, highlighter, etc.
  • Creating a mind map/presentation using PREZI

Your graphic organizer must include:

  • Pertinent information about utilizing each model for solving equations
  • 1-2 examples of how to use each model

Source: template created by Mika Fox

Algebra Tile/Balance Method Guided Practice

Visit the following website to complete guided practice of using algebra tiles to solve equations. The examples in the guided practice use bags and blocks.

Balancing Scales to Solve Equations

Use the recording sheet below to record your work and answers.

Access additional algebra tiles at the following website:

Virtual Algebra Tiles

Algebra Tiles/Balance Method Overview

Balancing Scales Recording Sheet


Bar Models for Solving Equations

Overview of using bar models to represent and solve linear equations in one variable.

Guided Practice-Bar Model

While watching the video above, complete your graphic organizer.

Then, using the worksheets provided below, select the highest tier worksheet that you are comfortable working on, and complete it with a partner in your group.

If you don't start on tier 3, progress through the levels until you complete through tier 3.

Guided Practice-Bar Model Tier 1


Bar Model-Tier 2


Bar Model-Tier 3


Traditional Algorithm Overview Video

View this video to learn the step-by-step "traditional" method.

Source: created by M. Fox

Independent Practice

Select one of the two games listed below to practice your selected method(s) for solving equations with variables on both sides.

  • You must complete at least 10 problems with equations with variables on both sides.
  • You may start with easier problems, but you must complete practice at the level of the standard.
  • Record your work on a separate sheet of paper and submit it to your teacher.

Algebra Four (partner):

Manga High (independent):

Google Form Assessment

Complete the Google Form Assessment after you have completed all of the stations and independent practice.