Course 2 Online!
Henrico County Public Schools, Virginia
7.14 - Equations
Number, Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
Patterns, Functions, and Algebra
Focus: Linear Equations

The student will
a)   solve one- and two-step linear equations in one variable; and
b)   solve practical problems requiring the solution of one- and two-step linear equations. 
Essential Knowledge and Skills 
  • Represent and demonstrate steps for solving one- and two-step equations in one variable using concrete materials, pictorial representations and algebraic sentences.
  • Solve one- and two-step linear equations in one variable.
  • Solve practical problems that require the solution of a one- or two-step linear equation.
Essential Understandings
  • When solving an equation, why is it important to perform identical operations on each side of the equal sign? An operation that is performed on one side of an equation must be performed on the other side to maintain equality.
Vertical Articulation
  • SOL 5.18abcd - a) investigate/describe concept of variable; b) write open sentence using variable; c) model one-step linear equations using add/sub; d) create problems based on open sentence
  • SOL 6.18 - solve one-step linear equations in one variable
  • SOL 8.15abc - a) solve multistep linear equations in one variable (variable on one and two sides of equations); b) solve two-step linear inequalities and graph results on number line; c) identify properties of operations used to solve
  • SOL A.4abcd - solve multistep linear/quad equation (in 2 variables) - a) solve literal equation; b) justify steps used in simplifying expressions and solving equations; c) solve quad equations (algebraically/graphically); d) solve multistep linear equations (algebraically/graphically); e) solve systems of two linear equation (2 variable-algebraically/graphically); f) solve real-world problems involving equations and systems of equations
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Equations (PDF) - Solving one and two step linear equations (Word)
  2. Virtual Manipulatives: Glencoe - select options from the menus
  3. Notes: Solving One-Step Add/Subtract Equations (ppt)
  4. Guided Notes: Using Algebra Tiles to Model Solving One-Step Equations (flipchart)
  5. Notes: Solving One-Step Multiplication Equations (ppt)
  6. Notes: Solving One-Step Multiply/Divide Equations (ppt)
  7. Guided Practice: One-Step Multiply/Divide Equations (doc)
  8. Notes: Modeling Two-Step Equations (flipchart)
  9. Notes: Modeling Equations from VDOE
  10. Guided Notes: Modeling with Shapes (flipchart)
  11. Activity: Solving Two-Step Equations Cut & Paste (doc)
  12. Activity: Two-Step Equation Race (doc)
  13. Activity: Two-Step Equation MATHO (flipchart)
  14. Activity: Pairs Matching - One-Step Equations (doc)
  15. VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)
Real World Lessons
  1. Mathalicious: An AppleCare a Day - Is it ever a good idea to buy an extended warranty?
  1. Worksheet: Solving and Modeling Addition & Subtraction Equations (doc)
  2. Worksheet: One-Step Equations Practice: Addition and Subtraction (doc)
  3. Quiz: One-Step Equations Practice: Addition and Subtraction (doc)
  4. Quiz: One-Step Equations and Graphs (doc)
  5. Self-Paced Equation Boot Camp (flipchart)
  6. Worksheet: Solving One-Step Equations (doc)
  7. Worksheet: One-Step Equations (doc)
  8. Worksheet: Modeling One- and Two-Step Balances (pdf)
  9. Worksheet: Two-Step Open Ended Word Problems #0 (doc)
  10. Worksheet: Two-Step Open Ended Word Problems #1 (doc)
  11. Worksheet: Two-Step Open Ended Word Problems #2 (doc)
  12. Worksheet: Solving Two-Step Equations (doc)
  13. Worksheet: Modeling Two-Step Equations (doc)
  14. Worksheet: Two-Step Equations Practice (doc)
  15. Quiz: Two-Step Equations (doc)
  16. Worksheet: Sample Balance Mat (doc)
SOL Mini Quiz
  1. SOL 7.14 Mini Quiz: Equations (pdf) | (doc)
  1. Mathematics Assessment Project
    • A05:Baseball Jerseys - Apprentice - In this task, you will help Bill to find the best price for buying printed jerseys for the baseball team.
    • A14:How old are they? - Apprentice - In this task, you will use equations to solve a number puzzle about three people's ages.
  2. Modeling Equations (doc)
  3. Equations: Penny Jars (doc)
  1. PH Solving Two-Step Equations
  2. PH Writing and Solving Two-Step Equations
  3. YouTube: Repeat it! Song
Explore Learning
  1. Modeling One-Step Equations - Activity A: Solve one‑step equations using an area model. Drag tiles into two bins, each representing a side of the equation, and isolate an x‑tile on one side.
  2. Modeling and Solving Two-Step Equations: Solve a two‑step equation using a cup‑and‑counter model. Use step‑by‑step feedback to diagnose and correct incorrect steps.
  3. Road Trip (Problem Solving): Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities.
  4. Solving Equations By Graphing Each Side: Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response.
  5. Solving Two-Step Equations: Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.
  1. Sadlier: Algebra Balance Scales
  2. Shodor: Fraction Four Game  - Connect Four game involving solving equations with fractions at Select Algebra from the list.
  3. NLVM: Balance Scales - virtual manipulatives at National Library of Virtual Manipulatives
  4. Two-Step Equations Practice - practice at
  5. Learn Alberta: Equations - Translating, modeling, and solving equations. Click on Equations.
  6. Interactive Notes - Solving Equations with Addition and Subtraction - notes and workout problems
  7. Interactive - One-Step Equations (Identifying Steps) at
  8. Aplusmath: Interactive - Solving Equations with Flash Cards - flash cards used for practicing 1-step and 2-step equations
VDOE Interventions
  1. VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra - The lessons focus on algebraic reasoning. Students learn to solve equations and inequalities, first by using manipulatives and then by working with symbols. They use modeling to collect data, and they learn to record data so that they can see the relationship that exists among tables, graphs, words, and equations. (pdf)
Common Core Standards