A.4bdf 
The student will solve multistep linear and quadratic equations in two variables, including
b) justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets;
d) solving multistep linear equations algebraically and graphically;
f) solving realworld problems involving equations and systems of equations.
Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions. 

Essential Knowledge and Skills 
 Solve equations, using the field properties of the real numbers and properties of equality, to justify simplification and solution.
 Solve multistep linear equations in one variable.
 Confirm algebraic solutions to linear equations, using a graphing calculator.
 Determine if a linear equation in one variable has one, an infinite number, or no solutions.

Essential Understandings 
 A solution to an equation is the value or set of values that can be substituted to make the equation true.
 The solution of an equation in one variable can be found by graphing the expression on each side of the equation separately and finding the xcoordinate of the point of intersection.
 Realworld problems can be interpreted, represented, and solved using linear equations.
 The process of solving linear equations can be modeled in a variety of ways, using concrete, pictorial, and symbolic representations.
 Properties of real numbers and properties of equality can be used to justify equation solutions and expression simplification.
 Equations can be used as mathematical models for realworld situations.
 Set builder notation may be used to represent solution sets of equations.


Vertical Articulation 
 SOL 7.14  a) solve one and twostep linear equations; b) solve practical problems in one variable
 SOL 7.16  apply properties w/ real numbers: a) commutative and associative properties for add/multi; b) distributive property; c) add/multi identity properties; d) add/multi inverse properties; e) multi property of zero
 SOL 8.15  a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve
 SOL AII.3  perform operations on complex numbers/express results in simplest form using patterns of the powers of i/ID field properties for complex numbers
 SOL AII.4  solve (algebraically/graphically) a) absolute value equation/inequalities; b) quadratic equations over complex; c) equations containing rational algebraic expression; d) equations containing radical expressions

Instructional Materials 
 VDOE ESS Lesson: Solving Linear Equations  Equations and Inequalities (PDF)  Exploring the functions of the graphing calculator; solving multistep linear equations (Word)
 Notes: Solving Equations with Variables on Both Sides (doc)  Answer Key (pdf)

Real World Lessons 

Practice 
 Worksheet: Solving Equations with Variables on Both Sides CW (doc)
 Worksheet: Solving Equations with Variables on Both Sides CW (doc)
 Quiz: Solving Equations with Variables on Both Sides (doc)
 ExamView Quiz: Solving MultiStep Equations
 ExamView Quiz: Solving Equations with Variables on Both Sides
 Prentice Hall Quiz #1
 Prentice Hall Quiz #2
 Prentice Hall Quiz #3

SelfAssessments 
 SOL Mini Quiz

Skills 

Videos 
 Video: PH Solving TwoStep Equations
 Video: PH Writing and Solving TwoStep Equations
 Video: PH Solving Equations with Variables on Both Sides
 Video: PH Consecutive Integers Problem
 Video: PH Solving Distance, Rate, Time Problems

Explore
Learning 
 Solving Formulas for any Variable  Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps.
 Modeling and Solving TwoStep Equations  Solve a two‑step equation using a cup‑and‑counter model. Use step‑by‑step feedback to diagnose and correct incorrect steps.
 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.
 Solving TwoStep Equations  Choose the correct steps to solve a twostep equation. Use the feedback to diagnose incorrect steps.

Websites 
 Interactive Notes: Solve Linear Equations  lessons and practice problems at Regentsprep.org
 Notes: Visual Equations  lesson on solving equations visually using tiles from Regentsprep.org
 Interactive Notes: Algebra Balance Scales  (Needs Internet Explorer browser) Interactive math manipulative that solves equations using a balance beam representation frommatti.usu.edu. Choose the Algebra Balance Scales icon from the list.

Old Website Links 

Common Core
Standards 
8.EE.7a 
8.EE.7b 
8.EE.8a 
8.EE.8b 
8.EE.8c 
ASSE.3a 
AAPR.1 
ACED.1 
ACED.2 
ACED.3 
ACED.4 
AREI.1 
AREI.3 
AREI.4a 
AREI.4b 
AREI.5 
AREI.6 
AREI.11 
FIF.8a 

