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: CoverUp Problems  Equations and Inequalities (PDF)  Deriving a method of solving simple equations in one variable (Word)
 VDOE ESS Lesson: Algebra Tiles and Equation Solving  Equations and Inequalities (PDF)  Using manipulatives to solve equations (Word)
 VDOE ESS Lesson: Solving Linear Equations  Equations and Inequalities (PDF)  Exploring the functions of the graphing calculator; solving multistep linear equations (Word)
 Notes: MultiStep Equations (doc)  Answer Key (pdf)

Real World Lessons 

Practice 
 VDOE ESS: Solving Equations Using AlgeTiles Worksheet (pdf)
 VDOE ESS: Solving Equations Using AlgeTiles  Jigsaw Puzzle #1 (pdf)
 VDOE ESS: Solving Equations Using AlgeTiles  Jigsaw Puzzle #2 (pdf)
 VDOE ESS: CoverUp Problems Worksheet (pdf)
 Worksheet: MultiStep Equations CW (doc)
 Worksheet: MultiStep Equations HW (doc)

SelfAssessments 
 SOL Mini Quiz

Skills 
 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.
 A19:Meal Out  Apprentice  In this task, you use equations to solve a problem with a restaurant check.
 JMU Pivotal Item: Justification Using Field Properties (doc)
 JMU PIvotal Item:Solving Linear Equations Graphically (doc)

Videos 
 Video: PH Solving MultiStep Equations Using Distributive Property
 Video: PH Solving MultiStep Equations by Combining Like Terms

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 

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 

