Patterns, Functions, and Algebra
Focus: Linear Relationships
The student will
a) solve multistep linear equations in one variable with the variable on one and two sides of the equation;
c) identify properties of operations used to solve an equation. 


Essential Knowledge and Skills 
 Combine like terms to simplify expressions.
 Solve two to fourstep linear equations in one variable using concrete materials, pictorial representations, and paper and pencil illustrating the steps performed.
 Identify properties of operations used to solve an equation from among:
 the commutative properties of addition and multiplication;
 the associative properties of addition and multiplication;
 the distributive property;
 the identity properties of addition and multiplication;
 the zero property of multiplication;
 the additive inverse property; and
 the multiplicative inverse property.

Essential Understandings 
 How does the solution to an equation differ from the solution to an inequality? While a linear equation has only one replacement value for the variable that makes the equation true, an inequality can have more than one.


Vertical Articulation 
 SOL 6.18  solve onestep linear equations in one
variable
 SOL 6.19abc  a) investigate/recognize identity
properties for add/mult; b) multiplicative
property of zero; c) inverse preperty for mult
 SOL 7.14ab  a) solve one and twostep linear
equations; b) solve practical problems in one
variable
 SOL 7.16abcde  a) apply properties w/ real numbers: commutative and associative properties for
add/mult; b) distributive property; c)
additive/ multiplicative identity properties;
d) additive/ multiplicative inverse properties;
e) multiplicative property of zero
 SOL A.2  perform operations on polynomials  a)
apply laws of exponents to perform ops on
expressions; b) add/subtract/multiply/divide polynomials; c) factor first and second
degree binomials/trinomials (1 or 2
variables)
 SOL A.4  solve multistep linear/quad equation (in
2 variables)  a) solve leteral 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 realworld
problems involving equations and systems of
equations

Instructional Materials 
8.15a
 VDOE Enhanced Scope and Sequence Lesson: Solving Equations (PDF)  Solving equations in one variable (Word)
 Notes: Solving TwoStep Equations (ppt)
 Notes: Solving TwoStep Equations #2 (ppt)
 Notes: Modeling Solving MultiStep Equations (flipchart)
 Notes: Using Algebra Tiles to Model Solving MultiStep Equations (doc)
 Notes: Using Algebra
Tiles to Model
Solving MultiStep Equations (flipchart)
 Activity: Solving MultiStep Equations Sort (xls)
 Notes: Solving Equations with Variables on Both Sides (ppt)
 Guided Notes: Solving MultiStep Equations
with Variables on Both Sides (doc)
 Guided Notes: Solving MultiStep Equations Using the Distributive Property and Modeling (doc)
8.15c
 VDOE Enhanced Scope and Sequence Lesson: Properties of Operations (PDF)  Identifying properties of operations (Word)
 WarmUp: Coin Traits & Like Terms (doc)
 Modeling Expressions with Algebra Tiles (flipchart)
 Guided Notes: Distributive Property & Simplifying Expressions (doc)
 Notes: Distributive Property & Like Terms (flipchart)
 Notes: How to Simplify Variable Expressions (doc)
 Activity Bundle: Combining Like Terms Notes, Activities, Group Work (pdf)

Real World Lessons 

Practice 
8.15a
 Worksheet: MultiStep Equations Practice (doc)
 Worksheet: MultiStep Equations Practice #2 (pdf)
 Worksheet: MultiStep Equations Practice #3 (doc)
 Worksheet: MultiStep Equations Practice #4 (doc)
 Worksheet: MultiStep Equations Quiz Review (doc)
 Worksheet: Equations Review (doc)
8.15c
 Worksheet: Justifications Practice (doc)
 Worksheet: Distributive Property & Simplifying Expressions (doc)
 Worksheet: Distributive Property & Simplifying Expressions #2 (doc)
 Quiz: Simplify Expressions and Distributive Property (doc)

SelfAssessments 
 SOL 8.15b MiniQuiz: Equations, Inequalities, and Properties

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.
 Equations: Number Puzzle (doc)

Videos 
 Video: PH Solving TwoStep Equations
 Video: PH Writing and Solving TwoStep Equations
 Video: PH Solving MultiStep Equations Using Distributive Property
 Video: PH Solving MultiStep Equations by Combining Like Terms
 Video: PH Solving Equations with Variables on Both Sides
 PH Identifying Properties of Real Numbers
 Video: PH Using Properties of Real Numbers

Explore
Learning 
 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: Solving two step equations  notes and workout problems from Math.com
 Interactive: Solving equations  applet that uses the "balance strategy" at Mathsnet.net
 Interactive: Solving Equations with Flash Cards  Flash cards used for practicing 1step and 2step equations from Aplusmath.com
 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  Interactive math manipulative that solves equations using a balance beam representation frommatti.usu.edu. Choose the Algebra Balance Scales icon from the list.
 Interactive Notes: Distributive Property with Tiles  lesson on solving equations visually using tiles at Regentsprep.org
 Interactive Notes: Properties of Real Numbers  lessons and practice problems at Regentsprep.org
 Interactive Notes: Properties with Integers notes and workout problems at Math.com
 Interactive Notes: Properties  defines the commutative, associative, distributive, and the identity properties of addition at aaamath.com. Click on Next Lesson to see the multiplication properties. This site has an interactive game at the bottom of each page.
 Like Terms Invaders  game from XPMath.com

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Using Order of Operations and Exploring Properties  (SOL 8.15c) The lessons focus on order of operations and evaluating numerical expressions. Students
will also investigate and recognize properties of real numbers used to solve an equation. (pdf)
 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 
7.EE.1 
7.EE.4a 
7.EE.4b 
8.EE.7a 
8.EE.7b 
