Patterns, Functions, and Algebra
Focus: Linear Equations
The student will
a) solve one and twostep linear equations in one variable; and
b) solve practical problems requiring the solution of one and twostep linear equations. 


Essential Knowledge and Skills 
 Represent and demonstrate steps for solving one and twostep equations in one variable using concrete materials, pictorial representations and algebraic sentences.
 Solve one and twostep linear equations in one variable.
 Solve practical problems that require the solution of a one or twostep 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 onestep
linear equations using add/sub; d)
create problems based on open
sentence
 SOL 6.18  solve onestep 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 twostep 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
variablealgebraically/graphically); f)
solve realworld problems involving
equations and systems of equations

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Equations (PDF)  Solving one and two step linear equations (Word)
 Virtual Manipulatives: Glencoe  select options from the menus
 Notes: Solving OneStep Add/Subtract Equations (ppt)
 Guided Notes: Using Algebra
Tiles to Model
Solving OneStep Equations (flipchart)
 Notes: Solving OneStep Multiplication Equations (ppt)
 Notes: Solving OneStep Multiply/Divide Equations (ppt)
 Guided Practice: OneStep Multiply/Divide Equations (doc)
 Notes: Modeling TwoStep Equations (flipchart)
 Notes: Modeling Equations from VDOE
 Guided Notes: Modeling with Shapes (flipchart)
 Activity: Solving TwoStep Equations Cut & Paste (doc)
 Activity: TwoStep Equation Race (doc)
 Activity: TwoStep Equation MATHO (flipchart)
 Activity: Pairs Matching  OneStep Equations (doc)
 VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)

Real World Lessons 
 Mathalicious: An AppleCare a Day  Is it ever a good idea to buy an extended warranty?

Practice 
 Worksheet: Solving and Modeling Addition & Subtraction Equations (doc)
 Worksheet: OneStep Equations Practice: Addition and Subtraction (doc)
 Quiz: OneStep Equations Practice: Addition and Subtraction (doc)
 Quiz: OneStep Equations and Graphs (doc)
 SelfPaced Equation Boot Camp (flipchart)
 Worksheet: Solving OneStep Equations (doc)
 Worksheet: OneStep Equations (doc)
 Worksheet: Modeling One and TwoStep Balances (pdf)
 Worksheet: TwoStep Open Ended Word Problems #0 (doc)
 Worksheet: TwoStep Open Ended Word Problems #1 (doc)
 Worksheet: TwoStep Open Ended Word Problems #2 (doc)
 Worksheet: Solving TwoStep Equations (doc)
 Worksheet: Modeling TwoStep Equations (doc)
 Worksheet: TwoStep Equations Practice (doc)
 Quiz: TwoStep Equations (doc)
 Worksheet: Sample Balance Mat (doc)

SOL Mini Quiz 
 SOL 7.14 Mini Quiz: Equations (pdf)  (doc)

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.
 Modeling Equations (doc)
 Equations: Penny Jars (doc)

Videos 
 PH Solving TwoStep Equations
 PH Writing and Solving TwoStep Equations
 YouTube: Repeat it! Song

Explore
Learning 
 Modeling OneStep 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.
 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.
 Road Trip (Problem Solving): Plan a crosscountry 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.
 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 
 Sadlier: Algebra Balance Scales
 Shodor: Fraction Four Game  Connect Four game involving solving equations with fractions at Shodor.org. Select Algebra from the list.
 NLVM: Balance Scales  virtual manipulatives at National Library of Virtual Manipulatives
 TwoStep Equations Practice  practice at HSTutorials.net
 Learn Alberta: Equations  Translating, modeling, and solving equations. Click on Equations.
 Math.com: Interactive Notes  Solving Equations with Addition and Subtraction  notes and workout problems
 Mathsnet.net: Interactive  OneStep Equations (Identifying Steps) at Mathsnet.net
 Aplusmath: Interactive  Solving Equations with Flash Cards  flash cards used for practicing 1step and 2step equations

VDOE Interventions 
 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.2 
7.EE.4a 
NQ.1 
NQ.2 
NQ.3 
