Course 3 Online!
Henrico County Public Schools, Virginia
8.15ac - Multistep Linear Equations
Number and Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
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 four-step 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
  1. SOL 6.18 - solve one-step linear equations in one variable
  2. SOL 6.19abc - a) investigate/recognize identity properties for add/mult; b) multiplicative property of zero; c) inverse preperty for mult
  3. SOL 7.14ab - a) solve one- and two-step linear equations; b) solve practical problems in one variable
  4. 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
  5. 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)
  6. 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 real-world problems involving equations and systems of equations
Instructional Materials

8.15a

  1. VDOE Enhanced Scope and Sequence Lesson: Solving Equations (PDF) - Solving equations in one variable (Word)
  2. Notes: Solving Two-Step Equations (ppt)
  3. Notes: Solving Two-Step Equations #2 (ppt)
  4. Notes: Modeling Solving Multi-Step Equations (flipchart)
  5. Notes: Using Algebra Tiles to Model Solving Multi-Step Equations (doc)
  6. Notes: Using Algebra Tiles to Model Solving Multi-Step Equations (flipchart)
  7. Activity: Solving Multi-Step Equations Sort (xls)
  8. Notes: Solving Equations with Variables on Both Sides (ppt)
  9. Guided Notes: Solving Multi-Step Equations with Variables on Both Sides (doc)
  10. Guided Notes: Solving Multi-Step Equations Using the Distributive Property and Modeling (doc)

8.15c

  1. VDOE Enhanced Scope and Sequence Lesson: Properties of Operations (PDF) - Identifying properties of operations (Word)
  2. Warm-Up: Coin Traits & Like Terms (doc)
  3. Modeling Expressions with Algebra Tiles (flipchart)
  4. Guided Notes: Distributive Property & Simplifying Expressions (doc)
  5. Notes: Distributive Property & Like Terms (flipchart)
  6. Notes: How to Simplify Variable Expressions (doc)
  7. Activity Bundle: Combining Like Terms Notes, Activities, Group Work (pdf)
Real World Lessons
Practice

8.15a

  1. Worksheet: Multi-Step Equations Practice (doc)
  2. Worksheet: Multi-Step Equations Practice #2 (pdf)
  3. Worksheet: Multi-Step Equations Practice #3 (doc)
  4. Worksheet: Multi-Step Equations Practice #4 (doc)
  5. Worksheet: Multi-Step Equations Quiz Review (doc)
  6. Worksheet: Equations Review (doc)

8.15c

  1. Worksheet: Justifications Practice (doc)
  2. Worksheet: Distributive Property & Simplifying Expressions (doc)
  3. Worksheet: Distributive Property & Simplifying Expressions #2 (doc)
  4. Quiz: Simplify Expressions and Distributive Property (doc)
Self-Assessments
  1. SOL 8.15b Mini-Quiz: Equations, Inequalities, and Properties
Skills
  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.
    • A19:Meal Out - Apprentice - In this task, you use equations to solve a problem with a restaurant check.
  2. Equations: Number Puzzle (doc)
Videos
  1. Video: PH Solving Two-Step Equations
  2. Video: PH Writing and Solving Two-Step Equations
  3. Video: PH Solving Multi-Step Equations Using Distributive Property
  4. Video: PH Solving Multi-Step Equations by Combining Like Terms
  5. Video: PH Solving Equations with Variables on Both Sides
  6. PH Identifying Properties of Real Numbers
  7. Video: PH Using Properties of Real Numbers
Explore Learning
  1. 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.
  2. 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.
  3. Solving Two-Step Equations: Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.
Websites
  1. Interactive Notes: Solving two step equations - notes and workout problems from Math.com
  2. Interactive: Solving equations - applet that uses the "balance strategy" at Mathsnet.net
  3. Interactive: Solving Equations with Flash Cards - Flash cards used for practicing 1-step and 2-step equations from Aplusmath.com
  4. Interactive Notes: Solve Linear Equations - lessons and practice problems at Regentsprep.org
  5. Notes: Visual Equations - lesson on solving equations visually using tiles from Regentsprep.org
  6. 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.
  7. Interactive Notes: Distributive Property with Tiles - lesson on solving equations visually using tiles at Regentsprep.org
  8. Interactive Notes: Properties of Real Numbers - lessons and practice problems at Regentsprep.org
  9. Interactive Notes: Properties with Integers- notes and workout problems at Math.com
  10. 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.
  11. Like Terms Invaders - game from XPMath.com
VDOE Interventions
  1. 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)
  2. 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