Download Solving Linear Equations Unit Guide Math 8 Big Idea (Cluster):

Solving Linear Equations
Unit Guide Math 8
Big Idea (Cluster):

Analyze and solve linear equations and pairs of
simultaneous linear equations (8.EE.7).
Edited 5/18/14
Renton School District
Domain: Expressions and Equations (8.EE.7)
Big Idea (Cluster): Analyze and solve linear equations and pairs of simultaneous linear equations
Standard 8.EE.7
Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these
possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a
= a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the
distributive property and collecting like terms.
2
This document is a draft and will continue to develop as we learn more about the Common Core State Standards and the SBAC assessment. (8.EE.7)
Relevant Math Practices and Student Actions
MP1 Make sense of problems and persevere in solving them.
 Perseveres when solving problems
 Understands what the problem asks and the relationship among the
problem’s parts
 Looks for an entry point into solving the problem
 Uses multiple strategies and representations
 Checks process, answers and ask “Does this make sense?”
MP 2 Reason abstractly and quantitatively.
 Interprets problems in context
 Uses representations to make meaning of problems
 Translates a problem from situation to equation
 Creates a situation for a given equation
 Explains connections between equation and situation
 Flexibly uses properties of operations and place value
MP 3 Construct viable arguments and critique the reasoning of
others.
 Makes conjectures and evaluates their accuracy
 Justifies conclusions with mathematical evidence and responds to
arguments of others
 Communicates and defends mathematical reasoning using objects,
drawings, diagrams, actions, examples and counterexamples
 Asks clarifying and probing questions to improve argument
 Attends to, questions, and evaluates the reasoning of others
MP 4 Model with mathematics.
 Describe, analyze, and solve problems arising in everyday life,
society and workplace
 Makes assumptions and approximations to make problems easier
 Identifies quantities necessary to solve a problem and uses
representations to map their relationships
MP 5 Use appropriate tools strategically.
 Selects tools strategically for visualizing, exploring, comparing,
predicting, and solving problems
 Uses technological tools and resources to pose problems, solve
problems and deepen understanding
MP 6 Attend to precision.
 Communicates mathematical thinking accurately both orally and in
writing
 Understands the meaning of mathematical symbols and vocabulary
and uses them appropriately
 Labels consistently and accurately graphs and diagrams
 Specifies the units of measure when labeling
 Calculates accurately and efficiently
 Pursues a level of precision appropriate to the context of the problem
 Formulates questions and explanations carefully
MP 7 Look for and make use of structure.
Looks for, identifies, develops and generalizes patterns and
relationships
 Makes connections to prior mathematical knowledge to solve new
problems
 Breaks down complex problems into manageable parts
 Views complicated quantities both as single objects or compilations
of several objects and uses operations to make sense of problems

MP 8 Look for and express regularity in repeated reasoning.
 Notices repeated calculations and looks for general methods and
shortcuts to solve a problem
 Identifies patterns to develop algorithm, formula, or calculation
 Evaluates reasonableness of intermediate and final results
3
This document is a draft and will continue to develop as we learn more about the Common Core State Standards and the SBAC assessment. (8.EE.7)
SBAC Required Evidence (Claim 1)


Student identifies and writes examples of linear equations in one variable with one solution, infinitely many solutions, or no solution (SBAC
Grade 8 Claim 1 Target D, required evidence #1).
Student solves linear equations in one variable with rational number coefficients, including equations with solutions that require expanding
expressions using distributive property and collecting like terms (SBAC Grade 8 Claim 1 Target D, required evidence #2).
A calculator is an allowable tool for this cluster of standards on an assessment. For more information on the assessment of this set of standards,
read the Grade 8 Claim 1 item specifications for Target D. This cluster of standards will also be assessed through Claim 2 Problem Solving (8.EE.C)
and Claim 3 Communicating Reasoning (8.EE.7 and 8.EE.8a) and Claim 4 Modeling and Data Analysis (8.EE.C). The “8.EE.C” means Grade 8
Expressions and Equations (EE) domain the third cluster (C).
Vocabulary
Mathematically proficient students communicate precisely by engaging in discussions about their reasoning using appropriate mathematical
language. Students should learn the following terms with increasing precision within the cluster. The bolded terms will be used on Smarter
Balanced assessment items.
coefficient
combining like terms
constant
distributive property
linear equation
ordered pair
property of equality
rational number
slope
solution
variable
x-coordinate
y-coordinate
y-intercept
4
This document is a draft and will continue to develop as we learn more about the Common Core State Standards and the SBAC assessment. (8.EE.7)
Domain: Expressions and Equations (8.EE.7)
Big Idea (Cluster): Analyze and solve linear equations and pairs of simultaneous linear equations
Standard 8.EE.7
Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these
possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a =
a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the
distributive property and collecting like terms.
See Grade 8 Common Core Flip Book pages 17-20 for explanations and examples of this standard.
Learning Objectives







Solve linear equations in one variable, including equations whose solutions require expanding expressions using the distributive property and
collecting like terms (SBAC Grade 8 Claim 1 Target D Achievement Level Descriptor, Level 3).
Solve mathematical and real-world linear equations in over variable.
Show a linear equation has one solution, no solution, or infinitely many solutions by transforming the equation into simpler form (SBAC Grade 8
Claim 1 Target D Achievement Level Descriptor, Level 3).
Know the conditions for which a linear equation will have a one solution, no solution of infinitely many solutions.
Classify a linear equation as either having no solution, one solution, or infinitely many solutions.
Write linear equation with either no solution, one solution, or infinitely many solutions compared to a given equation.
Compare equations that have no solution, infinitely many solutions, and one solution.
5
This document is a draft and will continue to develop as we learn more about the Common Core State Standards and the SBAC assessment. (8.EE.7)
SBAC Required Evidence (Claim 1)
Connections to Prior Learning
 Student identifies and writes examples of linear equations in one
variable with one solution, infinitely many solutions, or no solution
(SBAC Grade 8 Claim 1 Target D, required evidence #1).
 Student solves linear equations in one variable with rational number
coefficients, including equations with solutions that require
expanding expressions using distributive property and collecting like
terms (SBAC Grade 8 Claim 1 Target D, required evidence #2).
7.EE.1 Apply properties of operations as strategies to add, subtract, factor,
and expand linear expressions with rational coefficients.
A calculator is an allowable tool for this cluster of standards on an
assessment. For more information on the assessment of this set of
standards, read the Grade 8 Claim 1 item specifications for Target D.
This cluster of standards will also be assessed through Claim 2 Problem
Solving (8.EE.C) and Claim 3 Communicating Reasoning (8.EE.7 and
8.EE.8a) and Claim 4 Modeling and Data Analysis (8.EE.C).
Connections to Curricular Materials
Moving Straight Ahead investigation 3 introduces solving linear
equations in one variable but not to the depth required by 8.EE.7. The
investigation is more aligned to Grade 6 and 7 equation standards but
still lacking the use of rational numbers beyond integers for those grade
levels. Engage NY Grade 8 Module 4 lessons 1-9 can be used to
supplement this standard if building resources are not already
developed. If you have prior developed resources, check for alignment
with 8.EE.7a. Students will need to classify, compare, write and solve
linear equations with no solution, a unique solution and infinitely many
solutions.
7.EE.4 Use variables to represent quantities in a real-world or
mathematical problem, and construct simple equations and inequalities to
solve problems by reasoning about the quantities.
a. Solve word problems leading to equations of the form px +q = r
and p(x + q) = r, where p, q, and r are specific rational numbers.
Solve equations of these forms fluently. Compare an algebraic
solution to an arithmetic solution, identifying the sequence of the
operations used in each approach.
Additional Resources/Technology Resources
Engage NY Grade 8 Module 4 Lessons 3, 6 and 7
Linear Equations in one variable module (NPS)
Expressions and Equations progression of learning document
Solving Linear Equations in One Variable task (MAP)
Khan Academy Common Core Student Practice site for 8.EE.7
6
This document is a draft and will continue to develop as we learn more about the Common Core State Standards and the SBAC assessment. (8.EE.7)
The Engage NY Grade 8 Module 4 is being used to supplement this standard where CMP2 curricular materials do not provide resources aligned to Common Core Standard
8.EE.7. Please be selective in the resources within the Engage NY modules you use for your students in order to meet proficiency or higher on this standard. The Engage NY is
fairly absent of the Standards for Mathematical Practice which should be equally weighted with content on a daily basis in classroom instruction. For the time-being, teachers
will use the Engage NY resources as a foundation to access these standards. But, teachers are highly encouraged to improve the recommended tasks to be less direct instruction
based, have students engage in rich mathematical talk and provide opportunities for students to work collaboratively. The Engage NY modules are a temporary solution as we
transition to the Common Core State Standards for Mathematics.
Solving Linear Equations Unit Pacing Guide
Supplemental CCSS-M Aligned
Lessons
Engage NY Grade 8 Module 4
Lesson 1
Engage NY Grade 8 Module 4
Lesson 2
Engage NY Grade 8 Module 4
Lesson 3
Engage NY Grade 8 Module 4
Lesson 4
Engage NY Grade 8 Module 4
Lesson 5 (optional)
Engage NY Grade 8 Module 4
Lesson 6
Engage NY Grade 8 Module 4
Lesson 7
Engage NY Grade 8 Module 4
Lesson 8
Engage NY Grade 8 Module 4
Lesson 9 (extension)
PLC-developed common
assessment until 2015-2016
Alignment Notes
Students will write mathematical statements using symbols to represent numbers
Students will know the properties of linear and non-linear expressions in x and identify
expressions as linear and non-linear.
Students will know that a linear equation is a statement of equality between two expressions.
CCSS-M
7.EE.4
8.EE.7
8.EE.7
8.EE.7
Students will extend the use of the properties of equality to solve linear equations having rational
coefficients.
Students will apply knowledge of geometry to writing and solving linear equations
8.EE.7
Students will transform equations into simpler forms using the distributive property and combining
like terms. Students will also experience linear equations with no solution.
Students will learn the conditions for which a linear equation will have a unique solution, no
solution or infinitely many solutions.
Students will rewrite and solve equations that do not appear to be linear equations using properties
of equality.
Students will rewrite an exponential expression that represents a series as a linear equation.
8.EE.7
8.EE.7
8.EE.7
8.EE.7
8.EE.7
For understanding the content required to be assessed, see the rubrics at the end of the unit guide 8.EE.7
which is based on the SBAC Grade 8 Claim 1 item specifications for Target D. Based on the SBAC
item specifications for Target D, a calculator is an allowable tool during the assessment.
*SBAC ALD Level 3 or Level 4 means Smarter Balanced Achievement Level Descriptors for entering into a Level 3 or Level 4. Hard copies of
these lessons can be found at http://staff.rentonschools.us/renton/secondary-math/math-8-ccss-m-resources .
The following resources were used to create this curriculum guide: SBAC Item Specifications Claim 1 Target D, Grade 8 Common Core State
Standards Flip Book compiled by Melissa Hancock and Expressions and Equations progression of learning document.
7
This document is a draft and will continue to develop as we learn more about the Common Core State Standards and the SBAC assessment. (8.EE.7)
Standard 8.EE.7
Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these
possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a =
a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the
distributive property and collecting like terms.
4
In addition to being proficient on the

standard, student can demonstrate one or
more of the following:
 Applies understanding of standard to
unfamiliar situations and/or to solve
complex problems
 Use precise and relevant

communication to justify
mathematical thinking
 Connects knowledge to other
learning targets and/or advance
problem sets.
For example, analyze a student’s
conjecture on how to classify equations
in one variable and justify or refute the
conjecture with a chain of reasoning.

8.EE.7
3
Transform a given equation

into simpler forms in order to
demonstrate a system of linear
equations has one solution, no
solution or infinitely many
solutions (x=a, a=a, or a=b)
Write and solve linear
equations in one variable with
rational coefficients including
equations using distributive
property and collecting like
terms that have one solution, no
solution or infinitely many
solutions.
Rewrite expanded equations
using distributive property or
by collecting like terms
2
Write and solve linear
equations in one variable
with integer coefficients
that have one solution, no
solution or infinitely many
solutions.

1
With help, minimal
success solving linear
equations in one
variable with integer
coefficients that have
one solution, no
solution or infinitely
many solutions.
For more detail on the assessment of the standard, read the SBAC Grade 8 Item Specifications-Target D. This rubric was constructed from the SBAC Claim 1
item specifications and SBAC Achievement Level Descriptors. These rubrics should be further developed at the PLC level. Students will also be assessed on this
standard through Claim 2 Problem Solving (8.EE.C) and Claim 3 Communicating Reasoning (8.EE.7 and 8.EE.8a) and Claim 4 Modeling and Data Analysis
(8.EE.C) which is not reflected in the above rubric.
8
This document is a draft and will continue to develop as we learn more about the Common Core State Standards and the SBAC assessment. (8.EE.7)