Unit Concept Map
Grade Level: 8th Grade Pre-Algebra
Course Essential Question:
Subject: Mathematics
Unit Topic:
Unit 8: Systems of Linear Equations
Unit Essential Question:
How are systems of two linear equations solved and interpreted?
PA Standards/Anchors(Assessment Anchor/Eligible Content)
Assessment Anchor: M08.A-N.1 Demonstrate an understanding of rational and irrational
M08.B-E.3
Analyze and solve linear equations and pairs of simultaneous linear equations.
M08.B-E.3.1.3
Interpret solutions to a system of linear equations in two variables as points of
intersection of their graphs, because points of intersection satisfy both equations
simultaneously.
M08.B-E.3.1.4
Solve systems of two linear equations in two variables algebraically, and estimate
solutions by graphing the equations. Solve simple cases by inspection.
Example: 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot
simultaneously be 5 and 6.
M08.B-E.3.1.5
Solve real-world and mathematical problems leading to two linear equations in two
variables.
Example: Given coordinates for two pairs of points, determine whether the line
through the first pair of points intersects the line through the second pair.
Concepts: By the end of the unit, students will:
 Know the mathematical difference between systems of two linear
equations that have exactly one solution, no solutions, or infinitely
many solutions.
 Understand that a line is the set of all coordinate pairs that satisfy
an equation
 Comprehend that if two algebraic expressions are equal, they can
be interchanged within an algebraic equation.
 Know that multiplying an equation by a scalar does not change the
solution set.
Skills: By the end of the unit, students will:
 Identify if two linear equations intersect at exactly one point, at no
points (parallel), or at all points (same line)
 Graph a system of two linear equations
 Isolate a variable in a linear equation
 Substitute an algebraic expression for a variable
 Multiply an equation by a scalar value
Vocabulary
System of Linear
Equations
Substitution
Elimination
Parallel Lines/No Solution
Coinciding Lines/Infinite
Solutions
**Some of the vocabulary
terms may already be known
to students but are still
prudent to review**
 Add two equations
Formative Assessments Summative Assessment
Resources
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Daily exit tickets
(focused after each
lesson and can also
be spiraled to
include the previous
day’s content)
Give students a
system to solve and
have them explain
their reasoning for
choosing the
method that they
did
End of class quizzes

Summative Assessment:
o Solve graphically
o Solve using substitution
o Solve using elimination
o Write a system based on a realworld situation
o Justify solution method of choice
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Prentice Hall
Mathematics PreAlgebra
Prentice Hall
Mathematics Algebra
1
Study Island
Calculators
Suggest Unit Lessons:
 Solving systems by graphing
 Special solution sets (parallel and coinciding lines)
 Solving systems using the method of substitution
 Solving systems using the method of elimination
 Applications of Linear Systems
Key Lesson Questions:
1. How is a solution of a linear system represented on a coordinate plane?
2. How are the solution sets of parallel and coinciding lines unique?
3. How is the substitution method used to find the solution set of a system of linear equations?
What does it mean when a system is reduced to a statement that is either always true or always false?
4. How is the elimination method used to find the solution set of a system of linear equations?
What does it mean when a system is reduced to a statement that is either always true or always false?
5. How can systems of equation be used to solve real-world problems?
How is the best method for solving a system determined?