Grade 8
Unit 4 Table of Contents
Systems of Equations
Section
Page Number
Unit Description
Unit Standards
Unit Essential Questions
Unit Proficiencies (Learning Targets)
Unit Vocabulary and Language Support
Sample Unit Calendar and Possible Supporting Materials
Student Proficiencies Handout
Unit Assessments and Rubric/Commentary
2
2
3
3
4
6
8
10
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Grade 8
Content Unit 4
Unit Title:
Stage 1
Unit
Description:
Dates of Unit:
Weeks 24-30
Systems of Equations
Identify Desired Results
Students will develop understanding of the methods of which systems of equations and inequalities with two
variables can be used to model problem situations. In addition, students will develop skills in the graphing and
symbolic methods to solve those systems.
CCSS.MATH.CONTENT.8.EE.C.8
Analyze and solve pairs of simultaneous linear equations.
CCSS.MATH.CONTENT.8.EE.C.8.A
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their
graphs, because points of intersection satisfy both equations simultaneously.
CCSS.MATH.CONTENT.8.EE.C.8.B
Standards:
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.
Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot
simultaneously be 5 and 6.
CCSS.MATH.CONTENT.8.EE.C.8.C
Solve real-world and mathematical problems leading to two linear equations in two variables. For 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.
Essential
Question(s):
Proficiencies
(Learning Targets)
How can the solution for a system of equations be found?
Writing Equations Proficiency – “I can write a linear equation from a story, table, or graph.” (8.F.B4)
Graphing Equations Proficiency – “I can correctly graph a system of linear equations.”
Solving Systems on a Graph Proficiency – “I can analyze and solve pairs of simultaneous linear equations on a graph.” (8.EE.C.8)
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Understand Intersection Point Proficiency – “I can explain why the solution to a system of equations is the point of intersection.”(8.EE.C.8a)
Slope-Intercept & Standard Form Proficiency – “I can rewrite standard form linear equations into slope-intercept form and vice versa.”
Solving Systems Using Substitution Proficiency – “I can solve a system of equations using substitution.”
Solving Systems Using Combination Proficiency – “I can solve a system of equations using combination/elimination.”
Solving Systems Using Any Method Proficiency – “I can solve a system of equations using any method.”
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Stage 2
Determine Assessment Evidence
Academic Language Function(s):

Academic Language (What language will students need to sound like experts?)
Academic Language Stems:
Easy for Beginners
Academic Vocabulary:







Equation
System of linear equations
Solution of a one-variable equation or system of
linear equations
One solution
no solution
Infinitely many solutions
parallel lines
Assessment
Tools:
 Goals Rubric
 Assessment Checklist
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Medium for Intermediate
Difficult for Advanced and Fluent
Unit of Study Assessment Checklist
Student Name
B = Beginning
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D = Developing
P = Proficient
M=Mastery
Stage 3
Plan Learning Experiences and Instruction
SAMPLE UNIT CALENDAR
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Proficiency
Score
4
Percentage
3
83%
2
67%
1
50%
100%
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Description
WOW!
I have shown proficiency and deeper understanding by:

You got it 
I have shown proficiency by:

Help is needed
I have shown partial understanding by:

Uh-oh…
I have not yet shown my understanding of the math.
IITS Check-Up #2
Name ______________________
Date ______________ Period ___
Use any method you would like to solve the problem.
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2. Solve the system of equations using Equal Values Method:
3. Solve the system of equations using Substitution:
4. Solve the system of equations using Combination/Elimination:
5. Solve the system of equations using any method you would like:
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IITS Check-Up #3 Review
Name ___________________________
Date _________________ Period _____
1) Mrs. Hunt-Kievit did the Shamrock Run in Portland and it was a
40K race. She ran at a speed of 8 kilometers per hour and walked
at a speed of 4 kilometers per hour. She completed the race in
exactly 6 hours. Let x be the number of hours Mrs. Hunt-Kievit
ran and let y be the number of hours that she walked.
a) Write an equation that relates x and y to the total distance of 40 kilometers:
b) Write an equation that relates x and y to the fact that she finished in exactly 6 hours:
c) For each equation above, find at least three ordered pair solutions (x,y). Then, plot the
points with those coordinates and use the pattern to draw a graph of each equation:
x
y
x
y
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2) Determine the coordinates of the intersection point for the graphs in the last
problem. What do the coordinates tell you about Mrs. Hunt-Kievit’s race? Explain:
3) Write each equation in Ax + By = C form (standard form):
a. y = 7 + 2x
b. x = -3y + 5
4) Write each equation in y = mx + b form (slope-intercept form):
a. 4x + 8y = 16
b. -2x + 5y = 14
5) Maven thinks that the answer to the following system of
equations is (5, 7). Prove Maven correct or incorrect:
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y=x+2
2x – y = 3
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Proficiency
Score
4
Percentage
3
83%
2
67%
1
50%
100%
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Description
WOW!
I have shown proficiency and deeper understanding by:

You got it 
I have shown proficiency by:

Help is needed
I have shown partial understanding by:

Uh-oh…
I have not yet shown my understanding of the math.