enVision Mathematics Topic 5
8th Grade; January (4 weeks); 3rd Quarter
Embedded Files
Topic Title(s):
Analyze and Solve Systems of Linear Equations
Prepared Graduates:
MP1. Make sense of problems and persevere in solving them.
MP4. Model with mathematics.
MP6. Attend to precision.
MP7. Look for and make use of structure.
Standard(s):
2. Algebra and Functions
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
8.EE.C. Expressions & Equations: Analyze and solve linear equations and pairs of simultaneous linear equations.
Analyze and solve pairs of simultaneous linear equations. (CCSS: 8.EE.C.8)
Explain 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: 8.EE.C.8.a)
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: 8.EE.C.8.b)
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. (CCSS: 8.EE.C.8.c)
Solve problems involving linear equations and systems of linear equations. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
Solve problems that require a system of linear equations in two variables. (MP1)
Model real-world problems with linear equations and systems of linear equations, with variables defined in their real-world context. (MP4)
Solve equations and systems of equations and express solutions with accuracy that makes sense in the real-world context modeled by the equations. (MP6)
Recognize the structure of equations and of systems of equations that produce one, infinitely many, or no solution. (MP7)
Inquiry Questions
What is meant by a “solution” to a linear equation? What is meant by a “solution” to a system of two linear equations? How are these concepts related?
Why can’t a system of linear equations have a solution set other than one, zero, or infinitely many solutions?
What connections exist between the graphical solution and the algebraic solution of a system of linear equations?
Coherence Connections
This expectation represents major work of the grade.
In previous grades, students reason about and solve one-step and two-step, one-variable equations and inequalities, use properties of operations to generate equivalent expressions, and solve real-world and mathematical problems using numerical and algebraic expressions and equations.
In Grade 8, this expectation connects with understanding the connections between proportional relationships, lines, and linear equations and with investigating patterns of association in bivariate data.
In high school, students abstract and generalize about linear functions and how they compare and contrast to nonlinear functions. Students also reason about and solve systems of equations that include one or more nonlinear equations.
Academic Vocabulary & Language Expectations:
System of linear equations, solution of a system of linear equations
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 5
Let's Investigate! Tasks
Let's Investigate! A Honey of a Deal (TE) (relates to Lesson 5-2)
Notes:
Evidence outcome 8.EE.C.8.b is ambiguous with respect to which algebraic solution methods are required. The recommendation is for all students to demonstrate mastery with solving a system of linear equations using the substitution method while having exposure to the elimination method. Solving by substitution may require rewriting an equation in standard form to y = mx + b. All students do not need to demonstrate mastery with the elimination method in 8th Grade, as it is addressed again in Algebra 1.
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: Solutions of Systems of Linear Equations, Solving Systems of Equations by Substitution, Solve Real-World Systems of Equations
Coherence Map/Concept Progressions: 8.EE.C.8.a, 8.EE.C.8.b, 8.EE.C.8.c
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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