Students manipulate, graph, and model with two-variable linear equations and inequalities, are introduced to inverse functions, and continue studying linear systems of equations and inequalities.
In Unit 4, Linear Equations, Inequalities, and Systems, students become proficient at manipulating, identifying features, graphing, and modeling with two-variable linear equations and inequalities. Students are introduced to inverse functions and formalize their understanding on linear systems of equations and inequalities to model and analyze contextual situations. Proficiency of algebraic manipulation and solving, graphing skills, and identification of features of functions are essential groundwork to build future concepts studied in Units 5, 6, 7, and 8.
Topic A builds on work from Unit 3 to expand the idea of a solution to a coordinate point and to review identifying features of linear functions as well as graphing and writing equations in different forms to reveal properties. Students build on conceptual work from eighth grade on independence and dependence to define, create, and model with inverse functions.
Topic B expands students’ understanding of a single-variable inequality to linear inequalities. Students are expected to use tools of checking solutions strategically as well as attending to precision in notation and graphing.
Topic C combines learning from topics A and B to explore and model with systems of equations and inequalities. Students need to be precise in their calculations and choose efficient methods of solving as well as contextualize and decontextualize situations that can be modeled with a system of equations or inequalities. The unit concludes with a two-day, teacher-designed project.
Pacing: 18 instructional days (15 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 4 and should be given on the suggested assessment day or after completing the unit.
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
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Standard form | Inverse functions $${f^{-1}( x)}$$ |
Slope-intercept form & Point-slope form | Linear inequality |
Linear equation | Solution set |
Rate of change | Boundary line |
Slope/y-intercept/zeros | Systems of linear equations |
Constraint | Systems of linear inequalities |
Solve by substitution/Solve by elimination | Solution to a system |
A.SSE.B.3
A.REI.D.10
Identify the solutions and features of a linear equation and when two linear equations have the same solutions.
F.IF.B.4
A.SSE.B.3
F.IF.C.7.A
Write linear equations given features, points, or graph in standard form, point-slope form, and slope-intercept form.
F.IF.B.6
F.IF.C.7.A
F.IF.C.9
F.LE.A.1.A
Determine if a function is linear based on the rate of change of points in the function presented graphically and in a table of values.
F.IF.A.1
F.IF.A.2
F.IF.B.5
F.BF.B.4.A
Identify inverse functions graphically and from a table of values in contextual and non-contextual situations.
F.IF.B.6
A.CED.A.4
F.BF.B.4.A
Find inverse functions algebraically, and model inverse functions from contextual situations.
A.REI.D.12
Describe the solutions and features of a linear inequality. Graph linear inequalities.
A.CED.A.3
A.REI.D.12
Write linear inequalities from graphs.
A.CED.A.3
Write linear inequalities from contextual situations.
A.CED.A.3
A.REI.D.11
Solve a system of linear equations graphically.
A.CED.A.3
A.REI.D.12
Identify solutions to systems of inequalities graphically. Write systems of inequalities from graphs and word problems.
N.Q.A.2
A.CED.A.3
A.REI.C.5
A.REI.C.6
Solve linear systems of equations of two variables by substitution.
A.REI.C.5
Identify solutions to systems of equations algebraically using elimination. Write systems of equations.
A.SSE.B.3
A.REI.A.1
A.REI.C.6
Identify solutions to systems of equations using any method. Write system of equations and inequalities.
A.REI.C.6
Identify solutions to systems of equations with three variables.
2 days
Project
Teacher-designed project
Key: Major Cluster Supporting Cluster Additional Cluster
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