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.
Math
Unit 4
9th Grade
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.
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
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 |
Topic A: Properties and Solutions of Two-Variable Linear Equations and Inverse Functions
Topic B: Properties and Solutions of Two-Variable Linear Inequalities
Topic C: Systems of Equations and Inequalities
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 3
Linear Expressions & Single-Variable Equations/Inequalities
Unit 5
Functions and Transformations