Students become proficient at manipulating and solving single-variable linear equations and inequalities, and using them to model and interpret contextual situations.
Math
Unit 3
9th Grade
In Unit 3, Linear Expressions & Single-Variable Equations/Inequalities, students become proficient at manipulating and solving single-variable linear equations and inequalities, as well as using linear expressions to model contextual situations. Domain and range are introduced again through the lens of a “constraint” with inequalities. The understanding students develop in this unit builds the foundation for Unit 4, Unit 5, and Unit 6, as well as provides an algebraic outlet for modeling contextual situations started in Unit 1 and continued in Unit 2.
Unit 3 begins in Topic A with a review of creating equivalent expressions and equations, as well as solving equations using the properties of operations and equality. Students are introduced to the concept of a domain restriction by understanding that dividing by zero produces an undefinable expression. Students develop their understanding of how to construct viable arguments in producing equivalent equations and expressions, as well as making use of structure to efficiently manipulate and solve expressions and equations, using repeated reasoning to develop properties, and attend to precision in solutions. Topic B builds on this conceptual understanding and fluency with expressions and equations to develop algebraic models for contextual situations. Students begin by using pre-defined variables to model simple contextual situations and build up to identifying quantities, estimating constants, defining variables, and writing and revising algebraic models to illustrate and make generalizations about a contextual situation. This section of the unit has several opportunities to model contextual situations. Topic C expands students’ understanding of constraints through single-variable inequalities and requires students to make strong connections between algebraic, contextual, and graphical representations.
Pacing: 15 instructional days (12 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 3 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
Commutative property of addition and multiplication | Associative property | Distributive property |
domain restriction | coefficient | variable |
term | equivalence | properties of operations |
Proeprties of Equality | solve for [variable/quantity] |
compound inequality (and/or) |
solution |
Topic A: Properties and Solutions of Single-Variable Linear Expressions and Equations
Topic B: Modeling with Single-Variable Linear Equations
Topic C: Properties and Solutions of Single-Variable Linear 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 2
Descriptive Statistics
Unit 4
Linear Equations, Inequalities and Systems