Students become proficient at manipulating and solving single-variable linear equations and inequalities, and using them to model and interpret contextual situations.
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.
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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 |
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
This assessment accompanies Unit 3 and should be given on the suggested assessment day or after completing the unit.
A.SSE.A.1
A.SSE.A.2
A.REI.A.1
Identify properties of operations that result in equivalent linear expressions.
A.REI.A.1
Use properties of equations to analyze and write equivalent equations.
A.REI.A.1
A.REI.B.3
Solve single-variable linear equations using properties of equality.
F.IF.A.1
A.REI.B.3
Solve equations with a variable in the denominator.
A.CED.A.4
Solve for a variable in an equation or formula.
N.Q.A.1
F.BF.A.1
A.CED.A.2
A.CED.A.4
F.IF.B.5
Write equations using defined variables to represent a contextual situation.
N.Q.A.1
F.BF.A.1
A.CED.A.1
A.CED.A.2
A.CED.A.4
F.IF.B.5
Define variables; write and solve equations to represent a contextual situation.
N.Q.A.1
F.BF.A.1
A.CED.A.1
A.CED.A.2
A.CED.A.4
F.IF.B.5
Write and solve equations to represent contextual situations where estimations and unit conversions are required.
2 days
N.Q.A.1
F.BF.A.1
A.CED.A.1
A.CED.A.2
A.CED.A.4
F.IF.B.5
Model a contextual situation and make an informed decision based on the model.
A.SSE.B.3
A.CED.A.3
A.REI.A.1
A.REI.B.3
Solve unbounded single-variable inequalities in contextual and non-contextual situations.
A.CED.A.3
A.REI.B.3
Write and graph compound single-variable inequalities to describe the solution to contextual and non-contextual situations.
A.CED.A.3
A.REI.A.1
A.REI.B.3
Solve and graph compound inequalities where algebraic manipulation is necessary in contextual and non-contextual situations.
Key: Major Cluster Supporting Cluster Additional Cluster
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