HSA-REI.D.12

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- HSA-REI.D.10Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- HSA-REI.D.11Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*
- HSA-REI.D.12Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

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## HSA-REI.D.12

## Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

31 Lesson(s)

### Solving Two Variable Inequalities

Algebra I »
Unit: Extending Equations

Algebra I »
Unit: Extending Equations

Big Idea:

#### See how to use test points to determine how to determine the solution to a two-variable inequality.

Standards:

Favorites
(13)

Resources
(22)

Reflections
(1)

### Introduction to Linear Equations and Inequalities in One Variable

Algebra I »
Unit: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable

Algebra I »
Unit: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable

Big Idea:

#### Students demonstrate current knowledge through a pre-test and preview the big ideas of the unit.

Standards:

Favorites
(17)

Resources
(17)

Big Idea:

#### Life is full of constraints and usually more than one at a time. So what is allowed? Students use systems of inequalities to determine feasible values on the coordinate plane.

Standards:

Favorites
(7)

Resources
(18)

Reflections
(1)

### Graphing Inequalities (Vertical and Horizontal Boundaries)

8th Grade Math »
Unit: Relationships between Quantities/Reasoning with Equations

8th Grade Math »
Unit: Relationships between Quantities/Reasoning with Equations

Big Idea:

#### This lesson is actually a continuation of the Two Variable Inequality lesson. Again, the topic of inequalities is a great one for modeling with real world problems.

Standards:

Favorites
(1)

Resources
(13)

Reflections
(1)

### Modeling with Two Variable Equations and Inequalties

Algebra I »
Unit: Extending Equations

Algebra I »
Unit: Extending Equations

Big Idea:

#### Students will make a real life problem easier to understand by representing and solving it graphically.

Standards:

Favorites
(2)

Resources
(15)

Reflections
(1)

### Solving Two Variable Inequalities Part 2

Algebra I »
Unit: Linear Functions

Algebra I »
Unit: Linear Functions

Big Idea:

#### See how to use test points to determine how to determine the solution to a two-variable inequality.

Standards:

Resources
(12)

Reflections
(1)

### Two Variable Inequalities

8th Grade Math »
Unit: Relationships between Quantities/Reasoning with Equations

8th Grade Math »
Unit: Relationships between Quantities/Reasoning with Equations

### Solve the System of Inequalities to Find The Treasure!

Algebra I »
Unit: Systems of Equations

Algebra I »
Unit: Systems of Equations

Big Idea:

#### The point of this activity is for students to solve a system of inequalities to find a treasure, and be able to provide reasoning and feedback to other students.

Standards:

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(24)

Resources
(14)

### Unit Test: Systems of Equations and Inequalities in 2 Variables

Algebra I »
Unit: Making Informed Decisions with Systems of Equations

Algebra I »
Unit: Making Informed Decisions with Systems of Equations

Big Idea:

#### Students complete a unit assessment aligned to unit standards - provides excellent data source for teacher's to adjust and refine their curriculum and instruction!

Standards:

Resources
(5)

### Maximizing Profit: An Introduction to Linear Programming

Algebra I »
Unit: Systems of Equations and Inequalities

Algebra I »
Unit: Systems of Equations and Inequalities

Big Idea:

#### Now for the important question: How can we make the most money? After graphing a feasible region, students plot profit lines and learn the basics of linear programming.

Standards:

Favorites
(2)

Resources
(12)

Reflections
(1)

### Study Session for Unit Test on Systems of Equations and Inequalities in 2 Variables

Algebra I »
Unit: Making Informed Decisions with Systems of Equations

Algebra I »
Unit: Making Informed Decisions with Systems of Equations

Big Idea:

#### Students work on the important executive function skill of progress monitoring by identifying areas of need and working on those types of problems to be active participants in studying for a unit test!

Standards:

Resources
(3)

### Graphing and Solving Systems of Inequalities

Algebra I »
Unit: Making Informed Decisions with Systems of Equations

Algebra I »
Unit: Making Informed Decisions with Systems of Equations

Big Idea:

#### Students apply concepts learned about solving systems of equations and apply them to create, interpret and solve systems of inequalities!

Standards:

Favorites
(2)

Resources
(31)

Reflections
(3)

### Graphing Linear Inequalities

Algebra I »
Unit: Linear Inequalities

Algebra I »
Unit: Linear Inequalities

Big Idea:

#### Students will combine their knowledge of inequalities and linear functions to graph solution sets.

Standards:

Favorites
(9)

Resources
(14)

Reflections
(1)

### Graphing Systems of Linear Inequalities (Day 1 of 2)

Algebra I »
Unit: Linear Inequalities

Algebra I »
Unit: Linear Inequalities

Big Idea:

#### Students will combine their knowledge of systems of equations and linear inequalities to represent the solution in a simultaneous equation scenario.

Standards:

Favorites
(8)

Resources
(16)

Reflections
(1)

### SUPPLEMENT: Linear Programming Application Day 1 of 2

Algebra I »
Unit: Systems of Equations and Inequalities

Algebra I »
Unit: Systems of Equations and Inequalities

Big Idea:

#### This lesson gives students the opportunity to synthesize what they have learned before they begin to create their own linear programming problems.

Standards:

Favorites
(1)

Resources
(17)

Reflections
(2)

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