About This Chapter
Standard: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (CCSS.Math.Content.HSA-CED.A.1)
Standard: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (CCSS.Math.Content.HSA-CED.A.2)
Standard: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (CCSS.Math.Content.HSA-REI.B.3)
Standard: 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. (CCSS.Math.Content.HSA-REI.D.12)
About This Chapter
Students who have mastered these standards are able to work out and graphically solve various types of inequalities. When discussing these concepts, they will be able to identify and define the different inequality representations.
Lessons in this standard cover concepts such as:
- Graphing 1- and 2-variable inequalities
- Working with set notation, compound inequalities and systems of inequalities
- Solving and graphing absolute value inequalities
Students demonstrate the mastery of this standard when creating expressions that describe relationships or numbers. Mastery of these standards can support students through their education and career when they need to solve some math problems that have more than one solution.
How to Use These Lessons in Your Classroom
Here are some tips for how to use the lessons to support instruction in these standards:
Solving Linear Inequalities Lessons
Create a worksheet and show your students the video lessons regarding how to solve inequalities. In addition to passing out the worksheets, require your students to team up with one other student to complete the worksheet. Spend time at the end of the class having the groups come up and work out the inequalities in front of everyone.
Graphing Inequalities Lessons
Develop a worksheet that consists of different types of inequalities. Have the students watch all video lessons about graphing inequalities. Provide your students with graphing paper and the worksheet. Give your students time to graph the inequalities. Display the correct graphs on an overhead projector and explain the answers.
Compound Inequalities and Systems of Inequalities Lessons
Exhibit the video lesson 'Set Notation, Compound Inequalities and Systems of Inequalities.' Write various types of compound inequalities and systems of inequalities on the board. Call on students to identify the different examples and explain their answers.
1. What is an Inequality?
Deciding how to spend your money can be a tricky thing. Should you save it, invest it, or enjoy it? Learn how inequalities can help you make your decision!
2. Solving Linear Inequalities: Practice Problems
Linear inequalities may look intimidating, but they're really not much different than linear equations. In this lesson, we'll practice solving a variety of linear inequalities.
3. How to Graph 1- and 2-Variable Inequalities
So an inequality is just an equation with a less than or greater than symbol. But what is the difference between 1 and 2 variable inequalities? What does have a greater than or equal to symbol change? When do you use a number line instead of a coordinate plane? Get those answers here!
4. Set Notation, Compound Inequalities, and Systems of Inequalities
In this lesson, we'll explore the conditions of compound inequalities and learn how to express them using set notation and interval notation. Test you knowledge afterward with a short quiz.
5. Graphing Inequalities: Practice Problems
If you're already pretty familiar with what inequalities are and just looking for a place to practice your skills, this is the place. This lesson covers topics like 1-variable, 2-variable, compound, and systems of inequalities.
6. How to Solve and Graph an Absolute Value Inequality
Taking two skills and combining them to make a more complicated problem is a classic tactic in mathematics. If you feel confident with absolute values and inequalities, see if you can tackle them with their powers combined here!
7. Solving and Graphing Absolute Value Inequalities: Practice Problems
Solving and graphing absolute value inequalities brings a lot of different skills together in one place. The practice problems in this video will give you a good chance to see more examples of absolute value inequalities but will also test your general algebraic knowledge.
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Other chapters within the Common Core Math - Algebra: High School Standards course
- Common Core HS Algebra: Algebraic Expressions
- Common Core HS Algebra: Linear Equations
- Common Core HS Algebra: Quadratics
- Common Core HS Algebra: Exponents and Exponential Functions
- Common Core HS Algebra: Polynomials
- Common Core HS Algebra: Rational and Radical Expressions and Equations
- Common Core HS Algebra: Systems of Equations
- Common Core HS Algebra: Matrices
- Common Core HS Algebra: Sequences and Series
- Understanding Common Core Standards