Lesson 11 | Linear Expressions & Single-Variable Equations/Inequalities | 9th Grade Mathematics

Objective

Write and graph compound single-variable inequalities to describe the solution to contextual and non-contextual situations.

Common Core Standards

Core Standards

The core standards covered in this lesson

A.CED.A.3 — Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

Creating Equations

A.CED.A.3 — Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Reasoning with Equations and Inequalities

A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Foundational Standards

The foundational standards covered in this lesson

7.EE.B.4.B

Expressions and Equations

7.EE.B.4.B — Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Write an inequality that has both a minimum and a maximum value from a contextual situation. Identify this as a compound inequality.
Solve compound inequalities and identify the solutions as either inclusive, exclusive, or either a union or disjoint.
Use appropriate notation to algebraically write a compound OR inequality and appropriate notation to algebraically write a compound AND inequality (inclusive and exclusive).
Use appropriate notation to graphically show the solution set of a compound inequality (inclusive, exclusive, and, or).
Identify when an inequality is used inappropriately in either mathematical or contextual situations.
Describe why a compound inequality is necessary in contextual situations, and use $${x > 0}$$ and $${y > 0}$$ to denote positive solutions for a context.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

At Sea World, kids are only allowed into the Air Bounce if they are between 37 and 61 inches tall. They are only allowed on the Tide Pool Climb if they are 39 inches tall or under.

Show the allowable heights for the rides on separate number line, and represent each with inequalities.

Air Bounce:

Tide Pool Climb:

Using inequalities and a number line, describe the height of kids who can go on both the Air Bounce and the Tide Pool Climb.

Guiding Questions

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References

Illustrative Mathematics Height Requirements

Height Requirements, accessed on Sept. 14, 2017, 2:12 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

Which inequality in each row is valid? Draw a number line below the description to help explain your reasoning.

A number is greater than 10 and less than 5.	A number is greater than 5 and less than 10.
A number is less than 8 or greater than 4.	A number is less than 4 or greater than 8.
$${2<x>5}$$	$${2<x<5}$$
$${x<7}$$ or $${x>9}$$	$${x<9}$$ or $${x>7}$$

For the true inequalities written in words, write the inequality algebraically.
For the true inequalities written algebraically, write the inequality in words.

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Which one of these inequalities is valid? Explain your reasoning using a number line and in words.

Inequality 1: $${-1\leq x\leq 1}$$

Inequality 2: $${x\leq1}$$ or $${x\geq -1}$$

References

EngageNY Mathematics Algebra I > Module 1 > Topic C > Lesson 15 — Exit Ticket

Algebra I > Module 1 > Topic C > Lesson 15 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Write the inequalities shown in the graphs below.

Inequality 1:

Inequality 2:

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Include problems where students write a single inequality to represent the solution set of $${x>4 }$$ or $${x>6}$$. Describe how this is not a compound inequality.
Include problems where students need to graph inclusive and exclusive, bounded and unbounded inequalities written algebraically and in word form.
Include problems where students need to describe a compound inequality from a graph both algebraically and in word form.
Include problems where students distinguish the solution set of an equation graphed from the solution set of an inequality graphed.
Include error analysis problems where students identify a solution that is not in the solution set of a compound inequality. Use graphical and algebraic analysis to show that this student is not correct.

Illustrative Mathematics Fishing Adventures 1 — Write a compound inequality to describe the reasonable domain within the context of the problem.
Math Coach Blog "The 35 Game" for Compound Inequalities — This will need to be converted to problems or used as an extension in class.
EngageNY Mathematics Algebra I > Module 1 > Topic C > Lesson 15

Lesson 10

Lesson 12

Lesson Map

Topic A: Properties and Solutions of Single-Variable Linear Expressions and Equations

Identify properties of operations that result in equivalent linear expressions.

A.REI.A.1 A.SSE.A.1 A.SSE.A.2

Use properties of equations to analyze and write equivalent equations.

A.REI.A.1

Solve single-variable linear equations using properties of equality.

A.REI.A.1 A.REI.B.3

Solve equations with a variable in the denominator.

A.REI.B.3 F.IF.A.1

Solve for a variable in an equation or formula.

A.CED.A.4

Topic B: Modeling with Single-Variable Linear Equations

Write equations using defined variables to represent a contextual situation.

A.CED.A.2 A.CED.A.4 F.BF.A.1 F.IF.B.5 N.Q.A.1

Define variables; write and solve equations to represent a contextual situation.

A.CED.A.1 A.CED.A.2 A.CED.A.4 F.BF.A.1 F.IF.B.5 N.Q.A.1

Write and solve equations to represent contextual situations where estimations and unit conversions are required.

A.CED.A.1 A.CED.A.2 A.CED.A.4 F.BF.A.1 F.IF.B.5 N.Q.A.1

2 days

Model a contextual situation and make an informed decision based on the model.

A.CED.A.1 A.CED.A.2 A.CED.A.4 F.BF.A.1 F.IF.B.5 N.Q.A.1

Topic C: Properties and Solutions of Single-Variable Linear Inequalities

Solve unbounded single-variable inequalities in contextual and non-contextual situations.

A.CED.A.3 A.REI.A.1 A.REI.B.3 A.SSE.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.B.3

Solve and graph compound inequalities where algebraic manipulation is necessary in contextual and non-contextual situations.

A.CED.A.3 A.REI.A.1 A.REI.B.3

Linear Expressions & Single-Variable Equations/Inequalities

Objective

Common Core Standards

Core Standards

Creating Equations

Reasoning with Equations and Inequalities

Foundational Standards

Expressions and Equations

Criteria for Success

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem Set

Target Task

Problem 1

References

Problem 2

Additional Practice

Lesson Map

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