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Reading, Writing, and Graphing Inequalities

Lesson Plan

Reading, Writing, and Graphing Inequalities

Grade Levels

8th Grade, 9th Grade

Course, Subject

Algebra I, Mathematics
Related Academic Standards
CC.2.2.6.B.2 CC.2.2.6.B.2
Understand the process of solving a one-variable equation or inequality and apply to real-world and mathematical problems.
CC.2.2.HS.D.7 CC.2.2.HS.D.7
Create and graph equations or inequalities to describe numbers or relationships.
A1.1.3.1.3 A1.1.3.1.3
Interpret solutions to problems in the context of the problem situation (limit to linear inequalities).
M06.B-E.2.1 M06.B-E.2.1
Create, solve, and interpret onevariable equations or inequalities in real-world and mathematical problems.
M06.B-E.2.1.1 M06.B-E.2.1.1
Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
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  • Big Ideas
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Numerical quantities and calculations can be estimated by using numbers that are close to the actual values, but easier to compute.
    Patterns exhibit relationships that can be extended, described, and generalized.
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
    Two variable quantities are proportional if their values are in a constant ratio. The relationship between proportional quantities can be represented as a linear function.
    Mathematical relations and functions can be modeled through multiple representations and analyzed to raise and answer questions.
    Mathematical relationships among numbers can be represented, compared, and communicated.
    Mathematical relationships can be represented as expressions, equations, and inequalities in mathematical situations.
    Numerical quantities, calculations, and measurements can be estimated or analyzed by using appropriate strategies and tools.
    Patterns exhibit relationships that can be extended, described, and generalized.
  • Concepts
    Algebraic properties and processes
    Ratio and Rates
    Variables, Expressions, Equations
    Algebraic Equations
    Equations and Inequalities
  • Competencies
    Write mathematical expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems.
    Write, solve, graph, and interpret linear equations and inequalities to model relationships between quantities.
    Create and/or solve equations (including literal, polynomial, rational, radical, exponential, and logarithmic) both algebraically and graphically.
    Determine how a change in one variable relates to a change in a second variable.
    Interpret solutions to linear equations and inequalities.
    Interpret solutions to linear systems of equations and inequalities.
    Represent and analyze quantitative relationships between Independent and dependent variables.
    Solve and interpret one variable equations or inequalities in real world and mathematical problems.
    Use and/or explain reasoning while solving equations, and justify the solution method.
    Use exponents, roots, and/or absolute values to represent equivalent forms or to solve problems.

Rationale

This lesson is a foundation for students to be able to advance through the Algebra I course. This topic will eventually allow them to be able to graph solutions and write, solve, and graph systems of linear inequalities.

Vocabulary

Inequality - a statement that two quantities are not equal (using <, >, <, >, or not equal)

Solution of an Inequality - any value that makes the inequality true

 

***Vocab and definitions provided in the PowerPoint notes.***

Objectives

  • Write, graph, and solve inequalities
  • Identify solutions of inequalities
  • Solving and graphing inequalities

Lesson Essential Question(s)

How are relationships represented mathematically?
How can data be organized and represented to provide insight into the relationship between quantities?
How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
How can mathematics support effective communication?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How is mathematics used to quantify, compare, represent, and model numbers?
What makes a tool and/or strategy appropriate for a given task?

Duration

Three Days of 40-50 minute periods:

Day 1:  Notes & Guided practice

Day 2:  Notes, Independent Practice, & Review

Day 3:  Review & Quick Check Quiz 

 

Materials

Teacher Materials

Graphing Inequalities Graphic Organizer  (Day 1 with review as needed on subsequent days)

Inequalities Bell Ringer  (Day 3)

Section 3-1 Inequalities and Graphs Part 1  (Day 1)

Section 3-1 Inequalities and Graphs Part 2  (Day 2)

Translating Words into Algebraic Equations & Inequalities  (Bell Ringer Days 1 & 2)

Inequalities Activity (Day 2) 

Algebra 1 - Reading, Writing, & Graphing Inequalities  (Days 1-2) 

***Note:  There are 55 example problems in this packet.  You do not need to cover all 55 if your students are understanding.  Just be sure to cover a substantial number of problems of each type.  You may choose to complete problems by displaying this resource via overhead projector.  This could also be shared on your teacher website, wikispace, or blog, and students could access this through individual desktop, laptop, or tablet.

Translating Inequalities (Day 2-3)

Inequalities Mini Review  (Day 3)

Standardized Test Prep - Reading, Writing, & Graphing Inequalities (Day 3) 

Algebra 1 - Reading, Writing, & Graphing Inequalities Quiz  (Day 3)

Graphing Inequalities video (Day 1) 

Writing Inequalities from a Graph video (Day 2)



 

Student Materials

Suggested Instructional Strategies

W: Post weekly lesson plans on website.  Post daily agenda in classroom.
H: Bell ringers completed in small group or with partners.
E: Exploratory, completion of graphic organizers, notes, lecture, discussion, independent practice, audio-visual, Accelerated students can independently Inequality Activity (resource)
R: Bell ringers, homework, discussion 
E: Bell ringers, homework, discussion, graphic organizer, Thumb System (see below)
T: Teacher-provided notes, graphic organizer, examples, vocabulary, exploratory activities for below level learners
O: Exploring, teacher examples, guided practice, partner/small group, independent practice, quiz 

***There are accelerated and struggling learner strategies within the instructional procedures.***

***Thumb System

Thumb up - I really get this and need no help!

Thumb sideways - I sort of get this but may need help soon!

Thumb down - I need help right now!

Instructional Procedures

Day 1

 

Day 2:

 

Day 3:

 
 
 
 

***You may use the Thumb System at any point during the lesson when you feel you need immediate student self-reflection and feedback.***


Formative Assessment

Day 1:  Graphing Inequalities Graphic Organizer

Day 2:  Translating Inequalities

Day 3:  Algebra 1 - Reading, Writing, & Graphing Inequalities Quiz & Translating Inequalities

Related Materials & Resources

Extra practice - Writing Inequalities:  http://www.math.com/school/subject2/lessons/S2U1L4GL.html

 

At home re-teaching:  http://www.mathsisfun.com/algebra/inequality.html

Author

Mallory Hafer (IU 11, IU 17)

Date Published

February 10, 2014
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