# Linear Inequalities Investigation

```Conceptual Overview Template
Module 3: Assignment 1
Curriculum Conceptual Overview
Curriculum Title: Linear inequalities
Subject/Topic Areas: Intermediate Algebra
Key Words: solve; inequality; interval notation; infinity; Mobius strip; graph; number line
Curricular Context
Brief Summary of curricular context and goals that make this curriculum valid for a technology based
classroom:
21st Century learning outcomes Oklahoma Academic Standards : Priority Academic Student Skills (PASS)
Algebra Content Standards
3. Linear Inequalities and Graphs
a. Solve linear inequalities by graphing or using properties of inequalities.
b. Match inequalities (with 1 or 2 variables) to a graph, table, or situation and vice versa
Oklahoma has not adopted the Common Core Standards.
Big Idea /Concept: Solving Linear Inequalities
Enduring Understanding(s): Represent the solution set of an inequality in the three ways of : 1) an
inequality (using symbols), 2) using interval notation and 3) graph of the solution set on a number line.
What Essential Question(s) will be considered:
1) Where are inequalities used in some real-life occasions?
2) How is interval notation similar to the way you first learned how to express an inequality?
3) In what ways does the Mobius Strip relate to the concept of infinity?
Appropriate technologies and tools:
Students will investigate and practice exercises by logging into their Schoology accounts and following
the link for the www.coolmath.com and go to Algebra - Solving inequalities. Here they will be directed
to follow a series of lessons and then can practice.
What key knowledge, skills, & dispositions will students acquire as a result of this curriculum?
KNOWLEDGE = Content
Content students will remember:
The symbols used to express inequalities.
How to translate an inequality into interval notation.
The connection of the Mobius Strip to infinity.
SKILLS = Power verbs
Students will be able to: Express the solution set of an inequality in three different representations of
an inequality, in interval notation and by graphing the solution set on a number line.
DISPOSITIONS = attitude
Building students’ beliefs and values toward: Students will value the necessity of inequalities and how
they are representations of multiple/infinite solutions and how that differs from the usually single
solution of an equation.
ASSESSMENT: What evidence is used to show that students understand?
Formative: Homework assignments that are checked, students writing exercises and working solutions
on the board during class time, differing activities such as a scavenger hunt for solutions, short quizzes
and unit tests.
Summative: Semester test
Objectives from 6 Facets + Misconceptions:
From the curriculum, students will be able to:
EXPLAIN: Students will explain the meaning of the solution set of an inequality.
APPLY: Students will translate a word problem into an algebraic inequality.
INTERPRET: Students will describe the solution set of an inequality in the context of a word problem.
(This means they will experience word problems that contain the phrases "at least" and "at most".)
EMPATHIZE: Students will critique other student's translations of word problems involving inequalities
by rewriting the same word problem's translation and then indicating if they agree or disagree with the
original student's translation, as well as, writing a one sentence reason as to why they may agree or
disagree.
GAIN PERSPECTIVE: Students will develop the insight of multiple/infinite solutions of an inequality as
related to the concept of infinity.
GAIN SELF KNOWLEDGE: Students will discover the difference between a solution of an inequality and a
solution of an equation.
OVERCOME THE NAÏVE VIEW OF: (Misconceptions)
Inequalities do not relate to the concept of infinity.
There is only one value solution to an inequality.
Incorrect understanding of "at least" and "at most" phrases.
Intermediate Algebra
Name ___________________________
Linear Inequalities Investigation
After logging into Schoology, open the resources folder and select the www.coolmath.com account. Complete the
following below and fill in the blanks as you read each section.
(1) From the Home CoolMath page, select the Algebra flag on the left. Scroll down to the Algebra Help Lesson Topics
and select Solving Inequalities. After reading 1 - write the meaning of these inequalities in words and describe what it
means: x > 4 __________________________________________________________________
≤ −2 _______________________________________________________________
Use ____ or ____ , for closed dots
≤
Use ____ or ____ , for open dots
<
,
≥
,
>
(2) On the next page write the answers to the TRY IT! questions : 2 ≤  < 5 _________ ; 0 ≤  ≤ 7 ________
−6 <  < 4 _________ ; −10 <  < 0 _________
(3) Do the infinity symbols, −∞  ∞ , ALWAYS have parentheses beside them? Why or why not?
_______________________________________________________________________________________________
(4) Write your answers to the TRY IT! here.  ≥ 2 ______ ;  < 4 ______ ;  > 0 ______ ;  ≤ −3 _______
(5) Complete this...Remember way back when you used sets? "or" means " ________ " and we use "___".
(6) Do the TRY IT! here.  ≤ −5   > 0 ___________________ ;  ≤ 3   > 10 ____________________
< 0   > 2 ___________________ . Now go back to Menu 4 for this lesson.
(7) Click on the Crunch Some. The computer will generate problems for you.
Write the inequality _________________ now write it in interval notation ________ Graph
(8) Go back and now do (4) Solving Basic Guys. Do TRY IT! here. Write the interval and graph.
8 − 3 ≤ 13
10 − 7 > 4 + 35
(9) Back to the menu and do 5 - The Freaky Thing! What is the Freaky Thing?
___________________________________________________________________________________________
(10) Now do 6 - Compound Inequalities and do the TRY IT! here. Write the intervals and also graph them.
−5 < 3 + 1 ≤ 10
0 ≤ 5 − 2 ≤ 7
YAY! Time for some word problems!!!!
Go to this website:
Read Solving Word Problems in Algebra Inequality Word Problems; Word Problem Solving Strategies ; Inequality Key
Words ; Example 1 and Example 2 then Click on Click here to move onto the word problem practice problems.
After reading Solving Word Problems in Algebra Practice Problems and checking the answers, I want you to make up a
word problem of your own! Write it here:
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
Now Write out your solution in detail:
Exchange papers with another student (write his/her name here ___________________________)
Write his/her word problem here and solve it.
Now discuss whether you agree or disagree with one another's word problem if you think it is appropriate and if you
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
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