Compound Inequalities

Learning Context

Purpose/Rationale for Learning Experience:

The purpose of this lesson is for the students to be able to solve compound inequalities and graph them on a number line.  These skills are practical for solving and representing real life problems, for which a general understanding of compound inequalities is necessary.  Compound inequalities are used regularly to talk about a range of things such as time, money, temperature, weight, age, etc.  The students will be able to interpret a word problem and write a compound inequality that represents the given information.

Enduring Understanding(s):

Students should be able to evaluate and solve any compound inequality.  They should recognize and understand the language given in a word problem and how to represent the information in a linear compound inequality.  They should also be able to represent the compound inequalities on a number line.

Essential Question(s):

• What is one method that we can use to represent a range of data?
• What is an example of how we could use or solve compound inequalities in the world?
  
        Guiding Questions:
  
• What is a compound inequality?
• What are other phrases that mean the same thing as:  “less than”, “greater than”, “less than or equal to”, or “greater than or equal to”?
• How and when do you combine two inequalities?
• When do you flip the inequality symbol?
• When do you use an open/closed circle on a number line?
• What does inclusive mean?
• How do you represent a compound inequality on a number line?
• What is the difference between an ‘and’ statement and an ‘or’ statement?

Overview of what students need to know/ be able to do in order to succeed:

Prior to Learning Experience:

The students in this 8th grade class are in advanced math.  They are taking Integrated Algebra, which is a 9th grade curriculum.  These students are expected to follow all classroom rules and procedures.  In order for the class to run smoothly, it is especially important that the students:  follow the teacher’s directions immediately, return classroom materials to their proper places, take out their homework upon entering the classroom and wait quietly in their seats for the teacher to check it, and are responsible for making up any missed work.  Prior to this learning experience, the students should be able to solve multistep inequalities in one variable.  They should be able to graph simple inequalities on a number line, and should know when to use an open or a closed circle.

During the Implementation of the Learning Experience:

During this learning experience, students should be able to see the connection between basic linear inequalities and linear compound inequalities.  They should be able to see the difference and relationship between the two, in both the written and graphic forms. 

After the Implementation of the Learning Experience:

After this learning experience, students should be able to solve compound inequalities.  They should understand the differences between regular inequalities and compound inequalities.  The students should be able to write a compound inequality based on information given in a word problem.  They will be able to solve and graph all compound inequalities.

Key Subject-Specific Vocabulary:

• Linear Inequality- An inequality of the first degree (graph is a straight line).
• Compound Inequality- two or more simple inequalities joined by ‘and’ or ‘or’.
• Inclusive- including the specified extremes or limits as well as the area between them (uses the greater than or equal to, ≥ , and less than or equal to symbols, ≤).
• “More than”- uses a greater than symbol (x >)
• “Less than”- uses a less than symbol (x <)
• “As much as”- uses a less than or equal to symbol (x≤)
• “As little as”- uses a greater than or equal to symbol (x≥)
• “At most”- uses a less than or equal to symbol (x≤)
• “At least”- uses a greater than or equal to symbol (x≥)
• “Or more”- uses a greater than or equal to symbol (x≥)
  
• “Or less”- uses a less than or equal to symbol (x≤)

Classroom Rules

Classroom Procedures

Floor Plan

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