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3-5 The Logic of Inequality Solving

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Content Standards and Benchmarks:

I,1,1: Use patterns and reasoning to solve problems and explore new content. (Specifically the Intermediate Value Theorem)

 

Objective:

          After reading the lesson the night before, and hearing my short lecture regarding the logic of inequality solving, students will be able to solve inequalities algebraically and determine which steps are irreversible and why.

Students will also be able apply this knowledge to real world problems.

 

Anticipatory Set:

          I will begin the day by asking students to tell me what the lesson was about.  They will explain to me the objectives of this lesson.  If the students need it, I will lead them into the objectives that they miss.

 

Input:

     Properties of Inequalities and Operations (review)

     Multiplication of both sides of an inequality by a negative number is  reversible step.

     If f is a function and increasing throughout the domain or decreasing throughout the domain, the function is 1-1.

     Let f be a real function: If f is increasing throughout its domain, then its inverse is increasing throughout its domain. If f is decreasing throughout its domain, then its inverse is decreasing throughout its domain.

     If you apply an increasing function to an inequality the result is an inequality with the same sense. If you apply a decreasing function to an inequality it changes the sense of the inequality.

     Reversible Steps Theorem for Inequalities (Pg 179)

 

Modeling:

v    Answer student questions from the night before.

v    Tie in today’s objectives with the questions that are asked.

 

Guided Practice:

v    As the students get more comfortable with the content, I will ask them

to lead me through the problems.

v    I may even ask student to come up to the board to do the problems

that other students are confused about problems.

 

Independent practice:

v       Students will be given Lesson Master 3-5 for extra practice and they will be assigned lesson 3-6 to read and do the C.A.R. problems for the next day.

 

Closure:

        “If there was one theorem to know from this lesson, what would it be?”

        Was there anything that surprised you from this lesson?

        What are the reversible steps from this lesson?

        What reversible steps do we know about thus far?

            What steps are irreversible?

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