Content Standards and Benchmarks:

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

I,1,4: Explore patterns (graphic, numeric, etc.) characteristic of families of functions; explore structural patterns within systems of objects, operations or relations.

I,1,5: Use patterns and reasoning to solve problems and explore new content.

Objective:

          After reading lesson 3-5 and 3-6, hearing my lectures on the material, and going of examples in class, students should be able to do most of the problems assigned to them from these lessons.  I feel the students have not “gotten it” so we are review these concepts today

Anticipatory Set:

OH:   “Do you think we could maybe go through all of this stuff?  ‘Cause I have no idea what’s going on!”

SURE!!! J

Input:

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

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

Ø     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.

Ø     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.

Ø     Reversible Steps Theorem for Inequalities (Pg 179)

Ø     Chunking: thinking of an expression as a single variable

Ø     Zero Product Property for Functions: Let f, g, and h be functions.  If there exists a c such that h(c) = 0 and h = f*g, then either f(c) = 0 or g(c)  = 0 or both.  

Ø     When chunking…remember to substitute the original expression back in for the chosen!!

Modeling:

v    I will do a couple of examples that encompess the objectives from 3.5 and 3.6.

Guided Practice:

Students will form two groups and compete against each other to see which group can answer the most questions correctly.  Students will work on the problems in small groups for 10 minutes, they will then compare answers within their larger group and write the answer on the board (10min). I will then grade/go through these answers with the entire class (15 min) The remaining time the students will answer the final questions to see who will win.  The team with the most points at the end of class will win.

Independent practice:

Students will do the remaining Lesson Master Problems for 3-5 and 3-6. 

Closure:

Ø        Summarize what we have learned for each problem lead by students.