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
I,1,5: Use patterns and reasoning
to solve problems and explore new content.
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
OH: “Do you think we could maybe go through all of this stuff? ‘Cause I have no idea what’s going on!”
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
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!!
v I will do a couple of examples that encompess the objectives from 3.5 and 3.6.
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.
Students will do the remaining Lesson Master Problems for 3-5 and 3-6.
Ø Summarize what we have learned for each problem
lead by students.