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 Intermediate Value Theorem, students will be able to find an x value between an a and b value given an f(a) and an f(b) value.

Anticipatory Set:

          Give the students the challenge of rewriting the Intermediate Value Theorem in their own words within their groups.  After 10 minutes the class will present their solutions to the rest of the class.  Their classmates will determine whether or not they are correct, along with my guidance.

Input:

Ø     f is continuous on an interval if f(x) is an unbroken curve on that interval

Ø     Addition, subtraction, multiplication, and division (sometimes) preserves continuity

Ø     Tangent function not continuous over the set of reals b/c broken at

odd multiples of p/2

Ø     A function may be defined on the entire interval and not be continuous (floor or ceiling functions)

Ø     Intermediate Value Theorem: If a continuous function take two

distinct values on some interval, then it must take all values between these two. (Pg 170)

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 that other students are confused about problems.

Independent practice:

v       Students will be given Lesson Master 3-4 for extra practice and they will be assigned lesson 3-5 to read and do the C.A.R. problems for the next day.

Closure:

v      “What do we need to consider before we can use the Intermediate Value Theorem?”

Ø              If the function is continuous

v       “When do we tend to use the IVT?”

Ø  When trying to determine if a function has zeros