**Unit
1, Lesson 1, Investigation 1.2**

__Standards and Benchmarks Covered in this Lesson__

I,1,2: Analyze, interpret and translate among representations of patterns including tables, charts, graphs, matrices,
and vectors.

I,2,2: Develop a mathematical concept of function and recognize that functions display characteristic patterns of change
(e.g., linear, quadratic, exponential).

__Introduction__

1. Anticipatory Set:
Karate Chop scenario considering length and width of board and how that effects the breaking weight. (Class discussion)

2. Objectives: -After
a group experiment and discussion students, will be able to observe inverse and direct relationships and express them with
variables in equations.

-After a group activity students
will be able to identify how changes in one variable affect the values of the other variables in a multiple-variable relation
and express these changes as an inverse or direct equation.

__Presentation__

Input/ Modeling: Review what inverse and direct relationships are and what they look like in equation form.

§ Develop the math

§ Do a couple examples

__Collect Data__

Students will
use noodles as bridges and their desks as supports. They will hang weights from the noodles until the noodles break and record
the number it took. Desks will be placed different lengths apart and students will use different numbers of noodles for their
bridges (circulate).

Students will
begin to analyze their data and try to find a pattern.

__Guided Practice__

As a class we
will discuss the check point Pg 5.

How do you model the following:

one variable increases as the other increases?

one
variable decreases as another increases?

Given an equation relating three variables, how would you determine
how changes in one variable relate to each other?

__Independent Practice__

§ Students will complete
the "On Your Own" questions Pg 5

__Conclusion__

o
What is an inverse relationship? direct relationship?

o
How do you write both of these?

o
Is it possible to analyze a function with three
variable?