Unit 1, Lesson 1, Investigation 1.3 and
Lesson 1, Investigation 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:** Overhead “I have a secret for you! It will
make your mathematical life simpler. Would you like to know what it is?”
Use the calculator to review what we did yesterday in class.

2)
**Objectives:** -After a group experiment the day before, a group discussion and finishing
the Investigation 1 of Lesson 1, students will be able to clear express an inverse and direct relationship in equation form,
given a contextual scenario, observe inverse and direct relationships and express them with variables in equations.

-Students will begin working in groups on Lesson 1, Investigation 2.
As students work through the investigation they will reaffirm the affect of changing a variable in a three variable
equation (**Combined Variation**). At
the end of this investigation of leading questions, they will be able to compare the rates and times of situations in context
of the general form

and determine the result
of these changes in the variables.

__Investigation__

As students work through the investigation
in the tex, I will guide them to a deeper understanding of the content through multiple representations of the content and
carefully designed questions and examples.

__Conclusion__

v

What is the relationship between the variables in this equation?

v

If you discover a relationship such as

¨
Can we write z as a function
of k, y, and x?

¨
Can we write x as a function
of k, y, and z?