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?