Unit 2: Patterns of Change — an overview of various change patterns.
This unit will provide you with a broad picture of patterns of change so that linear models, as studied in the next unit, will be seen as a specific type of change.
Since this unit is an overview of patterns of change, mastery of each type of change is not expected.
Lesson 2.1: Related Variables
Key Questions
How do things relate?
How does one thing make something else change?Objectives
When you are finished with this lesson, you will have demonstrated how to
- identify key variables in the situation to be modeled
- collect data that will suggest the pattern relating those variables
- make a table and graph the data to look for patterns
- and make predictions that go beyond the data (extrapolations and interpolations).
Approximate completion time: 3 days
Lesson 2.2: What's Next?
Key Questions
What's next?
How do we know what will happen next?Objectives
When you are finished with this lesson, you will have demonstrated how to
- focus attention on patterns of change in variables
- explore iterative or recursive change
- examine equations relating NOW and NEXT
- and introduce and utilize the iteration capabilities of a graphing calculator or computer software.
Approximate completion time: 4 days
Lesson 2.3: Variables and Rules
Key Questions
How can we predict how much we will earn over time?
How can we model how much money a company makes?Objectives
When you are finished with this lesson, you will have demonstrated how to
- summarize patterns relating variables using rules
- utilize rules along with a graphing calculator or computer software
- illustrate the power of a rule and its capabilities when used with a graphing calculator or computer software
- and explore difficult questions relating variables by using rules and technology.
Approximate completion time: 6 days
Lesson 2.4: Linear and Nonlinear
Key Questions
How can we tell something will continue at the same rate?
How can we model the flight of an object?Objectives
When you are finished with this lesson, you will have demonstrated how to
- begin to understand and develop an appreciation for the power of technology-generated tables and graphs and the essential role of algebraic rules in providing directions to a calculator or computer software
- and recognize the connection between two-variable relationships and their graphs.
Approximate completion time: 4 days
Lesson 2.5: Looking Back
Approximate completion time: 2 days