1. By: Christopher Imm Johnson County Community College October 7, 2017
27th Annual Mathematics Technology Expo Using (Free) Web Tools to Engage the Flipped Classroom and online learning
By: Christopher Imm
Johnson County Community College
October 7, 2017

2. The Flipped Classroom:
At JCCC there is a movement toward the Learning Studio which promotes:
Group Learning
Inter(active) Learning
More student to student interaction
More student/teacher interaction
Individual and mobile computers for student and group exploration

5. Activities which drive the topic:
Use the Transformation of Functions Exploration to fill in the class notes

6. Activities to explore topics:
Match My Parabola Exploration

7. Inverse Function Exploration
After using this exploration, list a few generalizations about inverse functions.
If a point (x,y) is on a function, (y,x) is on the inverse.
Inverse functions are symmetric about the line y=x.
Sometimes the domain must be restricted for inverse functions to exist.

8. Explorations and projects used to help define mathematical topics and definitions: The Magic Carpet Ride Sequence
Linear Combination Exploration for visualization
Magic Carpet Ride Project (informal/concrete idealization)
Follow up Project (formalizes mathematical topics definitions)

9. Explorations which help visualize skills (Wolfram Demonstrations Projects)
Matrix Multiplication
Planes and Gaussian Elimination of a 3x3 Linear System
3x3 Determinants with Cofactor Expansion
Coordinates Relative to a Basis in 2D
The Gram Schmidt Process in 3D

10. Online Class Challenges
Providing students with tools to conceptualize the topics
Providing students with tools to interact with the topics
Providing students with tools to practice with the topics
Providing students with tools that offer instantaneous feedback

11. Applied Calculus Explorations College Algebra Explorations
Secant to Tangent Line Exploration
Continuity at a Point Exploration
Continuity at a Point Follow up Questions
Function or not
Even function exploration
Odd function exploration
Composition of functions exploration
Factors and zeros of polynomials
Quartic function Exploration
Rational function exploration
Exponential function exploration
Logarithmic function exploration

12. “Drillmaster Assignments”
Graph the Line Through Two Points
Point Slope Form of a Linear Equation
Composition of Functions
Computing Inverse Functions
Synthetic Division
Rational Function Attributes
Solving Logarithmic Equations

13. Quartic Function Exploration
What can you conjecture about polynomials from this exploration regarding:
End behavior
Zeros

14. Quartic Function Exploration (Cont.)
What theorems can you visualize?
The Conjugate Zeros Theorem
Polynomials of odd degree have at least one real zero
The Intermediate Value Theorem