• Algebra 1 / Grades 8 and 9

• Students are familiar with factoring trinomials.
• Students are familiar with solving equations using the zero-product property.
• Students have not been introduced to the quadratic equation at this time.

• Students are familiar with Mathematica
• Students will know the basic interactions with a notebook.
• The notebook will be set up in a manner that is intuitive to the students and could be followed with a brief instruction sheet (i.e. Shift + Enter to evaluate).

• The students will learn how to use a Computer Algebra System (Mathematica) as a tool for analyzing, visualizing, and solving mathematical problems.
• The students will learn how to use a Computer Algebra System (Mathematica) as a tool for analyzing, visualizing, and solving polynomial equations.

I would have the students use Mathematica to model a polynomial equation. Depending on my assumptions of their Mathematica skills, I would either have students input numbers into dialog boxes and have Mathematica generate the answers, or I would have the students calculate the answers themselves.

Lesson One:
• I would have them find values of y for given values of x.
• I would have them describe any patterns that they see from these values.
• I would have them graph the equation
• I would have them use the graph and value of the coordinates that they already know to identify what values of x would solve this equation.
• I would have the students find values of x when y equals zero.
• I would have students identify these values of x as solutions to the equation.
• I would then have the students factor the equation using methods they have used in class.
• I would then ask them if these answers correspond to the answers they found earlier, and have them explain how they do or don't correspond.

Lesson Two:
• I would have the students do three more given examples using the same methods they used in lesson one. One of these examples will not be factorable by the general methods gone over in class.
• If they have extra time, I would have the students create their own equations and check for solutions

• AP Calculus AB / Grade 12

• Students are familiar with the definition of differentiation.
• Students are familiar with the derivative of a constant function.
• Students are familiar with the sum, difference, product, and quotient rules of differentiation.
• Students are familiar with the power and chain rule of differentiation.
• Students are familiar with rates of change.
• Students are familiar with the derivatives of trigonometric functions
• Students are familiar with implicit differentiation.
• Students are familiar with higher derivatives.

• Students are familiar with Mathematica
• Students will know the basic interactions with a notebook.
• The notebook will be set up in a manner that is intuitive to the students and could be followed with a brief instruction sheet (i.e. Shift + Enter to evaluate).

• The students will learn how to use a Computer Algebra System (Mathematica) as a tool for analyzing, visualizing, and solving mathematical problems.
• The students will learn how to use a Computer Algebra System (Mathematica) as a tool for analyzing, visualizing, and solving related rates problems.