Integrating Technology into Secondary Math Classes

For this lesson/project on technology integration in math classes, I collaborated with Ms. Leanna Winstead and her Math 2 classes at Heritage High School. They are using a web based tool called "desmos" located at www.desmos.com. A description of the tool is listed on the student's Project Information Sheet listed below. In addition there are detailed instructions on how students are to complete the project.

Mathspiration Art Project

Objective: To create a piece of art using functions. Your job is to create a piece of art for an "Mathspiration Art Exhibit" at a local art gallery. This exhibit is all about showing that Math isn't just numbers on a page, it's about bringing things to life. So we don’t just want regular works of art. Your art must be made by graphing functions on a coordinate plane. The idea is that we don’t just want basic shapes, We want pictures! That means that there are some guidelines you should follow.

• You must use at least 5 different functions from the following list: Linear, quadratic, absolute value, square root, cube root, exponential, log, power or inverse variation.
• You must have at least 10 equations to form your picture.
• You must have a list of equations you used to create your picture. They should be turned in separately. Any equations you only use part of, you must include the domains (using inequalities).
• You must print out your picture and equations to turn in.  Your picture must be  colored..

You will use www.desmos.com which is an online graphing program to help you figure out how to do your picture.

• It will let you move your functions around using your transformations until you have your picture just the way you want it.
• When you are done:
  1. Add a link to your finished product to our class's "Digital Art Gallery" Padlet. You must comment, positively and constructively, on at least five other pieces of "Mathspirational" art.
  2. Print your picture. Then you will have to write your functions on your picture and color it.

This mini-project usually covers a day and a half but could be integrated with other areas of content. The finished student work will be added to a Padlet and students will complete a "Digital Art Gallery" walk and comment on each other's work. Another idea we had, and plan to do in the future, is to collaborate with the Art Teachers and actually host an "Mathspiration Art Exhibit" at the Spring "Meet the Teacher Night". That adds an authentic audience to the project and helps students see themselves in a real world situation. 

These are the Content Essential Standards that could be associated with the project.

• Reasoning with Equations & Inequalities       
  • A-REI Understand solving equations as a process of reasoning and explain the reasoning.
  • A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
    • Note:  Students should be able to justify the steps for any equation type solved in Math II.
  • A-REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
    • Note:  At this level, limit to inverse variation.

• Solve equations and inequalities in one variable.
  • A-REI.4 Solve quadratic equations in one variable.
  • b.  Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
    • Note:  Solve quadratic equations that have real solutions and recognize quadratic equations that do not have a real solution. (Writing complex solutions is not expected in Math II.)
• Solve systems of equations.
  • A-REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
• Represent and solve equations and inequalities graphically.
  • A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
    • Note:  At this level, extend to quadratics.
  • A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
    • Note:  At this level, extend to quadratic functions