Hands On Quadratic Equation Activity By: Corinne Shultis

“What goes up, must come down!” Algebra 1 Content : Grades 8 – 10 Goals Students will be able to make predictions about data and determine the best model for the situation presented. Students will create and determine the accuracy of a quadratic equation based on data points using different variables. Objectives Students will construct a quadratic equation based on the physical data collected from an experiment. Students will consider the effect of variables on the quadratic equation using the manipulation of the physical data collected. Given the quadratic equation and h(t) = −16t2 + v0t + h0, ,Students will compare two quadratic equations that represent the same data. New York State Common Core Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graph and tables in terms of quantities, and sketch graphs showing key features given a verbal description of the relationship. F.LE.4 Construct and compare linear, quadratic, and exponential models and solve problems. S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Materials Bean bag or Tennis ball Post Its or Tape Yard Sticks Stop Watches Clip board Data Sheets TI-84 Graphing calculator High Technology Version: (video activity and upload to the computer) Video camera to record the throwing of the object Motion detection attachment from Texas Instruments

Station Set Up Teachers will set up the station for activity. There will be up to 8 members in a group. Each group will toss a ball in the air and record the time that it takes to reach the ground. Students will consider the initial position of the ball. This station is set up for 4 markers, each person has a line of tape and they are positioned 2 feet apart from each other. There is a thrower, each ”marker” student has a phone ( stop watch) and a post it to mark the position the ball passes them.

There will be one student throwing the ball, the other students will be “markers.” As the ball passes each ”marker,” the student will record the time and the height at which it passes. Students will record on the data table. After completion of the table, students will return to classroom to complete activity.

Sample Data Data from parts one and two of the practice activity.

Using the calculator students will calculate the regression equation for the data points using the calculator cheat sheet. Students will then answer the questions regarding aspects of the quadratic equation.

Part One: Height vs Distance Students will be able to determine: The quadratic equation as height as a function of horizontal distance. The graphic representation of the quadratic equation. The time at which the maximum height is reached. The maximum height that is reached.

Part Two: Height vs Time Students will be able to determine: The quadratic equation as height as a function of time. The graphic representation of the quadratic equation. The time at which the maximum height is reached. The maximum height that is reached.

Reflection Students will compare the two equations and decide if they are an accurate representation of the activity. Students will be able to reason and provide examples and suggestions to validate the equations based on the activity. This activity requires the students to collect data, create a scatter plot, a quadratic equation based on quadratic regression, using a formula and data create a quadratic equation, and determine the maximum height of the quadratic. This also allows students to see the difference in the creation of quadratic equations.