Writing Equations for Rocket Paths: Math Lesson Example

Standards and Benchmarks CC F.IF.4 – For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. CC F.IF.5 – Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. CC F.IF.7 – Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases. 2

Standards and Benchmarks cont. CC F.IF.8 – Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. CC F.IF.9 – Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions. CC A.CED.1 – Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CC A.CED.2 – Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 3

Overview Rockets can be used to explain Quadratics and how all projectiles follow a Parabolic path. The equation of the path of the rocket will be determined using the Horizontal and Vertical distances. The equation for time will also be found with respect to height. 4

Tools Using the Estes AltiTrak altitude tracker you can measure the height of the rocket by standing a specific distance from the launch pad and using the tracker to find the exact angle. If the distance is too close, you can stand any distance away from the launch pad and use Trig to find the distance. This method will review other Mathematical functions. Using a stop watch you will find the time to apogee and finally touchdown. 5

Safety Always have a safety briefing prior to launching any rocket regardless of how small or big. Remind all students the required distance from the launch pad. Remind all students not to chase the rocket while in flight. When launching a rocket with a sealed nose cone make sure you angle the launch trajectory away from any pedestrians or buildings. If there is an ignition failure always wait 3 minutes before approaching the rocket. 6

Parabolic Path Apogee Initial Landing Point Height Distance or Time Y X Distance or Time Initial Landing Point 7

Using the Graphing Calculator to find the line of regression There are four main buttons we will be using: STAT Y= Window Graph 8

Using the Graphing Calculator to find the line of regression The process is lengthy at first but you will follow the same directions whether you are finding the equation for linear, quadratic, cubic, exponential or radical. You will insert your data points into the table (STAT, edit) You will calculate the line of regression (STAT, Calc, and find your specific regression) You will input your table names that you filled in first (2nd STAT) After given the equation, write that down and input into Y= After checking your window to make sure the min and max values are -10 to 10 you can push the graph button Students will be able to use this graph to find values (Trace) anywhere on the equation. 9

Lesson Expectations Students will be able to generate the equation given any number of points. In Algebra this is a very important skill that is on the Standards Based Assessment and the ACT. By using the steps learned in this lesson the students will be able to generate an equation with a linear, quadratic, cubic, rational, radical, or exponential function. With only a few more steps the students could also learn about statistical models and how predictions or trend lines are made. Learning how to determine which model is the most appropriate is an important skill set. 10