- Introduce students to what a Meteoroligist is and how they use sophisticated models to predict the occurence, duration and trajectory of weather events.
- Explain to students that meterologists build their models based on observations they have made in the past and by understanding how previous weather patterns evolved, meterologists can apply that knowledge to future weather events.
- Ask students to brainstorm and name of weather events that can be predicted by Meterologists.
- Next ask students to name mathematical models and/or tools that they think can assist Meterologists.
- Explain how Parametric Equations can be used to graph the path of an object in space. Give an example of how it can describe the path of a storm moving through an area, such as a Hurricane.
- Students will use historical storm data to trace the path of a hurricane by accessing the NOAA’s office fo Coastal Management. Model for the students how to search for a hurricane, reminding them that inland states typically do not have hurricanes. Zoom in to show the full hurricane path. Have students do the same and screen shot thier storm for copy/paste into their assginment heet.
- Students will create a table of values in their assignment sheet to track the storm’s horizontal and vertical movement with respect to time.
- Students will track their storm and collect data for 5 days and identify the latitude (x-value) and longitude (y-value).
- Model for the students how to create a mathematical model by creating two parametric equations and ask them what type of regression they expect I will use.
- Students will create their mathematical model and use their graphing calculator (Desmos.com) to create the formula for the model they have chosen and use the line (equation) of best fit. Students record two equations: x(t) and y(t).
- Next demonstrate for the students how to check their model by using t=0,1,2,3, and plugging into x(t) and y(t) and recording their results in Table 2. Have students do the same for their equations.
- Have the students graph their two sets of coordinates, Table 1 and Table 2, using their graphing calculator (Desmos.com). Remind the students that the two sets of data should be plotted in different colors. Students will screen shot their graphs into their assignment sheet.
- As a closure, provide the students with the following questions to compare the model points with the original points:
- How does your model compare with the actual path?
- Why did you choose the graph family that you did? Did you choose well? Why or why not?
- Is it possible to solve x(t) for t, substitute into y(t) to eliminate the parameter, t, and write its rectangular equation with x and y instead? Why or why not?
- For the next class period, create a gallery of student work so that the students can
-How to collect data, write parametric equations to model a real-world siutation, and graph their equations using a graphing calculator
Apply prior knowledge about parametrics to a real life situation.
– parameter- parametric equation- plane curve- eliminating the parameter
How can parametric equations can be used to graph the path of an object in space?
Modifications/Accommodations for Struggling Students
Students who need modifications can be provided the data and only work on obtaining the equations.
Modifications/Accommodations for Students Who Need a Challenge
Students can collect data for two different hurricanes and make comparisions betweent h paths, time and equations.
This lesson would occur at the end of a unit of study on parametric equations. Students will have already studied how to:• Evaluate sets of parametric equations for given values of the parameter.• Sketch curves that are represented by sets of parametric equations.• Rewrite sets of parametric equations as single rectangular equations by eliminating the parameter.• Find sets of parametric equations for graphs
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