Performance+Task

=Performance Task=

Standards

Enduring Understandings

Essential Questions

__** Goal: **__ Your goal is to evaluate your friend’s skateboarding performance and help her safely set new goals. You must convince your friend that the information you are giving your friend is accurate. **__Role:__** You are your friend’s coach. Your job is to help her set goals while maintaining her safety. __**Audience:**__ You are determining performance and safety information to share with your friend. __**Situation:**__ You are working with your extreme sport loving friend. __**Product, Performance, and Purpose:**__ You will create a report to show your friend graphically, in words, and symbolically her current performance data and the safe jumping distance with a second ramp. __**Standards and Criteria for Success:**__ Your report will be scored based on the inclusion of all the elements, your problem solving strategy, your conceptual understanding, your accuracy and your ability to communicate the mathematical ideas to your friend. Your friend is into extreme sports. She likes to jump off ramps on her skateboard. She keeps trying more daring stunts, and you want to help her be safe. Currently, she is jumping off a 4 ft ramp, but she wants to try a 6 ft and an 8 ft ramp. She also wants to try adding a second ramp for landing on. The second ramp will be a 4 ft ramp. Your friend needs your help evaluating her performance and making sure she is safe.

When your friend launches herself off the ramp, she continues to move in both a horizontal direction and a vertical direction. The vertical motion is independent of the horizontal motion. This means that vertical and horizontal motions are calculated using different formulas. Vertical motion can be modeled by the formula

h = -16t2 + v0t + h0

h0 = initial height (ft) t = time (s) v0 = initial velocity (ft/s) -16 is a constant that represents the force of gravity and has units of ft/s2 You will need to research the value of v0. You can check online to find an average speed for a skateboarder on flat ground and use that as your friend’s v0. Make sure you convert the number into the correct units (ft/s). ||
 * h = height (ft)

<span style="font-family: 'Comic Sans MS',cursive; margin: 0in 0in 10pt;">Your friend has asked you to answer the following questions for her.
 * 1) <span style="font-family: 'Comic Sans MS',cursive;">What will her path of motion look like? Use a diagram with labels to show your friend her start position, the ramp, ramp height, her path through the air, and her landing position. You must include a diagram for each ramp height/landing scenario.
 * 2) <span style="font-family: 'Comic Sans MS',cursive;">What will her maximum height be for each ramp height? //Hint:// the path of motion is symmetrical.
 * 3) <span style="font-family: 'Comic Sans MS',cursive;">How long will she be in the air for each ramp height?
 * 4) <span style="font-family: 'Comic Sans MS',cursive;">If she wants to reach a height of 10ft, what initial velocity is required for each ramp height? (use the values for t calculated in #3)
 * 5) <span style="font-family: 'Comic Sans MS',cursive;">What is the distance she will travel from the time she leaves the ramp to the time she lands on the ground? Calculate this for each ramp height used. //Hint:// Remember that vertical motion and horizontal motion are independent.
 * 6) <span style="font-family: 'Comic Sans MS',cursive;">Your friend wants to add a 4 ft ramp to land on. Where should the second ramp be positioned in relation to the first ramp so that she is able to safely land on it? Show the positioning with a diagram that includes her path of motion.
 * 7) <span style="font-family: 'Comic Sans MS',cursive;">Your friend is thinking about trying some other sports. Provide an explanation of how you might be able to help her with other sports.

<span style="font-family: 'Comic Sans MS',cursive;">Answer all of your friend’s questions.

<span style="font-family: 'Comic Sans MS',cursive;">Use an online graphing calculator to graph your equation for each ramp height. Print out the graphs and label them with the max height, the starting position of your jumper, and the landing position of your jumper. Be sure to label the parts of the graph that do not apply to your problem. You must provide the graph for the 4 ft, 6 ft, and 8 ft ramps.

<span style="font-family: 'Comic Sans MS',cursive;">Remember, you want to convince your friend that the information you provide to her is trustworthy. She doesn’t believe in magic math so you must show all your calculations and explain where all your numbers came from. You may solve the problems using any method, but you must explain your method. Your diagrams and graphs must be clear and easy to read. You must show your friend the connections between your diagrams, graphs and calculations. You must present the information in a report to your friend. You may organize the report in any way you like, but all the information requested must be included. The report does not need to be typed, but it must be written in ink.

<span style="font-family: 'Comic Sans MS',cursive;">Materials: <span style="font-family: 'Comic Sans MS',cursive;">· internet access and printer <span style="font-family: 'Comic Sans MS',cursive;">· You may use any online graphing calculator, but you can find one at: [] <span style="font-family: 'Comic Sans MS',cursive;">· Paper and pen

<span style="font-family: 'Comic Sans MS',cursive;">**Rubric**:


 * || <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">4 || <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">3 || <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">2 || <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">1 || <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">Score ||
 * <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive;">Content – Mathematics || <span style="font-family: 'Comic Sans MS',cursive;">The calculations, formulas, graphs and diagrams are all included and their connections are explained. || <span style="font-family: 'Comic Sans MS',cursive;">Three of the four math elements are included and only some connections are made between the elements || <span style="font-family: 'Comic Sans MS',cursive;">Two of the three math elements are included and no connections are made between the elements or connections are unclear || <span style="font-family: 'Comic Sans MS',cursive;">One of the math elements is included ||  ||
 * <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Content –Questions || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">All of the questions have been addressed || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Five of the questions have been addressed || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Four of the questions have been addressed || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">One to three of the questions have been addressed ||  ||
 * <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Conceptual Understanding || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">The solution shows a deep conceptual understanding of the problem including the ability to apply the correct mathematical concepts and the necessary information for its solution || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">The solution shows more than a basic comprehension of the problem and the main concepts necessary for its solution || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">The solution is incomplete showing parts of the problem are not understood || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">No solution or solution is not related to the questions and incorrect concepts are applied ||  ||
 * <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Problem Solving Strategy || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Uses a well organized and high level strategy that leads to a solution || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Uses a sound mathematical strategy and mathematical procedures are complete. || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Some mathematical strategy is evident, but procedures are incomplete || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">No clear plan evident in problem solving strategy ||  ||
 * <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Accuracy of Information || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Graph and all calculations are accurate and in proper units || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Graph and data are accurate but not in proper units || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Graph and calculations contain some errors or incorrect units || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Graph and calculations contain mostly errors or incorrect units ||  ||
 * <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Communication || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Explanation is clear and comprehensive. All steps and procedures are incorporated and include correct mathematical terminology. || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Explanation is clear and accurate. Use of Mathematical terminology is correct. || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Explanation is incomplete. Mathematical terminology is incorrect. || <span style="font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Solution is not explained or is not clear. ||  ||
 * ||  ||   ||   || <span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Total ||   ||