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toc =G.R.A.S.P.S= = = =Understanding(s)= • Students will understand that a linear relationship takes the form of y = mx + b. • Students will understand that linear relationships are characterized by a constant rate of change. • Students will understand that graphs can be drawn from equations and vice versa.
 * Goal || You are to create a snowboard park within certain dimensions to have a specified distance and slope appropriate for a specified skill level. ||
 * Role || You are a snowboard park designer hired to create a new snowboard park. ||
 * Audience || Your audience will be the Sugarloaf Board of Directors as well as Olympic Gold Medalist Seth Wescott. ||
 * Setting || The challenge is to create a park that is within your given dimensions and skill level. ||
 * Presentation || You need to create an equation of a linear equation with a skill appropriate slope and the distance fits within the dimensions provided. ||
 * Standards || **Product:** Mathematical Reasoning (20%), Working with Others (15%), Explanation (15%), Mathematical Concepts (20%), Appearance (15%), Neatness & Organization (15%)
 * Presentation:** Comprehension (25%), Preparedness / Attire (15%), Content (25%), Posture & Eye Contact (15%), Enthusiasm (10%), Collaboration with Peers (20%) ||

=Introduction= Sugarloaf is a popular ski destination located in western Maine. Over the years, the mountain has attracted hundreds, if not thousands, of new guests each year. To accommodate the growing interest in the mountain, Sugarloaf has decided that an expansion of the slopes has become a necessity. An open search will be conducted to see if there are any design firms that can come up with some great ideas for proposed slopes.

=Task= With an increasing amount of people wanting to snowboard over ski, Sugarloaf Ski Resort is looking for a snowboard park designer to create a new section of their snowboard park. Your architect firm, based out of Portland, Maine, has been given the task of designing a new snowboard park that would be appealing to all different experience levels. However, you will have space limitations and will need to create a slope that will be appropriate for your given skill level as well as an appropriate distance so that a snowboarder is not going faster than they should like to be. You and your design company will make your way out to Sugarloaf in order to convince the Sugarloaf Board of Directors as well as Olympic Gold Medalist Seth Wescott, as to why your snowboard park design is the best and is appropriate based on skill level. They are also interested in learning where your numbers came from, so be prepared to explain that. If your design company is chosen, your company’s design will be selected to be the new addition to the mountain but it will also increase your likelihood of being selected to create future expansions of the park. Good Luck!

=** Process **=

//Step 1: Slope// Your design firm will need to find out all that it can about solving for the slope of a line. Since most ski slopes are downhill, there should be altitudes that can be used to to create two points in which slope can be found. Preferably, these two points should be at the beginning and end of the ski trail. The x-value for the starting point at the top of the mountain should be (0,y), and the point at the end of the slope should be (x,0). For more information on slope and ways to calculate it, please visit this [|site].

//Step 2: Distance// In order to determine the distance of your ski trail, two points are also going to be necessary. The points that should be used are the same ones that were in your slope equation. The Sugarloaf Board are interested in seeing what your design company feels would be an appropriate length for each given ski trail. For information on finding the distance of your ski trail, please visit this [|site].

//Step 3: Midpoint// Sugarloaf feels that it is important for it's guests to know how far along in their trails they are so that if they are feeling tired or just do not want to continue, they know how much longer they would have to travel. Using the midpoint formula, you and your design firm need to figure out what the midpoint of the trail would be so that Sugarloaf can put up signs to let their visitors know. For more information on finding the midpoint of your proposed ski trail, please visit this [|site].

//Step 4: Velocity// Sugarloaf Board Members want to also inform it's guest as to how long it would take them to reach the bottom at a specific rate of velocity. If someone is less experienced, it will probably take them longer to reach the bottom of the trail since they would want to travel at a slower velocity. They also want guests to know the opposite, if they travel at a certain velocity the entire way down, how long would they expect it to take them to reach the bottom. For more information on finding the velocities of the skiers, please visit this [|site].

//Step 5: General Facts About Skiing!// In order for you and your design company to come up with the best possible ski slope for Sugarloaf to create at their resort, it would seem reasonable to have a general background of the skiing industry. Some facts that may be of interest would be finding out what common velocities are seen in each of the experience levels. Also, what should the slope of the ski trail be for each of those experience levels. Below are some websites that give some information about skiing. Students are welcome to search for their own websites, however, they **__//MUST//__** be a site that is approved by your teacher. Sites cannot be used otherwise.

[|www.wildsnow.com] - This article contains information about appropriate grades for ski slopes and specific experience levels. [|Yahoo! Answers] - This is conversation from several different people placing their input on ski slope grades.

//Step 6: Glogster Tutorials// The media that students will be using to create their final projects on will be Glogster. In order to become more familiar with Glogster, your design company members should watch the following tutorials and then experiment with the product yourselves. One of the best ways to become more familiar with new technology is to experiment with it.

[|Tutorial 1] - This tutorial was created by Traci Blazosky [|Tutorial 2] - Glogster tutorial from schooltube.com

//Step 7: Create Your Glogster!// In order to persuade the Sugarloaf Board of Directors and Olympic Gold Medalist Seth Wescott that your ski trails are the best options to be added to the resort, they have asked that all design companies wishing to create slopes create a Glogster poster to show them what you have come to for numbers. They are very interested in seeing the math that was done to achieve the number being presented so be sure to include your process in finding numbers. They also want to know why your design company feels like it has come to the best slopes, distances, and velocities possible for their new ski trails.

//Step 8: The Presentation...// Your company will be invited to Sugarloaf Resort to present your Glogsters directly to the Board of Directors. They want to see all of the people behind the creation of the numbers, not just one person representing the entire firm. Your and your design firm will be housed for one night free of charge as a thank you for participating in their search for the best ski trail design.

=Conclusion= The Sugarloaf Board of Directors are thankful of your submission for a possible expansion to their park. The Board has realized that the planning process of expanding the park is not easy and finding appropriate dimensions for the slopes and distances require a good mathematical background. Knowing about linear relationships and their properties, such as slope, distance and velocity, will all affect how the new terrain park turns out. Good luck in your presentation to the Board!