Skiing is a popular sport, but avid skiers are constrained by the seasons, weather conditions, time of day, and more. Indoor ski slopes are gaining in popularity as they allow for the control of many of these constraints and could provide year-round fun. Still, the most interesting indoor ski slopes are probably yet to be designed. Try your hand at it!

The Task:

You are going to explore various existing indoor ski slopes and then develop a plan for an indoor ski center of your own. You’ll need a healthy background knowledge of coordinate planes, slopes, lines, and graphing linear equations (those equations that produce straight lines.) Your task is to graph the mathematical slope of various existing indoor ski slopes and design three unique ski slopes for varying abilities. Your ski slopes should be drawn carefully on graph paper and include the linear equations for the straight segments.

The Process: Use the following directions to explore five different world indoor ski slopes.

  1. Out of class assignment: Gather information on five indoor ski slopes that will allow you to graph the mathematical slope of the ski slope. You will need at least two of the three necessary pieces of information: length of the slope; distance of the drop from the top of the hill to the bottom; length of indoor space needed to accommodate the slope and drop. (If you have two, you can determine the third number! You’ll find out how later on.)
  2. You can begin with the sites below and then conduct an Internet search using the following keyword phrase: “indoor ski slope”
  3. For each slope, write down a descriptive sentence describing the ski slope, such as: “The Skidome Nicky Broos ski facility in Ruchpen, the Netherlands features a run that is 160 meters long with a 25 meter drop.”
  4. Graph the overall slope from the highest point to the lowest (realizing that no slope is a straight line). Note: in most cases, the information you will find on the Internet will be the drop (height) and the slope length (the hypotenuse of a right triangle.) You will have to use the Pythagorean theory to determine how much indoor length is required to accommodate the slope and drop. Show your equation and work for each ski slope calculation.
  5. Identify the run and rise of each line drawn.
  6. Write the equation to calculate the mathematic slope of each line drawn.
  7. Write a paragraph comparing and contrasting the five ski slopes you selected.
Resources and Practice
  1. Lines and Slope lessons from the Math Forum:
  2. Graphing Equations and Inequalities from
  3. Worksheets on Linear Equations from
  4. Coordinate Graphing from SCORE Mathematics:
  5. A more advanced description of line graphing by Wiki Books:
  6. What’s the Point? – an interactive point plotting exercise for basic coordinate pairs:
  7. Java applets for exploring functions and algebra concepts from Shodor Interactive:
  8. Algebra resources from the Spartanburg, SC school system:
  9. The “Hand Squeeze” graphing activity – optional assignment:
  10. The “Stressed Out” graphing activity – optional assignment for more advanced students:

PBL UNIT Documents