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[Teacher's Guide]
 
 
  There's Gotta Be an Angle

OverviewProcedures
Students will examine the external variables that affect a downhill skier in the quest for speed. Students will manipulate the formula for speed (speed=distance/time) by utilizing ratios and percentages. Students will use angle measurement to correctly map and model local and idealized terrains.


Grade Level:

8


Subject Matter:

Math


Curricular Uses:

This Challenge includes practical applictions of ratios, percentages, and decimals in manipulating a formula. Students solve multi-stage problems during these applications.

This lesson Challenge also applies angle measurement in calculating an optimum ski slope and constructing contour maps. Scale is practically applied.


Extensions:

Science and Math: Ski length varies with the height of the skier. Have students search and find the recommended ratios of ski length to a skier's height. They should calculate the best ski length for various members of the class and staff. Why do some skiers prefer to use the new short skis?

Science: Different kinds of snow are present on the ice pack of the slopes. The type of snow depends on temperature, as well as the amount of sun and time between snowfalls. Students should explain how the snow is classified. They should then explain how each type of snow formed.

Relate the types of ski wax to the different kinds of snow. Get examples of the different waxes, and compare their physical properties. Test the effects by putting the wax on different blocks and sliding them down the ramp.

Ecologists and ski resort developers often do not agree on the development of the ski area. Ask students: Who are the residents of these habitats? How is the ecosystem affected by building a resort?

Social studies: Ask students the following: What kind of mountains are at Nagano? How did they form? Where else can these kinds of mountains be formed? Explain why two of these places are also ski slope sites, and why two others are not.

Language Arts: Write to various ski resorts, and ask what amenities the resort owners feel must be offered to attract guests.


Objectives


Students will be able to:

  • Manipulate the speed formula (speed = distance/time).
  • Work with ratios and percentages in calculating and comparing speeds.
  • Work with decimals and the metric system.
  • Experiment to find the optimum angle for a ski slope.
  • Measure and draw a contour map of local terrain.
  • Demonstrate how to overcome the effects of air resistance.
  • Make a scale model of a geological feature.
  • Compare a scale model and a contour map.
  • Accurately measure the angles of elevation of local terrain.