A ski hill's trail map shows its lifts, which carry skiers up, and its runs, which they ski down. In North America each run is marked by how hard it is: a green circle is easiest, a blue square is more difficult and a black diamond is most difficult. A lift's speed is often given in meters each second, and a hill's stations by their height above sea level. The ski hill on these pages, Snowcap Mountain, and its runs are made up.
Six pages about one ski hill, Snowcap Mountain. Page 1 is its trail map with seven questions: how long a run is, which runs start at a lift's top, and how far a route of two runs goes. Page 2 has the map again: follow four sets of directions to find where you end up, then find the one way from the Summit to the Lodge on green runs only and the shortest way on green and blue runs. Page 3 works out each lift's ride time from its length and speed (the shortest lift has the longest ride), then fills in a morning's schedule of waits, rides and runs with each start and end time. Page 4 uses a scale of heights above sea level to find each run's drop and each lift's rise, then asks which of two runs is steeper. Page 5 is speed: a rate table and six problems on how far, how long and how fast. Page 6 is six word problems. The first problem on pages 1 to 5 is worked as an example.
Put the trail map up and trace a route together before page 2: a lift goes up, a run goes down, and each run starts where the last one ended. On page 3, work out one ride time on the board: length ÷ speed gives seconds, and ÷ 60 gives minutes. For page 4, ask why two ways down from the same place to the same place always drop the same.
Look at a real ski hill's trail map online together and find its greens, blues and blacks. Ask how far a route would be, or how long a lift ride takes if you know its length and speed.
This pack supports the following Common Core State Standards for Mathematics:
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A trail map of a made-up ski hill, with its lifts, its green, blue and black runs and the heights of its stations, for distance, time and speed problems. Students read run lengths off the map, follow directions and find the shortest way down, work out lift ride times and a morning's schedule, find each run's drop and solve speed and word problems.
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