Lesson 4: Slope
Module 4: General Relations
Lesson 4: Slope
Focus
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Mountain biking was first included in the Summer Olympics at the 1996 Games in Atlanta, Georgia. There are three other Olympic cycling disciplines: road cycling, track cycling, and BMX, which is short for bicycle motocross. All of the cycling disciplines include both men’s and women’s events.
What are some of the requirements for an Olympic mountain-bike course? The course needs to test the physical endurance and bike-handling skills of riders as they manoeuvre around trees, branches, rocks, and streams. It should include a variety of terrain—forest roads and trails, earth or gravel paths, and significant amounts of climbing and descending. Typically, mountain-biking courses are designed so top competitors will finish them in about two hours.
Since 1996, Olympic mountain-bike courses have varied in length, and riders must complete a specified number of laps. The 2000 Summer Olympics in Sydney, Australia, had a 7-km mountain course that featured steep drops, sharp turns, and paths as narrow as 50 cm. For the 2004 Summer Olympics in Athens, Greece, the 6.1-km mountain-biking course was built in the pine and oak forests of Mount Parnitha. At the 2008 games in Beijing, China, the Laoshan mountain-bike course was shortened to 4.6 km; it had a hard-pack single track covering a series of small climbs through heavy brush and wood and it included berms (banked curves), drops, and rocks, as well as challenging climbing and descent sections.
Designers of mountain-biking trails need to have strong math skills. Because these trails need to have more gradual grades than hiking trails do, a well-designed bike trail will generally follow a contour line across the hill. If the course is built on a steep mountain, there will be several switchbacks. The trail will also slope across the hill at a slight downhill angle; this will encourage water to run off the side of the trail and downhill.
In this lesson you will explore slope. You will investigate what the direction of the slope means and how you can calculate the slope of a line.
Outcomes
At the end of this lesson, you will be able to
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determine the slope of a line segment by measuring or calculating the rise and run
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classify lines in a given set as having positive or negative slopes
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explain the meaning of the slope of a horizontal or vertical line
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explain why the slope of a line can be determined by using any two points on that line
Lesson Questions
In this lesson you will investigate the following questions:
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How can slope be used to describe the properties of objects?
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Why is it possible to use any two points to determine the slope of a line?
Lesson Completion and Assessment
As you work through each lesson, complete all the questions and learning activities in your binder using paper and pencil, clearly labeling your work (they refer to this as your course folder). These include the Are you Ready, Try This, Share and Self Check questions. Check your work if answers are provided. Remember that these questions provide you with the practice and feedback that you need to successfully complete this course.
Once you have completed all of the learning activities, take the Lesson Quiz. This is the assessment for each lesson and is located under the Assess tab or by using the Quizzes link under the Activities block.
** Note – Share questions may have to be done on your own depending on your learning situation**
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