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The middle school in the district where I work is quite old.  Dedicated in 1959, and once serving as the district high school, the building is a Frankenstein of aging classrooms, newer additions, and inconsistent heat. One feature of the building is the network of ramps used to shuttle students from wing to wing, and supplies in and out.

Recently, I worked with a team of 8th grade algebra I teachers to develop an activity which would utilize the many ramps, get kids moving and measuring, and reinforce slope as a measure of steepness. The teachers had great ideas for leading students through measurement activitites. My initial idea of having students choose points along the ramp, then measuring the rise and run between points, was discussed and improved. The teachers used blue painter’s tape to create guiding triangles along the bricks on the walls along two of the ramps. Another teacher noted that railings could be used to connect parallel lines to slopes, and triangles utilizing the railing were also provided.

Students measured the slope of two ramps using the provided triangles, then were led outside, where both a pedestrian ramp and a custodian’s ramp were measured.  The outside ramps were additional challenges, as no guiding tape marks were provided.  Wacthing student reactions and approaches to these ramps was intriguing.  Some students attempted to use the bricks on the building to trace their own triangles, while another group discovered that the level ground along the freight ramp could be used as the “run”.

After the activity, the class discussed and compared their results.  In one class, the unusual steepness of one ramp in our building was questioned, and related to the legal limits of handicapped ramps.  The class agreed that the ramp seems to be an original part of the building, and that an elevator had been installed alongside the ramp for our disabled friends.  Further discussion could include the requirements of the Americans with Disabilities Act, which contains the following requirements for ramps:

The least possible slope shall be used for any ramp. The maximum slope of a ramp in new construction shall be 1:12. The maximum rise for any run shall be 30 in (760 mm) . Curb ramps and ramps to be constructed on existing sites or in existing buildings or facilities may have slopes and rises as allowed in 4.1.6(3)(a)  if space limitations prohibit the use of a 1:12 slope or less.

As a follow-up, students found pictures of objects or places which they felt represented interesting slopes.  Geometer’s Sketchpad was then used to measure and compare the slopes in their pictures: