This lesson will give students a strong knowledge of right angle trigonometry/geometry.   Our school, Central, has an entrance ramp at one of the entrances of the school, but it is not the most convenient entrance for people entering the school at sporting events.

I would like the students to assess the area around an alternate entrance for the location of a possible ramp.   They will need to take into consideration what the shape of the ramp will be and at what angle and how long the ramp will be.   Trigonometry and geometry will be used in determining the ramp angle, and Pythagorean theorem in determining the ramp length(s).

The students will be given the problem and they will be asked to investigate the needs (using the school code and actually surveying the area).   The students will create a plan for a new ramp and then build a model to present to the school.   They will then revise/finalize their model based on the feedback of the school panel.

Mathematics

Standard 1. Level IV. Uses a variety of strategies in the problem-solving process

Standard 4. Level IV. Understands and applies basic and advanced properties of the concepts of measurement

Standard 5. Level IV.   Understands and applies basic and advanced properties of the concepts of geometry

Standard 8. Level IV. Understands and applies basic and advanced properties of functions and algebra

Students will be able to:

• understand (Investigate) the needs of the consumer (school and persons using the ramp)
• use the requirements of the school code to design a ramp for persons needing access to the school in ways other than stairs
• calculate the “ ideal length and angle of the ramp.   (the ramp height will be fixed to the current height of the stairs)
• build a model of the new ramp (to scale) to present to the school.
• research possible building materials and costs, while taking into consideration, weight, cost, resistence to rain/snow/other conditions

geometry textbook

knowledge of trigonometric functions

• cardboard
• clay
• wooden craft sticks
• glue
• tape
• stapler
• ruler, yardstick, or tape measurer

Before starting this project the students should have a solid knowledge of basic trigonometric functions and the Pythagorean theorem.  

1. Take the students to an area where a ramp would be beneficial either in your school or in a building in the near community.   Describe the problem to the students and have them investigate the problem and come up with various solutions.   The students will need to use their knowledge of angles and slope to design the ramp.   They will also need to take into consideration the placement of the ramp (i. e. will it be an obstruction to anything).

2. The students are to come up with a design including the calculations (length, height, angle) that they used to design their ramp.

3. Students are to research various building materials online that could be used to build this ramp.   Things to take into consideration: price, material type and weather resistency, cost to install.

4. Students should build a model of their ramp to scale out of any building materials listed above in resources, or otherwise desired but should be approved by the instructor.

5. Students submit a proposal to you as an instructor with all of their calculations, a drawing of their design, any model they have built, and a rough estimate of material and installation costs.

6. Students do a presentation to someone at your school or in the community who has the authority to put their idea into action.