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## Roll It! Creating an Entrance Ramp

By Heather Endres, January 27, 2010

• High School

### Category

• City of Neighborhoods

• Mathematics

### Lesson Time

150 minutes for classroom activities and 60 minutes for homework

### Introduction

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.

### National Standards

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

Standard 9. Level IV.  Understands the general nature and uses of mathematics

Common Core Standards

Key Ideas and Details:

Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

Craft and Structure:

Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

Integration of Knowledge and Ideas:

Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.

Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.

Range of Reading and Level of Text Complexity:

Read and comprehend complex literary and informational texts independently and proficiently.

Anchor standards for Speaking and Listening:

Comprehension and Collaboration:

Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others' ideas and expressing their own clearly and persuasively.

Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

CCSS.ELA-LITERACY.CCRA.SL.3Evaluate a speaker's point of view, reasoning, and use of evidence and rhetoric.

Presentation of Knowledge and Ideas:

Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations.

Adapt speech to a variety of contexts and communicative tasks, demonstrating command of formal English when indicated or appropriate.

Anchor standards for Language:

Conventions of Standard English:

Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Vocabulary Acquisition and Use:

Acquire and use accurately a range of general academic and domain-specific words and phrases sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when encountering an unknown term important to comprehension or expression.

### Objectives

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

### Resources

geometry textbook

knowledge of trigonometric functions

computer with internet access

### Materials

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

N/A

### Procedures

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.

### Assessment

The students will be assessed on their design model and their presentations, both delivery and content.  They will also be assessed on the calculations of their design, both accuracy and the write-up of proposal.

### Enrichment Extension Activities

Students could go into the community and identify two areas where a ramp or a sloped surface may be beneficial and then they could determine how they might propose effecting these changes.
1. Being clear about who the user is and what problem needs to be solved is essential to the design process. I think this lesson does a phenomenal job at both of these items. I feel like the “problem” of creating a ramp for the school is something that students are able to connect to immediately and can brainstorm solutions in very unique ways. Using the requirements of the school code to design a ramp for persons needing access to the school in ways other than stairs can be answered uniquely, despite the restrictions. The creation of a ramp absolutely requires mathematical skills and allows students to make concrete connections to math and its application in the real world. As an additional extension, students could brainstorm how to answer the accessibility question not only answered with ramps.

2. Very relevant and practical project for students. This lesson has some physics applications as well as mathematics. To extend this to physics, students could determine which materials produce the best friction for the users who will be using this ramp.