Slippery Slope

By Viktoriya D'Agostino, January 15, 2009

Grade Level

  • High School

Category

  • Other

Subject Area

  • Mathematics

Lesson Time

Three Block Periods (about four and a half hours)

Introduction

This lesson will be used after teaching a unit called Linear Functions. In this unit students will learn how to graph linear functions and write equations when given different types of information. Students will relate this unit to real life by designing wheelchair ramps and analyzing slopes of stairs.

National Standards

Uses expressions, equations, inequalities, and matrices to represent situations that involve variable quantities and translates among these representations
Understands that mathematics provides a precise system to describe objects, events, and relationships and to construct logical arguments
 

Common Core Standards

Anchors for Reading:

Key Ideas and Details:

CCSS.ELA-LITERACY.CCRA.R.1 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.

Integration of Knowledge and Ideas:

CCSS.ELA-LITERACY.CCRA.R.7 Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.

Range of Reading and Level of Text Complexity:

CCSS.ELA-LITERACY.CCRA.R.10 Read and comprehend complex literary and informational texts independently and proficiently.

Anchor Standards for Writing:

Text Types and Purposes:

CCSS.ELA-LITERACY.CCRA.W.1 Write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and sufficient evidence.

CCSS.ELA-LITERACY.CCRA.W.3 Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details and well-structured event sequences.

Production and Distribution of Writing:

CCSS.ELA-LITERACY.CCRA.W.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

CCSS.ELA-LITERACY.CCRA.W.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.

Research to Build and Present Knowledge:

CCSS.ELA-LITERACY.CCRA.W.7 Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding of the subject under investigation.

Range of Writing:

CCSS.ELA-LITERACY.CCRA.W.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.

CCSS.ELA-LITERACY.CCRA.W.8 Gather relevant information from multiple print and digital sources, assess the credibility and accuracy of each source, and integrate the information while avoiding plagiarism.

Anchor standards for Speaking and Listening:

Comprehension and Collaboration:

CCSS.ELA-LITERACY.CCRA.SL.1 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.

CCSS.ELA-LITERACY.CCRA.SL.2 Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

Anchor standards for Speaking and Listening:

Comprehension and Collaboration:

CCSS.ELA-LITERACY.CCRA.SL.1 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.

CCSS.ELA-LITERACY.CCRA.SL.2 Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

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

Presentation of Knowledge and Ideas:

CCSS.ELA-LITERACY.CCRA.SL.4 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.

CCSS.ELA-LITERACY.CCRA.SL.6 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:

CCSS.ELA-LITERACY.CCRA.L.1 Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

CCSS.ELA-LITERACY.CCRA.L.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Knowledge of Language:

CCSS.ELA-LITERACY.CCRA.L.3 Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.

 Vocabulary Acquisition and Use:

 CCSS.ELA-LITERACY.CCRA.L.5 Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

CCSS.ELA-LITERACY.CCRA.L.6 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

1. Students will be able to use slope to design wheelchair ramps. 2. Students will be able to graph functions. 3. Students will be able to find slope by measuring stairs.

Resources

Worksheets
Internet for research if needed
Neighborhood

Materials

Ruler
Tape Measure
Stairs
Worksheets
Graph Paper

Vocabulary

Slope - measures steepness of a line
Thread - horizontal distance that you step on
Riser - vertical distance that you step up

Procedures

1. First a unit on linear functions will be taught (all definitions will be discussed, and all methods will be discuss).
2. Discuss the legal requirements of slopes for stairs and wheelchair ramps and slopes for stairs.
          a.) ADA recommends a 1:12 slope which means every 1" of vertical rise requires one foot of ramp (5 degrees of incline)
          b.) Ideal slope for stairs is 0.7
3. Discuss all rules for this lesson.
4. We will take a field trip around the neighborhood to observe different types of ramps (wheelchair and others) and different types of stairs. Students will take notes on things they see in their environment (ex: ramp seemed too        steep, stairs didn't look functional, and so on).
5. Students will then have a discussion about what they saw.
6. Students will then go back to their environment (home, school, neighborhood), and focus on one wheelchair ramp. They will measure the rise and the run and the length of the ramp. They will then compute the slope of the ramp and analyze their results.
Did the ramp meet the legal requirements? What can be done to meet the requirements? Discuss some issues with designing ramps?
7. Students will then design a wheel chair ramp for a building of their choice near the school. They must follow ADA requirements.
8. Moving on to stairs. Discuss all parts of stairs, how to analyze them, how to measure them, and so on.
9. Students will follow the instructions in the worksheet. They will measure 5 different types of stairs, they will analyze them and finish the worksheet.
10. Students will write a letter and describe their research and make suggestions to improve staircases and wheelchair ramps.

Assessment

Informal observations
Grade students letter
Grade all steps along the way
Formal observations
Discussions

Enrichment Extension Activities

Students can design a staircase for a given building and discuss their reasoning.
  1. I plan on implementing this lesson in my Algebra 1 class. Including the legal requirements for the wheelchair ramps was a nice part of this lesson since often times students ask how math relates to the real world. The research element of this lesson is a part I would want to expand more. I would want to add how to report the research in a formal research format and teach elements of technical writing to the students.

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