Slopes


Author:

Tyler Styons

Unit Title:

Slopes

Grade:

8th

Subject:

Mathematics

Estimated Duration:

7 Days

Unit Activities:

Activity 1: Interview

Activity 2: Concept of Slope

Activity 3: Slope Triangles

Activity 4: Four Corners

Activity 5: Ramp Build

Background Knowledge: 

Students must have a basic understanding of measurement that is measuring the lengths of a given object.

Students must have a basic understanding of the coordinate grid system. 

Date:

July 2014

The Big Idea (including global relevance)

The Big Idea for this unit will revolve around the topic of handicap accessibility. Students will learn about assistive devices and biomedical engineering that is involved with basic structural engineering concepts. They will demonstrate their knowledge of slope while constructing a portable wheelchair ramp.

The Essential Question

How can effective engineering designs enable handicapped access to wheelchair bound citizens.

Justification for Selection of Content

This content was chosen due to its relevance to the Common Core Academic Content Standards as well as past student performance. Historically, although this concept is touched on briefly in 7th grade as students begin to analyze liner relationships, the 8th grade content extends this understand making it more difficult for students. 

The Challenge

Design, build, and test a small scale portable wheelchair ramp

The Hook

Students will be participating in an interview with a wheelchair bound individual. They will present questions about how he maneuvers in his daily life to gain perspective on a person who lives their life in a wheelchair. 

Teacher's Guiding Questions
  1. What is life like when you are forced to roll from place to place?
  2. What architectural designs are in place to assist individuals in wheelchairs?
  3. What makes a ramp safe or unsafe?
  4. How can slope be seen in a graphed line?
  5. What is going to be true about the proportions of triangles constructed from a line?
  6. What makes a ramp safe or unsafe?
  7. How does the length of the ramp affect the safety?
  8. How does the steepness of the ramp affect the safety?
  9. How do you find the slope of line?
  10. How do you write slope once you find the rise and the run?
ACS (Real world applications; career connections; societal impact)

Real World Application

Students will learn about biomedical and structural engineering. They will learn how slope of objects applies in the real world, for example stairs and wheelchair ramps. This will be addressed in the activity in which students will measure the rise and run of a given set of stairs and then compute the slope, and also in their construction of the final wheelchair ramp.

Career Connections

Occupations such as a civil engineer, carpenter, material engineer, and structural engineer will all be addressed in the calculation of the slope from the stairs as well as building their individual wheelchair ramp.

Societal Impact

People that are restricted to wheelchairs need to be able to access structures that are not handicapped accessible. This will be addressed in the calculation of slope from the stairs as well as designing and building their own wheelchair ramp.  

Engineering Design Process (EDP)

The Challenge will include each step of the EDP. 

  1. Identify and Define: Students will identify the problem when they receive their individual height requirement that they have to meet.
  2. Gather Information: Students will research ADA guidelines and the guidelines of current companies that design wheelchair ramps.
  3. Identify Alternatives: Each group member will be required to design blueprint of what the ramp should look like.
  4. Select Best Solution to Try: Each group must discuss the pros and cons of each design and decide which one will best meet the challenge.
  5. Implement Solution: Students will create a final design drawing that includes labeled dimensions and materials.  They will then construct the prototype.
  6. Test and Evaluate: Each group will test their solution. Then they will describe the test and results.  They will also explain whether the design was effective and provide reasons.
  7. Communicate: Each group will give a short presentation on their ramp which will include the dimensions and how and why their ramp meets the ADA guidelines. 
Unit Academic Standard

8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the y = mx + b for a line intercepting the vertical axis at b.

Unit Activities

Lesson 1: Gaining perspective on life in a wheelchair and basic slope definition.

a. Lesson 1 will focus on giving students an understanding of what life is like in a wheelchair for them to start thinking about once technology are available to these people to access various buildings. Once the concept of slope is introduced, through the activities of rolling down ramps, students will begin to understand slope as the change in height over a change in distance.

i.    Activity 1: Interview with a citizen in a wheelchair and developing Essential Questions. They will be given the challenge of designing, testing, and building a small scale wheel chair ramp.

ii.    Activity 2: Begin examining wheel chair ramps and stair around our school building. Students will begin to develop guiding questions surrounding topics such as: What makes a ramp safe or not safe? How does the length of the ramp affect safety? How does the steepness of the ramp affect safety?

Lesson 2: Students will begin working with slope on a coordinate grid. They will then research the appropriate slope guidelines for ramp construction, begin their construction of the ramp, and finally finish a completed line.

i.    Activity 1: Developing slope from similar triangles

ii.    Activity 2: Four corner slope challenge

iii.    Activity 3: Students will be given the criteria of their challenge which will force them to do research and follow out the EDP in building their ramp.

Where the CBL and EDP appear in the Unit
  • Activity 1
  • Activity 3
Misconceptions
  1. Students may confuse x and y when calculating slope
  2. Students may confuse the terms of rise and run
  3. Students may forget that the “rise” value is divided by the “run” value when determining slope
  4. Students may not understand turning a fraction into a decimal
Additional Resources
  1. Kuta Math
  2. Youtube
  3. Presentation Notes
  4. Illuminations worksheet
Pre-Unit Assessment Instrument
Post-Unit Assessment Instrument
How to Make This a Hierarchical Unit
  1. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.    

a. In using this standard for high school an instructor could discuss how the angles created by the ramp lead to the ratio of the sides. This would lead into a discussion of the trigonometric ratios for acute angles.