Summary
In this lesson, students will explore angles of incline on different wheelchair ramps by measuring side lengths and finding missing angle measures using inverse trigonometric functions. Students will compare their results with the Americans With Disabilities Act (ADA) accessibility standards to determine if their measured ramps are accessible. Prerequisites for this lesson include knowing how to find the angle of elevation using inverse trigonometry. This is the second lesson in the "Elevating Angles" lesson duo.
Essential Question(s)
How is trigonometry used to find the measures of unknown angles?
Snapshot
Engage
Students consider accessibility and learn how civil engineers consider ADA compliance.
Explore
Students recall and use their knowledge of inverse trigonometric functions to find the angles of elevation given ADA accessibility standards for wheelchair ramps.
Explain
Students recall their knowledge of angle of elevation and expand their vocabulary to include angle of depression and the relationship between the two.
Extend
Students measure ramps on their campus and determine if the angles of incline are within the ADA's accessibility standards and complete a report with their findings.
Evaluate
Students reflect on their learning and if they are interested in becoming a civil engineer through the use of the Fist to Five strategy.
Materials
Lesson Slides (attached)
ADA Compliance Check handout (attached; one per pair; printed front only)
Accessibility Standards handout (attached; one per student; printed front only)
Visual Vocabulary handout (attached; one per student; printed front only)
Compliance Report handout (attached; one per pair; printed front only)
Tape measure (one per pair)
Scientific calculator (one per student)
Pencil
Paper
Access to wheelchair ramps on campus (alternative activity provided)
Ramps on Campus handout (optional; attached; one per student; printed front only)
Engage
10 Minute(s)
Introduce the lesson using the attached Lesson Slides. Display slide 3 to share the lesson’s essential question with students. Go to slide 4 to share the lesson’s learning objective. Review each of these with students to the extent you feel necessary.
Show slide 5 and tell students that they are going to be thinking about accessibility today. Share with students the following:
The American With Disabilities Act (ADA) is a civil rights law that prohibits discrimination against individuals with disabilities.
The U.S. Department of Education is a federal agency that promotes student achievement and educational excellence and is tasked to ensure equal access to education.
Transition to slide 6 and pose the question: What types of considerations need to be made to ensure education is accessible? Have volunteers share their ideas and facilitate a short discussion. Ask guiding questions as needed to encourage the response of needing wheelchair ramps to get to class.
Display slide 7 and introduce the video on the slide: “K20 ICAP - Accommodations and Civil Engineering.”
The video introduces civil engineer Bobby Williams, who shares his profession and how he takes accessibility into account in his work.
Explore
15 Minute(s)
Have students find a partner or assign students partners. Give each pair a copy of the attached ADA Compliance Check handout which contains the scenario of students being hired as engineers to check if wheelchair ramps on campus are ADA compliant.
After students read the handout, display slide 8. Give each pair a copy of the attached Accessibility Standards handout and a calculator. Instruct students to read the handout and find the angle of elevation for each given diagram using inverse trigonometric functions.
Explain
10 Minute(s)
Display slide 9 and give each student a copy of the attached Visual Vocabulary handout. Use this handout and the slide to review the definition of angle of elevation with the class and tell them that angle of incline or inclination are alternatives to angle of elevation. Direct students to label the picture on their handout to match what they see on the slide. Consider having the class write a definition in their own words for angle of elevation.
Transition to slide 10 and repeat with the vocabulary: angle of depression. Let students know that it is also known as the angle of decline or declination.
Use the note above to determine how to best use slide 11 and help students see that the angle of elevation and angle of depression are congruent.
Have students add this handout to their math notebooks if that is a classroom norm.
Extend
35 Minute(s)
Display slide 12 and give pairs a tape measure and scratch paper. Then have pairs find two wheelchair ramps on campus to measure. Instruct them to record their measurements on scratch paper.
Have students apply the appropriate inverse trigonometric function to the ratios they measured. The result should be an angle that is either less than, equal to, or greater than the angle recommended by the ADA. Ask students to record their findings, explain whether the ramp meets the ADA's standards, and justify their reasoning. If they are unsure, encourage them to remeasure to be certain.
After students record their findings, show slide 13. Have two pairs who measured the same ramp work together as a group of four to check one another’s work and discuss what was discovered.
Move to slide 14 and give each group a copy of the attached Compliance Report handout. Have students work in their groups to complete the handout.
Have the original pairs of students find another pair of students who both measured the same second ramp form a new group. Give the new groups a clean copy of the Compliance Report and repeat these steps for their second measured ramp.
Collect the Compliance Report handouts to assess student understanding.
Evaluate
5 Minute(s)
Display slide 16 and have students use the Fist to Five strategy to reflect on what they've learned during the lesson and see who is interested in becoming a civil engineer. As time allows, ask for a few volunteers with differing opinions to share their reasoning.
Resources
K20 Center. (n.d.). Fist to Five. Strategies. https://learn.k20center.ou.edu/strategy/68
K20 Center. (n.d.). Commit and Toss. Strategies. https://learn.k20center.ou.edu/strategy/119
K20 Center. (May 2023). K20 ICAP - Accommodations and Civil Engineering. YouTube. https://youtu.be/DD4nSV5eQ00
Department of Justice. (2010, September 15). 2010 ADA Standards for Accessible Design. https://archive.ada.gov/regs2010/2010ADAStandards/2010ADAStandards.pdf