Lesson Plan ID: 
24056 
Title: 
Take a Hike! An exploration into finding slopes of inclines 
Overview/Annotation: 
Students will work in small groups to analyze a topographical map of the Fiery Gizzard hiking trail on the Cumberland Plateau in southeastern Tennessee. They will use the map key to determine distance traveled and elevation gained to determine the slope of a short portion of the trail with a steep incline. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.

Content Standard(s): 
MA2013(6)  3. Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3]  MA2013(7)  1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1]  MA2013(8)  7. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5]  MA2013(912) Algebra  46. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [SID7] 

Local/National Standards: 
Calculus: Finding Average Rates of Change. 
Primary Learning Objective(s): 
Students will analyze a topographical map and assess the slope of inclines. 
Additional Learning Objective(s): 
Create a concept of how an average rate of change over a period of time can be compared to the instantaneous rate of change at a specific time. This discussion could lead to the definition of a derivative. Students must also convert units of measure from miles to feet or likewise. 
Approximate Duration of the Lesson: 
31 to 60 Minutes 
Materials and Equipment: 
Projector A calculator for each student 
Technology Resources Needed: 
A computer with internet connection Digital projector 
Background/Preparation: 
Students must be familiar with the definition of slope. The definition of slope should be presented to the students. 
Procedures/Activities: 
1.)Divide students into groups of three or four. The students will observe a hike from the Fiery Grizzard Trail to the Cumberland plateau. Display the map on the digital projector. The teacher will need to reveal all of the detail during the trail, and may reward students by allowing them to explore the trail. Explain to students how topo lines are used to determine elevation.
2.)The teacher will explain to the students the following: After a refreshing swim at Blue Hole Falls, we are going to take a left onto Dog Hole Mine Trail. The trail immediately elevates in altitude. Find the slope of the incline over the climb. The interval has been indicated over this gap in picture.
3.)Students may need help determining the point where the slope begins and ends. Estimations from groups may vary. Referring back to the map, ask a student to demonstrate on the screen the methods needed to determine the length of the indicated segment of the trail.
4.)Students will then use the slope formula to determine the slope of the incline. Ask students to write an explanation justifying this result. Answers will vary. Allow students to watch the video or view an attached photo of views from the trail. ( www.thumb15.webshots.net) Scenic view from atop the Cumberland Plataue.
5.)Homework: Students will research Mt. Everest and determine the average slope of the climb from Base Camp to the summit. They can also write a short story of a climb to the top including cultural background of the Sherpa guides.

Attachments:**Some files will display in a new window. Others will prompt you to download. 
map.pdf
Indicated Section of Trail.jpg

Assessment Strategies: 
Monitor students' participation in groups. Evaluate and correct each groups' justifications of their slopes. Answers will vary. Give students necessary feedback to make corrections. 
Extension: 
Discuss how this slope is an average rate of change over a given interval. Finding instantaneous rates of change at specific points on the trail will be explored in calculus. 
Remediation: 
Students can be remediated by finding the slope of lines going through two points. 

Each area below is a direct link to general teaching strategies/classroom
accommodations
for students with identified learning and/or behavior problems such as: reading
or math performance below grade level; test or classroom assignments/quizzes at
a failing level; failure to complete assignments independently; difficulty with
shortterm memory, abstract concepts, staying on task, or following directions;
poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material

Environment 
Time Demands 
Materials 
Attention 
Using Groups and Peers 
Assisting the Reluctant Starter

Dealing with Inappropriate
Behavior 
Be sure to check the student's IEP for specific accommodations.

Variations Submitted by ALEX Users: 
