Designing Ski Slopes
by Jill Doga, jdoga@acadia.k12.la.us

Content Area(s)
Math

Grade Level(s)
9, 10, 

Overview
Students will investigate linear algebraic expressions to determine the appropriate equations needed in order to find the best slopes to use in designing a ski resort.

Software
powerONE Graph and WordToGo

Technology
(1)Projector connected to Internet-connected workstation and access to United Streaming.com
(2)Template in WordToGo that has investigative questions for lesson.

The following resource could be used if classroom is not equipped with handhelds but has access to Internet-connected computers for each pair of students.

Graph It! by Cool Math
http://www.coolmath.com/graphit/index.html

Objectives
1. Students will test theories about how slope changes.
2. Students will graph solutions for algebraic expressions to find slope.
3. Students will sue a real-world application to learn the relevance of math problems.

Procedures
1. Teacher will introduce the concept of slope using the United Streaming Video segment, “What is slope?” in the full video, “Operation Algebra: Slope of a Line”. The teacher will then discuss the lesson on building a ski resort. The students will have to develop 3 equations for 3 different ski slopes, a beginner’s, an intermediate, and an advanced slope.
2. Teacher will divide the students into pairs whereby each pair of students will use two handhelds. One handheld will have a Word To Go document opened that lists a set of questions related to analyzing slope and equations. The other handheld will have the software, powerOne Graph.
3. Teacher will ask each pair of students to answer question 1, “What would an equation that helps you to design the slope of one ski run look like?” It will be answered in the Word To Go document.
4. Students will open the powerOne Graph software on handheld 2 of each pair of students. The main calculator should be seen.
5. The teacher will instruct the students to enter the equation of y=x in the My Graphs section and then tap Graph.
6. The students will then answer the question, “What does the slope look like of this equation?” in the Word To Go document.
7. After taping DONE in the powerOne Graph software, create a new equation with the slope of y= x+1. Before choosing GRAPH, choose a different color for the line. Notice the two lines graphed and tap DONE.
8. Now use subtraction and enter a new equation y=x-2. (Change the color of this line.) After noticing all three graphs, answer the questions, “What did you learn about adding and subtracting a value to the first equation? How does it affect the graph of the equation?”
9. Tap DONE, and uncheck the last two equations (y=x+1 and y=x-2).
10. Use multiplication to create another slope. Create new equations using y=2x and y=3x. Examine the graphs.
11. Use division to create another slope. Create a new equation using y=.5x. Compare the graphs and answer the question in the Word To Go document, “Explain how multiplying or dividing has affected the slope of the graph.”
12. Explain why in the Word To Go document:” The smaller the number (slope number), the less the slope inclines. The larger the number, the greater the slope inclines.”
13. Explain in the Word To Go document: ”What equations would you use to create a beginner’s, intermediate, and advanced slope at your ski resort?”.
14. Assignment to investigate in the Word To Go document.:
a. What would these slopes look like? y = (1/4)x, y = (4)x, y = - (1/4)x , y = - (4) x.
b. What skill level would skiers need to use for each of them?
15. Students will then send their completed Word To Go document to the printer after their names are added to the document for assessment.

Other Supporting Material
Slope%20Questions

Submitted on: 7/25/2005 4:50:43 PM