Resources Needed:

A computer lab with Internet access (enough computers so students can work in groups of 3), scratch paper, graph paper, pencils, straight edges and copies of activity packet.

Exposition:

1. Students should be familiar with the terms: Pythagorean Theorem and slope or tangent. Simply mention the terms and ask the students for formulas that correspond with them.

Pythagorean Theorem a2 + b2 = c2

slope rise over run

tangent opposite over adjacent

2. Some students may not have had exposure to trigonometry. Explain to the students that slope and tangent are basically the same thing. They are both ratios between two points on a line.

Experience/Procedure:

3. Split class into 3 member cooperative learning teams.

4. Assign each member a position. The teams consist of a "Captain," the leader of the team; a "Transcription Expert," the recorder; and the "Research Specialist," this person runs the computer and does the searching on the Internet.

5. Pass out the activity packet.

6. Read the first page (Mission Debriefing) to them. Tell them not to turn to the next page until instructed.

7. Have each team choose a team name.

8. Assign teams to computers.

9. Instruct students to turn to next page (Mission Assignment). Have groups get started on activity. (Optional--read Mission Assignments instructions as a class.)

Critical Thinking:

10. Architects and engineers use the formulas for Pythagorean Theorem and slope when designing buildings, roads, and structures. In what ways did the engineers design and build objects before these formulas existed?

Interactive Learning:

11. Students will work in cooperative learning teams and use the Internet to get more information to complete activity assignment. Students will draw a diagram of their inclined plane on graph paper.

Assignment:

12. Students will complete problems 1 - 4 on page 3 (Mission Log). One packet will be turned in per team.

Resources:

(1998). IV.13 Inclined Plane. http://galileo.imss.firenze.it/museo/4/eiv13.html

(1998). Pythagorean triples. http://www.cut-the-knot.com/

(1998). Graphing slope of a line. http://library.advanced.org/10030/6soal.htm

(1998). Tangents and slopes. http://aleph0.clarku.edu/~djoyce/java/trig/tangents.html

Team Name: Date:

Captain:

Transcription Expert:

Research Specialist:

Mission Debriefing

Your mission is to travel back in time to the year 1610 and assist Galileo Galilei with the design of an inclined plane used to measure the acceleration of falling bodies.

You will leave today taking with you your Internet access, mini-hand-held, traveling, research computer, your assignment packet, graph paper, a straight edge, and your pencils. No textbooks or calculators!!!

Let me quickly debrief you on the situation you will encounter when you reach the office of Galileo.

1. Galileo has been trying to construct an inclined plane to run his experiments on acceleration of falling bodies.

2. Galileo must use the material around his office to construct the plane. The materials available include one sheet of wood, a hand saw, and a measuring stick.

3. Using your mini-hand-held, traveling, research computer, research the situation and design an inclined plane for Galileo.

Good Luck on your mission!!!

Team: Date:

Mission Assignment

You have successfully arrived in the year 1610, at Galileo Galilei's office. You must first check your mini-hand-held, traveling, research computer for Internet link.

Turn on your computer.

Download your Internet browser program.

You must now check the research at site HTTP://galileo.imss.firenze.it/museo/4/eiv13.html

Read in information about Artifact IV.13.

Galileo shows you the materials available.

Interestingly the measuring stick has no marks or numbers on it.

You will call the length of the measuring stick 1 Galileo or 1Ga.

You measure the sheet of wood in Ga's.

Your calculations are 30Ga by 49Ga.

Galileo informs you that he needs the length of the incline (hypotenuse) to be 53Ga and the slope close to 6/11 Ga. Important: All sides of the plane must be integers in Galileo's. This means they must be whole units, no fractions or decimals.

You need to:

1. Find the length of all sides of the inclined plane.

Go to these sites for formulas on Pythagorean Triplets. http://www.cut-the-knot.com .

2. Find the exact slope of the inclined plane.

Go to these sites about slope and tangents http://aleph0.clarku.edu/~djoyce/java/trig/tangents.html

http://library.advanced.org/10030/6soal.htm

3. Draw a scaled diagram of your inclined plane, showing units, on graph paper.

4. Show all work, formulas and calculations on your log & graph paper.

Remember: The inclined plane is a right triangle.

Team: Date:

Mission Log

Show all work, formulas and calculations on your paper.

1. Is there real documentation showing Galileo's inclined plane?

2. Find the length of all sides of the inclined plane.

3. Find the exact slope of the inclined plane.

4. Draw a scaled diagram of your inclined plane, showing units, on graph paper.

Captain:

Transcription Expert:

Research Specialist:

Mission Log Calculations and Answers

Show all work, formulas and calculations on your paper.

1. Is there documentation showing Galileo's inclined plane? no

2. Find the length of all sides of the inclined plane.

30 Ga, 49Ga c=53GA

Students should realize that 302 + 492 = 900 + 2401 = 3301 = (57.454)2

Using the formula from HTTP://www.cut-the-knot.com/ Go to Pythagorean Triples

a = n2 - m2, b = 2nm, c = n2 + m2

We know that c = 53 = n2 + m2

We know that all sides must be integers, therefore this formula for triples will help us.

By trial and error students must determine n & m to satisfy equation 53 = n2 + m2

n = 7, m = 2 are solutions, therefore a = (7)2 - (2) 2 = 49 - 4 = 45, b = 2(7)(2) = 24

45< 49 & 24< 30 therefore it will fit in the piece of wood provided.

3. Find the exact slope of the inclined plane.

a = 45 & b = 24

slope = rise over run

slope = 24/45 = .53333

Galileo need a slope close to 6/11 = .5454 therefore this slope satisfies.

4. Draw a scaled diagram of your inclined plane, showing units, on graph paper.

Allow students to be creative, Drawing should include units and be to scale.