Calculating the shortest distance between two points

Lesson is designed for two days

Grade Level: 8

Materials: Pens, paper, pencil, calculator, tables, overhead, chalkboard, tape , foot, helicopter and brochure from Miami Seaquarium.

Objectives: The student, after the teacher's explanation and demonstration on finding the length of the third side of a right triangle, will be able to calculate the distance between the two points. This is known as the hypotenuse side of a right triangle.

Mathematical Concepts:
Right triangle, Hypotenus, Legs, Square, Square Roots, Distance, Geometry

NCTM Standards:
Standard 4: Mathematical connection
Standard 5: Number and Number Relationship
Standard 6: Number System & Number Theory
Standard 7: Computation and Estimation
Standard 8: Patterns and Functions
Standard 13: Measurements

Procedures :
1. Field trip to the Miami Seaquarium.
2. Have students get into small groups of 3-4 students.
3. Teacher demonstrates the way how to obtain the distances by using the measuring tape or by using their feet.
4. The teacher picks two points A and B measures
the distance between the two points and log in the distance.
5. The teacher picks two more points B and C with B as the previous point and C as the new point C, measures and records the distances. Now we have the measurements for two sides of the triangle This process is done until the students have obtained all the measurements.
6. The teacher shows the students how to use this information and assuming that the shape is a right angle triangular use the data collected and the given formula c2 = a2 + b2 to find the missing side.
7. The teacher will explain to the class that the side "c" is the length of the hypotenuse side , "b" is one of the given side adjacent to the hypotenuse side and the other side "a" is opposite to the hypotenuse side. The sides of the triangles are called "legs".
8. The students will follow the directions of the teacher and find the sides of each assigned triangles. The teacher will let the students know that they are dealing with right angle triangles.
9. Explains to the students that a right angle triangle is 900

Assessment :
(a) Given a right angle triangle ABC , side AB = 3 feet, and BC = 4 feet . Calculate the distance of side CA.
( Hint angle "B" is a right angle, it is equal to 900)
(b) Given a right angle triangle DEF, side DE = 6 feet, and EF = 8 feet. Calculate the distance of side DF ( Hint: angle "E" is the right angle)
(c) The height of the flag pole is 12 feet, the distance from the base of the flag pole to the curb is 16 feet. Calculate the distance from the top of the pole to the curb.

Name your triangle with letters. (Note that the hypotenuse side is opposite to the right angle)

References: Miami Administrations, Architects, Personnel office for Seaquarium, Phone number (305) 361 - 5705
Address: 4400 Rickenbacker Cswy., Miami, Florida 33149

Web Site: http://orchid.isle.com/adventur/aquarium.htm

Harcourt Brace Jovanoich: Mathematics Plus, 1993 , grade 7, p. 244 - 245. Authors: Grace M. Burton, Ph.D. Professor in the Department of Curricular Studies at University of North Carolina. Howard C. Johnson, Ph.D. Chairman of Mathematics Education at Syracuse Universit.

Contributors:Major: Mignon L. Griffith, Mathematics teacher, West Miami Middle School
Minor: Carol A. Marinas, Professor of Mathematics and Computer Science at Barry University
Rosa Rivas, Chairperson Mathematics Department, at West Miami Middle School.

Use table to record all of the measurements


Right Triangle      Length of   Length of      Length of   
                    first side  second side    third side         
                    ( Legs )    ( Legs )      ( hypotenuse )    
                                                                     

                                                                               

                                                                               

                                                                               

                                                                               



Some extra problems

1. Given a side AB of length 15 feet and the side BC of length 45 feet, where the end point of the side BC lies across a canal. Find the length of the side AC . Note the triangle is a right angle triangle. (Hint: student can use a boat to go over to the other side of the canal and measure the distance.)

2. Given the hypotenuse side of the triangle AB with side equals 25 feet, the length of another side BC of the triangle is 15 feet. Find the length of the third side AC.