Mignon Griffith
S0802474
CALCULATING THE SHORTEST DISTANCE BETWEEN TWO POINTS
GRADE LEVEL: 10
MATERIALS: Pen, paper, pencil, hand calculator, tables, overhead, chalkboard, measuring tape, and the use of student's foot. ( Use helicopter to obtain
any measurement which might be difficult to obtain.
OBJECTIVES: The student, after the teacher's explanation and demonstration, will be able
to calculate the distance between two points. (This distance is known as the
hypotenuse side of a right triangle.)
MATHEMATICAL
CONCEPTS: 1. Measurements
2. Multiplication
3. Estimation
4. Conversion ( English to Metric )
5. Hypotenuse
6. Square
7. Square Roots
8. Legs of a Triangle
NCTM
STANDARDS: Standard 1: Mathematics As Problem Solving
Standard 4: Mathematical Connections
Standard 5: Number And Number Relationships
Standard 6: Number And Number Theory
Standard 7: Computation And Estimation
Standard 13: Measurements
PROCEDURES: 1. Field trip to the Miami Seaquarium.
2. Teacher shows the students the areas which will be use for their
assignment. The brochures are collected from the information
centre.
3. Teacher demonstrates how to measure distances using the measuring
tape or student's foot for estimating the distances.
4. Pick two points A and B, call the side "d" and measure that distance
using the measuring tape.
5. Pick two other points using B as one point from the previous selection and C as the other point so that ABC is a right triangle.
call the side " e" and measure the distance. 6. These distances are recorded in the students log books.
7. The teacher shows the students how to use this collected data to calculate the distance of the missing sides. Assuming that the shape
is a right triangle.
8. Find the missing sides by using the Pythagorean Theorem. The given
formula is C2 = A2 + B2
9. Have the students get into small groups of 3 - 4 students and begin to work on their assigned areas.
10. The students will follow the directions of the teacher using the assigned points. These assigned points are from the Miami Seaquarium's brochure which show the locations of the different attractions.
( e.g. The Flipper show #4 , The Killer Whale show #5 and The Shark presentation #6. These attraction formed a right triangle.)
11. The teacher will explain to the students that the triangle must be a
right triangle in order to use the given formula.
12. The teacher will draw some shapes of right triangles on the chalkboard
in order to help the students understand what the right triangle looks like.
13. The teacher will explain that sometimes it will be difficult to measure
the distances because of the obstacles.
14. As a homework problem the teacher will have the students calculate
the third side. Given the hypotenuse side as one of the sides and the side that is adjacent to the hypotenuse side, they will be able to find the
missing side. The teacher shows the students how to change around
given formula and to find any required side. See the attached sheets for
the homework problems.
REFERENCES: Rexene, D. B. (1995). Bringing Pythagoras To Life. The Mathematics
Teacher, 88 (3), 744 - 747.
Donna B. Erickson @cmuvm.csv.c.mich.edu
Officials of Miami Sequarium
Address: 4400 Rickenbacker Cswy
Miami, Florida 33149
Phone number (305) 361 - 5705 Ext. 284
CONTRIBUTORS: Major: Mignon Griffith, Mathematics Teachers Seaquarium
Minor: Carol A. Marinas, Professor of Mathematics and Computer Science at
Barry University
Rosa Rivas, Mathematics Chairperson, West Miami Middle
Letisha Brown, Mathematics Teacher
NOTEPAD
DATA TO BE USED FOR CALCULATING THE MISSING SIDES
Right Triangle Length of first Length of second Length of third
side side side
( hypotenuse)
ABC AB = 9 feet BC = 10 feet AC = ?
LMN LM = 6 feet MN = 8 feet LN = ?
RST RS = 12 feet ST = 16 feet RT = ?
XYZ XY = 3 feet YZ = 4 feet XZ = ?
NOTE: Students must first change around the formula to find the missing side
C2 = A2 + B2
B2 = C2 - A2
A2 = C2 - B2
Right Triangle Length of first Length of second Length of third
side side side
( Hypotenuse)
ABC AB = 9 feet BC = ? feet AC = 15 feet
LMN LM = ? feet MN = 8 feet LN = 10 feet
RST RS = 12 feet ST = ? feet RT = 20 feet
XYZ XY = ? feet YZ = 4 feet XZ = 5 feet
ANSWERS
1. AC = 15 feet
2. LN = 10 feet
3. RT = 20 feet
4. XZ = 5 feet
5. BC = 10 feet
6. LM = 6 feet
7. ST = 16 feet
8. XY = 3 feet