VECTORS 

Albert Oldenburg               Lindblom Tech High School
                               6130 So. Wolcott            
                               Chicago, IL

OBJECTIVES:
      To define a vector and its rules. To use as a tool to help clarify its use 
with motion and forces. To have students discover these relation-ships with the 
use of various simple equipment and a computer.  


MATERIALS:
      Three pieces of heavy yarn of different colors, preferably blue, orange, and 
green. Three pieces of chalk of different colors, blue, orange, and green. A large 
blackboard protractor. Several meter sticks and 2-meter meter sticks. Three bricks 
wrapped in plastic. A side clamp for the front desk. A computer with a large 
monitor. Four large pieces of paper with E,W,N,S printed on them. 

STRATEGY:
     Post the four large signs representing the directions on the four opposite 
walls in the classroom before class begins. Ask a student to move a brick from the 
front desk to his seat. Make it known to the class the direction that the brick 
was moved and that it might represent the change in position of any object from 
one position to another. Ask the class to enter into the description of this 
change in position of the brick (to elicit an answer of "displacement"). Have 
students take out a sheet of paper and pencil to record a simple data table you 
place on the board, having length in meters and angle in degrees for each of the 
three sides of the triangle. Label the sides A,B,C respectively. Also the angles 
are labelled as alpha, beta, and gamma. Ask those students with calculators to 
raise their hands, then divide the class into groups of three or four people so 
each group would have access to a calculator. Challenge each group to find one of 
the sides and angles, then record them on the board. Then graphically have the 
students record them on their graph paper. Show students how to graphically add 
vectors "head to tail", by putting the head of the second vector to the head of 
the first vector and so forth until all vectors for that problem have been added. 
While writing vector equations remind the students to indicate above each 
algebraic symbol a small arrow representing a vector. 
     After graphing, a chalk and talk review of vectors takes place. At this point 
the students would be advised to record these notes for future reference. The main 
concepts revealed here were the addition of parallel vectors (positive or 
negative) depending on their direction, then adding two vectors at 90 degrees was 
shown. A third but more realistic way to add vectors at any direction (not 90 or 
180 degrees) was also shown. Here we introduced the use of the Law of Sines. 
     For another class period an interesting computer review was prepared for the 
students with a dialogue on the computer and displayed on the large monitor. There 
were several parts to the dialogue. The student takes out a paper and pencil and 
writes down the answers to the definitions asked for on the first part of the 
dialogue. A student is asked to operate the computer at the teachers' command. The 
best answer on the monitor screen is not revealed until the definition is rather 
thoroughly discussed. The computerized review of the problems are revealed step by 
step on the monitor with the students recording it. The problem is broken down 
step by step and reconstructed with complete agreement on each step along the way. 
First a problem involving parallel vectors was used and repeated a number of 
times. Then the vector problems using right angles was reviewed. The vectors at 
various angles were shown to be quite simplified by using this method. A ditto 
sheet is then passed out and a few "homework" problems are printed on it to review 
2
them. With the use of the computer monitor we substituted some of the homework 
problem variables in it and proceeded to demonstrate to the students how to solve 
the problems by breaking them down into steps and reconstructing them.