# Vectors and Maps

Can your students read a map? Vectors are multidimensional numbers used for making maps. Vectors are used by surveyors, archeologists, cartographers, and of course, physicists. Below are simple activities that will work for introducing vectors in elementary school as part of map making and reading exercises.

Objective: Students will learn how to write and read vectors by doing activities which use vectors.

### Part 1: Distance-Distance Vectors

 Distance-Distance vectors represent how far over and how far forward. They are properly written like: However for ease they are frequently written as [2, 3].

#### Activity 2: Chess board Vectors

Label two edges of a chess board with the numbers 1 through 8. Have students place pieces on the board and identify the vector to the location of the piece. Be sure they count over-up not up-over. Have them discuss the difference between [ 5, 2] and [2, 5].

#### Activity 3: Applied Vectors and maps.

• Most street maps substitute one of the dimensions as letters rather than numbers. Students may replace the letters on the map with number and give the map vector for various locations.
• On a map of the world the equator and Greenwich mean time are the standard lines for marking vectors. Notice that locations to the west or south require the use of negative numbers in the vectors.
• Center city Philadelphia is laid out such that vectors may be used to assign addresses. The East-West starting point is the River with street going 1 to 23 going west. City Hall is the starting point moving north and south with address going up by 100 for each block moved north.
• Archeologists use vectors to map their sites. Many pictures of digs show a set of strings stretched across the dig to the the vector to objects.

#### Activity 4: Vector Addition

Adding distance-distance vectors is very easy. Students may discover the method using the following reasoning: The first vector represents a starting point, the second vector represents how far someone moved and the sum represents where they ended up.
 Here are student started at a point 3 steps over and 5 steps forward. She then moved over 4 more steps and up 6 more steps to stop at 7 steps over, 11 forward. This may be demonstrated by moving pieces on the chessboard or having students walk out the steps in the classroom.

### Part 2: distance angle vectors

Distance angle vectors represent how far and at what angle. They may be written as 3/45 -that's 3 followed by the angle symbol followed by 45.

#### Activity 6: Applied Vectors for discussion

• Surveyors use distance angle vectors when they plot out land. The surveyor holding the striped pole is marking an exact point. The device that the other surveyor looks through calculates the angle and distance to the striped pole.
• Look at the north pole on a globe. The line radiating from it represent angle and the circles may be used to calculate distance (Notice how this is not true at the equator where the line represent distance-distance vectors.)
• Pilots use maps that show the distance and angle from various airports.