Author: Robin A. Ward, California Polytechnic State University-San Luis Obispo

Audience: Grades 4 - 6

Mathematical Topics: subtraction, introduction to coordinate graphing, introduction to the integers, spatial sense

Rationale: For grades K - 4, the NCTM Standards state that students should model, explain, and develop reasonable proficiency with basic facts and algorithms related to whole numbers. In grades 5 - 8, the Standards recommend that students be presented with opportunities to compute with whole numbers, fractions, decimals, integers, and rational numbers. Students in grades 4- 6 should also describe and represent relationships using tables and graphs.

In grades K-4, the Standards also emphasize the importance of developing and sharpening students' spatial sense. Spatial sense is an intuitive feel for one's surroundings. To develop spatial sense, students must have experiences that focus on the direction, orientation, and perspective of objects in space. Students also need to learn how to describe objects in relation to each other using such terms as above, below, behind, near, etc.

The Standards also emphasize making links across the curriculum. This activity integrates geography and mathematics by allowing students to learn about different state and country capitals while performing subtraction.

Overview: In this activity, students will subtly be introduced to coordinate graphing by using latitude and longitude coordinates to find distances between cities. Students will find the distance (measured in degrees) between cities by subtracting their respective latitude and longitude coordinates. The teacher can purposefully choose latitude and longitude coordinates of cities that are whole numbers (for younger students) or those that are decimal and/or negative (for students in the upper grades.) Thus, the teacher should take care in using those numbers (wholes, rational, integers) that are most appropriate for their students.

In the first activity, students will learn the meaning of the terms "latitude" and "longitude" and will visually see how latitude and longitude lines precisely determine the location of a particular city. Students will then view a map of the United States and approximate the latitude and longitude coordinates of certain cities. Then students will compute the distance (measured in degrees) between cities using their latitude and longitude coordinates.

This first activity can also serve as an introduction to, or as a real-life application of, the Pythagorean Theorem for those students in grades 7 and higher. Or, for those students studying algebra 2, this activity can serve as a lead into the distance formula.

PLEASE NOTE: For simplicity sake, let us make the assumption that the world is flat so that we can apply the distance formula to this problem. Certainly, the earth is round! Thus, the distances computed in this activity will not be as exact as if we were considering the curvature of the earth. However, given that the coordinates of latitude and longitude clearly define a specific location, we will use this opportunity to compute the distance between two locations.

In the second activity, primarily designed for elementary level students, students will physically engage in a spatial skills activity whereby they will take turns positioning themselves on a coordinate grid, mapped out with masking tape on the classroom floor. Once positioned, the students will describe their position and locate other students' positions using the masking tape, which serves as lines of latitude and longitude.

Materials:

One other way of providing students practice with working with lines of latitude and longitude would be to provide the students with the latitude and longitude coordinates of various NASA sites.

Students can plot these locations as shown below.

Next, ask students to verbally describe how they might travel from one location to another. For example, using the map below, ask students the following: "How would you travel from NASA Dryden to NASA Ames if you could only move along the latitude and longitude lines?"

Based on the map, NASA Dryden is located (approximately) at 117 degrees longitude and 34 degrees latitude. NASA Ames is located (approximately) at 122 degrees longitude and 37 degrees latitude.

In order to travel from NASA Dryden to NASA Ames, students might describe the following path:

Notice that while students are mapping out the travel path from one location to another, not only are they introduced to coordinate graphing, but they are also provided practice with subtraction.

Using the options listed below, students can find the distance between:

(1) their favorite city and their partner's favorite city
(2) a city that begins with the same first initial of their first name and a city with the same first initial as their last name.
(3) two randomly drawn cities. (Prior to class, the teacher can record the names of various cities on index cards. Students will draw two cards out of a box and find the distance between those two cities.)

Recall that we are making the assumption that the world is flat so that we can apply the distance formula to this problem. Certainly, the earth is round! Thus, the distances computed in this activity will not be as exact as if we were considering the curvature of the earth. However, given that the coordinates of latitude and longitude clearly define a specific location, we will use this opportunity to compute the distance between two locations.

In the second activity, prior to class, the teacher will create a coordinate grid on the classroom floor by laying strips of masking tape running horizontally and vertically on the floor. The lines should be perpendicular to each other and labeled in some fashion (see below).

The teacher may label the lines with latitude and longitude values of his/her choice. Notice that some negative values for longitude were chosen. Depending on the students and on the intent of the lesson, the teacher can choose to make these values positive or negative, and large or small in magnitude.

Ask one student to position himself/herself anywhere on the grid. Ask another student to identify this student's coordinates and write it neatly on piece of paper for the first student to hold. Ask another student to stand anywhere on the grid and then ask another volunteer to identify and record the coordinates of the second individual. The remaining students will work in pairs to determine the distance between the students if they were to travel along the lines of latitude and longitude. Repeat this activity with different pairs of students.

For fun, after one student has chosen his or her location, ask another student to stand on the same latitude line as the first student. Ask students to compute the distance between the two students. Did the students get a zero value for longitude? Can the students explain why?

In bringing this activity to closure, the teacher could pose the question, "Is there a 'quicker' way to travel from one city to the next, without moving along their latitude and longitude lines?" Most students will respond that by drawing a straight line between the two cities would be the shortest distance. Thus, for students in grades 7 and higher, this activity can be used as a lead in to the Pythagorean Theorem or the distance formula.

Enrichment Activity:

Come plan a flight across the US or around the world!

Allow students to use the Internet to view the Earth. By entering the latitude and longitude of any city, students can view this city from space.


Return or go to:

Math Activities for Grades K - 4

Math Activities for Grades 5 - 8

Math Activities for Grades 9 -12

Algebra Activities

Environmental Research Aircraft and Sensor Technology (ERAST) Program Activities

Airborne Sciences Program Activities

Math Activities Home Page

Funded by the NASA Dryden Flight Research Center

The below icon appears to help us track statistics on our website.