The time for the lesson will be an additional 15-20 minutes if the students are asked to build their own set of axes.

The purpose of this lesson is to teach students about the three dimensional Cartesian coordinate system. It is important for structural engineers to be confident graphing in 3D in order to be able to describe locations in space to fellow engineers.

Engineers use a coordinate system whenever they create engineering drawings of something, and the Cartesian coordinate system described in this lesson is used most often. Cartesian coordinate system plane axes graphing Some experience with the two dimensional Cartesian coordinate system would be helpful, but is not necessary At the end of the lesson the student should be able to find a point in space given the X, Y, and Z coordinates. At the end of the lesson the student should be able to give the X, Y, and Z coordinates, given a point in space relative to a specified coordinate system and origin. Use a flat surface such as a piece of paper, or a table top. Put your finger at a point on the surface, and ask the students how they would describe the location of that point. If they have had experience graphing on the XY plane, they will probably figure out that they can give the coordinates of that point relative to a particular corner (over 5 inches, up 9 inches). If they do not get this on their own, ask leading questions to help them. For example, "Well how far away is the point from the side of the paper?" Once the students grasp this, move your finger so that it is above the surface you are using. Then ask them again how they would describe the location of that point. They may say something like "above the paper." Ask them to be more specific. The goal is to get them to give a description such as "5 inches over from the left side, 9 inches up, and 6 inches above." Ask them to give you the three coordinates necessary to describe the location of the points. Next, spend a short time discussing the terms in the vocabulary section. It may also be helpful to describe concrete examples of how the 3D coordinate system is used in everyday life. For example, when you are describing the location of an office within a building, you are essentially using coordinates: "Go up 3 floors, do down the hall past 4 doors and turn right, it's the 2nd room on your left." City blocks are another example of the use of a coordinate system. Directions from one house to another might read, "Go three blocks, then take a right and go 4 blocks." This is an example of a two dimensional coordinate system. The purpose of this lesson/activity is to teach students the basics of graphing in three dimensions. Use the associated activity "A Place in Space" to accomplish this. It has a worksheet which allows the students to first review finding points on the 2D (XY) plane, and then move on to finding and describing points in a 3D space (X,Y,Z). In order to get the most out of the lesson, the groups will need their own set of axes. Instructions for how to build these as well as supplies needed are described in the procedure of the activity. A dimension is a measure of special extent. What we see around us is a three-dimensional world, because objects have 3 dimensions (length, width, and height). A line is in one dimension, an area (such as a rectangle drawn on a piece of paper) is in two dimensions, and a box has three dimensions. In math, an axis is a line used as a reference to describe the location of a point. For example, in the Cartesian Coordinate System (see definition below) an axis is a line marked zero at a certain point (see origin definition below). An object's location can then be described by measuring how far away (on the line) it is from this origin, and in what direction. In many ways, an axis is like a number line that goes on forever in both directions (positive and negative). An axis is one dimensional. A plane is the set of all points between two intersecting lines. A plane is two dimensional, so it is a flat surface. A flat table top, for example, can be thought of as a plane. An ordered pair is used to describe the location of a point within a plane, relative to a specified reference point. For example, if you are told that the front left corner of your desk is the origin, and you want to find a point given the ordered pair (2, 3) and you know that the unit you are using is inches, you would start at that front left corner of your desk, move two inches to the right, and then 3 inches toward the back of the desk, and you would be at that point. A graph is a visual representation of a mathematical function or set of numbers. In the previous definition for ordered pair, if your desk surface could be thought of as a graph, and you graphed the point (2,3), this means you represented those numbers visually (or graphically). The specified reference point [(0,0,0) in most coordinate systems] The rectangular coordinate system developed by the famous mathematician Descartes. It consists of 2 or 3 axes (X, Y, and Z) all at right angles to each other, and all intersecting at a specified origin. A Place in Space A coordinate system is used by engineers in all designs. The coordinate system is used to specify dimensions for products. When an engineer designs a part, the engineer specifies where each point on the part is located using a Computer Aided Design program (CAD). Often, parts can be manufactured by sending a CAD drawing file to a machine that is designed to interpret the file and create the part. We have learned how to locate a point given an origin, and the X, Y, and Z coordinates. We can also describe the location of a point by providing this information. If students were able to satisfactorily complete the activity worksheet with little or no help from teachers or peers then they have demonstrated a sound understanding of the basics of plotting coordinates in three dimensions. Students should be able to locate a point in space, given its coordinates and an origin. Students should be able to describe the location of a given point in space relative to some origin using coordinates. A practical way to apply what students have learned in this lesson/activity is to design a basic structure such as a bridge or a tower using a computer aided design (CAD) program like the West Point Bridge Builder.