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Here is a picture of two axes in a plane:
A man named René Descartes invented the system that we use to graph points in the plane. (You can see some pictures of René Descartes at the MacTutor Math History Archive.) The word Cartesian means "from Descartes," so people often talk about the Cartesian plane when they are using this system.
A chameleon is a kind of lizard. Chameleons have long, sticky tongues for catching bugs. They can change color to warm up or cool off. Chameleons also change color when they are angry or scared.
A coordinate is a number that tells you where to find a point. Sometimes you need several coordinates to find exactly where a point is. You can think of a point's coordinates as its address.
Some people talk about "the coordinate plane" to show that you can use coordinates to find every point in the plane.
An object's dimension tells you how many directions a creature living inside it could move. Forward and backward count as the same direction.
The word "dimensional" is an adjective that explains how many dimensions something has. For example, a line is one-dimensional, because a creature that lived on a line could only move forward or backward. A plane is two-dimensional, because a creature living in a plane could move forward or backward and up or down.
Our universe is three-dimensional, because we can move forward or backward, up or down, and side to side. Of course, we can move diagonally or follow a curved path, too. However, these are really combinations of the three basic directions. You can reach any point just moving front or back, up or down, and side to side. Try it!
Estimate means "make a smart guess." For example, if you saw a bunch of kids in a playground, you might estimate that there were fifteen children playing. You wouldn't guess 500 children, unless it was a huge playground, and you wouldn't guess 0 children, because you know there are some kids there. Whenever you estimate, you should check to see that your answer makes sense.
In math, a line is always straight. Lines go on forever in both directions.
Here is a picture of a line. A real line is only one-dimensional, but the picture is bigger, so you can see it more easily.
A negative number is a number less than 0. We use this symbol for negative numbers: "-". For example, -10 means negative ten. You can imagine this as a temperature ten degrees below zero.
An ordered pair is a list of two numbers, where the order of the numbers is important. We write the coordinates of a point as an ordered pair, inside parentheses. Some examples of ordered pairs are (1, 2) and (6, 77).
In this picture of a plane, the origin has been marked with a red dot:
A plane is two-dimensional. It seems flat, like a thin piece of paper. However, unlike pieces of paper, planes have no edges. A bug could crawl along a plane forever without falling off.
Here is a picture of part of a plane. It has been colored green to make it easier to see.
A point is one place in space. Points are really zero-dimensional. Of course, we can't draw something that has no dimensions. When we want to show where a point is, we usually draw a dot, like this: . You can imagine that the real point is in the exact center of the dot.
The distance between marked points on a graph or numberline is called its scale. These two numberlines use different scales:
A chameleon's skin is covered with flat, hard objects. These are also called scales. The word scale has several other meanings. How many can you find?
Please send questions, comments, and suggestions
to Ursula Whitcher
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