6th Grade Math: Graphing Integers

Up until 6th grade, most students work with positive whole numbers. Starting in 6th grade, you'll learn about integers, which include negative numbers. You'll learn to locate positive and negative integers on a number line and also plot points on the coordinate plane.

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How to Find Integers and Points

In 6th grade, you'll use both number lines and coordinate planes for graphing. Number lines are used for locating integers, which include all of the negative and positive numbers as well as zero. Number lines usually have zero at the center and list the positive numbers to the right of zero and the negative numbers to the left, like this: …-3, -2, -1, 0, 1, 2, 3… Some number lines are written vertically, with the positive numbers counted upward from zero and the negative numbers counted downward. A thermometer is a good example, since it shows both positive and negative temperatures.

The integers on a number line are in order, and they're usually labeled to make them easy to find. For instance, negative 12 (-12) will be in between -13 and -11. You may also be asked to locate rational numbers, like decimals, on a number line. These are usually not labeled, but you can find them if you know which integers they fall in between. For instance, 15.5 would be in between 15 and 16.

Graphing Points on the Coordinate Plane

A coordinate plane is composed of two perpendicular number lines. They cross at zero, with one positioned vertically and the other positioned horizontally. The vertical number line is called the y-axis, and the horizontal number line is the x-axis. Coordinate points are points on the graph that are represented by ordered pairs.

Ordered Pairs

An ordered pair is a simple set of directions to the coordinate point, and they're written like this: (2, 3). The first number in the ordered pair tells you where the coordinate point is in relation to the x-axis, and the second number describes the coordinate point's position relative to the y-axis.

Finding Coordinate Points

To find a coordinate point that is represented by an ordered pair, place your pencil at zero on your graph. Since the first number in the ordered pair represents the point's relation to the x-axis, move your pencil right or left on that axis to the point specified in the ordered pair. For instance, if the ordered pair is (2, 3), you would move your pencil to the right to positive two; if your ordered pair is (-4, -5), you would move it to the left to negative four.

Now, it's time to locate the coordinate point relative to the y-axis, which is the second number in your ordered pair. You start at whatever point the first number in the ordered pair specified, and the move up or down relative to the y-axis.

For the ordered pair (2, 3), you would move your pencil up from two on the x-axis until it was parallel with three on the y-axis. This is the location of the coordinate point (2, 3).

For (-4, -5), you would move your pencil down from negative four on the x-axis until it was parallel with negative five on the y-axis. This is where the point (-4, -5) is located.

How to Practice

To practice graphing integers on number lines and coordinate points on the coordinate plane, it's helpful to have a pad of graph paper. You can draw number lines and coordinate planes on it, and then practice finding points. You can make up the points by drawing numbers out of a hat or by asking a friend or adult to make them up for you.

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