Use input-output tables in fifth-grade math to help students learn the concepts of mathematical functions by plotting the values on a graph. Each input value, graphed on the horizontal axis, has a corresponding output value that is graphed on the vertical axis. By plotting several of these points, students can find the pattern that determines the function.
Input-output tables should have at least four sets of numbers in them, but only two points are needed for a line. As an example point, assume that one of the inputs is two, and the output is five. Starting from the origin point, count two spaces over and five up, marking the point. Assume the next input and output to be three and six, and the next ones to be four and seven then five and eight. Mark each of these points on the graph and look at the line. In this example, the relationship between the input and output is to add three.
To check the work, take a ruler and extend the line several points over, taking the input of one and adding three to it. The result should fall on the line. Learning these simple operations paves the way for more complex linear equations such as "y = 3x - 2" that require multiple operations to complete.