As an introduction to graphing I completed an activity with my students that I call Graphing a Story. I have two paper bags. In one paper bags are units of time that are used to label the horizontal axis. In the other paper bag are different things to represent the vertical axis.
Students are put into pairs and asked to pick one paper from each bag and tape them to their graph.
Next, I give each pair of students a die. The first roll of the die will complete the ordered pair (0, ). The next roll will complete the ordered pair (1, ), etc. The students plot the points and connect those points. I tell students that the scale of each axis does not have to go by 1.
Finally, students create a story that would "fit" the graph. My hopes for this activity were to determine if students could read a graph. As you can see from one story below the students believed that each point was a sum of the previous points, something I need to fix. Below are a few samples of students' work, worts and all. Here is a link to the file if you are interested.