# More Thinking about the Graph

Say "graph" to most people, and they will visualize a nice, continuous curve describing the relationship between two variables. However, not all graphs are continuous. It is important for students to understand the difference between continuous and discrete situations, and how the graphs of those situations are similar and different.

Suppose you were plotting a graph that shows how shoe size is related to foot length. For example, a man's shoe size of 9.5 corresponds to a foot length of 10.5 inches, while a man's shoe size of 10 corresponds to a foot length of 10.69 inches.

However, it is meaningless to inquire about a shoe size of, say 9.6 or 9.7. Shoe sizes are designated only in whole numbers or in numbers that are exactly 0.5 greater than whole numbers. Thus, a graph that shows how shoe size is related to foot length would not include any points corresponding to shoes sizes strictly between 9.5 and 10.

Prediction: What do you think the students think? Will they connect the dots, or not? View "Points and a Line" to find out.

Classroom Clip Reflection:

• How does Ms. England's questioning help (or not help) her students understand whether to connect the points on the graph?
• Do you agree with her answer to her students? How would you answer and why?
• What other thoughts or strategies might you use with your students?