Monday’s Lesson: Graph Literacy: Interpolation
Graphs are powerful tools for visualizing data, but too often students are unable to gain insights from them because they never learn the fundamentals of “reading” graphs. The Graph Literacy project is designed to help. We have cataloged the basic steps necessary for interpretation of simple graphs and developed a set of activities to address these steps.
Graph literacy is the ability to identify the important features of a wide variety of graphs and relate those features to the context of the graphs—in other words, to increase student understanding of the meaning of graphs. Graph literacy is emphasized in both the Common Core State Standards for Mathematics and the Next Generation Science Standards. The math standards suggest, for example, that by the eighth grade, students should learn about lines of best fit and what they mean.
Here, we focus on scatter plots and line graphs, both of which are widely used in STEM subjects. In the "Interpolation" activity, middle school students identify and use scales while interpolating between points on a graph. By the end of the activity, students will be able to 1) identify a linear relationship in scatter plot data, 2) find a trend in noisy, experimental data, and 3) use a linear relationship to interpolate points on a graph.
The storyline for the activity is based on crickets and their signature adaptation for communication (Figure 1). Interestingly, the rate of a cricket’s chirping is related to the ambient temperature. Students must find a relationship between chirps per minute and temperature.
Finding the trend and slope
Students first find the trend in some noisy data “by eye” and interpolate based on the trend. To define a line they tap two points on the graph, then move the points until they are satisfied they have found the line of best fit (Figure 2). If their line is not within acceptable bounds of the true best-fit line, a sequence of scaffolds guides them to the correct line. (Graph Literacy activities provide hints for all incorrect answers.)
Next, students find the slope. If they need help, the activity breaks down the sequence of steps, showing first the change in y, then the change in x. Finally, when students have found the mathematical relationship between temperature and chirp rate, they use it to determine the algebraic equation of the line from the graphical trend.
Following the activity students can create a conversion graph for Celsius to Fahrenheit from two known points—the temperatures of freezing and boiling water. Seeing this common conversion represented as a graph removes the mystery around the formulas on which students usually rely, and gives them the confidence to figure out the conversion even if they forget the formulas.
Free Graph Literacy activities
Other Graph Literacy activities include identifying general graph features, recognizing basic functions of graphs, and linking stories and graphs to any common function. Each activity is accompanied by a lesson plan, which details connections to the standards and provides suggestions for classroom use, discussion questions and a related activity. The six activities are available on our website or as a free app for the iPad at the App Store on iTunes.
This material is based upon work supported by the National Science Foundation under grant DRL-1256490. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.