Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Applying Connections
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Imagine that you have been busy collecting data, and now it is time to consider the best way to represent your data in graphical form. Although there are many ways to graph data, for this scenario your options are line plots, bar graphs, stem-and-leaf plots, histograms, and line graphs. Let's take a quick look at each.

Line Plots

A line plot is a "quick sketch" of numerical data. To make a line plot, draw a number line in the range of the expected data, then chart an X above the corresponding value on the number line for each piece of data.

Here is an example of a line plot showing the ages of the siblings of a class of first-graders:

Bar Graphs

Several graphs are similar to bar graphs; pictographs, real graphs (using real objects to make them), tallies, and line plots are all types of bar graphs. Students in the early grades can begin with real graphs, keep track of their numbers using graph paper, and then connect these early graphs to more formal bar graphs.

The following bar graph represents the same data as in the line plot:

 The Ages of Our Brothers and Sisters

Stem-and-Leaf Plots

In stem-and-leaf plots, numeric data is shown by using the actual numerals. Stem-and-leaf plots are especially useful when you have a lot of data that has a wide range.

The following stem-and-leaf plot shows the record of wins for the Eastern Conference NBA teams:

In this case, 17 is the lowest number of wins and 76 is the greatest number of wins, so we are going to group the data by tens (rather than, say, hundreds). First, set up the "stem" using the tens digits:

Now make the "leaves" by recording the ones digits next to the appropriate tens digit. For example, since the 76ers won 48 games, we record an 8 (which represents eight ones) next to the 4 (which represents four tens):

Continue entering the data from the ones place. At this point, we can draw some conclusions from our data. For example, we can see that most of the teams had between 30 and 49 wins. We can see that 76 was the greatest number of wins. Seventy-six is also considered an outlier -- a value that lies pretty far outside the rest of the data.

To get more information, we can quickly order the ones-place digits to complete the graph:

Histograms

A histogram is a form of bar graph in which the categories are consecutive equal intervals on the horizontal axis. This histogram shows the results of tossing two number cubes 30 times. Since the possible outcomes (2-12) are consecutive, we place the bars so that they are adjacent:

Line Graphs

A line graph is used to show a continuous change in data. For instance, we might use a line graph to show the growth of a plant over time. The line connecting the points indicates that the change is continuous -- it doesn't occur in discrete values or steps.

Here are examples of questions you might use with your students when working with this type of graph:

1. How would you describe the growth of the plant as shown by this graph?

2. Why do you think the line is at 0 in the month of August?

3. Which months show the most growth? Why do you think this is so?

In the following activity, you will be given some data. You will select the type of graph you think is most appropriate and then graph your data. As you work on this activity, think about how the data connect to other subjects or to everyday experiences. And, although you are applying your own knowledge in this section, you may also want to think about some of these topics for your own students to explore!

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