Creating and Analyzing Line Graphs
Graph with Missing Title and Labels |
Students in Ms. Apo's class are shown this graph that is missing its title and many of its labels. The students are asked what a line graph measures (change over time). The students are asked how they know this graph shows change over time (the x-axis shows the months of the year). The students are identify the missing parts of the graph. They are also asked to consider how hard it is to interpret the graph without the title. Students predict what the graph shows. Students should be asked to consider the trends in the data. Ms. Apo's class noticed that January had the greatest value, and the trend decreased after January until the value was zero from May to October. Students then noticed an increasing trend from October to December. After a short discussion, the students made reasonable predictions that the graph had to do with something that changed during different times of year, and that the winter months had the greatest values. |
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Only after successfully predicting the subject of the graph with justifications are the students shown the missing components of the graph.
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In the Computer Lab, students then used the following website to create their own line graphs:
http://nces.ed.gov/nceskids/createagraph/
The students are given the data from the following table:
Students are taught to use the components of the table to help them label the line graph, converting the information in the table to another graphic form, such as a line graph. Students can evaluate the usefulness of the two different representations.
The students are shown how to use the website to add the data and the labels. One benefit of the website is that students can preview the graph to see what is missing and then revise. Students worked in pairs after a quick demonstration to create the following graph. (The class was told to focus on the first three cities). In pairs, students successfully completed the graph. Below is an example of one of the graphs the students made.
After completing the graph, Ms. Apo's class analyzed the data. It is important for students to make generalizations and conclusions about the data presented in graphs. The analysis is often more difficult than creating the graph itself. They noticed:
1. In Melbourne, from February to March the temperature decreased by 5º.
2. In Fairbanks, from July to December, the temperature decreased by 71º.
3. In Washington, DC, from July to December, the temperature decreased by 41º .
4. In Fairbanks, from January to February, the temperature increased by 5º.
5. In September, it is 7º hotter in Melbourne than in Fairbanks.
6. There is a 16º difference in temperature in July between Washington, DC and Fairbanks (July is the hottest month in both cities).
7. In February, it's 80º in Melbourne and 7º in Fairbanks. So it's 73º colder in Fairbanks.
8. In the month of April, there is only a 1º difference in the high temperatures of Washington, DC and Melbourne. |
Ms. Apo's class did a good job of comparing some of the values in specific months between two cities. It is much harder for students to generalize trends in the data and make conclusions. Follow-up questions would include:
What trends do you notice in the data for the three cities?
How are the trends similar between the three cities?
How are the trends different between the three cities?
How would you compare winter in Washington, DC to winter in Fairbanks?
Why is the shape of the Melbourne data so much different than the shape of the data for Washington, DC and Fairbanks?
In Ms. Zamora's class, students interpreted a different line graph about the money in a teacher's bank account throughout the year.
First, students made observations about the graph, explaining the trends they noticed, the greatest values and the least values. Students were then encouraged to infer why the trends went from increasing to decreasing to increasing.
Above, the students wrote their observations on yellow post-its and their inferences or conclusions on blue post-its. The two observations were:
It is first increasing from January to May.
It is decreasing from May to September.
Making observations about the data is not as difficult. When students are asked to analyze data, they typically make simple observations. The students were encouraged to make and record those observations. To encourage the students to make inferences or generalizations about the data, the students were asked questions such as:
Why would a teacher's salary decrease in the summer?
Why was the increase from November to December only $300.
On blue post-its, the students wrote their analysis:
Mr. Love is a teacher and in the summer, kids are not there so his money decreases.
His money decreases because it was summer vacation.
The blue post-its require analysis and higher order thinking skills.
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Indicators:
4.4.2.1 organize and display data in a variety of ways, including line plots and line graphs.
4.4.3.1 analyze and interpret line plots, line graphs, and circle graphs.
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