Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Bill Stevenson explains to his sixth-grade class that each group will receive an envelope with a secret location. They're to decide, as a group, how many people will be present in that location at each hour of the day, starting at midnight and going until the next midnight. They record the information in a table.
Once they have the table, each group creates a line graph that will show this information.
Finally, Mr. Stevenson leads a wrap-up discussion in which students discuss the features of the graphs and try to guess what location the graphs might represent.
An Exploration for Teacher Workshops
Materials: grid paper
Imagine a supermarket, or wherever you buy your groceries. Think about what it's like at different times of the day.
Work in pairs to make a table with 24 entries labeled by the 24 hours of the day, starting at midnight and ending the following night at 11 p.m. Record how many people you think will be in the market each hour. Think of it as a snapshot: how many are in the market at midnight? How many at 1:00 a.m.? Continue for the remaining hours.
Finally, make a display that shows how the number of people in the market changes over time.
- How did you and your partner decide how many people were there? How did you record your data?
- What kind of display did you make? Why did you choose that kind of display? What kinds of representations are appropriate for this kind of data?
- What makes a representation clear and communicative?
- These instructions were fairly open-ended. What additional structure (if any) would you give to students?
- What's the mathematical value of this activity?
Additional Discussion Topics
Here are some additional ideas for discussion that arise in the video:
- What group skills did these students demonstrate? How experienced or inexperienced do they seem to be at working in groups? How do they compare with your classes?
- Discuss the connections this activity makes with places outside school. What purpose does this activity serve outside mathematics?
- Activities like this one occasionally raise sensitive issues such as family structure and lifestyle. How would you handle these issues if they arose in your math class?
- How would it have been different if students did the activity alone instead of in groups? What happened in the group conversations about the data?
Teaching and Learning About Graphs
- This was the students' introduction to line graphs. Yet the teacher did not tell the students how to make one. Instead, he asked questions about what you need for a line graph and had the students answer. How did Mr. Stevenson orchestrate this introduction?
- What did students need to know to make this introduction to line graphs work?
- Mr. Stevenson prompted students making presentations to describe what the features on the graphs meant in real life. For example, when someone said the graph "went down," the teacher remarked that people were leaving the location. Discuss the importance of this correspondence and difficulties students seem to have in understanding it.
These questions appear at the end of the video. Here are some follow-up ideas and prompts to help get a discussion going.
What is the value of having students generate, record, and graph their own data?
What is the difference between the "made-up " data the students used and data generated by a simulation or collected from the real world? Discuss the use of "made-up " versus "real " data. Sometimes the data students generated were unrealistic, for example, the librarians getting in at 5:00 a.m. to set up. Mr. Stevenson did not intervene. In what circumstances, and how, would you intervene to correct unrealistic estimates?
Discuss Mr. Stevenson's decision not to supply grid paper.
How might the lesson have gone differently if they had large grid paper to make their graphs? What are the advantages of using grid paper?
Students spent a lot of time just scaling the axes correctly. What mathematics are students doing as they set up the graphs? When is that time worth spending, and when is it a waste?
What kinds of graphs would grid paper inhibit?
Brainstorm the use of line graphs in other disciplines.
A student mentioned using line graphs in the stock market. What other uses can you think of for line graphs?