Subject Area: Mathematics Science
(Check all that apply) Language Arts Social Sciences
Curricula Type: OR Facilitator program.
Topic: Emergence, Modeling, and Measurement
Abstract/Summary:
Students control traffic lights in a city. The mayor of the city of Gridlock has asked them to help improve the traffic situation. To explore traffic control, each student either manually switches his lights or sets a phase for his light – set the time in the cycle when his light switches. This serves as a jumping off point for students to discuss different metrics for "quantifying" traffic. Students will develop mathematical ways of quantifying their verbally described metrics, and use these to input back to the mayor the best traffic strategy.
Prerequisites:
Teacher Notes/Procedures:
This activity requires, in addition to a complete Navigator system and Netlogo software, Netlogo model Gridlock.nlogo and Navigator activity AAA – Gridlock.
Before logging into the Navigator activity, you should set up the Netlogo model and have it ready to go. When you load the model, a startup routine will run that prepares the model for use with a class of 9. All that will remain is for you, the teacher, to add a TI-83+ widget to the model. The NetLogo interface has a "prompter" to help with steps for using the model.
You can adjust the grid to roughly match the number of students in your class. The sliders Grid-Size-X and Grid-Size-Y adjust the number of roads going vertically and horizontally, respectively. If you adjust these numbers, hit the setup button. It is better to have too few than too many lights in the activity - an unattended light will definitely cause gridlock!
When the students log in to activity Gridlock, they will be asked to pick a light in the model. As the teacher, assign students to row 1,2,3, etc and column 1,2,3, etc. This numbering begins in the upper left corner.
Then the students choose between Manual and Automatic. This is also a switch in the Netlogo model - "Auto?". Turn "Auto?" off, and have your students choose Manual, and the students will each be able to directly control a light by pressing the ENTER button.
Turn on
the TI-83+ widget and the DRIVE button in the Netlogo model. The cars will
begin driving, and will soon start getting backed up. Students switch their
light by pressing the enter button. Give them several tries at the activity to
become acquainted with the interface.
Students may try many strategies to improve traffic. If the students ask how to improve traffic, try one of these responses:
· Shrug your shoulders and say "I don't know."
· Say something obvious, like "Keep traffic moving," or, best of all
· Ask your students what they mean by "improve traffic" - how they would measure an improvement in traffic.
The goal is for the students to determine what it means to improve the traffic situation, how this improvement might be quantified, and how to accomplish that improvement goal.
Encourage students to try different strategies. After they've tried several, ask them to decide which worked best. How do they determine "best?" Facilitate a discussion in which students begin describing good and bad traffic. What factors do they look at? The number of stopped cars (the quantity currently graphed in the model)? Or are your students more concerned that cars have a short wait time? Higher average speed? etc. Many metrics are possible - encourage students to think of reasons to use different ones.
The students have a worksheet where they can record their thoughts on what it means to improve the traffic situation. They record what they would seek to measure, and also outline how they would quantify that in real life and in the model. Once they've had the chance to develop their thoughts individually or in small groups, ask students to present their ideas. Keep track of the quantities the students want to measure and of their strategies for optimizing those quantities. To allow the students to explore various metrics, the NetLogo model can send back the data from the simulations to the calculators. (Press "sample and send".)
Now that the students have presented their ideas, check them. Let each group direct the class in trying their strategy. How do different strategies compare? Does a particular strategy work well for every metric the students came up with?
Many extensions are possible for this activity. Instead of operating in manual mode, the class can work in auto mode, where the students set the phase (actually, the clock time) when their light changes. Or, with some small modifications to the Netlogo model, the students could work individually with the Netlogo model in the computer lab to try various strategies. This could open a unit on statistics, where you collect real world information. Or students could begin extending the model themselves, adding code to the NetLogo model to compute the particular metrics they decided upon.
Time Considerations:
Curriculum Standards:
From the NCTM standards –
Data Analysis and Probability –
· Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
Problem Solving –
· solve problems that arise in mathematics and in other contexts
· apply and adapt a variety of appropriate strategies to solve problems
Connections –
· recognize and use connections among mathematical ideas
· understand how mathematical ideas interconnect and build on one another to produce a coherent whole
· recognize and apply mathematics in contexts outside of mathematics
Representation –
· use representations to model and interpret physical, social, and mathematical phenomena
Curriculum Objectives:
As the students decide upon various metrics, they form connections between the model and the mathematics they decide to use. They will also try several strategies, and have the opportunity to tie together many ideas from mathematics and social behavior.
Equipment/Materials Needed:
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Navigator Components:
Component Name Component Number
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UT - Gridlock |
01-03-200-002363-001 |
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Keyword Field: Words that you think teachers would use when looking for an activity like this.
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Traffic |
Phase |
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Average |
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Student Handouts: 0107gridlock_handout.htm
Watch Variables to monitor: These would be the variable that are currently viewed on the Teacher Monitor: