Activity Content Sections
GETTING READY
Cut the foam core into sections about 20″ long by 4″ wide. Use markers to draw a center line and direction arrows to represent a section of highway. Also mark which direction is north, south, east, and west.
Use wooden blocks and highway sections to create a highway intersection, with one road passing over the other. You may want to use masking tape to hold this intersection together.
Cut rope into sections ranging from 12″ to 20″. Each team should have a supply of 15–20 sections. (Teams can cut their own rope lengths from a spool of rope; subsequent groups can use the cut pieces from earlier groups.)
Intersection of I-635 and US Route 75 in Dallas, Texas. Credit: Austrini
It is also helpful to put your interchange model on a large piece of cardboard so that participants can swivel it around when making their rope connections.
INTRODUCTION
Give participants the following information, adapted to their age: Modern highways are filled with cars, each trying to go somewhere. To get where they want to go, cars often need to move from one roadway to another using on and off ramps. These ramps are called highway interchanges. Engineers design highway interchanges to keep cars as safe as possible, which means not making them have to cross lanes of traffic or come to a stop as they move from one highway to another. Before engineers plan the construction of these interchanges, they must figure out how the roadways will connect to each other. Otherwise, with cars traveling on many roadways going in many directions, the ramps will become a confusing, dangerous tangle.
Did you know that there are different kinds of mathematics? To figure out how roadways should connect to each other, engineers use the kind called topology, the mathematics of how things are connected.
Instructions
Ask participants about their experiences with being a passenger in a car on the highway. If there is an adult driver present, ask that person to describe what highway driving is like (shifting lanes, merging into traffic on the ramp, etc.).
Show participants the foam core model of two highways and which way is north, south, east, and west on your model. Younger participants may benefit from a brief discussion of how important these compass points are when driving or traveling by any means, even walking, and why they often work better than just saying “turn here” or “turn left.”
Pose the following question: If a driver who is headed north wants to switch highways and head east, what ramp would you have to build? Use rope and paperclips to show how to put that ramp onto your model. Use your finger (or model car) to show the path of the car from one highway, onto the ramp, then onto the next highway, so that everyone knows how the model works.
Now pose this question: Suppose the driver who is headed north wants to go west. What ramp would you need to build? Take suggestions and ask, “Are there any other ways to do this?”
Demonstrate two ways to build ramps so that the northbound driver can turn either east or west. One uses an overpass to turn west. The other uses a cloverleaf to turn west. Make sure younger participants know what shape a cloverleaf is.
 Example model showing overpass. |
 Example model showing cloverleaf. |
To make the model less abstract and more comprehensible, have one or two of the participants use a finger to follow the traffic flow. Ask any participants of driving age to describe what it’s like to use on and off ramps to also make the model more real: “I get into the right lane, slow down, watch for the sign…”
Place participants in small teams and state the challenge: Design an interchange so that drivers starting in any direction can leave the interchange in any other direction. Instruct them to use pieces of rope and clips to indicate their interchange, as you showed them.
Distribute team materials. Encourage each team to talk through several options and to play with the ropes as they try out different ideas. They can also make signs to clarify how cars should use the interchange they choose.
Ask teams to demonstrate their interchange for the other teams. Decide as a whole group which interchanges would work best and why.
ACTIVITY VARIATIONS
Label the north-south highway as HWY 1 and the east-west highway as HWY 2. Now make little signs to put on your model that show drivers where to turn. For example: HWY 1 South, Next Right.- For older participants: Design the ramps needed for a three-way interchange. (They should consider: Does every roadway need to connect to every other roadway, or can you get from the first to the third by passing through the second, thereby reducing the number of ramps?)
- Print out photos of actual interchanges so that participants realize that you’re not making this up: they are actually very complicated in real life. Participants can look for patterns such as cloverleaves in the actual photos.
- Print out diagrams of a variety of highway interchange designs for people to peruse.
Label the north-south highway as HWY 1 and the east-west highway as HWY 2. Now make little signs to put on your model that show drivers where to turn. For example: 
Illustration credits: Ruby SS; Artur Jan Fijałkowski; Ruby SS; Sharshar; Ruby SS (Wikipedia Creative Commons).
Relevant Terminology
Constraint: A real-world limitation, such as the amount of space or money or time you have to build something.
Cloverleaf: A type of interchange where cars go left by making right-hand turns and looping 270o around a large ramp that looks like the leaf of a clover.
Interchange: A place where multiple highways or roadways cross each other.
On ramp / Off ramp: A roadway that allows cars to enter or exit a highway.
Overpass / Underpass: A section of roadway that passes over (or under) another roadway. This can be accomplished with a bridge, ramp, or tunnel.
Topology: The branch of mathematics that studies how things are connected
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