Building Cities with Geometry
I’ve been framing my first unit in geometry around the concept of street maps and city grids. Curious? Read on…
Reflective Question: How would you describe to someone how to get from your house to your school without using any street names? What landmarks would you use? How would you describe where to turn? When they’ve gone too far? How do you describe streets when they don’t have names (cue a U2 song).
Discussion: Without names, you describe streets by their landmarks. We naturally use lots of nice geometry words: intersection, same street (ie: collinear), parallel, etc. You can even discuss elevation (cities on mountains vs cities in valleys – this works nice for Tucson, which is itself in a valley), which later ties into coplanar.
Activity: Have your class make up the rules for naming a street in the most precise way possible (additional discussion: what does ‘precise’ mean in this context? argue that it means least number of letters and symbols). Debate it, then decide on a naming scheme. Hopefully it’ll be similar to what the accepted geometric notation rules are. Additional fun: students will (hopefully) realize on their own that the order of points doesn’t matter, which can be hard for some students if this rule is told via exposition rather than constructed via discussion.
Connection: We name points, lines, and angles this same way. Surprise!
Further activities: Use google maps to examine street views of your town, turn landmarks into points, take away the map and discuss the figure, do all the procedural stuff that students need to know (classify angles as acute, obtuse, etc; identify collinear points; etc). Then describe a street layout to them and have them make the figure that matches it.
Disclaimer: This isn’t actually how my first few weeks have gone – after botching several lessons and taking a detour into solving linear equations, this is how I wish my first week had gone. Next year, I’m doing all of the above.
Culminating activity: Design your own cities. This is what I’m trying tomorrow. The worksheet: http://bit.ly/rhZ6IL.
How it works: My students work in groups of four. In the document above, cut the first two pages in half so you have four half-sheets – each half-sheet has a different city description on it. Give each student in the group a different half sheet. Have them create the city (ie: draw the figure) on a white sheet of paper. They check their answers with their group. Everyone in the group must agree. When they do, call the instructor over. After everything is verified, give the group the third page from the handout, requiring them to combine their drawings together to form a metropolis (Los Angle-les: the City of Angles. I think I’m so clever. My students don’t…). Havethem tape/staple their sheets of paper together or, if you have butcher paper/poster paper, redraw their diagrams on a larger sheet. Extra stuff: get creative and decorate it. Continue designing and labeling the cities. Added benefit: you will have student work you can hang in your classroom. If time at the end, have each group present their metropolis. Additional writing exercise: have the group give several points names (ie: B is the Bakery) then describe why certain locations are connected together. In essence: give their city a history.
I’m trying this worksheet tomorrow. I put it together from an idea I had a few days ago – If anyone has any feedback, I’d love to hear it.