Project-Based Geometry Outline

As a complement to my Geometry Skills List, here is my planned outline of Geometry projects. As I describe in a previous post, I’ve increased the project-based component of my math classes a little bit each year, and this year my goal is to have a sequence of overarching projects driving the course content. Direct instruction to provide background knowledge for the projects will fit in as needed, but not be the predominant mode of learning.

  • Quarter 1: Patterns & Motion
  • Week 1: Review of measurement skills, then 1-day (90-minute) Volume Project wherein students measure, convert, then find volume and surface area of a classroom
  • Weeks 2-4: Tiling Project drives learning of regular shapes, transformations, & symmetry
  • Weeks 5-6: Similarity, dilation, proportion are discussed, culminating in application mini-projects on creating scale drawings and indirect measurement
  • Weeks 6-7: Fractal Project drives understanding of self-similarity, iteration, and fractal dimension, while reinforcing ideas of perimeter, area, and volume
  • Weeks 8-9: Students use nets, toothpicks, gumdrops, straws, pipe cleaners to build polyhedra, then do the Euler Characteristic Project, plus we prove why there are only five platonic solids
  • Quarter 2: Construction & Measurement
  • Weeks 9-10: We discuss understanding measurement at a deeper level, converting between units of measure (dimensional analysis), choosing appropriate units, and measurement in the coordinate plane
  • Weeks 10-11: Triangle Construction & Proof Project, where students investigate which pieces of information are sufficient to determine/construct a triangle; this ties directly into proofs of triangle congruence and other triangle-related proofs
  • Week 12: Pythagorean Proof Project – After learning about and applying the Pythagorean Theorem, students research varying proofs and write a research paper detailing one particular proof
  • Week 13: Sine Exploration Project connects with earlier discussion of similarity and proportion, leading  to an understanding of the three trigonometric ratios and their application
  • Week 14: Students use triangles and triangulation to break harder problems down into easier problems (relating to area, angles, and art museum security)
  • Weeks 14-16: Circle Construction Project deals with multiple ways of constructing circles and their measurable parts – students construct circles with compass going through 1, 2, or 3 points (connecting back to theorems about isosceles triangles and perpendicular bisectors), then construct, measure, and calculate lengths/areas for parts within a large circle
  • Week 17: Return to measurement of volume and surface area; students empirically verify the relationship between prisms and pyramids (or cylinders/cones) with the same base
  • Week 18: Students summarize learning in a culminating Portfolio

Hope this sounds interesting to you! I’m looking forward to creating some new projects and modifying existing ones to encompass more and better learning.

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6 Comments

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6 responses to “Project-Based Geometry Outline

  1. Dan

    This is very interesting stuff. In geometry this year I’ll be trying out a couple of larger projects that have similar goals. Keep us updated to how the projects go!

    • nyates314

      Thanks! I shall keep you posted. I hope to give an update on the big tessellation project later this week or early next.

      What do you have planned for your larger projects?

  2. Cool! I’ve done some of those projects you outlined (or variations of such), and I’m always driving my class half with projects and half with direct approach. (I find that projects alone tend to encompass “too much” and kids don’t really know which specific skills they’re supposed to get out of the project, so even with my projects, I wrap them up with a few days of directed skills practice before quizzes/tests.)
    Anyway, last year I did a whole unit of active measurements of volumes and heights and “irregular” measurements, culminating in talking about net weight, density of liquids and irregular shapes, conversions between English and metric units, and similarity concepts for heights. It was way cool! This year, I’ve tried various new projects and have liked them a lot. We should definitely trade notes!

    • nyates314

      Just checked out your tessellation posts on your blog – they sound cool, and some insights I hadn’t known about before!

      I hope to return in the measurement recap during my second quarter to irregular area and volume measurements, and since our academy is engineering-themed, I would love to draw some connections to density, weight/mass, center of gravity etc. Did you write a blog post about your activities on measurements?

  3. Only this very rough brainstorming post: http://untilnextstop.blogspot.com/2009/10/unconventional-measurement-methods.html I ended up fleshing the unit out quite a bit more. I’ll dig around for a unit outline if you’re interested.

  4. Pingback: Fractal Difficulties « Maryland Math Madness

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