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Architecture and Area Project (Geometry)

Finally! I finished putting the final touches on my Architecture and Area project for Geometry.  My students completed this project for the first time back in March, but I was revising, reorganizing, and perfecting what I have so far.  There are so many extensions to this project, but I chose the ones I felt most suitable for my students.  Let me tell you more about this project (teacher resources at the bottom)...

Students work in pairs to build their own model home (physical model or digital model).  Not only do they use area formulas to calculate their square footage, but they also have to calculate how much it would cost to paint, tile, and carpet the home.  On top of that, I had my students do some algebra review by calculating the cost of their home, the selling price they desire, and finally the asking price.  Whew! 

Why I love this project:  The students were really into it.  Their reflections had nothing but awesome things to say about it such as, "This is the best thing we have done all year, and "I learned so much math I can actually use."  Students collaborated and I facilitated.  In fact, my goal was to see what would happen if I used a strictly constructivist approach with this project.  I did absolutely NO direct instruction.  I explained the project, gave them a few ideas and sent them on their way!  For two weeks of class they worked and I assisted when needed with guiding questions.  They did amazing!  I had students using trig to discover how to find the area of a regular octagon, using triangles and rectangles to derive a formula for trapezoids, and applying the circumference formula to find the area needed to paint a round wall!  I was blown away!

What I would do different:  I would use this project as a quarter project rather than a unit project and incorporate more concepts taught in Geometry.  For example, we used similarity in polygons and area, but you can apply so much more.  The chapters that could potentially be taught within this unit are trigonometry, similar triangles/polygons, area, surface area and volume, and quadrilaterals.  In addition, there is plenty of algebra review.

Overall, I loved seeing my students come to class with a smile, work hard for an hour each day, and leave with a plan.  We did no homework during this unit because they were so involved with their projects.  Here are some sample projects (you can find the project description, rubric, and student handouts in my TpT store.):

Sample Student Projects (the math)

The pictures:

Teacher Resources:
- Here is a list of web or iPad apps my students used to complete the project.  There were benefits of using the digital model and disadvantages.  I let students pick.  Digital is not as messy and is more cost effective; however, they did not get to actually work hands-on.  Some of the physical models, on the other hand, took a long time to build, taking away from calculation time.
  • (my students' favorite, easy to share, easy to use, can use irregular figures)
  • (easy to use, but some students had issues with their projects disappearing)
  • RoomPlanner (a free iPad app, but doesn't have too many features)
  • 3D Home Builder ($8 iPad app, my students liked this one, but I didn't see the benefit over the free web apps)
  • iBlueprint ($0.99, my fellow Geometry teacher had students using this, but none of my students used it)
- Direct Instruction?  I would challenge you to lead your students to the formulas for discovery rather than giving them the formulas.  It takes some patience and some great questioning to get them there, but it is rewarding to see the students get to the formulas themselves!  Also, they will remember how to derive them and use them rather than just memorizing another chapter.

- Quality of Work: To get the best quality of work, I had a panel of judges (teachers and administrators on campus).  On the due date we had all the projects from every Geometry class on campus in the same room.  We had the judges walk around with 3 tickets each (ended up being 5 because there were so many projects to vote on) and place tickets in cups of the projects they liked the best.  It had nothing to do with math, strictly design.  The winning team was treated to lunch by myself and the other Geometry teacher.  It was a great motive for students, knowing not only that their other teachers were going to be there, but that all of their friends were going to see their work as well.  Additionally, we had them create ads to sell their houses (not part of the project).  I had my students go onto to get an idea of a brief house description that would capture the judges' eyes.

- Have fun!  This project is so much fun if executed correctly.  Enjoy watching the learning happen!


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