# Welcome to Grade 8 Geometry and Technology!

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**Goal / Objective: **

In this Grade 8 mathematics seminar, students learned the principles of Euclidean Geometry, and explored the connection of these concepts to a variety of areas including music, architecture, physics, and engineering. They will also explored geometry-based technologies including 3-D printing, algorithms, and soap bubbles. In addition, they participated in the Purple Comet International math competition, explored Group Theory, learned about discrete math concepts as applied to computer science, explored the basics of Arduino microcontroller programming and circuitry, and built and tested a Sea Perch Remotely Operated Vehicle.

In the process of doing this, they became familiar with digital fabrication technologies based upon geometric concepts, including InkScape vector graphics, SketchUp and/or Solidworks CAD software, and Rapman 3-D printing, and applied these technologies to the construction of various models. The MIT Department of Computer Science and Artificial Intelligence (CSAIL) has generously donated a 3D printer to the Middle School which will be utilized in this course( http://www.csail.mit.edu/node/1781 ).

This course was taught using a blended-learning model, consisting of textbook study, an online interactive lecture, online exercises and problems, and an online discussion board, combined with in-class discussion of the more challenging problems.

The course also included lecture-demonstrations by guest speakers from MIT, Northeastern University, Weston High School, and elsewhere.

Most of the formal lectures, discussion, and homework took place online, in conjunction with **The Art of Problem Solving** (**http://www.artofproblemsolving.com**/) online Geometry course, Sept 24th 2012- March 5th 2013. The online course also included homework( answered or submitted online to AOPS), and the Alcumus, an adaptive learning system.

Other highlights of the course included a full-day field trip to MIT, where they met with Professors Erik Demaine and Daniela Rus is the Computer Science Department, took part in research experiments in robotics, and met with AOPS Geometry Instructor Sam Elder in the Mathematics Department, and PhD student Caitlin Mueller in the Architecture Department.

This was an advanced course for a small cohort of students who completed Grade 8 Advanced Algebra while in Grade 7.

Grading of the course was pass-fail. Except for the guest university lecturers, there was very little in-class lecturing; most problems were discussed by the students independently. All students took and passed the Weston High School Honors Geometry final exam.

Available facilities included both Mac and PC computer labs, electronics lab, woodshop, and 3D Printer. Off-site access to a laser-cutter may be done through the Artisan's Asylum ( http://artisansasylum.com/ ) and or Danger!Awesome ( http://dangerawesome.co/ ).

A major influence on the students is **Mathemusician Vi Hart- See http://www.nytimes.com/2011/01/18/science/18prof.html?_r=0. **

Below*: STL Mesh of Foot for 3D Printing*

**Syllabus**

**Assignments and Activities**

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**Geometry: The Art of Problem Solving**

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**Projects: Making Stuff**

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**Purple Comet International Math Competition**

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**Embedded Computing-**

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**Discrete Math**

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**Geometry Review**

**Sea Perch ROV **

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**References and Further Readings *** ** *

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