Model Problems and Examples

Links below, organized by chapter, contain examples of students' work on many of the ideas and problems in this course. We appreciate these students' willingness to share their thoughts and ideas.

• Chapter 1: Polygons and Angle Relationships
  • [AP 1.3] Project: Triangle and Quadrilateral Angle Sums by
    Tearing
    • Triangle Sums by Christy Horn (PDF: 125 KB)

    • Quadrilateral Angle Sums by Jessica Booth (PDF: 93 KB)

• Chapter 2: Quadrilaterals and Their Definitions
  • How some students make sense of the ideas of definitions and properties.
    • Definitions and Properties by Lindsey Lewis (PDF: 1.16 MB)

      This colorful project gives Lindsey's way of making sense of definitions (good and bad ones) and properties. She gives examples from real life and from geometry.

    • To Me a Parallelogram is... by Carrie Duncan (PDF: 20 KB)

      Rachelle and Amber are trying to figure out a good definition for a parallelogram. Their bantering back and forth is cleverly captured in this short novelette by Carrie Duncan.

    • Definitions and Properties by Atsuhiro Narisawa (PDF: 262 KB)

      Cute examples from real life and geometry are given by Atushiro illustrating ideas of definitions versus properties.

    • Rhombuses by Jennifer Richardson (PDF: 220 KB)

      Two different ways to define a rhombus are described in this project. Jennifer also shows how to check through paper folding if a figure satisfies these definitions.

  • Project: To Me a Kite Is...
    
    Student examples of work on a project exploring possible good and bad definitions of a kite are given. Several different good defintions are given; bad definitions are also given with examples showing why they are bad. You can see the Project Assignment sheet through this link.
    • To Me a Kite Is: A shape with several properties & possible definitions!! by Christine Ramey (PDF: 145 KB)

      Christine's colorful and clear description of how she sees this question is very well done.

    • Samples from Students' Work on the Kite Project by Various Students (PDF: 369 KB)

• Chapter 3: Constructions by Paper Folding
  • Project: Two Basic Paper Folding Constructions and Why They Work!
    
    Four students' examples of a project which involves finding perpendicular bisectors and angle bisectors are given below. The "Why do they work?" parts are interesting and slightly different for each student. The Project Assignment sheet can be accessed through this link.
    • Crystal Davis (PDF: 117 KB)

    • Janell Eck (PDF: 208 KB)

    • Cheryl Jenkins (PDF: 206 KB)

    • Jacqueline McLemore (PDF: 144 KB)

• Chapter 5: Areas
  • Students' ways for making sense of the ideas in this chapter:
    • Take-Away by Emily Lanie (PDF: 256 KB)

    • The Trouble with Trapezoids by Kendel Lewellen (PDF: 593 KB)

• Chapter 8: Pythagorean Theorem and Perimeter
  • Students' ways for making sense of the ideas in this chapter:
    • Estimating Perimeter on a Geoboard (with examples from the class of Ms. James) by Joni Prodanov (PDF: 368 KB)

      (What do you think of the last "stop sign" example in this project?)

• Chapter 17: Symmetries of Mandalas
  • [AP 17.7] Express Yourself with a Mandala
    
    Creative examples of mandalas by geometry students are in the files given below.
    • Mandalas created Spring 1999 (PDF: 1.51 MB)

    • Mandalas created Fall 1999 (PDF: 212KB)

• Chapter 18: Borders
  • [AP 18.5] Borders: Make Your Own Display
    
    Several examples of students' work on this project or similar projects are given below
    • Border Projects — 2001 (PDF: 2.16 MB)

    • Border Projects — 2004 (PDF: 735 KB)

  • Border Projects — 2000:
    • Borders by Dalee Adams (PDF: 94 KB)

    • Borders by Sara Kelly (PDF: 152 KB)

    • Borders by Joey Brown (PDF: 76 KB)

    • Sports Borders by Jocelyn Crow (PDF: 210 KB)

• Chapter 19: Escher Style Tessellations
  • [AP 19.4] Mini-Project: Recognizability
    
    Fun and imaginative examples of student work on this mini project are given in the following files.
    • Recognizability — 1999 (PDF: 244 KB)

    • Recognizability — 2004 (PDF: 1.22 MB)

    • Dana Eskridge's Creations (PDF: 166 KB)

  • [AP 19.8] Project: Making Escher Style Tessellations
    
    A collection of tessellations related to this activity page is given below. Please enjoy!
    • Tessellations — 1999A (PDF: 2.98 MB)

    • Tessellations — 1999B (PDF: 2.69 MB)

    • An Elf with a Reindeer by Misti Martin (PDF 145 KB)

    • Starman (TCTC) by Annie Black (PDF: 205 KB)

    • Young Boy (TGTG) by Emily Kern (PDF 195 KB)

    • Dani Redmen's TCTC (PDF: 674 KB)

    • Leslea Davis's C4 Tessellation (PDF: 185 KB)

    • A Tessellation Project by Brandy Moore (PDF: 496 KB)