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
 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.
 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.
 Chapter 5:
Areas

Students' ways for making
sense of the ideas in this chapter:
 Chapter 8:
Pythagorean Theorem and Perimeter

Students' ways for making
sense of the ideas in this chapter:
 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.
 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
 Chapter 19:
Escher Style Tessellations

[AP 19.4] MiniProject:
Recognizability
Fun and imaginative examples of student work on this mini project
are given in the following files.

[AP 19.8] Project: Making
Escher Style Tessellations
A collection of tessellations related to this activity page is given
below. Please enjoy!