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Mathematics projects

Table of Contents

Research Projects
Research Settings
Teacher Handbook
Mathematics Tools
Completed Student Work

Research projects
Contributors: Al Cuoco, Michelle Manes, Ken Levasseur, Nina Shteingold, and Joshua Abrams
Key for levels
Title Mathematical Area Where you're at
Marion Walter’s Theorem
algebra, geometry level 3-45
Inspi (a Logo program)
number theory level 2-4
Patterns in Pascal's Triangle
geometry, combinatorics, number theory level 1-4
Problems in Probabilistic Number Theory
algebra, number theory, calculus level 4-4
The Game of Set
combinatorics, probability level 3-4
The Simplex Lock
combinatorics, algebra level 3-4
Patterns in Polynomials algebra, trigonometry level 4-4
Postage Stamp Arithmetic algebra, number theory level 3-4
Subsets in Sequence computer science, number theory level 1-4
Raw Recruits patterns and reasoning level 1-4
Trains patterns and reasoning level 1-4
Amida-kuji patterns and reasoning level 1-4

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Research settings
Connect the Dots
Pythagorean Triples
Fraction Equations and Other Research Settings
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Mathematics Research Skills
Primary Author: Joshua Abrams     Contributor: Lisa Honeyman

Mathematics Research in the Classroom

   Introduction to Research in the Classroom (FAQ)    HTML  |  PDF     Help with PDFs
   Setting and Sharing Goals      HTML  |  PDF
   Student and Teacher Affect     HTML  |  PDF
   Getting Stuck, Getting Unstuck!     HTML  |  PDF
   Building Collaborative Skills     HTML  |  PDF
   Assessment and the Use of Classtime     HTML  |  PDF
   Presenting Your Research     HTML  |  PDF
   Resources     HTML | PDF

Mathematics Research Skills

   Introductory Explorations and the Research Cycle     HTML  |  PDF
   Definitions     HTML  |  PDF
   Problem Posing     HTML  |  PDF
   Examples, Patterns, and Conjectures     HTML  |  PDF
   Proof     HTML  |  PDF
   Getting Information     HTML  |  PDF

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Mathematics tools


  Conditional Statements
Mathematical Induction
Proof by Contradiction
Parity Arguments
Pigeonhole Principle
Number Theory
  Modular Arithmetic
Euclid’s Algorithm
Fermat’s Little Theorem
The Chinese Remainder Theorem
The Fundamental Theorem of Arithmetic
Pascal’s Triangle
The Geometry of Complex Numbers
Numbers and Infinity
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Completed Student Work

Problems in Probabilistic Number Theory

Joe Noss, Interim Report, January 2001

Joe Noss, Final Report, November 2001
(PDF Version, requires Adobe Acrobat Reader)

Patterns in Polynomials

Jeremy Warshauer, Final Report, January 2002
(PDF Version, requires Adobe Acrobat Reader)

Leon Yu Mao Loo, Final Report, May 2002
(PDF Version, requires Adobe Acrobat Reader)

The Simplex Lock

Emily Weiss, Rebecca Kalauskas, & Alex Cole, Arlington High School, Arlington, MA, April 1999


Megan Lojek, February 1999

Jackie Ou, Program in Mathematics for Young Scientists, 1999

Erik Elwood, Program in Mathematics for Young Scientists, 1999


David Senft, Final Report, July 2002

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