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Selected InterMath Investigations
number Concept

Basic Facets of Number Sense

Rational Numbers: Decimals, Fractions …

Irrational Numbers:

Complex Numbers:

Natural Number, Whole Numbers:


Order Relationships:

Square Roots and Other Roots:

Mathematical Induction and Inductive Reasoning:

Enjoyment/Beauty of Numbers:

Distinctions between Countable and Uncountable:

Large and Small Numbers:



History of Numeration

Numeration Systems (Hindu, Arab, Egyptian, Roman, etc.):

Development of the Concept of Zero:

Place Value:

Exploration of Infinity:


Divisibility Properties of Integers

 Divisibility Rules:

 Greatest Common Factor (GCF), Least Common Multiple (LCM):


Prime Numbers and Composite Numbers

Prime and Composite Numbers:

Sieve of Eratosthenes:

Infinitude of Prime Numbers

Abundant, Deficient, and Perfect Numbers:


Special Sets of Numbers and Sequences

Pascal's Triangle:

Fibonacci Sequence:

Geometric Sequence & Series:

Gauss Strategy (sum of counting numbers):

Pythagorean Triples:

Figurate Numbers:


Concepts of Operations

Operations on Sets of Numbers:

 Identity Elements:

 Inverse Operations:

Alternative Algorithms:

Exploration of Other Bases:

Modular Arithmetic:

 Proportional Reasoning:

Other Components of Number Theory:

Historically noteworthy problems from number theory (Goldbach's Conjecture, Fermat's Last Theorem, etc.)