Learning Outcomes for 3450:140 Fundamentals of Mathematics for Primary Educators                                            Students are expected to be able to:

• Understand and apply basic problem solving strategies.
• Understand the structure of numeration systems (Roman, Mayan, Babylonian and Hindu-Arabic in base-10 and other bases) and be able to convert numbers between the Hindu-Arabic base-10 numeration system and the other numeration systems.
• Understand the representation and properties of the following subsets of real numbers: whole numbers (including other bases), integers, rational numbers, and real numbers, as well as perform mathematical operations on them.
• Understand the basics of the following topics from number theory and use them in solving problems: parity, multiples, factors, divisors, divisibility tests, and factorization.
• Understand the meanings and connections between ratios, proportions, and percents, as well as solve problems involving them.

Topical Outline:

• Problem Solving Strategies (Polya’s Principles, Guess and Check, Lists, Diagrams, Working Backwards, Eliminating Possibilities, Pigeonhole Principle, Finding Patterns)
• Numeration Systems (Egyptian, Roman, Babylonian, Mayan, Hindu-Arabic, Other Bases for Hindu-Arabic)
• Operations with Whole Numbers (Including other bases)
• Addition (Adding on, Putting together, Minimum representations with base blocks, Partial sums, and Standard algorithm)
• Subtraction (Taking away, Comparison, and Missing addend)
• Multiplication (Repeated addition, Rectangular grids, Partial products, Standard algorithm with and without partial sums, Lattice)
• Division (Sharing equally aka partitive, Repeated subtraction aka measurement and the Standard algorithm
• Number Properties (Closure, Identity, Associative, Commutative, Distributive)
• Laws of Exponents
• Order of Operations
• Number Theory
• Parity, Multiples, Factors, Divides, Divisor,
• Divisibility Tests (2, 3, 4, 5, 6, 8, 9, 10)
• Prime and Composite Numbers (sieve of Eratosthenes, Factorization, Factor Trees, Number of Factors, GCF (aka GCD) and LCM
• Integers (Representations with number lines and tiles, Operations, Additive Inverses)
• Fractions (As part to whole, division or ratios, equivalence, Improper, Mixed numbers, Operations, Density, and Fraction sense)
• Decimals (Expanded Form, Representations with rectangular grids, Operations, Rounding, and Converting repeating decimals to fractions and vice-versa)
• Rational, Real and Irrational Numbers (Defining and Identifying)
• Ratios (Equivalent, Proportions, and Constant of Proportionality)
• Percents (Connection to fractions and decimals, and Finding percents of numbers and percent changes)
• Sets (Venn diagrams, Intersections, Unions, Compliments, Subsets, and Disjoint)