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)