ModelCourses/Math for Elementary Education

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Mathematics for Elementary Educators
PREP 2011 Model Course
Prepared by Mike Diehl and Jonathan Duncan



This is a model course for a two-term Mathematics for Elementary Educators course. Below is a list of topics and sub-topics arranged in an order that is common for many texts on the subject.

To Do

  • Finish writing/finding problems (have approximately 240, need approximately 30 more)
  • Write set header files
  • Create PDF files for homework assignments
  • Tag written problems for NPL
  • Write solutions
  • Shamelessly copy Multi-variable Calculus wiki layout

List of Topics

First Term

Problem Solving Strategies

Problem set for this unit
  • General Strategies
  • Patterns
  • Algebra
  • Logical Reasoning

Sets and Functions

Problem set for this unit
  • Sets and Set Operations
  • Counting with Sets and Venn Diagrams
  • Functions and Their Properties
  • Function Applications
  • Numeration Systems
    • Ancient Numeration Systems
    • The Hindu-Arabic System
    • Bases Other than Ten

Whole Number Arithmetic

Problem set for this unit
  • Addition
  • Subtraction
  • Multiplication
  • Division

Number Theory

Problem set for this unit
  • Divisibility
  • Tests for Divisibility
  • Primes and Prime Factorization
  • Greatest Common Divisors and Least Common Multiples

Integers, Fractions, and Rational Numbers

Problem set for this unit
  • Integer Operations
  • Modeling Fractions
  • Fractional Number Sense
  • Fraction Operations

Decimals and Real Numbers

Problem set for this unit
  • Irrational and Real Numbers
  • Decimal Computation and Applications

Proportions and Percents

Problem set for this unit
  • Ratios and Proportions
  • Percents

Second Term

  • Coordinate Geometry
    • Cartesian Coordinate System
    • Graphing and Applications
    • Connecting Algebra and Geometry
  • Geometric Figures
    • Figures in the Plane
    • Polygons
    • Figures in Space
  • Symmetry and Transformations
    • Similarity Transformations
    • Types of Symmetry
    • Tiling the Plane
  • Measurement: Length, Area and Volume
    • Units of Measure
    • Area and Perimeter
    • Pythagorean Theorem
    • Similarity
    • Volume and Surface Area
  • Statistics
    • Organizing Data
    • Populations and Sampling
    • Measures of Center
    • Measures of Variation
    • Measures of Relative Standing
  • Probability
    • Introduction to Probability
    • Principles of Counting
    • Theoretical Probability
    • Random Variables and Expected Value

Other Model Courses

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