ModelCourses/Math for Elementary Education

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

Description

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

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

Problem set for this unit

• Cartesian Coordinate System
• Graphing and Applications
• Connecting Algebra and Geometry

Geometric Figures

Problem set for this unit

• Figures in the Plane
• Polygons
• Figures in Space

Symmetry and Transformations

Problem set for this unit

• Similarity Transformations
• Types of Symmetry
• Tiling the Plane

Measurement: Length, Area and Volume

Problem set for this unit

• Units of Measure
• Area and Perimeter
• Pythagorean Theorem
• Similarity
• Volume and Surface Area

Statistics

Problem set for this unit

• Organizing Data
• Populations and Sampling
• Measures of Center
• Measures of Variation
• Measures of Relative Standing

Probability

Problem set for this unit

• Introduction to Probability
• Principles of Counting
• Theoretical Probability
• Random Variables and Expected Value