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

[ModelCourses/Math4Teachers/FirstTerm/ProblemSolvingStrategies|Problem Solving Strategies]]

Problem set for this unit

• General Strategies
• Patterns
• Algebra
• Logical Reasoning

[ModelCourses/Math4Teachers/FirstTerm/SetsAndFunctions|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

[ModelCourses/Math4Teachers/FirstTerm/WholeNumberArithmetic|Whole Number Arithmetic]]

Problem set for this unit

• Addition
• Subtraction
• Multiplication
• Division

[ModelCourses/Math4Teachers/FirstTerm/NumberTheory|Number Theory]]

Problem set for this unit

• Divisibility
• Tests for Divisibility
• Primes and Prime Factorization
• Greatest Common Divisors and Least Common Multiples

[ModelCourses/Math4Teachers/FirstTerm/IntegersFractionsRationals|Integers, Fractions, and Rational Numbers]]

Problem set for this unit

• Integer Operations
• Modeling Fractions
• Fractional Number Sense
• Fraction Operations

[ModelCourses/Math4Teachers/FirstTerm/DecimalsReals|Decimals and Real Numbers]]

Problem set for this unit

• Irrational and Real Numbers
• Decimal Computation and Applications

[ModelCourses/Math4Teachers/FirstTerm/ProportionsPercents|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