ModelCourses/Math for Elementary Education

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

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Contents

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

List of Topics

First Term

Unit 1 - Problem Solving Strategies

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

Unit 2 - 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

Unit 3 - Whole Number Arithmetic

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

Unit 4 - Number Theory

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

Unit 5 - Integers, Fractions, and Rational Numbers

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

Unit 6 - Decimals and Real Numbers

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

Unit 7 - Proportions and Percents

Problem set for this unit
  • Ratios and Proportions
  • Percents

Second Term

Unit 1 - Coordinate Geometry

Problem set for this unit
  • Cartesian Coordinate System
  • Graphing and Applications
  • Connecting Algebra and Geometry

Unit 2 - Geometric Figures

Problem set for this unit
  • Figures in the Plane
  • Polygons
  • Figures in Space

Unit 3 - Symmetry and Transformations

Problem set for this unit
  • Similarity Transformations
  • Types of Symmetry
  • Tiling the Plane

Unit 4 - Measurement: Length, Area and Volume

Problem set for this unit
  • Units of Measure
  • Area and Perimeter
  • Pythagorean Theorem
  • Similarity
  • Volume and Surface Area

Unit 5 - Statistics

Problem set for this unit
  • Organizing Data
  • Populations and Sampling
  • Measures of Center
  • Measures of Variation
  • Measures of Relative Standing

Unit 6 - Probability

Problem set for this unit
  • Introduction to Probability
  • Principles of Counting
  • Theoretical Probability
  • Random Variables and Expected Value

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