# ModelCourses/Math for Elementary Education

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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

## List of Topics

# First Term

### Unit 1 - Problem Solving Strategies

- General Strategies
- Patterns
- Algebra
- Logical Reasoning

### Unit 2 - Sets and Functions

- Sets and Set Operations
- Counting with Sets and Venn Diagrams
- Functions and Their Properties
- Function Applications
- Numeration Systems

### Unit 3 - Whole Number Arithmetic

- Addition
- Subtraction
- Multiplication
- Division

### Unit 4 - Number Theory

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

### Unit 5 - Integers, Fractions, and Rational Numbers

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

### Unit 6 - Decimals and Real Numbers

- Irrational and Real Numbers
- Decimal Computation and Applications

### Unit 7 - Proportions and Percents

- Ratios and Proportions
- Percents

# Second Term

### Unit 1 - Coordinate Geometry

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

### Unit 2 - Geometric Figures

- Figures in the Plane
- Polygons
- Figures in Space

### Unit 3 - Symmetry and Transformations

- Similarity Transformations
- Types of Symmetry
- Tiling the Plane

### Unit 4 - Measurement: Length, Area and Volume

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

### Unit 5 - Statistics

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

### Unit 6 - Probability

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