# ModelCourses/Math for Elementary Education

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PREP 2011 Model Course<br /> | PREP 2011 Model Course<br /> | ||

Prepared by Mike Diehl and Jonathan Duncan<br /> | Prepared by Mike Diehl and Jonathan Duncan<br /> | ||

+ | |||

+ | {{UnderConstruction}} | ||

== Description == | == Description == | ||

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

− | many texts on the subject | + | many texts on the subject. |

− | + | ||

− | == | + | == To Do == |

− | * Finish writing/finding problems (approximately | + | * Finish writing/finding problems (have approximately 240, need approximately 30 more) |

* Write set header files | * Write set header files | ||

* Create PDF files for homework assignments | * Create PDF files for homework assignments | ||

* Tag written problems for NPL | * Tag written problems for NPL | ||

+ | * Write solutions | ||

+ | * Shamelessly copy Multi-variable Calculus wiki layout | ||

== List of Topics == | == List of Topics == | ||

− | + | = First Term = | |

− | + | === Unit 1 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/ProblemSolvingStrategies|Problem Solving Strategies]] === | |

− | + | :[[file11|Problem set for this unit]] | |

− | + | * General Strategies | |

− | + | * Patterns | |

− | + | * Algebra | |

+ | * Logical Reasoning | ||

− | + | === Unit 2 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/SetsAndFunctions|Sets and Functions]] === | |

− | + | :[[file12|Problem set for this unit]] | |

− | + | ||

− | + | * Sets and Set Operations | |

− | + | * Counting with Sets and Venn Diagrams | |

+ | * Functions and Their Properties | ||

+ | * Function Applications | ||

* Numeration Systems | * Numeration Systems | ||

− | |||

− | |||

− | |||

− | + | === Unit 3 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/WholeNumberArithmetic|Whole Number Arithmetic]] === | |

− | + | :[[file13|Problem set for this unit]] | |

− | + | ||

− | + | * Addition | |

− | + | * Subtraction | |

+ | * Multiplication | ||

+ | * Division | ||

+ | |||

+ | === Unit 4 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/NumberTheory|Number Theory]] === | ||

+ | :[[file14|Problem set for this unit]] | ||

+ | |||

+ | * Divisibility | ||

+ | * Tests for Divisibility | ||

+ | * Primes and Prime Factorization | ||

+ | * Greatest Common Divisors and Least Common Multiples | ||

+ | |||

+ | === Unit 5 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/IntegersFractionsRationals|Integers, Fractions, and Rational Numbers]] === | ||

+ | :[[file15|Problem set for this unit]] | ||

+ | |||

+ | * Integer Operations | ||

+ | * Modeling Fractions | ||

+ | * Fractional Number Sense | ||

+ | * Fraction Operations | ||

+ | |||

+ | === Unit 6 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/DecimalsReals|Decimals and Real Numbers]] === | ||

+ | :[[file16|Problem set for this unit]] | ||

+ | |||

+ | * Irrational and Real Numbers | ||

+ | * Decimal Computation and Applications | ||

+ | |||

+ | === Unit 7 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/ProportionsPercents|Proportions and Percents]] === | ||

+ | :[[file17|Problem set for this unit]] | ||

+ | |||

+ | * Ratios and Proportions | ||

+ | * Percents | ||

+ | |||

+ | = Second Term = | ||

+ | |||

+ | === Unit 1 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/CoordinateGeometry|Coordinate Geometry]] === | ||

+ | :[[file21|Problem set for this unit]] | ||

+ | |||

+ | * Cartesian Coordinate System | ||

+ | * Graphing and Applications | ||

+ | * Connecting Algebra and Geometry | ||

− | + | === Unit 2 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/GeometricFigures|Geometric Figures]] === | |

− | + | :[[file21|Problem set for this unit]] | |

− | + | ||

− | + | ||

− | + | ||

− | * | + | * Figures in the Plane |

− | * | + | * Polygons |

− | * | + | * Figures in Space |

− | + | ||

− | + | ||

− | + | === Unit 3 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/SymmetryTransformations|Symmetry and Transformations]] === | |

− | + | :[[file22|Problem set for this unit]] | |

− | + | ||

− | * | + | * Similarity Transformations |

− | * | + | * Types of Symmetry |

− | * | + | * Tiling the Plane |

− | === | + | === Unit 4 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/Measurement|Measurement: Length, Area and Volume]] === |

+ | :[[file23|Problem set for this unit]] | ||

+ | |||

+ | * Units of Measure | ||

+ | * Area and Perimeter | ||

+ | * Pythagorean Theorem | ||

+ | * Similarity | ||

+ | * Volume and Surface Area | ||

− | + | === Unit 5 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/Statistics|Statistics]] === | |

− | + | :[[file24|Problem set for this unit]] | |

− | + | ||

− | + | ||

− | * | + | * Organizing Data |

− | ** | + | * Populations and Sampling |

− | * | + | * Measures of Center |

− | * | + | * Measures of Variation |

+ | * Measures of Relative Standing | ||

− | + | === Unit 6 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/Probability|Probability]] === | |

− | + | :[[file25|Problem set for this unit]] | |

− | + | ||

− | + | ||

− | * | + | * Introduction to Probability |

− | * | + | * Principles of Counting |

− | * | + | * Theoretical Probability |

− | * | + | * Random Variables and Expected Value |

− | + | ||

− | + | ||

− | + | =[[ModelCourses|Other Model Courses]]= | |

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | + | [[Category:PREP 2011]] | |

− | + | [[Category:Events]] | |

− | + | [[Category:Model Courses]] | |

− | + | ||

− | + |

## Latest revision as of 11:52, 10 March 2013

Mathematics for Elementary Educators

PREP 2011 Model Course

Prepared by Mike Diehl and Jonathan Duncan

## 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

- 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