Difference between revisions of "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 ==
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== List of Topics ==
  
== List of Topics ==
   
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=== First Term ===
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= First Term =
   
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* Problem Solving Strategies
  
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=== Unit 1 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/ProblemSolvingStrategies|Problem Solving Strategies]] ===
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** General Strategies
  
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:[[file11|Problem set for this unit]]
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** Patterns
  
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* General Strategies
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** Algebra
  
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* Patterns
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** Logical Reasoning
  
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* Algebra
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* Logical Reasoning
   
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* Sets and Functions
  
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=== Unit 2 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/SetsAndFunctions|Sets and Functions]] ===
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** Sets and Set Operations
  
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:[[file12|Problem set for this unit]]
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** Counting with Sets and Venn Diagrams
  
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−
** Functions and Their Properties
  
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* Sets and Set Operations
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** Function Applications
  
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* Counting with Sets and Venn Diagrams
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* Functions and Their Properties
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* Function Applications
 
* Numeration Systems
  
* Numeration Systems
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** Ancient Numeration Systems
  
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** The Hindu-Arabic System
  
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** Bases Other than Ten
  
   
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* Whole Number Arithmetic
  
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=== Unit 3 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/WholeNumberArithmetic|Whole Number Arithmetic]] ===
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** Addition
  
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:[[file13|Problem set for this unit]]
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** Subtraction
  
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−
** Multiplication
  
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* Addition
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** Division
  
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* Subtraction
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* Multiplication
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* Division
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  +
=== Unit 4 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/NumberTheory|Number Theory]] ===
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:[[file14|Problem set for this unit]]
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  +
* Divisibility
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* Tests for Divisibility
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* Primes and Prime Factorization
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* Greatest Common Divisors and Least Common Multiples
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  +
=== Unit 5 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/IntegersFractionsRationals|Integers, Fractions, and Rational Numbers]] ===
  +
:[[file15|Problem set for this unit]]
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  +
* Integer Operations
  +
* Modeling Fractions
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* Fractional Number Sense
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* Fraction Operations
  +
  +
=== Unit 6 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/DecimalsReals|Decimals and Real Numbers]] ===
  +
:[[file16|Problem set for this unit]]
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  +
* Irrational and Real Numbers
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* Decimal Computation and Applications
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  +
=== Unit 7 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/ProportionsPercents|Proportions and Percents]] ===
  +
:[[file17|Problem set for this unit]]
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  +
* Ratios and Proportions
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* Percents
  +
  +
= Second Term =
  +
  +
=== Unit 1 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/CoordinateGeometry|Coordinate Geometry]] ===
  +
:[[file21|Problem set for this unit]]
   
−
* Number Theory
  
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* Cartesian Coordinate System
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** Divisibility
  
  +
* Graphing and Applications
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** Tests for Divisibility
  
  +
* Connecting Algebra and Geometry
−
** Primes and Prime Factorization
  
−
** Greatest Common Divisors and Least Common Multiples
  
   
−
* Integers, Fractions, and Rational Numbers
  
  +
=== Unit 2 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/GeometricFigures|Geometric Figures]] ===
−
** Integer Operations
  
  +
:[[file21|Problem set for this unit]]
−
** Modeling Fractions
  
−
** Fractional Number Sense
  
−
** Fraction Operations
  
   
−
* Decimals and Real Numbers
  
  +
* Figures in the Plane
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** Irrational and Real Numbers
  
  +
* Polygons
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** Decimal Computation and Applications
  
  +
* Figures in Space
   
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* Proportions and Percents
  
  +
=== Unit 3 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/SymmetryTransformations|Symmetry and Transformations]] ===
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** Ratios and Proportions
  
  +
:[[file22|Problem set for this unit]]
−
** Percents
  
   
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=== Second Term ===
  
  +
* Similarity Transformations
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* Types of Symmetry
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* Tiling the Plane
   
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* Coordinate Geometry
  
  +
=== Unit 4 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/Measurement|Measurement: Length, Area and Volume]] ===
−
** Cartesian Coordinate System
  
  +
:[[file23|Problem set for this unit]]
−
** Graphing and Applications
  
  +
−
** Connecting Algebra and Geometry
  
  +
* Units of Measure
  +
* Area and Perimeter
  +
* Pythagorean Theorem
  +
* Similarity
  +
* Volume and Surface Area
   
−
* Geometric Figures
  
  +
=== Unit 5 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/Statistics|Statistics]] ===
−
** Figures in the Plane
  
  +
:[[file24|Problem set for this unit]]
−
** Polygons
  
−
** Figures in Space
  
   
−
* Symmetry and Transformations
  
  +
* Organizing Data
−
** Similarity Transformations
  
  +
* Populations and Sampling
−
** Types of Symmetry
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* Measures of Center
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** Tiling the Plane
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* Measures of Variation
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* Measures of Relative Standing
   
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* Measurement: Length, Area and Volume
  
  +
=== Unit 6 - [[ModelCourses/Math_for_Elementary_Education/FirstTerm/Probability|Probability]] ===
−
** Units of Measure
  
  +
:[[file25|Problem set for this unit]]
−
** Area and Perimeter
  
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** Pythagorean Theorem
  
−
** Similarity
 
−
** Volume and Surface Area
  
   
−
* Statistics
  
  +
* Introduction to Probability
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** Organizing Data
  
  +
* Principles of Counting
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** Populations and Sampling
  
  +
* Theoretical Probability
−
** Measures of Center
  
  +
* Random Variables and Expected Value
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** Measures of Variation
  
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** Measures of Relative Standing
  
   
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* Probability
  
  +
=[[ModelCourses|Other Model Courses]]=
−
** Introduction to Probability
 
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** Principles of Counting
  
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** Theoretical Probability
  
−
** Random Variables and Expected Value
  
   
 
[[Category:PREP 2011]]
  
[[Category:PREP 2011]]

Latest revision as of 10:52, 10 March 2013

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

Construction.png This article is under construction. Use the information herein with caution until this message is removed.

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

Other Model Courses

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