Math 236: Foundations of Geometry, Statistics, and Probability

Course Description: This course is designed to provide students with the opportunity to acquire knowledge related to the following topics and / or concepts: Basic concepts and methods of probability, statistics, and geometry, including discrete probability, random events, and conditional probability. Analysis of data, informational display, measurement, and geometry (as approached through similarity and congruence, coordinates, and transformations). Problem solving emphasized. 

Prerequisite: MATH 133.  Listed as MATH 1351 in the Texas Common Course Numbering 

System.  

Learning Objectives

Upon completion of this course, a student should be able to:

  1. Compute theoretical and empirical probabilities
  2. Apply permutations and combinations in probabilities
  3. Use and understand variety of statistical graphs
  4. Understand and can compute Measures of central tendency and variation
  5. Understand and can use basic geometric vocabularies
  6. Understand and can apply theorems involving angles
  7. Understand the properties of basic three-dimensional figures and can construct basic three-dimensional figures
  8. Understand and can apply the congruence properties and similarity properties
  9. Use a compass and a straightedge to copy a line segment, circle, and angle; bisect a segment, angle;
  10. Construct a perpendicular or parallel
  11. Understand and convert the English system of measure, the metric system of measure
  12. Compute the distance, area, and volumes of basic geometric figures
  13. Understand motions of the plane

Required Reading / Textbook: A Problem Solving Approach to Mathematics for Elementary School Teachers, 12th edition  with MyMathLab Student Access Kit Package  Billstein, Rich | Libeskind, Sholmo | Lott, Johnny. Publisher: Pearson

Recommended Reading: 

Mathematics for Elementary Teachers: A Conceptual Approach, 10th Edition By Albert Bennett and Laurie Burton and Ted Nelson and Joseph Ediger. ISBN10: 0078035651, ISBN13: 9780078035654

Problem Solving Approach to Mathematics for Elementary School Teachers – 12th edition. ISBN13: 9780321987297. ISBN10: 0321987292

Major Assignments/Exams

  • Homework
  • Quizzes
  • Exams
  • Final Exam

List of discussion/lecture topics

Topics and Schedule for the course:

  1. Probability (Weeks 1, 2, 3)
    1. Determining Probabilities
    1. Multistage Experiments and Modeling Games
    1. Simulations and Applications in Probability
    1. Permutations and Combinations in Probability
  2. Data Analysis/Statistics: An Introduction (Weeks 4, 5, 6)
    1. Designing Experiments/Collecting Data
    1. Displaying Data: Part I
    1. Displaying Data: Part II
    1. Measures of Central Tendency and Variation
    1. Abuses of Statistics
  3. Introductory Geometry (Weeks 7, 8)
    1. Basic Notions
    1. Curves, Polygons, and Symmetry
    1. More About Angles
    1. Geometry in Three Dimensions
  4. Congruence and Similarity with Constructions (Weeks 9, 10)
    1. Congruence Through Constructions
    1. Additional Congruence Theorems
    1. Additional Constructions
    1. Similar Triangles and Other Similar Figures
  5. Congruence and Similarity with Transformations (Weeks 11, 12, 13)
    1. Translations and Rotations
    1. Reflections and Glide Reflections
    1. Dilations
    1. Tessellations of the Plane
  6. Area, Pythagorean Theorem, and Volume (Weeks 14, 15)
    1. Linear Measure
    1. Areas of Polygons and Circles
    1. The Pythagorean Theorem, Distance Formula, and Equation of a Circle
    1. Surface Areas
    1. Volume, Mass, and Temperature

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