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Math for Educators (MATH 010A and 010B CID120)

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Math for Educators (MATH 010A and 010B CID120)

Mathematics
Author
Lynn Mann
Publisher
LibreTexts
Source
LibreTexts
License
Mixed
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 185 sections
  1. 01: Teaching Elementary Mathematics
  2. 1.01: Importance of the Teacher's Skills
  3. 1.02: Understanding Mathematical Content Knowledge
  4. 1.03: Pedagogical Content Knowledge
  5. 1.04: Common Core Standards for Mathematics
  6. 1.4.01: Kindergarten Standards Overview
  7. 1.4.02: Grade 1 Standards Overivew
  8. 1.4.03: Grade 2 Standards Overview
  9. 1.4.04: Grade 3 Standards Overview
  10. 1.4.05: Grade 4 Standards Overview
  11. 1.4.06: Grade 5 Standards Overview
  12. 1.4.07: Grade 6 Standards Overview
  13. 1.4.08: Grade 7 Standards Overview
  14. 1.4.09: Grade 8 Standards Overview
  15. 1.4.10: High School Number and Quantity Standards
  16. 1.4.11: High School Algebra Standards
  17. 1.4.12: High School Functions Standards
  18. 1.4.13: High School Modeling Standards
  19. 1.4.14: High School Geometry Standards
  20. 1.4.15: High School Statistics and Probability Standards
  21. 1.05: Teaching Techniques in Mathematics
  22. 1.5.01: Number and Operations
  23. 1.5.1.01: Introduction
  24. 1.5.1.02: Addition- Dots and Boxes
  25. 1.5.1.03: Subtraction- Dots and Boxes
  26. 1.5.1.04: Multiplication- Dots and Boxes
  27. 1.5.1.05: Division- Dots and Boxes
  28. 1.5.1.06: Number Line Model
  29. 1.5.1.07: Area Model for Multiplication
  30. 1.5.1.08: Properties of Operations (Part 1)
  31. 1.5.1.09: Properties of Operations (Part 2)
  32. 1.5.1.10: Division Explorations
  33. 1.5.1.11: Problem Bank
  34. 1.06: Building a Supportive Math Learning Environment
  35. 1.07: Math Anxiety
  36. 1.08: Assessing and Reflecting on Teaching Practices
  37. 1.09: Common Mistakes Math Teachers Make
  38. 02: Historical Counting Systems
  39. 2.01: Introduction
  40. 2.02: The Number and Counting System of the Inca Civilization
  41. 2.03: The Hindu-Arabic Number System
  42. 2.04: The Development and Use of Different Number Bases
  43. 2.05: The Mayan Numeral System
  44. 2.06: Addition and Subtraction with Other Bases
  45. 2.07: Exercises
  46. 03: The Real Number System
  47. 3.01: Introduction to the Real Number System
  48. 3.02: Whole and Natural Numbers
  49. 3.03: Integer Numbers
  50. 3.04: Rational Numbers
  51. 3.05: Irrational Numbers
  52. 3.06: Real numbers and the Number Line
  53. 3.07: Absolute Value
  54. 3.08: Adding and Subtracting Integers
  55. 3.09: Multiplying and Dividing Integers
  56. 3.10: Fractions
  57. 3.11: Review of Decimals and Percents
  58. 3.12: Exponents and Square Roots
  59. 3.13: Order of Operations
  60. 3.14: Scientific Notation
  61. 3.15: Approximation and Estimation
  62. 3.16: Real Numbers - Algebra Essentials
  63. 3.17: Challenges and Misconceptions
  64. 3.18: Summary and Review
  65. 04: Number Theory
  66. 4.01: Introduction to Number Theory
  67. 4.02: Primes and Composite Numbers
  68. 4.03: The Sieve of Eratosthenes
  69. 4.04: Even and Odd Numbers
  70. 4.05: Factors and GCF
  71. 4.06: Euclidean Algorithm
  72. 4.07: Digital Roots and Divisibility
  73. 4.08: Division Algorithms
  74. 4.09: The Meaning of Multiplication
  75. 4.10: Multiplication Algorithms
  76. 4.11: The Meaning of Division
  77. 4.12: LCM and other Topics
  78. 4.13: Modular Arithmetic
  79. 4.14: Arithmetic Sequences
  80. 4.15: Geometric Sequences and Series
  81. 05: Problem Solving
  82. 5.01: Problem Solving
  83. 5.02: George Polya's Strategy
  84. 5.03: John Van de Walle's Strategy
  85. 5.04: Marilyn Burns' Strategy
  86. 5.05: Use a Problem-Solving Strategy
  87. 5.06: Recognizing Patterns
  88. 5.07: Beware of Patterns
  89. 5.08: Careful Use of Language in Mathematics
  90. 5.09: Exercises and Applications
  91. 06: Mathematical Reasoning
  92. 6.01: Introduction on Mathematical Reasoning
  93. 6.02: Types of Reasoning
  94. 6.03: Logical Connectives and Statements
  95. 6.04: Proof Techniques
  96. 6.05: Common Logical Fallicies
  97. 6.06: Strategies for Teaching Mathematical Reasoning
  98. 6.07: Practical Applications
  99. 07: Logic
  100. 7.01: Introduction
  101. 7.02: Statements and Quantifiers
  102. 7.03: Compound Statements
  103. 7.04: Constructing Truth Tables
  104. 7.05: Truth Tables for the Conditional and Biconditional
  105. 7.06: Equivalent Statements
  106. 7.07: De Morgans Laws
  107. 7.08: Logical Arguments
  108. 7.09: Chapter Summary
  109. 7.9.01: Key Terms
  110. 7.9.02: Key Concepts
  111. 7.9.03: Videos
  112. 7.9.04: Projects
  113. 7.9.05: Chapter Review
  114. 7.9.06: Reasoning and Logic
  115. 7.9.07: Basic Arguments- Using Logic
  116. 7.9.08: Review Exercises
  117. 7.9.09: Chapter Test
  118. 08: Algebraic Thinking
  119. 8.01: The Language of Algebra
  120. 8.02: Solving Equations with Addition and Subtraction Properties of Equality
  121. 8.03: Solving Equations with the Division and Multiplication Properties of Equality
  122. 8.04: Solving Equations with Variables and Constants on Both Sides
  123. 8.05: General Strategy to Solve Linear Equations
  124. 8.06: Solving Equations with Fractions or Decimals
  125. 8.07: Solving a Formula for a Specific Variable
  126. 8.08: Arithmetic Operations with Functions
  127. 8.09: Graphing and slope
  128. 8.10: Equations of lines
  129. 8.11: Parallel and perpendicular lines
  130. 8.12: System of Equations - Graphing
  131. 8.13: Systems of Equations - The Substitution Method
  132. 8.14: System of Equations - The Addition Method
  133. 8.15: Applications with systems of equations
  134. 09: Probability Topics
  135. 9.01: Introduction
  136. 9.02: Terminology
  137. 9.03: Independent and Mutually Exclusive Events
  138. 9.04: Two Basic Rules of Probability
  139. 9.05: Contingency Tables
  140. 9.06: Tree and Venn Diagrams
  141. 9.07: Probability Topics (Worksheet)
  142. 9.E: Probability Topics (Exericses)
  143. 10: Descriptive Statistics
  144. 10.01: Prelude to Descriptive Statistics
  145. 10.02: Stem-and-Leaf Graphs (Stemplots) Line Graphs and Bar Graphs
  146. 10.03: Histograms Frequency Polygons and Time Series Graphs
  147. 10.04: Measures of the Location of the Data
  148. 10.4E: Measures of the Location of the Data (Exercises)
  149. 10.05: Box Plots
  150. 10.06: Measures of the Center of the Data
  151. 10.07: Skewness and the Mean Median and Mode
  152. 10.08: Measures of the Spread of the Data
  153. 10.09: Descriptive Statistics (Worksheet)
  154. 10.E: Descriptive Statistics (Exercises)
  155. 11: Geometry
  156. 11.01: Introduction
  157. 11.02: Tangrams
  158. 11.03: Triangles and Quadrilaterals
  159. 11.04: Polygons
  160. 11.05: Platonic Solids
  161. 11.06: Painted Cubes
  162. 11.07: Symmetry
  163. 11.08: Geometry in Art and Science
  164. 11.09: Problem Bank
  165. 12: Congruence and Similarity with Constructions
  166. 12.01: Similar Triangles
  167. 12.1.01: Proportions
  168. 12.1.02: Similar Triangles
  169. 12.1.03: Transversals to Three Parallel Lines
  170. 12.1.04: Pythagorean Theorem
  171. 12.1.05: Special Right Triangles
  172. 12.1.06: Distance from a Point to a Line
  173. 13: Area Pythagorean Theorem and Volume
  174. 13.01: Lines
  175. 13.02: Parallelograms
  176. 13.03: Other Quadrilaterals
  177. 13.04: Regular Polygons
  178. 13.05: Circles
  179. 13.06: Metric Units of Measurement
  180. 13.07: Temperature Scales
  181. 13.08: Temperature and Time
  182. 13.8.01: Exercises
  183. 13.09: Dilations on a Square Grid
  184. 13.10: More Dilations
  185. 14: Transformations