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

by Lynn Mann

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Subjects
Mathematics
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Mixed licences (each page states its own), as LibreTexts states it
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Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Teaching Elementary Mathematics
  7. 1.1: Importance of the Teacher's Skills
  8. 1.2: Understanding Mathematical Content Knowledge
  9. 1.3: Pedagogical Content Knowledge
  10. 1.4: Common Core Standards for Mathematics
  11. 1.4.1: Kindergarten Standards
  12. 1.4.2: Grade 1 Standards
  13. 1.4.3: Grade 2 Standards
  14. 1.4.4: Grade 3 Standards
  15. 1.4.5: Grade 4 Standards
  16. 1.4.6: Grade 5 Standards
  17. 1.4.7: Grade 6 Standards
  18. 1.4.8: Grade 7 Standards
  19. 1.4.9: Grade 8 Standards
  20. 1.4.10: High School Number and Quantity Standards
  21. 1.4.11: High School Algebra Standards
  22. 1.4.12: High School Functions Standards
  23. 1.4.13: High School Modeling Standards
  24. 1.4.14: High School Geometry Standards
  25. 1.4.15: High School Statistics and Probability Standards
  26. 1.5: Teaching Techniques in Mathematics
  27. 1.5.1: Number and Operations
  28. 1.5.1.1: Introduction
  29. 1.5.1.2: Addition- Dots and Boxes
  30. 1.5.1.3: Subtraction- Dots and Boxes
  31. 1.5.1.4: Multiplication- Dots and Boxes
  32. 1.5.1.5: Division- Dots and Boxes
  33. 1.5.1.6: Number Line Model
  34. 1.5.1.7: Area Model for Multiplication
  35. 1.5.1.8: Properties of Operations (Part 1)
  36. 1.5.1.9: Properties of Operations (Part 2)
  37. 1.5.1.10: Division Explorations
  38. 1.5.1.11: Problem Bank
  39. 1.6: Building a Supportive Math Learning Environment
  40. 1.7: Math Anxiety
  41. 1.8: Assessing and Reflecting on Teaching Practices
  42. 1.9: Common Mistakes Math Teachers Make
  43. 2: Historical Counting Systems
  44. 2.1: Introduction
  45. 2.2: The Number and Counting System of the Inca Civilization
  46. 2.3: The Hindu-Arabic Number System
  47. 2.4: The Development and Use of Different Number Bases
  48. 2.5: The Mayan Numeral System
  49. 2.6: Addition and Subtraction with Other Bases
  50. 2.7: Exercises
  51. 3: The Real Number System
  52. 3.1: Introduction to the Real Number System
  53. 3.2: Whole and Natural Numbers
  54. 3.3: Integer Numbers
  55. 3.4: Rational Numbers
  56. 3.5: Irrational Numbers
  57. 3.6: Real numbers and the Number Line
  58. 3.7: Absolute Value
  59. 3.8: Adding and Subtracting Integers
  60. 3.9: Multiplying and Dividing Integers
  61. 3.10: Fractions
  62. 3.11: Review of Decimals and Percents
  63. 3.12: Exponents and Square Roots
  64. 3.13: Order of Operations
  65. 3.14: Scientific Notation
  66. 3.15: Approximation and Estimation
  67. 3.16: Real Numbers - Algebra Essentials
  68. 3.17: Challenges and Misconceptions
  69. 3.18: Summary and Review
  70. 4: Number Theory
  71. 4.1: Introduction to Number Theory
  72. 4.2: Primes and Composite Numbers
  73. 4.3: The Sieve of Eratosthenes
  74. 4.4: Even and Odd Numbers
  75. 4.5: Factors and GCF
  76. 4.6: Euclidean Algorithm
  77. 4.7: Digital Roots and Divisibility
  78. 4.8: Division Algorithms
  79. 4.9: The Meaning of Multiplication
  80. 4.10: Multiplication Algorithms
  81. 4.11: The Meaning of Division
  82. 4.12: LCM and other Topics
  83. 4.13: Modular Arithmetic
  84. 4.14: Arithmetic Sequences
  85. 4.15: Geometric Sequences and Series
  86. 5: Problem Solving
  87. 5.1: Problem Solving
  88. 5.2: George Pólya's Strategy
  89. 5.3: John Van de Walle's Strategy
  90. 5.4: Marilyn Burns' Strategy
  91. 5.5: Use a Problem-Solving Strategy
  92. 5.6: Recognizing Patterns
  93. 5.7: Beware of Patterns!
  94. 5.8: Careful Use of Language in Mathematics
  95. 5.9: Exercises and Applications
  96. 6: Mathematical Reasoning
  97. 6.1: Introduction on Mathematical Reasoning
  98. 6.2: Types of Reasoning
  99. 6.3: Logical Connectives and Statements
  100. 6.4: Proof Techniques
  101. 6.5: Common Logical Fallicies
  102. 6.6: Strategies for Teaching Mathematical Reasoning
  103. 6.7: Practical Applications
  104. 7: Logic
  105. 7.1: Introduction
  106. 7.2: Statements and Quantifiers
  107. 7.3: Compound Statements
  108. 7.4: Constructing Truth Tables
  109. 7.5: Truth Tables for the Conditional and Biconditional
  110. 7.6: Equivalent Statements
  111. 7.7: De Morgan’s Laws
  112. 7.8: Logical Arguments
  113. 7.9: Chapter Summary
  114. 7.9.1: Key Terms
  115. 7.9.2: Key Concepts
  116. 7.9.3: Videos
  117. 7.9.4: Projects
  118. 7.9.5: Chapter Review
  119. 7.9.6: Reasoning and Logic
  120. 7.9.7: Basic Arguments- Using Logic
  121. 7.9.8: Review Exercises
  122. 7.9.9: Chapter Test
  123. 8: Algebraic Thinking
  124. 8.1: The Language of Algebra
  125. 8.2: Solving Equations with Addition and Subtraction Properties of Equality
  126. 8.3: Solving Equations with the Division and Multiplication Properties of Equality
  127. 8.4: Solving Equations with Variables and Constants on Both Sides
  128. 8.5: General Strategy to Solve Linear Equations
  129. 8.6: Solving Equations with Fractions or Decimals
  130. 8.7: Solving a Formula for a Specific Variable
  131. 8.8: Arithmetic Operations with Functions
  132. 8.9: Graphing and slope
  133. 8.10: Equations of lines
  134. 8.11: Parallel and perpendicular lines
  135. 8.12: System of Equations - Graphing
  136. 8.13: Systems of Equations - The Substitution Method
  137. 8.14: System of Equations - The Addition Method
  138. 8.15: Applications with systems of equations
  139. 9: Probability Topics
  140. 9.1: Introduction
  141. 9.2: Terminology
  142. 9.3: Independent and Mutually Exclusive Events
  143. 9.4: Two Basic Rules of Probability
  144. 9.5: Contingency Tables
  145. 9.6: Tree and Venn Diagrams
  146. 9.7: Probability Topics (Worksheet)
  147. 9.E: Probability Topics (Exericses)
  148. 10: Descriptive Statistics
  149. 10.1: Prelude to Descriptive Statistics
  150. 10.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
  151. 10.3: Histograms, Frequency Polygons, and Time Series Graphs
  152. 10.4: Measures of the Location of the Data
  153. 10.4E: Measures of the Location of the Data (Exercises)
  154. 10.5: Box Plots
  155. 10.6: Measures of the Center of the Data
  156. 10.7: Skewness and the Mean, Median, and Mode
  157. 10.8: Measures of the Spread of the Data
  158. 10.9: Descriptive Statistics (Worksheet)
  159. 10.E: Descriptive Statistics (Exercises)
  160. 11: Geometry
  161. 11.1: Introduction
  162. 11.2: Tangrams
  163. 11.3: Triangles and Quadrilaterals
  164. 11.4: Polygons
  165. 11.5: Platonic Solids
  166. 11.6: Painted Cubes
  167. 11.7: Symmetry
  168. 11.8: Geometry in Art and Science
  169. 11.9: Problem Bank
  170. 12: Congruence and Similarity with Constructions
  171. 12.1: Similar Triangles
  172. 12.1.1: Proportions
  173. 12.1.2: Similar Triangles
  174. 12.1.3: Transversals to Three Parallel Lines
  175. 12.1.4: Pythagorean Theorem
  176. 12.1.5: Special Right Triangles
  177. 12.1.6: Distance from a Point to a Line
  178. 13: Area, Pythagorean Theorem, and Volume
  179. 13.1: Lines
  180. 13.2: Parallelograms
  181. 13.3: Other Quadrilaterals
  182. 13.4: Regular Polygons
  183. 13.5: Circles
  184. 13.6: Metric Units of Measurement
  185. 13.7: Temperature Scales
  186. 13.8: Temperature and Time
  187. 13.8.1: Exercises
  188. 13.9: Dilations on a Square Grid
  189. 13.10: More Dilations
  190. 14: Transformations
  191. Back Matter
  192. Index
  193. Glossary
  194. Detailed Licensing
  195. Detailed Licensing