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Math 27: Number Systems for Educators

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Math 27: Number Systems for Educators

This text focuses on the development of quantitative reasoning skills through in-depth, integrated explorations of topics in mathematics, including real number systems and subsystems. Emphasis is on comprehension and analysis of mathematical concepts and applications of logical reasoning. (Photo Credit: by Joshua Eckstein on Unsplash)

Mathematics
Author
Ashley McHale
Publisher
Las Positas College
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 111 sections
  1. 01: Overview of Elementary Common Core Mathematics
  2. 1.01: How to Read this Textbook
  3. 1.02: The Importance of Mathematics for Elementary School Students
  4. 1.03: How Did We Get Here
  5. 1.04: Showing Students' Thinking
  6. 02: Problem Solving
  7. 2.01: Introduction to Problem Solving
  8. 2.02: Problem or Exercise
  9. 2.03: Problem Solving Strategies
  10. 2.3.01: George Polya's Four Step Problem Solving Process
  11. 2.04: Beware of Patterns
  12. 2.05: Problem Bank
  13. 2.06: Careful Use of Language in Mathematics
  14. 2.07: Explaining Your Work
  15. 2.08: The Last Step
  16. 03: Numeration Systems and Bases
  17. 3.01: The Why
  18. 3.02: Units of Measurement
  19. 3.03: Historical Counting Systems
  20. 3.3.01: Introduction and Basic Number and Counting Systems
  21. 3.3.02: The Number and Counting System of the Inca Civilization
  22. 3.3.03: The Hindu-Arabic Number System
  23. 3.3.04: The Development and Use of Different Number Bases
  24. 3.3.05: The Mayan Numeral System
  25. 3.3.06: Roman Numerals
  26. 3.3.07: Exercises
  27. 3.04: Different Bases and Their Number Lines
  28. 3.05: Converting Between (our) Base 10 and Any Other Base (and vice versa)
  29. 3.06: Place Values with Different Bases
  30. 3.07: Operations in Different Bases
  31. 04: Arithmetic and Mental Mathematics
  32. 4.01: The Why
  33. 4.02: Addition and Subtraction
  34. 4.03: Multiplication
  35. 4.04: Division
  36. 4.05: Estimation and Rounding
  37. 4.06: Personal Referents
  38. 4.07: Calculating Percentages
  39. 4.08: Extension - Methods of Teaching Mathematics
  40. 05: Rational Numbers
  41. 5.01: The Why
  42. 5.02: What are Fractions
  43. 5.03: Add Subtract Multiply and Divide Fractions
  44. 5.04: Understanding Fractions With The C-Strips
  45. 5.05: Rational Numbers
  46. 5.06: Facts About Comparing Fractions
  47. 5.07: Decimals
  48. 5.08: Definition of Real Numbers and the Number Line
  49. 5.09: Models and Operations with Integers
  50. 5.10: Number comparisons using and
  51. 5.11: Homework
  52. 06: Number Theory
  53. 6.01: The Why
  54. 6.02: Number Theory
  55. 6.03: Divisibility Rules
  56. 6.3.01: Digital Roots and Divisibility
  57. 6.04: Primes and GCF
  58. 6.05: The Greatest Common Factor
  59. 6.06: LCM and other Topics
  60. 6.07: The Least Common Multiple
  61. 6.08: Homework
  62. 07: Geometry
  63. 7.01: The Why
  64. 7.02: Introduction
  65. 7.03: Tangrams
  66. 7.04: Triangles and Quadrilaterals
  67. 7.05: Polygons
  68. 7.06: Polygons
  69. 7.07: Linear Unit Conversions
  70. 7.08: Platonic Solids
  71. 7.09: Painted Cubes
  72. 7.10: Symmetry
  73. 7.11: Area Surface Area and Volume
  74. 7.12: Area Surface Area and Volume Formulas
  75. 7.13: Geometry in Art and Science
  76. 7.14: Problem Bank
  77. 08: Additional Activities
  78. 8.01: 1. Power of Patterns- Domino Tiling
  79. 8.02: 2. Regular Tiling
  80. 8.03: 3. Festive Folding
  81. 8.04: 4. Platonic Solids
  82. 8.05: 5. Egyptian Pizza
  83. 8.06: Semi Regular Tilings
  84. 09: Appendix
  85. 9.01: Appendix A- Common Core State Standards Mathematics K-6
  86. 9.02: Appendix B- Mathematical Practices for Teachers
  87. 9.03: Appendix C- Solutions for Partner Activities
  88. 9.04: Appendix D- Solutions to Practice Problems
  89. 9.05: Appendix E- Material Cards (Harland)
  90. 9.5.01: Coins
  91. 9.5.02: A-Blocks
  92. 9.5.03: Value Label Cards
  93. 9.5.04: Models for Base Two
  94. 9.5.05: Unit Blocks
  95. 9.5.06: Base Two Blocks
  96. 9.5.07: Base Three Blocks
  97. 9.5.08: Base Four Blocks
  98. 9.5.09: Base Five Blocks
  99. 9.5.10: Base Six Blocks
  100. 9.5.11: Base Seven Blocks
  101. 9.5.12: Base Eight Blocks
  102. 9.5.13: Base Nine Blocks
  103. 9.5.14: Base Ten Blocks
  104. 9.5.15: Base Eleven Blocks
  105. 9.5.16: Base Twelve Blocks
  106. 9.5.17: Supplementary Longs
  107. 9.5.18: Centimeter Strips
  108. 9.5.19: Counters
  109. 9.5.20: Number Squares
  110. 9.5.21: Fraction Circles
  111. 9.5.22: Strips and Arrays