An example on how can be used to help in designing new materials.

After a while of organizing information by term, grade level and page number (URLs for OER materials) on current and past elementary and secondary school mathematics materials, there is always a temptation to be creative with this much information. While actually producing materials is beyond the scope of, as it requires years of working in the learning community that the materials are being developed for. But by examining content from a broad range of materials as does, it does become apparent that there are patterns that dictate where content will appear. Patterns beyond what is the most likely grade level that a content item will appear in. For example, the concept of exponents depends on an understanding that exponents are related to repeated multiplication; and that repeated multiplication requires an understanding of multiplication; and multiplication is, of course, repeated addition; and repeated addition depends on an understanding of what is addition; and finally on counting. The last “sentence” illustrates one of several such patterns that require multiple grade levels to successfully achieve understanding.

With the patterns of information available in, the following provides one version of what content could appear in the Kindergarten to fifth grade materials to “complete” CK-12’s mathematics textbook series. (January 8, 2014)

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    Content, and content distribution (Spreadsheet):

  1. Set, Logic and Basic Number terms:

  2. Whole Numbers terms:

  3. Fraction terms:

  4. Decimal and Integer terms:

  5. Rational, Real and Complex number terms:

  6. Measurement and Standard units terms:

  7. Length, Area, Volume terms:

  8. Point, Line and Angle terms:

  9. Triangle, Quadrilateral, Polygon terms:

  10. Circle, Plane, Polyhedron terms:

  11. Trigonometry, Vector, Transformation Geometry terms:

  12. Relation and Exponent terms:

  13. Coordinate System terms:

  14. Equation and Function terms:

  15. Equations with 2 vaiables and Polynomial terms:

  16. Rational Expressions and Quadratic terms:

  17. Problem Solving and Statistics terms:

  18. Probability and Sequence terms:

  19. Logarithm and Calculus terms:

    Content by grade level:

  1. Kindergarten (Average age: 5 years old)

  2. First grade (Average age: 6 years old)

  3. Second grade (Average age: 7 years old)

  4. Third grade (Average age: 8 years old)

  5. Fourth Grade (Average age: 9 years old)

  6. Fifth Grade (Average age: 10 years old)

The mathematics terms (or their synonyms) that are used in the following spreadsheets are part of the lesson proper. Lesson proper means the explanation or the development of the terms through an interaction between teacher and learner. In learning communities where written textbooks exist, the interaction is aided by a written explanation using the terms.

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