 The Visual / Auditory / Symbolic / Kinesthetic Approach to Algebra

 Even Before Representation

Manipulatives Theory
Unit 1. Term Tiles - OVERVIEW Unit 1. Tiles, Tokens, & Toys Unit 1. Manipulatives As A Language Unit 1. Manipulative Use Unit 2. Play, Work, Visualize, Debrief, Extend Unit 2. Longer Assignments and Projects Term Tiles & Tokens Work Areas - READ THIS
Unit 3. Storing Tiles During Use Unit 3. Display Areas During Use Unit 3. Moving Tiles Signed Number & Math Suggestions
Unit 4. Skip Manipulative Use If Your Students Already Know The Material Unit 4. Think Money Unit 4. The Good Guys and The Bad Guys Or ģ Unit 4. The Signed Number Hundreds Board Representation & Tough Topics to Teach
Unit 5. A Number Unit 5. Zero Unit 5. The Opposite Unit 5. "Zero In" and "Zero Out" to Simplify. Unit 6. Represent Expressions. Evaluate Expressions. Verify Statements. Unit 7. More, Less, The Sum, The Difference, Double, Triple Unit 8. "Five Decreased by a Number" Vs. "A Number Decreased by Five" Unit 9. "The Other Number If The Sum Of Two Numbers Is Five" Unit 10. Of: The Opposite of ģ, Two Of ģ, The Square Of ģ Unit 11. Perimeter and Area Unit 11. Vocabulary Unit 11. Tile Representation of Area Unit 11. Tile Representation of Perimeter Unit 12. Exercises Creation & Interpretation
Unit 13. Make Experts Using Creation and Interpretation Activities. Unit 13. Digital Manipulatives Spread Sheets
tiles.xls create.xls hot.xls Operation

Integer Computation
Unit 14. Integer Addition Unit 14. Integer Subtraction Unit 15. Integer Multiplication Unit 15. Integer Division Algebraic Computation & Factoring
Unit 16. Algebraic Addition Unit 16. Algebraic Subtraction By "Adding the Opposite" Using "Take Away" Unit 17.Distributive Property of Multiplication over Addition Unit 17.Algebraic Multiplication Unit 18.Algebraic Division Unit 19.Factoring Factor - A Noun and A Verb Algebraic Factoring Unit 20. Special Products Unit 20. Binomial Squared and Cubed Unit 20. Binomial Squared Unit 20. Binomial Cubed Unit 20. The Squares and Cubes of the Sums and Differences of Two Numbers Unit 21. Sums and Differences of Squares and Cubes Unit 21. Difference Two Squares Unit 21. Sum of Two Squares Unit 21. Difference of Two Cubes Unit 21. Sum of Two Cubes Solution of Equations and Inequalities

Unit 22. Solve Equations and Inequalities. Unit 22. Solve A Linear Equation By Undoing One Operation. Unit 23. Solve A Linear Equation By Undoing Two or More Operations. Unit 24. Solve All Linear Equations. Unit 25. Solve A Linear Inequality. Unit 26. Solve A Quadratic Unit 27. Solve A Proportion. Unit 30. Rational Expressions, Fractions Unit 28. Fraction Representation and Computation
Unit 29. Represent Rational Expressions Unit 29. Tilted Tile Display Unit 29. Numerator / Denominator Display Unit 30. Multiples, Equivalent Fractions, Reduced Fractions Unit 30. Term Tiles Require Multiplication to Create Equivalent Fractions. Unit 31. Reduced Fractions Unit 10. (A-B)/(B-A) is -1. Unit 32. Add Two Fractions Unit 33. Subtract Two Fractions Unit 34. Multiply Fractions and Mixed Numbers Unit 35. Divide Two Fractions Unit 36. Solve An Equation with Fractions. Unit 39. Find A Common Denominator. Unit 37. Solve A Linear System Unit 38. Solve A Linear System by Substitution. Unit 39. Solve A linear System by Linear Combination. Extend the Pattern.

Unit 40. Dimensions Unit 41. Sets of Numbers Unit 42. Factorial, Permutations, Combinations Unit 43. Binomial Expansion Presented Symbolically and Pascal's Triangle Unit 44. Term Tiles and Binomial Expansions Appendix / Masters

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