Contents of This Table of Contents  
 Even Before Representation
 Manipulatives Theory
 Term Tiles & Tokens Work Areas  READ THIS
 Signed Number & Math Suggestions
 REPRESENTATION & Tough Topics to Teach
 OPERATION
 CREATION & INTERPRETATION
 Integer Computation
 Algebraic Computation & Factoring
 Solution of Equations and Inequalities
 Advanced Topics  Fractions, Linear Systems, Binomial Expansion
 Appendix / Masters
 Source Material
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 …
 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 …, Two Of …, The Square Of …
 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
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.
 Undo addition.
 Undo subtraction.
 Undo division.
 Undo multiplication.
 Undo multiplication by 1.
 Undo multiplication by a fraction.
Unit 23. Solve A Linear Equation By Undoing Two or More Operations.
 Undo more than one operation.
 Solve an equation with a binomial on each side.
 Solve an equation with complicated expressions on each side.
Unit 24. Solve All Linear Equations.
 Solve an equation with 1 solution.
 Solve an equations with no solution.
 Solve an equation in which all numbers are solutions.
Unit 25. Solve A Linear Inequality.
Unit 26. Solve A Quadratic
Unit 27. Solve A Proportion.
 Remind Me. Why Is It Legal to Cross Multiply?
 Check for extraneous roots.
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. (AB)/(BA) 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
 Contents
 Basic Tile & Token Set:
front
back
 Extended Tile & Token Set:
front
back
 Additional Variable Tile & Token Set:
front
back
 Paper Folded Solids
x³ and a 1 cube 
x³ 1 cube  
x², x, y², y, and 1 
x², x, y², y, and 1

x²y 
x²y  
xy² 
xy² 
y³ and y³  
 Digital Manipulatives Spread Sheets:
(for students, basic tiles only) tiles.xls
(for students, basic + hot cells) create.xls
(for teacher and to supplement students', all tiles, tokens, hot cells) hot.xls
(for teacher to demonstrate the cube of the sum or difference of two numbers) cubes.xls
 A Journey with SelfAssessment as a Compass,
and related pages © 1995, 1998, 2001, A. Azzolino
and related pages
 "algebraic fractions" © 2006 A. Azzolino
 Algebraic inequalities & graphing on a number line, © March 2008, A. Azzolino
 area © 2005, Agnes Azzolino
 Common Denominator, © 2006, Agnes Azzolino
 compute.xls, © 2008, A. Azzolino
 Features of the Languages of the Math Classroom © 1998, 2005 Agnes Azzolino
 I Got Your Number, RATIONAL Computation, © 2005, Agnes Azzolino
 MATH SPOKEN HERE!  an arithmetic and algebra dictionary © 2005, Agnes Azzolino
 Multiple Strips & Fraction Bars, © 2005, Agnes Azzolino
 Multiples, © 2005, Agnes Azzolino
 "Options" © 2008, Agnes Azzolino
 perimeter © 2005, Agnes Azzolino
 prime.xls, © 2003, 2008, A. Azzolino
 "Remind Me Why "Invert and Multiply" Works When Dividing Fractions." © 2008 A. Azzolino
 So, What Is A Fraction? © 2005, Agnes Azzolino
 "Solve A Systems of Linear Equations by Substitution" © 2008, A. Azzolino
 Solve linear equation w/many operations  page 3, © 2005, A. Azzolino
 Solve linear equation w/more than one operation in the expression, pg 2, © 2007, A. Azzolino
 Solve linear equation w/paper & pencil, © 2005, 2007, A. Azzolino
 "Solving Quadratics" © 2007, Agnes Azzolino
 Spreadsheet Notes & Index © 2006, Agnes Azzolino
 "The distance formulas used for a line, a plane, or in space" © 2003, 2006, 2007 A. Azzolino
 The Hundreds Board, © '98, '01, Agnes Azzolino
 "Use Linear Combination to Solve Systems of Equations and Inequalities" © 2004, A. Azzolino
 Write 21, © September 29, 2003, A. Azzolino
 Writing one operation equations, expressions, statements, © 2001, 2007, A. Azzolino
 Written notes on factoring, © 2005, A. Azzolino
