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
- 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|
- 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
- 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
- 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.
- Undo addition.
- Undo subtraction.
- Undo division.
- Undo multiplication.
- Undo multiplication by -1.
- Undo multiplication by a fraction.
Unit 24. Solve All Linear Equations.
- Undo more than one operation.
- Solve an equation with a binomial on each side.
- Solve an equation with complicated expressions on each side.
Unit 25. Solve A Linear Inequality.
- Solve an equation with 1 solution.
- Solve an equations with no solution.
- Solve an equation in which all numbers are solutions.
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 37. Solve A Linear System
- 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.
Extend the Pattern.
- Unit 38. Solve A Linear System by Substitution.
- Unit 39. Solve A linear System by Linear Combination.
- 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
- Basic Tile & Token Set:
- Extended Tile & Token Set:
- Additional Variable Tile & Token Set:
- Paper Folded Solids
|x³ and a 1 cube ||
-x³ -1 cube |
x², x, y², y, and 1 ||
-x², -x, -y², -y, and -1
|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 Self-Assessment 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