The Visual / Auditory / Symbolic / Kinesthetic Approach to Algebra

For PreAlgebra & Early Algebra I


1st: Introduce yourself to those around you, your partners.
2nd: Sort the Tiles and Tokens in descending order.
3rd: Think of one topic in which you could use tiles to enhance the presentation.
4th: Share your choice and strategy of presentation with partners.


Manipulatives are made to be outgrown.
Consider manipulatives as a language.
Introduce with the concrete (manipulative).
Summarize with the abstract (pictures, written and spoken words and symbols).


A Number , Zero, The Opposite
"Zero In" and "Zero Out" to Simplify.
Qu. 1 - 3: Represent then simplify.
1. three
2. three in a way not already used
3. a number
4. double the value of three less than a number
Qu. 5 - 6: Prepare to explain out loud
5. how to simplify the given expression.
6. a starting expression, what was done, the final expression for the work below.
Qu. 7 - 10: Represent
7. four decreased by a number
8. four increased by a number
9. a number decreased by four
10. double the sum of a number and three
Tough Topics to Teach
  • "Five Decreased by a Number" Vs. "A Number Decreased by Five"
  • Of: The Opposite of , Two Of , The Square Of
  • "The Other Number If The Sum Of Two Numbers Is Five"
  • Perimeter and Area
To Improve OPERATION skills, spend more time with REPRESENTATION.


by "Signed Number Board,"
by "take away," and by "add the opposite."
Multiply and Distribution
Add, Subtract, Simplify, Combine Like Terms
Subtract (x+1) - (2x+3)
Simplify (x-4) - (-3x+2)
Simplify (x +2x-4) - (2x +3)
Algebraic Division
Factor x - 4
Factor 2x-x-6
Evaluate when x is ... and Verify ...
Solve linear equations.
Solve x/4 = 2
Solve -x = -4
Solve 3 + 2x = -1
Solve A Linear Inequality.
Solve -2x > 4.
Solve A Quadratic
Solve x² + 5x = -6.
Solve A Proportion.


Current Tile Set: front back
See for more info.

www.   © 2008, A. Azzolino