The Visual / Auditory / Symbolic / Kinesthetic Approach to Algebra

Represent Expressions. Evaluate Expressions. Verify Statements.

      Once the idea of "a number" is introduced, skills like "evaluate an expressions" and "verify a statement" can easily be coupled with "write and expression or equation." The ideas reinforce each other, but, it is the teacher or the text that decides the blend.

      EVALUATE and VERIFY and "a number" may be introduced BEFORE signed numbers, but, here we assume signed number computation has been introduced.

      Mental computation should be encouraged and the reader is reminded tiles, and manipulative computation, is designed to be outgrown.

      Represent (as shown in "Integer Computation" and below) comes first, then evaluate may stand alone or be required after represent.

1st:Represent the expression to be evaluated in the storage area above the display area.
2nd:Place the value of the variable in the place of the variable in the display area.

      Example 3b. is tricky for some students. It requires one to take the opposite of the number 3. Example 3c. is even more difficult.

Verify or Disprove.
1st:Represent the first number, the minuend.
    Represent each expression in its own display area, positioning the areas because of the relation symbol.
2nd:Move each representation to the storage area just above the display area.
3rd:In each display area, evaluate the expression with the given value of the variable.
5th:Judge if the statement or equation is true.

Verify or disprove.
ex. 6.             If x+2 = 6, then x = 3.
            The statement is false because it would mean 5 is equal to 6.
  • For more info on solutions, see: "Solve A Linear Equation Which Does Not Have a Unique Solution."
  • For more info on inequalities, see: "Solve A Linear Inequality.", Unit 6   © 2008, A. Azzolino