OBJECTIVES
Provide a visual model to help students develop conceptual understanding for variables as unknown values.
Build conceptual understanding of solving equations.
Construct meaning for algebraic solutions of equations.
The value of each piece is determined by its area.
A new piece is created by developing
a new dimension, “x”.
for practical reasons, “x” is not a multiple of the dimension
representing “1”.
The value of this piece is
x, because 1 x = x.
ALGEBRAIC EXPRESSIONS
1
x
MODEL THE EXPRESSION
-2(3x -1) Begin inside the parenthesis.
-6x + 2
3x - 1 There are two sets,
and their signs are opposite of the
originals.
SOLVING EQUATIONSMODEL 2x + 1 = 5
To solve, SUBTRACT 1 tile from each side. NEW EQUATION 2x = 4
Isolate x by DIVIDING into two groups
=
x = 2
2x = 4
x = 2
SOLVING EQUATIONS
2x + 3 = 7
2x = 4 2 2
Subtract 3 from each side of the equationDivide by 2 on each side of the
equation
The operations and the result are exactly the same.
x = 2=-3 -3