Download Expressions and Equations with Tiles

Expressions and Equations
A Look At Expressions and Equations
A manipulative, like algebra tiles,
creates a concrete foundation for the
abstract, symbolic representations
students begin to wrestle with in
middle school.
2
What do these tiles represent?
1 unit
Area = 1 square unit
1 unit
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Unknown length, x units
Area = x square units
1 unit
x units
x units
Area = x2 square units
The red tiles denote negative quantities.
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Modeling expressions
x+5
5+x
4
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Modeling expressions
x-1
5
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Modeling expressions
x+2
2x
6
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Modeling expressions
x2 + 3x + 2
7
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Simplifying expressions
x2 + x - 2x2 + 2x - 1
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zero pair
Simplified expression
-x2 + 3x - 1
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Simplifying expressions
2(2x + 3)
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Simplified expression
4x + 6
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Two methods of illustrating the Distributive
Property:
Example: 2(2x + 3)
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Solving Equations
How does this concept progress as we move through middle school?
6th grade:
6.18 The student will solve one-step linear equations in one variable involving whole
number coefficients and positive rational solutions.
7th grade:
7.14 The student will
a)
solve one- and two-step linear equations in one variable; and
b)
solve practical problems requiring the solution of one- and two-step linear equations.
8th grade:
8.15 The student will
a) solve multistep linear equations in one variable on one and two sides of the
equation;
b) solve two-step linear inequalities and graph the results on a number line; and
c) identify properties of operations used to solve an equation.
** What does this mean for Course 2 students who go to Algebra 1?
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Solving Equations
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Solving Equations
6.18 The student will solve one-step linear equations in one variable involving whole
number coefficients and positive rational solutions.
x+3=5
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Solving Equations
6.18 The student will solve one-step linear equations in one variable involving whole
number coefficients and positive rational solutions.
Pictorial Representation:
Symbolic Representation:
Condensed Symbolic Representation:
x+3=5
x+3=5
̵3 ̵3
x=2
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x+3=5
̵3 ̵3
x=2
Solving Equations
6.18 The student will solve one-step linear equations in one variable involving whole
number coefficients and positive rational solutions.
2x = 8
15
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Solving Equations
7.14
The student will solve one- and two-step linear equations in one variable;
and solve practical problems requiring the solution of one- and two-step linear equations.
3=x-1
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