Expressions and Equations

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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.

What do these tiles represent?

Tile Bin

1 unit

1 unit Area = 1 square unit

1 unit

Unknown length, x units

Area = x square units

x units

x units

Area = x2 square units

The red tiles denote negative quantities.

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Modeling expressions

Tile Bin

5 + x

x + 5

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Modeling expressions

Tile Binx - 1

5

Modeling expressions

Tile Binx + 2

2x

6

Modeling expressions

Tile Binx2 + 3x + 2

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Simplifying expressions

Tile Binx2 + x - 2x2 + 2x - 1

zero pairSimplified expression

-x2 + 3x - 1

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Simplifying expressions

Tile Bin2(2x + 3)

Simplified expression

4x + 6

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Two methods of illustrating the Distributive Property:

Example: 2(2x + 3)

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Solving EquationsHow 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 willa) solve one- and two-step linear equations in one variable; andb) 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 EquationsTile Bin

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Solving Equations

Tile Bin x + 3 = 5

6.18 The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions.

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Pictorial Representation:

Symbolic Representation: Condensed Symbolic Representation:

x + 3 = 5

x + 3 = 5 * 3 * 3

x = 2

x + 3 = 5 * 3 * 3

x = 2

6.18 The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions.

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Solving Equations

Tile Bin 2x = 8

6.18 The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions.

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Solving Equations

Tile Bin 3 = x - 1

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.

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Solving Equations