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Expressions and Equations

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. Tile Bin. 1 unit.

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Expressions and Equations

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  1. Expressions and Equations

  2. 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

  3. What do these tiles represent? 1 unit Tile Bin 1 unit Area = 1 square unit Unknown length, x units Area = x square units 1 unit x units x units Area = x2 square units The red tiles denote negative quantities.

  4. Modeling expressions Tile Bin x + 5 5 + x

  5. Modeling expressions Tile Bin x - 1

  6. Modeling expressions Tile Bin x + 2 2x

  7. Modeling expressions Tile Bin x2 + 3x + 2

  8. Simplifying expressions Tile Bin x2 + x - 2x2 + 2x - 1 zero pair Simplified expression -x2 + 3x - 1

  9. Simplifying expressions Tile Bin 2(2x + 3) Simplified expression 4x + 6

  10. Two methods of illustrating the Distributive Property: Example: 2(2x + 3)

  11. 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 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. 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?

  12. Solving Equations Tile Bin

  13. Solving Equations Tile Bin 6.18 The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions. x + 3 = 5

  14. x + 3 = 5 x + 3 = 5 ̵ 3 ̵ 3 x = 2 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.

  15. Tile Bin 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

  16. Tile Bin 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-steplinear equations. 3 = x - 1

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