Algebra Tiles Pp Version 2

Let’s Do Algebra Tiles REL HYBIRD ALGEBRA RESEARCH PROJECT Adapted from David McReynolds, AIMS PreK-16 Project and Noel Villarreal, South Texas Rural Systemic Initiative November , 2007

Algebra Tiles ,[object Object],[object Object],[object Object]

Algebra Tiles ,[object Object],[object Object],[object Object],[object Object]

Algebra Tiles ,[object Object],[object Object]

Zero Pairs ,[object Object],[object Object],[object Object]

Addition of Integers ,[object Object],[object Object],[object Object],[object Object],[object Object]

Addition of Integers ,[object Object],[object Object],[object Object],[object Object]

Addition of Integers ,[object Object],[object Object],[object Object],[object Object],[object Object],+2 -1

Subtraction of Integers ,[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Subtraction of Integers -1 +3

Subtracting Integers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],+8 -5

Subtracting Integers ,[object Object],[object Object],[object Object]

Multiplication of Integers ,[object Object],[object Object],[object Object],[object Object],[object Object]

Multiplication of Integers ,[object Object],[object Object],[object Object],Two groups of three positives Three groups of four negatives +6 +12

Multiplication of Integers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],= -6 = +3

Multiplication of Integers ,[object Object],[object Object]

Division of Integers ,[object Object],[object Object],[object Object]

Division of Integers ,[object Object],[object Object],[object Object],[object Object]

Division of Integers ,[object Object],[object Object],[object Object],[object Object],[object Object],-5

Division of Integers ,[object Object],[object Object],+4

Polynomials ,[object Object],[object Object]

Distributive Property ,[object Object],[object Object],[object Object],[object Object]

Distributive Property ,[object Object],[object Object],[object Object],3 · x + 3 · 2 = 3 x + 6

Modeling Polynomials ,[object Object],[object Object],[object Object]

More Polynomials ,[object Object],[object Object],[object Object],[object Object]

More Polynomials ,[object Object],[object Object]

More Polynomials ,[object Object],[object Object],[object Object]

More Polynomials ,[object Object],Combine like terms to get three x ’s and five positives = 3 x + 5

Substitution ,[object Object],[object Object]

Substitution ,[object Object],[object Object],[object Object],[object Object],let x = 4

Solving Equations ,[object Object],[object Object],[object Object]

Solving Equations ,[object Object],[object Object],[object Object],[object Object],-2 -2 x = 1

Solving Equations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Solving Equations ,[object Object],[object Object],[object Object],· -1 · -1

Solving Equations ,[object Object],[object Object],[object Object],• 3 • 3 x = - 6

Solving Equations ,[object Object],[object Object],[object Object],[object Object],- x - x x + 3 = -5 + -3 + - 3 x = -8

Solving Equations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Multiplication ,[object Object],[object Object],[object Object],[object Object]

Multiplication using “Area Model” ,[object Object],[object Object],10 x 10 = 10 2 = 100 10 x 2 = 20 10 x 3 = 30 2 x 3 = 6 10 x 2 = 20

Multiplying Polynomials ,[object Object],x 2 + 2 x + 3 x + 6 = x 2 + 5 x + 6 Fill in each section of the area model Combine like terms

Multiplying Polynomials ,[object Object],= x 2 + 3 x – 4 Fill in each section of the area model Make Zeroes or combine like terms and simplify x 2 + 4 x – 1 x – 4

Multiplying Polynomials ,[object Object],[object Object]

Factoring Polynomials ,[object Object],[object Object],[object Object],[object Object]

Factoring Polynomials ,[object Object],[object Object],= 3 · ( x + 1) = 2 · ( x – 3) Note the two are positive, this needs to be developed

Factoring Polynomials ,[object Object],= ( x + 2)( x +4)

Factoring Polynomials ,[object Object],= ( x – 2)( x – 3)

Factoring Polynomials ,[object Object],= ( x + 2)( x – 3)

Factoring Polynomials ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Dividing Polynomials ,[object Object],[object Object],[object Object]

Dividing Polynomials ,[object Object],[object Object],= ( x + 6)

Dividing Polynomials ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Conclusion ,[object Object],[object Object],[object Object],[object Object]

Resources ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Algebra Tiles Pp Version 2

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