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Name: ____________________________ Addition/Subtraction of Real Numbers Date: ___________ 1. Expression Tile Model Written Description of Procedure Mathematical Procedure (Algorithm) (+3) + (+1) (-2) + (-1) (+3) + (-1) (+3) + (-4)

Algebra tiles graphic organizers

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Different ways of organizing work for students using algebra tiles and modeling in mathematics. The worksheets are designed to intentionally connect the model, student thinking (through written explanation), and the mathematical algorithm.

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Page 1: Algebra tiles graphic organizers

Name: ____________________________ Addition/Subtraction of Real Numbers Date: ___________1.

Expression Tile ModelWritten Description of

Procedure

Mathematical Procedure

(Algorithm)

(+3) + (+1)

(-2) + (-1)

(+3) + (-1)

(+3) + (-4)

Page 2: Algebra tiles graphic organizers

Name: ____________________________ Addition/Subtraction of Real Numbers Date: ___________2.

Expression Tile ModelWritten Description of

Procedure

Mathematical Procedure

(Algorithm)(+5) – (+2)

(-4) – (-3)

(+3) – (-5)

(-4) – (+1)

(+3) – (-3)

Page 3: Algebra tiles graphic organizers

Name: ________________________ Multiplication of Real Numbers Date: ___________3.

Problem ModelWritten Description of

ProcedureMathematical Procedure

(Algorithm)

(+2)(+3)

(+3)(-4)

(-2)(+3)

(-3)(-1)

Page 4: Algebra tiles graphic organizers

Name: ________________________ Division of Real Numbers Date: ___________4.

Problem ModelWritten Description of

ProcedureMathematical Procedure

(Algorithm)

(+6)/(+2)

(-8)/(+2)

(+10)/(-2)

(-12)/(-3)

Name: ____________________ Simplifying the Distributive Property using Algebra Tiles

Date: ___________5.

Page 5: Algebra tiles graphic organizers

Expression Tile ModelWritten Description of

Procedure

Mathematical Procedure

(Algorithm)3(x + 2)

3(x – 4)

-2(x + 2)

-3(x – 2)

Page 6: Algebra tiles graphic organizers

Name: _________________ Simplifying Polynomials using Algebra Tiles Date: ___________ 6.

Expressions Tile Model Mathematical Procedure (Algorithm)

2x + 3

4x – 2

2x + 4 + x + 2

- 3x + 1 + x + 3

Page 7: Algebra tiles graphic organizers

Name: _________________ Simplifying Polynomials using Algebra Tiles Date: ___________ 7.

Expressions Tile Model Mathematical Procedure (Algorithm)

3x – 1 – 2x + 4

(2x2 + 5x – 3) + (-x2 + 2x + 5)

(2x2 – 2x + 3) – (3x2 + 3x – 2)

Substitution:3 + 2x for x = 4

Page 8: Algebra tiles graphic organizers

Name: ____________________ Solving/Modeling Equations using Algebra Tiles Date: ___________ 8.

Equation Tile ModelWritten Description of

ProcedureMathematical Procedure

(Algorithm)

x + 2 = 3

-5 = 2x

Page 9: Algebra tiles graphic organizers

2 x + 3 = x – 5 9.

3(x – 1) + 5 = 2x – 2

Name: _________________ Solving/Modeling Equations using Algebra Tiles (Jigsaw Date: _________ 10.

Page 10: Algebra tiles graphic organizers

Page 1)

Equation Tile ModelWritten Description of

ProcedureMathematical Procedure

(Algorithm)

2x = -8

1. One negative x is equal to 52. Take the opposite of each side of the equation3. One x is equal to five negative units

3x = 2 + x -x -x2x = 2 ÷2 ÷ 2 x = 1

Name: _________________ Solving/Modeling Equations using Algebra Tiles (Jigsaw

Page 2)Date: ___________11

Page 11: Algebra tiles graphic organizers

Equation Tile ModelWritten Description of

ProcedureMathematical Procedure

(Algorithm)

2x + 1 = 5

1. Three negative x’s and two units are same as 52. Subtract two units from each side of the equation3. Divide both sides of the equation into two equal groups4. Flip both sides of the equation to make them opposites5. One x is equal to one negative unit

2 x - 3 = 2 + x -x -x x – 3 = 2

+3 +3x = 5

Page 12: Algebra tiles graphic organizers

Name: _________________ Multiplying Polynomials using Algebra Tiles Date: __________12

Expressions Tile Model Mathematical Procedure (Algorithm)

(12)(13) = (10+2)(10+3)

(x + 2)(x + 3)

(x – 1)(x +4)

(x + 2)(x – 3)

Name: _________________ Multiplying/Factoring Polynomials using Algebra Tiles Date: __________13

Page 13: Algebra tiles graphic organizers

Expressions Tile Model Mathematical Procedure (Algorithm)

(x – 2)(x – 3)

3x + 3

2x – 6

x2 + 6x + 8

Page 14: Algebra tiles graphic organizers

Name: _________________ Multiplying/Factoring Polynomials using Algebra Tiles Date: __________14

Expressions Tile Model Mathematical Procedure (Algorithm)

x2 – 5x + 6

x2 – x – 6

x2 + x – 6

x2 – 1

x2 – 4

2x2 – 3x – 2

2x2 + 3x – 3

-2x2 + x + 6

Name: _________________ Dividing Polynomials using Algebra Tiles Date: __________15

Expressions Tile Model Mathematical Procedure (Algorithm)???

Page 15: Algebra tiles graphic organizers

x 2 + 7 x +6 x + 1

x 2 + 7 x +6 x + 1

2 x 2 + 5 x – 3 x + 3

x 2 – x – 2 x – 2

x 2 + x – 6 x + 3

Name: _______________________ Addition of Fractions (Jigsaw Page) Date: ___________16

Problem Model Simplified Mathematical Procedure(Algorithm) Simplify

Page 16: Algebra tiles graphic organizers

Model

½ + ¾

2/3 + 1/6

(2/3 • 2/2 = 4/6)4/6 + 1/6

5/6

9/6 = 1 3/6

1 3/6 = 1 1/2