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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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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)
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)
Name: ________________________ Multiplication of Real Numbers Date: ___________3.
Problem ModelWritten Description of
ProcedureMathematical Procedure
(Algorithm)
(+2)(+3)
(+3)(-4)
(-2)(+3)
(-3)(-1)
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.
Expression Tile ModelWritten Description of
Procedure
Mathematical Procedure
(Algorithm)3(x + 2)
3(x – 4)
-2(x + 2)
-3(x – 2)
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
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
Name: ____________________ Solving/Modeling Equations using Algebra Tiles Date: ___________ 8.
Equation Tile ModelWritten Description of
ProcedureMathematical Procedure
(Algorithm)
x + 2 = 3
-5 = 2x
2 x + 3 = x – 5 9.
3(x – 1) + 5 = 2x – 2
Name: _________________ Solving/Modeling Equations using Algebra Tiles (Jigsaw Date: _________ 10.
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
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
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
Expressions Tile Model Mathematical Procedure (Algorithm)
(x – 2)(x – 3)
3x + 3
2x – 6
x2 + 6x + 8
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)???
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
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