Using Algebra Tiles - Texas State University System: Mathematics
Transcript of Using Algebra Tiles - Texas State University System: Mathematics
![Page 1: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/1.jpg)
Using Algebra Tiles
You Can “Feel”
the Mathematics
Sandra Richardson , Ph.D.Dept. of Mathematics
Lamar UniversityBeaumont, TX
![Page 2: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/2.jpg)
2
TEKS & Algebra Tiles
Grade 7: 7.1(C), 7.2(C), 7.5A
Grade 8: 8.14
Algebra I: A.4, A.10, C.3(B), C.4(B), D.2(A)
Algebra II: C.2(E)
![Page 3: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/3.jpg)
3
3 Tiles
x
x Area of large square = x (x) = x2
x Area of rectangle = 1 (x) = x
Area of small square = 1 (1) = 1
1
11
Each tile represents an area.
![Page 4: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/4.jpg)
4
Units Tile
X Tile
X2 Tile
POSITIVE ALGEBRA TILES NEGATIVE ALGEBRA TILES
![Page 5: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/5.jpg)
5
Algebra Tiles Template
![Page 6: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/6.jpg)
6
Big Ideas Using Algebra Tiles
A & S Integers; Zero PrincipleModeling Linear Expressions Solving Linear Equations Simplifying Polynomials Solving Equations for Unknown Variable M & D PolynomialsCompleting the Square Investigations
![Page 7: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/7.jpg)
7
Additive Inverses
A combined negative and positive tile of the same area produces a zero pair.
![Page 8: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/8.jpg)
8
Use Algebra Tiles to Model Integer Addition
2 + 1 =
-2 + -1 =
![Page 9: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/9.jpg)
9
Use Algebra Tiles to Model Integer Addition
3 + -1 =
3 + -3 =
![Page 10: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/10.jpg)
10
Use Algebra Tiles to Model Integer Subtraction
5 – 2 =
-4 – (-3) =
![Page 11: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/11.jpg)
11
Use Algebra Tiles to Model Integer Subtraction
3 – (-5)
-4 – 1
![Page 12: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/12.jpg)
12
MODELING LINEAR EXPRESSIONS
![Page 13: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/13.jpg)
13
Grouping with Algebra TilesEx: 3x means 3 rows of x
3x - 6 means 3 rows of x and 6 negative units
**Try representing 2x2 + X - 3
![Page 14: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/14.jpg)
14
Distributive Property
3(X + 2)
3(X – 4)-2(X + 2)-3(X – 2)
![Page 15: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/15.jpg)
15
Simplifying Polynomials
Simplify 2x + 4 + x + 2.
Simplify -3x + 1 + x + 3.
Simplify (2x2 – 2x + 3) – (3x2 + 3x – 2).
![Page 16: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/16.jpg)
16
SOLVING EQUATIONS
![Page 17: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/17.jpg)
17
Use Algebra Mats to Solve Equations
![Page 18: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/18.jpg)
18
Use algebra tiles to find value of X.
X + 2 = 3
Try 2X – 4 = 8.
![Page 19: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/19.jpg)
19
Use algebra tiles to find value of X.
2X + 3 = X – 5
![Page 20: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/20.jpg)
20
Substitution
Evaluate 3 + 2x if x = 4
Evaluate 3 - 2x if x = -4
![Page 21: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/21.jpg)
21
MULTIPLYING POLYNOMIALS
![Page 22: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/22.jpg)
22
Multiplying Polynomials
(x + 2)(x + 3)
![Page 23: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/23.jpg)
23
Multiplying Polynomials
(x – 1)(x +4)
![Page 24: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/24.jpg)
24
Multiplying Polynomials
(x + 2)(x – 3)
(x – 2)(x – 3)
![Page 25: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/25.jpg)
25
FACTORING POLYNOMIALS
![Page 26: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/26.jpg)
26
Factoring Polynomials
3x + 3
2x – 6
![Page 27: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/27.jpg)
27
Factoring Polynomials
x2 + 6x + 8
![Page 28: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/28.jpg)
28
Factoring Polynomials
x2 – 5x + 6
![Page 29: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/29.jpg)
29
Factoring Polynomials
x2 – x – 6
![Page 30: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/30.jpg)
30
Factoring Polynomials
x2 + x – 6 x2 – 1 x2 – 4 2x2 – 3x – 2 2x2 + 3x – 3 -2x2 + x + 6
![Page 31: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/31.jpg)
31
DIVIDING POLYNOMIALS
![Page 32: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/32.jpg)
32
Dividing Polynomials
x2 + 7x +6x + 1
![Page 33: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/33.jpg)
33
Dividing Polynomials
x2 + 7x +6x + 1
2x2 + 5x – 3x + 3
x2 – x – 2x – 2
x2 + x – 6x + 3
![Page 34: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/34.jpg)
34
INVESTIGATIONS
![Page 35: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/35.jpg)
35
Investigations with Algebra Tiles
Use algebra tiles to show that (x + 1)2 and (x2 +1) are not equivalent.
(x + 1)2 = (x+1)(x+1) = x2 + 2x + 1
x2 +1
![Page 36: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/36.jpg)
36
COMPLETING THE SQUARE
![Page 37: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/37.jpg)
37
Using Algebra Tiles to Complete Square
What is needed to create a perfect square trinomial for x2 + 4x + ?
Use algebra tiles to create a square. What tiles will be needed to complete the square?
?
![Page 38: Using Algebra Tiles - Texas State University System: Mathematics](https://reader035.fdocuments.us/reader035/viewer/2022071600/613d0ed1736caf36b758d034/html5/thumbnails/38.jpg)
38
Completing the Square
What is needed to create a perfect square trinomial for x2 - 6x + ?