Algebra Tiles Powerpoint
By
Jon Hyatt
Created 3 years ago
Duration 0:00:00
1024
NUCC lesson shared with Utah Teachers through PBWorks Wiki as part of Secondary Math II; TOPIC: Algebra Tiles

Embed

Social
Select the file type you wish to download
Slide Content

Slide 1  Let’s Work With Algebra Tiles

Slide 2  2
 Algebra Tiles
 Algebra tiles can be used to model operations involving integers.
 Let the small green square represent +1 and the small pink square represent 1.
 The green and pink squares are additive inverses of each other.

Slide 3  3
 Algebra Tiles
 Algebra tiles can be used to model operations involving variables.
 Let the green rectangle represent +1x or x and the pink rectangle represent 1 x or x .
 The green and red rods are additive inverses of each other.

Slide 4  4
 Algebra Tiles
 Let the green square represent x2. The pink square represents x2.
 As with integers, the green squares and the pink squares form a zero pair.

Slide 5  5
 Zero Pairs
 Called zero pairs because they are additive inverses of each other.
 When put together, they model zero.

Slide 6  Practice with Integers
 Algebra tiles can be use to model adding, subtracting, multiplying, and dividing real numbers.
 Remember, if you don’t have enough of something, you can add “zero pairs”
 6

Slide 7  Modeling Addition/Subtraction
 2 – 3
 Start with 2
 Take away positive 3. But wait, I don’t have 3 so I must add zero pairs!
 Now remove positive 3
 You are left with 5
 7

Slide 8  Modeling Addition/Subtraction
 1 + 3
 Start with 1
 Now, add positive 3
 Now, you must remove any “zero pairs”
 You are left with 2.
 8

Slide 9  You try
 5 + 3
 1 + 4
 4 – 2
 2 + 3
 9

Slide 10  Modeling Multiplication
 2 x 3
 This means I need 2 rows of 3
 Which is 6
 This could also mean “the opposite of 3 rows of two”
 10

Slide 11  You try
 1 x 4
 3 x 3
 2 x 4
 2 x 2
 11

Slide 12  Modeling Division
 6 2
 The “6” is called the dividend. The “2” is called the divisor.
 Place the “2” outside, and then line up the 6 inside.
 You answer is what fits on top, which is 3. (called the quotient)
 12

Slide 13  You Try
 4 / 2
 8 / 4
 6 / 3
 3 / 1
 13

Slide 14  14
 Modeling Polynomials
 Algebra tiles can be used to model expressions.
 Model the simplification of expressions.
 Add, subtract, multiply, divide, or factor polynomials.
 To solve equations with polynomials.

Slide 15  15
 Modeling Polynomials
 2x2
 4x
 3 or +3

Slide 16  16
 More Polynomials
 2x + 3
 4x – 2

Slide 17  17
 Adding Polynomials
 Use algebra tiles to simplify each of the given expressions. Combine like terms. Look for zero pairs. Draw a diagram to represent the process.
 Write the symbolic expression that represents each step.

Slide 18  18
 Adding Polynomials
 (2x + 4) + (x + 1)
 Combine like terms to get three x’s and five positive ones
 = 3x + 5

Slide 19  19
 Adding Polynomials
 (3x – 1) – (2x + 4)
 Now remove 2x and remove 4. But WAIT, I don’t have 4 so I must add zero pairs.
 Now remove 2x and remove 4
 And you are left with x  5

Slide 20  You Try
 (2x – 1) + (x + 2)
 (x + 3) + (x – 2)
 (2x – 1) – (x + 5)
 (3x + 5) + (x – 1)
 (4x – 3) – (3x – 2)
 20

Slide 21  Adding Polynomials
 This process can be used with problems containing x2.
 (2x2 + 5x – 3) + (x2 + 2x + 5)
 (2x2 – 2x + 3) – (3x2 + 3x – 2)
 21

Slide 22  Distributive Property
 Multiplying a monomial to a polynomial
 3(x – 2)
 = 3x  6

Slide 23  Distributive Property
 2(x  4)
 23
 = 2x + 8

Slide 24  You try
 4 (x + 2)
 2 (x – 3)
 2 (x + 1)
 2 ( x – 1)
 24

Slide 25  Multiplying Polynomials
 (x + 2)(x + 3)
 x2 + 2x + 3x + 6 = x2 + 5x + 6
 Fill in each section of the area model
 Combine like terms

Slide 26  Multiplying Polynomials
 (x – 1)(x +4)
 = x2 + 3x – 4
 Fill in each section of the area model
 Make Zeroes or
 combine like terms
 and simplify
 x2
 + 4x
 – 1x
 – 4

Slide 27  27
 You Try
 (x + 2)(x – 3)
 (x – 2)(x – 3)
 (x – 1) ( x + 4)
 (x – 3) (x – 2)

Slide 28  28
 Dividing Polynomials
 Algebra tiles can be used to divide polynomials.
 Use tiles and frame to represent problem. Dividend should form array inside frame. Divisor will form one of the dimensions (one side) of the frame.
 Be prepared to use zero pairs in the dividend.

Slide 29  29
 Dividing Polynomials
 x2 + 7x +6
 x + 1
 = (x + 6)

Slide 30  Dividing Polynomials
 x2 – 5x + 6
 x – 3
 = (x – 2)

Slide 31  31
 You Try
 x2 + 7x +6
 x + 1
 2x2 + 5x – 3
 x + 3
 x2 – x – 2
 x – 2
 x2 + x – 6
 x + 3

Slide 32  32
 Factoring Polynomials
 Factoring is the process of writing a polynomial as a product.
 Algebra tiles can be used to factor polynomials. Use tiles and the frame to represent the problem.
 Use the tiles to fill in the array so as to form a rectangle inside the frame.
 Be prepared to use zero pairs to fill in the array.

Slide 33  33
 Factoring Polynomials
 3x + 3
 2x – 6
 = 3 ·
 (x + 1)
 = 2 ·
 (x – 3)

Slide 34  You Try
 Factor 4x – 2
 Factor 3x + 6
 Factor
 Factor
 34

Slide 35  Factoring Polynomials
 x2 + 6x + 8
 = (x + 2)(x + 4)

Slide 36  Factoring Polynomials
 x2 – 5x + 6
 = (x – 2)(x – 3)
 Remember: You must form a RECTANGLE out of the polynomial

Slide 37  Factoring Polynomials
 x2 – x – 6
 = (x + 2)(x – 3)
 This time the polynomial doesn’t form a rectangle, so I have to add “zero pairs” in order to form a rectangle.

Slide 38  You Try
 x2 + 3x + 2
 x2 + 4x + 3
 x2 + x – 6
 x2 – 1
 x2 – 4
 2x2 – 3x – 2

Slide 39  Solving Equations
 We can use algebra tiles to solve equations.
 Whatever you do to one side of the equal sign, you have to do to the other to keep the equation “balanced”.

Slide 40  Solving Equations
 3x + 4 = 2x – 1
 First build each side of the equation
 Now remove 2x from each side.
 Next, remove 4 from each side. But wait, I don’t have 4 so I must add “zero pairs”
 Remove 4 from each side
 You are left with x = 5
 =

Slide 41  Solving Equations
 4x + 1 = 2x + 7
 First, build each side of the equation
 Next, remove 2x from each side.
 Remove 1 from each side.
 Now divide each side by 2.
 Your result is x = 3.
 =

Slide 42  You Try
 2x + 3 = x – 2
 x – 4 = 2x + 1
 3x + 1 = x – 5
 8x – 2 = 6x + 4

Slide 43  Credits
 Adapted by Marcia Kloempken, Weber High School from David McReynolds, AIMS PreK16 Project