Algebra Tiles Powerpoint

NUCC lesson shared with Utah Teachers through PBWorks Wiki as part of Secondary Math II; TOPIC: Algebra Tiles

UtahNUCCSecondary Math II

Algebra Tiles Powerpoint

Created 3 years ago

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NUCC lesson shared with Utah Teachers through PBWorks Wiki as part of Secondary Math II; TOPIC: Algebra Tiles
Slide Content

2. 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.
3. 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.
4. 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.
5. Slide 5 - 5

• Zero Pairs
• Called zero pairs because they are additive inverses of each other.
• When put together, they model zero.
6. 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
7. Slide 7 - Modeling Addition/Subtraction

• -2 – 3
• 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
8. Slide 8 - Modeling Addition/Subtraction

• -1 + 3
• Now, you must remove any “zero pairs”
• You are left with 2.
• 8

• -5 + 3
• -1 + 4
• 4 – -2
• 2 + -3
• 9
10. 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

• 1 x -4
• 3 x -3
• -2 x 4
• -2 x -2
• 11
12. 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

• 4 / 2
• 8 / -4
• -6 / 3
• 3 / -1
• 13
14. 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.
15. Slide 15 - 15

• Modeling Polynomials
• 2x2
• 4x
• 3 or +3
16. Slide 16 - 16

• More Polynomials
• 2x + 3
• 4x – 2
17. Slide 17 - 17

• 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.
18. Slide 18 - 18

• (2x + 4) + (x + 1)
• Combine like terms to get three x’s and five positive ones
• = 3x + 5
19. Slide 19 - 19

• (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
20. 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
21. 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
22. Slide 22 - Distributive Property

• Multiplying a monomial to a polynomial
• 3(x – 2)
• = 3x - 6

• -2(x - 4)
• 23
• = -2x + 8
24. Slide 24 - You try

• 4 (x + 2)
• 2 (x – 3)
• -2 (x + 1)
• -2 ( x – 1)
• 24
25. 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
26. 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
27. Slide 27 - 27

• You Try
• (x + 2)(x – 3)
• (x – 2)(x – 3)
• (x – 1) ( x + 4)
• (x – 3) (x – 2)
28. 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.
29. Slide 29 - 29

• Dividing Polynomials
• x2 + 7x +6
• x + 1
• = (x + 6)
30. Slide 30 - Dividing Polynomials

• x2 – 5x + 6
• x – 3
• = (x – 2)
31. 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
32. 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.
33. Slide 33 - 33

• Factoring Polynomials
• 3x + 3
• 2x – 6
• = 3 ·
• (x + 1)
• = 2 ·
• (x – 3)
34. Slide 34 - You Try

• Factor 4x – 2
• Factor 3x + 6
• Factor
• Factor
• 34
35. Slide 35 - Factoring Polynomials

• x2 + 6x + 8
• = (x + 2)(x + 4)
36. Slide 36 - Factoring Polynomials

• x2 – 5x + 6
• = (x – 2)(x – 3)
• Remember: You must form a RECTANGLE out of the polynomial
37. 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.
38. Slide 38 - You Try

• x2 + 3x + 2
• x2 + 4x + 3
• x2 + x – 6
• x2 – 1
• x2 – 4
• 2x2 – 3x – 2
39. 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”.
40. 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
• =
41. 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.
• =
42. Slide 42 - You Try

• 2x + 3 = x – 2
• x – 4 = 2x + 1
• 3x + 1 = x – 5
• 8x – 2 = 6x + 4
43. Slide 43 - Credits

• Adapted by Marcia Kloempken, Weber High School from David McReynolds, AIMS PreK-16 Project