Algebra Tiles Powerpoint

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

UtahNUCCSecondary Math II
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Algebra Tiles Powerpoint

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NUCC lesson shared with Utah Teachers through PBWorks Wiki as part of Secondary Math II; TOPIC: Algebra Tiles
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Slide Content
  1. Let’s Work With Algebra Tiles

    Slide 1 - Let’s Work With Algebra Tiles

  2. 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. 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. 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. 5

    Slide 5 - 5

    • Zero Pairs
    • Called zero pairs because they are additive inverses of each other.
    • When put together, they model zero.
  6. Practice with Integers

    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. Modeling Addition/Subtraction

    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
  8. Modeling Addition/Subtraction

    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
  9. You try

    Slide 9 - You try

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

    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
  11. You try

    Slide 11 - You try

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

    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
  13. You Try

    Slide 13 - You Try

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

    Slide 15 - 15

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

    Slide 16 - 16

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

    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.
  18. 18

    Slide 18 - 18

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

    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
  20. You Try

    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. Adding Polynomials

    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. Distributive Property

    Slide 22 - Distributive Property

    • Multiplying a monomial to a polynomial
    • 3(x – 2)
    • = 3x - 6
  23. Distributive Property

    Slide 23 - Distributive Property

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

    Slide 24 - You try

    • 4 (x + 2)
    • 2 (x – 3)
    • -2 (x + 1)
    • -2 ( x – 1)
    • 24
  25. Multiplying Polynomials

    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. Multiplying Polynomials

    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. 27

    Slide 27 - 27

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

    Slide 29 - 29

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

    Slide 30 - Dividing Polynomials

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

    Slide 33 - 33

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

    Slide 34 - You Try

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

    Slide 35 - Factoring Polynomials

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

    Slide 36 - Factoring Polynomials

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

    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. You Try

    Slide 38 - You Try

    • x2 + 3x + 2
    • x2 + 4x + 3
    • x2 + x – 6
    • x2 – 1
    • x2 – 4
    • 2x2 – 3x – 2
  39. Solving Equations

    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. Solving Equations

    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. Solving Equations

    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. You Try

    Slide 42 - You Try

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

    Slide 43 - Credits

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