Topic 3 Multiplying Whole Numbers

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    TOPIC THREE Multiplying Whole Numbers

     
    ****It is extremely important to learn your facts****

    Lesson One
     
    Objective:  identify and apply the Commutative, Associative, Identity, and Zero Properties of Multiplication
     
    Vocabulary:
     
    Commutative Property of Multiplication - You can multiply two numbers in any order and get the same product.
    7 x 5 = 5 x 7
     
    ***  You may have heard this as a turn around or a flip.    However, now that you are in fifth grade you need to use the proper terminology.
     
    Associative Property of Multiplication - You can change the groupings of three or more factors and get the same product.
     
    (6 x 2) x 3 = 6 x (2 x 3)
           12 x 3 = 6 x 6
                36 = 36

    Identity Property of Multiplication - Any number multiplied by 1 is that number.

    6 x 1 = 6                                     1 x 45 = 45                             578 x 1 = 578
     
     

    Zero Property of Multiplication - Any number multiplied by 0 is 0.

    7 x 0 = 0                                    0 x 56 = 0                              698 x 0 = 0

     
     
    Lesson Two
     
    Objective:  mentally compute products of whole numbers using place value patterns and the properties of multiplication
     
    Vocabulary:

    Factors:   numbers that are multiplied together

    Product:  answer to a multiplication problem

    Multiple:  a product of a whole number and another whole number
     
    Knowing 3 x 7 can help you solve 30 x 7 and 300 x 7
    3 x 7 = 21
    30 x 7 = 210
    300 x 7 = 2100

    You can use the Associative Property to solve more difficult problems:

    50  x  32  x 2                                                             4  x  33  x  25
    50  x  2  = 100                                                            4  x 25  = 100
    100  x 32  = 3200                                                      100  x 33  = 3300
     
     
    Lesson Three 
     
     Objective:  use estimating to determine the product

    Vocabulary:    underestimate - when you estimate low
                          overestimate - when you estimate high

    24  x  39 =
    Estimate 24 to 20 and 39 to 40
    20  x  40  = 800

    75  x  28
    80  x  30  = 2400

    97 x 15
    100  x 15
    1500
     
     
    Lesson Four

    Objective:  use exponential notation
     
    Vocabulary:    base - the number to be multiplied
                          exponent  - the number that tells how many times the base is used as a factor
                          expanded form - 5 x 5 x 5
                          standard form - 125 (answer to the problem)
                                                              3
                         exponential notation   5

    You can also read these to the second, third, fourth power......etc.
    The second power is squared.
    The third power is cubed.


     
     
    Lesson Five
     
    Objective:  use the Distributive Property to simplify expressions and solve equations.
    Think about how you can break apart numbers and "Distribute" them.

    7 x 86                                                            132 x 8
    ( 7 x 80) + ( 7 x 6)                                          (100 x 8) + ( 30 x 8) + ( 2 x 8)
    560 + 42                                                            800      +     240    +   16
    602                                                                                    1056
     
     
    Lesson Six
     
    Objective:  multiply multi-digit numbers by one digit numbers
     
      22
      567
      x  3
     1701
     
     
     
    Lesson Seven and Eight 
     
    Objective: multiply multi-digit numbers by multi-digit numbers


        36                                                                            472
      x23                                                                            x36
       108                                                                          2562
     +720                                                                       +12810
       928                                                                       15372


    Lesson Nine

    Objective:  use diagrams and write equations to solve problems


    Assessment - What do you need to Know?????