Operations on Decimal Numbers by j7rBzHO0

VIEWS: 53 PAGES: 55

									        Place Value
    The place value chart below shows 1247.63
Thousands   Hundreds Tens   Ones   Decimal   Tenths   Hundredths
                                   Point
    1          2       4      7       .        6           3


   The number 1248.63 is one more than 1247.63

  The number 1147.63 is one hundred less than 1247.63

  The number 1247.83 is two tenths more than 1247.63
         Review
   Where is the decimal place?

       34
       $5698
       508
       67.89
                  HIDDEN DECIMAL
          Review
   Arrange each set of numbers from greatest
    to least! What strategy did you use?
       A) 1.8, 2.8, 1.9


       B) 365.7, 358, 365.9
     Review – Learn Alberta Place Values
http://www.learnalberta.ca/content/memg/index.html?term=Division02/Place_Value/index.html
          Review – Adding and Subtracting Decimals
What do you need to do?

1.   Line up the decimals
2.   Add zeros into place values that are empty (if you wish)

3.   Ex: 12.3 + 2. 4 =      12.3           12.3
                           + 2.4         + 02.4
                            14.7           14.7
          Review – Adding and Subtracting Decimals
What do you need to do?

1.   Line up the decimals
2.   Add zeros into place values that are empty (if you wish)

3.   Ex: 187.415 + 34.6 =
                                                  187.415
                187.415
         +       34.6                       +     034.600
    2.1 Add and Subtract Decimals
     Student Outcome: I can use different strategies to estimate decimals.


   Pg 44 Vocabulary:
     Estimate:

           to approximate an answer
       Overestimate:
           Estimate that is larger than the actual answer
       Underestimate:
           Estimate that is smaller than the actual answer
                  Front-End Estimation
        Student Outcome: I can use different strategies to estimate decimals.

Front End Estimation:
keep the leading (front) digit and then add zeros behind

Example #1
      87.85 + 14.60 + 273.52 = 375.97
      80.00 + 10.00 + 200.00 = 290.00



       Using front-end estimation: 290 is an ok estimation
                 Front-End Estimation
       Student Outcome: I can use different strategies to estimate decimals.

Front End Estimation:
keep the leading (front) digit and then add zeros behind

Example #2
      537.85 - 174.60 = 363.25
      500.00 - 100.00 = 400.00



    Using front-end estimation: 400 is a good estimation
               Front-End Estimation
     Student Outcome: I can use different strategies to estimate decimals.

Front End Estimation:
keep the leading (front) digit and then add zeros behind

Example #3            49.45 + 239.99 + 87.06 = 376.50
                      ____ + _____ + ____ = _______

Example #4            708 – 45.89 = 662.11
                      ___ - ____ = _________
                          Relative Size
        Student Outcome: I can use different strategies to estimate decimals.


Use Relative Size:
     Estimating each number to the nearest ten, hundred, thousand etc.

Example #1
      87.85 + 14.60 + 73.52 = 175.97
        87.85 is between 80 and 90, and closer to 90.00

        14.60 is between 10 and 20, and closer to 10.00

        73.52 is between 70 and 80, and closer to 70.00




       90.00 + 10.00 + 70.00 = 170.00
       Using relative size: 170.00 is a good estimation
                          Relative Size
        Student Outcome: I can use different strategies to estimate decimals.


Use Relative Size:
     Estimating each number to the nearest ten, hundred, thousand etc.

Example #2              39.01 + 62.77 = 101.78
                        ____ + ____ = ________

Example #3              567.28 – 21.99 + 38.34 = 583.63
                        _____ - ____ + _____ = _______
                        Compensation
        Student Outcome: I can use different strategies to estimate decimals.


Use Compensation: (try to round up - round down)
     Estimating each number to the nearest ten, hundred, thousand etc.

Example #1
       87.85 + 14.60 + 73.52 = 175.97
        87.85 is closer to 90.00 (round up)

        14.60 is closer to 10.00 (round down)

        73.52 is closer to 70.00 (round down)




             90.00 + 10.00 + 70.00 = 170.00
       Using compensation: 170 is a good estimation
                        Compensation
        Student Outcome: I can use different strategies to estimate decimals.


Use Compensation: (try to round up - round down)
     Estimating each number to the nearest ten, hundred, thousand etc.

Example #2              12.45 + 71.12 – 19.43 = 64.14
                        ____ + ____ - ____ = ____

Example #3              567.89 – 123.00 = 444.89
                        _____ - _____ = _____
           Compatible (Friendly) Numbers
         Student Outcome: I can use different strategies to estimate decimals.


Use Compatible numbers: (5’s, 10’s 50’s 100’s 1000’s)

Example #1
                87.85 + 14.60 + 73.52 = 175.97

         87.85 is closer to 90 or 85
         14.60 is closer to 10 or 15
         73.52 is closer to 70 or 75

                  Two possible answers, but still others
              90+10+70 = 170       or       85+15+75 = 175
    Try It On Your Own!
   Rewrite each question using front-end
    estimation.
       A) 45 + 33 + 92 = 170
         ____ + ____ + ____ = ____


       B) $475.12 - $210.38 = $264.74
         _________ - ________ = ________
         Is your estimate higher or lower than the calculated
           answer? _____________
    Try It On Your Own!
   Use any strategy to estimate the answers.

       A) 45 + 33 + 92 = 170
         ____ + ____ + ____ = ____
         ____ + ____ + ____ = ____


       B) $475.12 - $210.38 = $264.74
          ________ - ______ = _______
          ________ - ______ = _______
    Try It On Your Own!
   Using estimation, where would you put the
    decimal point in the answer? Why?
       A) 631.5 + 902.4 + 217.83 = 175173
          ______ + ______+ ______ = _______


       B) $475.12 - $210.38= $26474
           _______ - _______ = _______
    Try These On Your Own!
   For Homework Due Tomorrow!
   Pg 48. #4, 7, 8ac, 10ac, 14, 20, 21
   Extend 22, 24, 25

   Page 2.1 worksheet
                 Practical Quiz #1
Using Estimation, fill in the blanks where would
    you put the decimal point in the answer?
          A) 81     + 14.074 + 201.897 = 296971
            ______ + ______    + ______   = _______


                B) $782.56 - $258.76 = $5238
                   _______ - _______   = _______
Assignment – Let’s go shopping
 Student’s will receive their handout to
     select their items and money to
         purchase merchandise.


            $500.00
         Multiplying Decimal Numbers
             Student Outcome: I can estimate by +,-,x,÷ decimals.


   Problem: Page 52
       Ashley and Marshall’s family keep busy travelling
        across the country by solving sudoku puzzles!
        During a stop, they look in a convenience store for
        more puzzles.
       Marshall finds sudoku books on sale for $1.69. he
        wants to buy five books and has $9.00.
       Help him estimate the total cost of the five puzzle
        books!
       $1.69 x 5 = ______?
             Multiplying Decimal Numbers
                Student Outcome: I can estimate by +,-,x,÷ decimals.


   1. Marshall estimates the total bill as $5.00
       a) How do you think Marshall got his estimate?
       b) Is Marshall’s estimate over or under the total?
            How do you know?
   2. Ashley estimates the total bill as $10.00
       a) How do you think Ashley got her estimate?
       b) Is Ashley’s estimate over or under the total?
          How do you know?
                                 DID YOU
                                 KNOW!!!!
       Sudoku
 Sudoku was invented hundreds
of years ago, and traded around
the world by ancient
mathematicians.
Each digit from 1 to 9 must occur
in:
   Each row
   Each column
   Each 3 x 3 square.
                   Multiplying Decimals
               Student Outcome: I can estimate by +,-,x,÷ decimals.


   Use front-end estimation and relative size to
    estimate:
       2.65 x 3.72
            Front-End Estimation:



            Relative Size:
             Multiplying Decimals
         Student Outcome: I can estimate by +,-,x,÷ decimals.


Estimate to make sure your answer is reasonable!
 Multiply 1.54 x 25




   What strategy will you use?
                  Multiplying Decimals
              Student Outcome: I can estimate by +,-,x,÷ decimals.


   Use a calculator to solve the equation:
    Multiply 1.54 x 25

          Things I know:     25 x 1 = 25
          Things I know      25 x 2 = 50

          Why would the answer lie between 25 and 50.
              Multiplying Decimals
          Student Outcome: I can estimate by +,-,x,÷ decimals.


   Using paper and pencil
   Multiply without decimals add decimals to
    product
   Estimate an answer. Why?

   Ex: 2.6 x 3.7=                26
                                x 37
                                  962
      Multiplying Decimals Learn Alberta



http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10

Slides 1-5
      Practice Makes Perfect
   Page 57
   3, 6ab, 9, 13, 14,17
   Extend 20, 21
             Dividing Decimal Numbers
             Student Outcome: I can estimate by +,-,x,÷ decimals.

   Example 1:
       A) 15.4 ÷ 3.6 = 4.27778

Front-End Estimation:
    Things I know: 15 ÷ 3 = 5

            The answer closest to 5 is 4.27778
Dividing Decimal Numbers Using a Number Line


Ex: 10 ÷ 2 =
        Use Estimation to Place the Decimal Point.
                Student Outcome: I can problem solve using decimals.


   Example #2:
Four friends buy 1.36L of pure orange juice and
  divide it equally.
       A) Estimate each person’s share.
       B) Calculate each person’s share.
        Use Estimation to Place the
        Decimal Point.
   Solution:
       A) To estimate, round 1.36L to a number that is
        easier to work with.
            Try 1.2                                12 ÷ 4 = 3 So
                                                    1.2 ÷ 4 = 0.3
                 1.2 ÷ 4 = 0.3 Underestimate
            Try 1.
                 1.6 ÷ 4 = 0.4 Overestimate

             16 ÷ 4 = 4 So                     Things I know
             1.6 ÷ 4 = 0.4
                   Dividing Decimals
            Student Outcome: I can problem solve using decimals.


   Problem Questions:
       1. How many pens do you think you can buy
        with $6.00 if one pen costs $0.40
          Use both front-end estimation and relative

           size estimation to find your educated guess.

    Strategy Used:
         Working Together!!
   Pg 66 #10
        A package of 7 fish hooks costs $17.99
        How much will one fish hook cost?
          1)   Estimate
          2)   Calculate- by hand and with calculator
          3)   Did you over/under estimate?

    ANSWER:        $17.99 ÷ 7 = $2.57
        Working Together!
   Pg 66 #11
       Ashley wants to find how many 355 mL cans
        of juice are in a 2-L bottle.
            A) Show Ashley how to estimate the answer

            B) Show Ashley how to calculate the answers
           Practical Quiz #2
What is the cost of each purchase before tax?

Show your work!!

       3 oatmeal cereal bars for $7.50
Dividing Decimals Learn Alberta
http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10

Slides 6-10
Assignment
   Page 65 – 67
   #4, 8, 12, 13, 14, 17, 19
   Extend #21, 22
                        BEDMAS
Student Outcome: I can solve problems using order of operations.



    Remember the order by the
     phrase
    B - BRACKETS
    E - EXPONENTS
    D/M – DIVIDE OR MULTIPLY
    A/S – ADD OR SUBTRACT
                   The “B” and “E”
    Student Outcome: I can solve problems using order of operations.

   The “B” stands for items in brackets
   Do all items in the brackets first

                   (2 + 3)
    The “E” stands for Exponents
    Do anything that has a exponent (power)

                           8 2
                     The “DM”
Student Outcome: I can solve problems using order of operations.


     Represents divide and multiply
     Do which ever one of these comes first
      in the problem

             Work these two operations
             from left to right
                      The “AS”
Student Outcome: I can solve problems using order of operations..


   Represents Add and Subtract
   Do which ever one of these comes first
   Work left to right
   You can only work with 2 numbers at a
    time.
1) 5 + (12 – 3)   2) 8 – 3 x 2 + 7
   5+ 9              8 - 6 +7
     14                2 + 7
                          9
3) 39 ÷ (9 + 4)
   39 ÷ 13
     3
4)   10 + 8 ÷ 2 – 6   5)   15 x 103
      10 + 4 - 6           15 x 1,000
        14 - 6               15 000
            8
6)   36 ÷ (1 + 2)2     7) 3 x 104
      36 ÷ 32              3 x 10 000
      36 ÷ 9                30 000
         4
8)   (5 – 1)3 ÷ 4   9)   14 + 3(7 -2) – 2 x 5
        43 ÷ 4            14 + 3 x 5 - 2 x 5
        64 ÷ 4            14 + 15 - 2 x 5
          16               14 + 15 – 10
                              29 – 10
                                19
    Order of Operations – Learn Alberta
    http://www.learnalberta.ca/content/mejhm/index.html?ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.
     INTE&lesson=html/object_interactives/order_of_operations/use_it.html
                 Let’s Practice
Student Outcome: I can solve problems using order of operations.


   Place the operations shown in square
    brackets to make each statement true.
   9__ 5__5 = 50     (+, x)

   15 __ 3 __2 = 24 (x,-)
                 Let’s Practice
Student Outcome: I can solve problems using order of operations.


   What are the missing numbers?

   A) _____ + 5 x 6 = 32

   B) _____ - 3.2 ÷ 0.5 = 5
             Practical Quiz #3
Solve. Show all your steps.
a) On the front:   18 + 3 – 3 x 5

b)   On the back   (2 x 3) – 4 + 8 ÷ 4
Assignment
   Page 71-73
   # 5, 6ab, 7ab, 9ab, 11, 14, 17, 18a, 19
   Extend #22, 23, 24
Assignment – Chapter Review
   Page 74-75
   #1-4, 5ab, 6ab, 7ab, 8, 9ab, 10-12,
    13ab, 14ab, 15, 16, 17ab, 18ab, 19ab,
    20ab
Assignment – Wrap it Up!!
   Page 77

   This will be completed at home using a
    computer. Please fill in all blanks with
    parent.
   Student to receive handout for support.
GAME – Page 78

								
To top