HAVING FUN WITH DECIMALS

By 

Jannyce Y. Omueti 

This lesson was created as a part of the SMART website and is hosted by the Illinois Institute of Technology

INTRODUCTION::  The following lesson is for teachers to direct students who may need extra help with understanding the concept of  decimals.  It can also be used as your introductory or revision lesson to teach decimals.  The lesson is focused on children between the ages 7 to 12 or grades 3-6. The link below will give you information on other aspects of decimals to choose from. 

 

http://www.proteacher.com/cgi-bin/outsidesite.cgi?external=http://www.teachingideas.co.uk/maths/decimals/contents.htm&original=http://www.proteacher.com/100014.shtml&title=Decimals%20Activities  

The lessons will be focused on place value and dividing with decimals.  There is also a revision exercise on the division of whole numbers.

REVISION:. Dividing Whole Numbers 

 

 

Division involves equal groups.  We divide for two reasons: 

  1. When you know the original amount and number of shares and you want to know the size of each share.

    2. Example 1 :  A cake is cut into 10 pieces.  Five students want equal shares.  How many pieces will each person get? 

    You know:   You need to know  

    original amount

    number of shares  

    		   ______ 

      ______ 

    size of one share

    10 ÷ 2 =

    		   ______ 

      ______ 
    How many slices will each person get?

      ___________ 

     

    Fill in the blanks above, and then check your answers below.

     

     

     


     

     

     

  2. When you know the original amount and the size of one share, you divide to find the number of shares.

    Example 2:   A hamburger uses 2 buns.  How many hamburgers can you make with 24 buns? 

    You know:   You need to know  

    original amount

    size of one share  

    		   ______ 

      ______ 

    how many  shares

    24 ÷ 2 =

    		   ______ 

      ______ 
    You can make _____ hamburgers.

    Fill in the blanks above, and then check your answers below.

     

Click on the link below to get more revision exercises on dividing whole numbers.  Follow the prompts to review what you need.

http://www.mathleague.com/help/decwholeexp/decwholeexp.htm#dividingwholenumberswithremainders

Test 1

Name________________________

Divide One- and Two-Digit Dividends with One-Digit Divisors for One-Digit Quotients 

Print and solve the following division problems.

   1.                      2.                  3.                      4.                   5.                    6.                  7. 

  ____    ____    ____     ____    ____    ____    ____ 
 9)18     4)24    8)56     4)28    9)36    5)75    8)72


 8.       9.     10.      11.      12.     13.     14.

  ____    ____    ____     ____    ____    ____    ____ 
 5)30    6)12    1)8      9)81    5)40    3)27    7)21
 15.      16.    17.      18.      19.     20.     


  ___     ____    ____     ____    ____    ____    ____ 
 9)54    4)16    7)49     1)0     2)12    5)35    


TEST 2
     
 1.       2.     3.       4.       5.       6.     
  
  ____    ____    ____     ____    ____    ____    ____ 
 7)28    9)54    1)6      5)35    6)48    7)14    



 7.       8.     9.       10.      11.     12.    13.
  ____    ____    ____     ____    ____    ____    ____ 
 6)36    6)18    3)24     2)0     6)30    5)5     2)22  

 14.      15.    16.      17.      18.     19.     20.

  ____    ____    ____     ____    ____    ____    ____ 
 2)10    6)42    8)24     6)54    5)10    7)42    8)48

www.scienceacademy.com/BI/divide.htm

Answers to the above:  Example 1  Amount is 10, shares are 5, each person to get 2 slices.
                                  Example 2  Amount is 24, one share size 2, 12 hamburgers will be made.
 
Once you have finished with these exercises you should be ready to to begin the lesson on decimals.  Have fun.
 
 
LESSON 1:  Decimals  Place Value
                    Decimal numbers are numbers written using place value.  We use a decimal point to separate the whole- number places from the places less  than one. 
 
Greater than one   ®     8.45   ¬ Less than one

^
|
|
| 		 
  Decimal Point  

         

When you read a decimal name aloud, the place value you read is the place value of the digit farthest to the right. 

               Example:  For the decimal 0.065, the digit.5 is the farthest digit to the right.  It is in the thousandths place.  Therefore 0.065 is  "sixty-five thousandths."

                 QUIZ      1.   0.013 is thirteen           ____________________________

                           2.  0.078 is seventy-eight  ____________________________ 

                                         3.  0.2 is                           ____________________________ 

                                         4.  0.15 is                         ____________________________ 

                                         5.  0.590 is                       ____________________________

 

 

 

The following links will give the teacher lessons plans and worksheets to help students better understand place value
                                                                           
http://www.teachervision.com/lesson-plans/lesson-3153.html
http://www.teachervision.com/lesson-plans/lesson-3157.html
http://www.gomath.com/htdocs/lesson/decimal_lesson1.htm

Decimal Place Value Chart

 

Units Decimal Tenths Hundredths Thousandths
  .      
  .      
  .      
  .      
  .      
  .      
  .      
  .      
  .      
 
http://205.126.22.50/math/dailymath/decimalplacev.html
Write the answer on the line to indicate the value of the digit in bold type.
Tenths, hundredths, or thousandths.
PLACE VALUE TEST 1
 
1.    What is the place value of the following digit     3  in  15.23   ________________________
2.                                                                           6  in    1.62   ________________________
3.                                                                           8  in  25.68   ________________________  
4.                                                  4  in  20.034 _______________________
5.                                                  9  in  73.90   ________________________ 
 
 6.    What is the numeral for six thousandths? 
      A.  6000   B.  0.06    C.   0.006    D.  0.0006
 7.     What is the numeral for one thousandths?
         
         A.  0.0001   B.  0.001   C.  1.000   D. 1000
 
 8.    What is the numeral for five hundredths?
         A.  500   B.  0.05    C. 0.005   D.  0.0005
 9.    What is the numeral for nine hundredths?
  
         A.  0.09   B.  0.009   C.  0.9    D.  900  
 
10.    What is the numeral for seven hundredths
         A.  7.00   B.  0.007   C.  0.07   D. 700
 
PLACE VALUE TEST 2 
FILL IN THE BLANKS
 
1.  In the number 2.03, what place is the 3 in?         _______________________          
2.  In the number 70.102 what place is the 1 in?      _______________________
3.  What is the value of the 6 in 5.1360?                  _______________________
4.  What is the value of the 4 in 9. 0214?                 _______________________
5.  The number 0.0900 is nine                                  _______________________
6.  The number 1.600 is six                                      _______________________
7.  0.055 is fifty-five                                                 _______________________
8.  0.933 is nine hundred thirty-three                         _______________________
9.  0.12 is twelve                                                      _______________________
10.  0.8 is eight                                                         _______________________
 
 
 

LESSON 2:   DIVIDING DECIMALS 
                       You divide decimals the same way you divide whole numbers.  The only difference is that you place a decimal point in the quotient.
Remember from the lesson above a decimal point is a dot  .  separating the ones and tenths places in a decimal number.
                
DIVIDING A DECIMAL BY A WHOLE NUMBER 
                        You must remember when you divide a decimal by a whole number, you must put a decimal point above the decimal point in the dividend.  Then divide, putting the digits in the quotient.  Make sure you always write zero in the quotient if a dividend digit is too small.  In the example below both dividend  digits 3 and 1 are smaller than the divisor 5.
 EXAMPLE: 
                                                    0.00602 
                                                 5)0.03010
 
Quiz      1.    4)8.12             2.   3)0.186           3.   5)40.5           4.   6)18.24 
 
 
                 5.    7)280.63         6.   32)3.360         7.   21)10.5         8.   9)18.207 
 
 
 
                 9.   7)35.7           10.   3)0.918           11.   4)12.64       12.   15)30.045
 
 
     
Click here http://www.aaamath.com/dec56a-divdeciint.html for more information.   You will get instructions on how to divide a decimal by a whole number and activities to determine how well you understood.
                        

http://www.321know.com/dec.htm

 

DIVIDING A DECIMAL BY A DECIMAL

                        You should now be ready to move to the next step.  More things to remember.  When a student divides a decimal by a decimal

he must start by moving both decimal points until the  divisor is a whole number. 

EXAMPLE:           0. 35)0.735             35.)73.5          Move both decimal points until the divisor is 35,  a whole number.  

                                                               35.)73.5           Then put a decimal point for the quotient. 

                                                                35.)73.5            Now divide 35 into 73.5.  the quotient is 2.1. 

Here is another link to help you.  http://www.aaamath.com/dec56b-divdeci.html

 

QUIZ:        1.   0.8)64.8       2.   0.05)0.45         3.   0.36)1.80       4.   0.4)12.88       5.   0.08)2.48 

             

                   6.   1.6)7.68       7.   0.16)24.32       8.   0.12)0.276      9.  .4)68.4          10.  .03)7.86 

 

                 11.  .5)1.55         12.  .30).720          13.    .5)7.65         14.  .06).744        15.  .23).299 

 

                 16.  1.5).480        17.  .37).740          18.  .16).320        19.  4.3)1.72         20.  2.5).525  

 

DIVIDING A WHOLE NUMBER BY A DECIMAL

Now that you have mastered the above procedures, let us move on.  When the number inside the bracket (dividend), put a decimal point at the right of that number.  Then move both decimal points until the divisor is a whole number. 

EXAMPLE:           0.6)54                0..6)54.0         Put a decimal point and a zero inside the division bracket 

                                        6.)540.       Move both decimal points until the divisor is 6, a whole number. Put a decimal point in the quotient. 

                                                            6)540           Divide 6 into 540. The quotient is 90. 

                                                                

QUIZ :            1.  0.3)93        2.   1.5)135       3.    0.12)132      4.   .06)48         5.   .03)165 

 

                        6.  3.2)960        7.   .9)972         8.    .06)78            9.   .9)189       10.   2.4)768 

 

                      11.  .04)284       12.   .8)248       13.   .11)55           14.  .02)36        15.    .4)128 

 

                      16.   .7)210         17.  1.8)54       18.  0.6)624          19.  .05)45     2O.   0.4)484   

 

Continue with your practice and review by clicking on the following. 

http://www.mathleague.com/help/decwholeexp/decwholeexp.htm

http://www.aaamath.com/B/dec56bx2.htm

 

                   

click here http://www.aaamath.com/B/dec51bx2.htm if you need further help on place value and decimals.  Also contained in this link are other areas of sixth grade mathematics you may want to review.

ANSWERS 

DIVISION EXAMPLE 1                                                    EXAMPLE 2 

original amount 10                                                                  original amount 24 

number of shares 5                                                                 size of one share 2

each person gets  2 slices                                                        hamburgers to be made 12

2 into 10 = 5                                                                           2 into 24 = 12 

DIVISION OF ONE & TWO-DIGIT  DIVIDENDS 

TEST 1

1. 2    2. 6   3. 7    4.  7    5.  4    6.  15    7.  9   8.  6    9.  2    10.  8 

11.  9   12.  8   13.  9    14.  3   15.  6    16.  4  17.  7    18.  0   19.  6   20.  7 

TEST 2 

1.  4    2.  6   3.  6   4.  7   5.  8   6.  2   7.  6    8.  3   9.  8    10.  0 

11.  5   12.  1   13.  11   14.  5   15.  7   16.  3   17.  9   18.  2   19.  6   20.  6

PLACE VALUE QUIZ                           PLACE VALUE TEST 1

1. thousandths  2.  thousandths                                  1.  hundredths  2.  tenths  3.  hundredths  4.  thousandths  5.  tenths 

3. thousandths  4.  fifteen-hundredths                         6.  C    7.  B   8.  B    9.  A      10.  C 

5. five hundred ninety-thousandths 

PLACE VALUE TEST 2 

1.  hundredths  2.  tenths   3.  thousandths  4.  ten-thousandths  5.  hundredths   6.  tenths   7.  thousandths  8.  thousandths

9.  hundredths   10.  tenths 

DIVIDING A DECIMAL BY A WHOLE NUMBER 

QUIZ  

1.  2.03    2.  0.062    3.  08.1    4.  03.04    5.  040.09    6.  0.105    7.  0.5    8.  0.2023     9.  05.1 

10.  0.306    11.  03.16    12.  2.003 

DIVIDING A DECIMAL BY A DECIMAL 

QUIZ 

1.  81    2.  9    3.  5    4.  32.2    5.  31    6.  4.8    7.  152    8.  2.3    9.  171    10.  262 

11.  3.1    12.  2.4    13. 15.3    14.  12.4    15.  1.3    16.  .32    17.  2    18.  2    19.  .4    20.  .21 

DIVIDING A WHOLE NUMBER BY A DECIMAL 

QUIZ 

1.  310    2.  90    3.  1100    4.  800    5.  5500  6.  300    7.  1080   8.  1300    9.  210    10.  320 

11.  7100    12.  310    13.  500    14.  1800    15.  320    16.  300    17.  30   18.  1040  19.  900   20.  1210 

 

When students have completed the quizzes for each section and passes the tests with 70% they should have mastered the concept and can move to the next topic.  If you don't attain these scores keep trying.  Don't give up.  HAVE FUN!

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