DIGITAL NUMERICS

BY:

ESTELLVENIA SANDERS


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

Several methods of counting and calculating on the fingers were used in ancient times and some of them are still in use. References on the writings of Greek authors from Aristophanes (466 B. C.) to Plutarch (A. D. 46) show that finger counting was used in ancient Greece and Persia. The use of finger counting technique became so common that arithmetic books had to contain detailed explanations if they were to be considered complete.

NUMBERS ONE THROUGH TEN:

The method consists of counting on the bones or the joints of four fingers on one hand, using the thumb of the same hand. The four fingers have a total of twelve bones. The thumb is excluded because the operation is performed by means of it.

1--> Place thumb inside of the palm of your right hand touching the first open space on the third finger

2--> Place thumb inside of the palm of your right hand touching the second open space on the baby finger

3--> Place thumb inside of the palm of your right hand touching the third open space on the baby finger

4--> Place thumb inside of the palm of your right hand touching the top open space on the third finger

5--> Place thumb inside of the palm of your right hand touching  the second open space on the third finger

6--> Place thumb inside of the palm of your right hand touching the third open space on the third finger

7--> Place thumb inside of the palm of your right hand touching the top open space on the second finger

8--> Place thumb inside of the palm of your right hand touching the second open space on the second finger

9--> Place thumb inside of the palm of your right hand touching the third open space on the second finger

10-> Place thumb inside of the palm of your right hand touching the top open space on the first finger

The numbers 1 - 12 ( although I showed you how to count 1 - 10 are counting on the finger bones of the right  hand using the right thumb. The system of finger counting is still used in parts of Iraq, Turkey, Iran, and India.

Fingermath

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Fingermath is wonderful! My 3rd grade son still has trouble remembering basic math facts and all the little tricks that you can teach him don't seem to help. He can't remember those, either. But when you use your hands as an abacus, the answer is always at your fingertips. He finally got to the point where using his fingers was annoying and he started to remember the answer! I am also teaching it to my kindergartner. She is just learning the basic concepts of addition and subtraction and while she is struggling to remember such things as 7+8 she can use fingermath to get the answer until it becomes automatic.

The concept is incredibly simple. The right hand is the ones. The left hand is the tens. You hold your hands over the table with your fingers spread.

 
O O O O

O O O O




O O

The diagram above represents your two hands placed over the table, but not touching it. The two lower O's in the middle represent your left and right thumb respectively. The four O's to the left are the other fingers of your left hand, and the four O's to the right are the other fingers of your right hand. When an X replaces an O, that means that finger is touching the table and is counted.

We will work with the right hand only first. Remember to keep your fingers extended and do not curl them under your palm. Press your right index finger to the table and say "one".


X O O O
O

"One"

Then press your middle finger to the table and say "two".


X X O O
O

"Two"

Continue until you have four fingers on the table. That's four.


X X X O
O

"Three"


X X X X
O

"Four"

Then "flip" your thumb to the table at the same time you lift all the other fingers off the table. That's five.


O O O O
X

"Five"

Then keeping your thumb on the table, put your index finger down again and say "six".


X O O O
X

"Six"

Keep going until all four fingers are back on the table. That's nine.


X X O O
X

"Seven"


X X X O
X

"Eight"


X X X X
X

"Nine"

Now we will use both hands. For ten you press the index finger of your left hand and lift your right hand at the same time.

O O O X

O O O O




O O

"Ten"

If you look at your hands now, you will see that you have a 1 on the left and 0 on the right. If your child writes a 1 and a 0 on his paper, he will see that he has just written ten! If you keep your left index finger pressed and continue to add fingers on the right hand, you will continue to count through the teens.

O O O X

X O O O




O O

"Eleven"

O O O X

O O O O




O X

"Fifteen"

O O O X

X X X X




O X

"Nineteen"

After all the fingers are pressed on the right hand, then you lift the right hand at the same time you press the next finger on the left hand. Now you have twenty.

O O X X

O O O O




O O

"Twenty"

You can count up to 99 that way. Practice counting all the way to 99. Don't forget to flip between 40 and 50, just as you did between 4 and 5. Below is an example of going from 49 to 50.

X X X X

X X X X




O X

"Forty-nine"

O O O O

O O O O




X O

"Fifty"

Practice counting up to 99, then practice 99 back to 0. Be sure to remove your pinky finger first and work back toward your index finger. Flips will be in reverse. With small children have them work up to 4 first, then teach them the flip to 5 and back. Once they master that, then teach them 6-9. They need to be able to "read" their fingers. One through 5 is pretty easy, but they may have trouble "reading" 6, 7, 8, and 9. If they don't recognize those numbers off their fingers right away, have them start with 5 at the thumb and continue counting the other fingers they have down to get to 6, 7, 8, or 9.

Once you have the counting and the finger action down pat, you are ready to do Fingermath. To add, simply press the first number you want to add, then start adding fingers up to the amount of the second number you want to add. For instance, how many first graders do you know who can add 5 and 5 no problem, but panic when they see 5 plus 6? Press 5, count out 6 more fingers and you suddenly see a 1 on the left hand and a 1 on the right hand. Even my kindergartner doesn't need a degree in brain surgery to know to write down a 1 and a 1 and then she can see she has written 11. But she could never tell you off the top of her head that 5 plus 6 makes 11, at least not yet.

Subtraction is just the reverse of addition. When you raise fingers off the table, you do it in reverse order, baby finger first.

My 3rd grader is still struggling with basic math facts such as 16 minus 7, but by using fingermath, he just has to read the answer off his fingers. This method has even worked well with mentally handicapped children and blind children.

We are also using it to a certain degree for multiplication. To multiply 6 x 8, we count:
1, 2, 3, 4, 5, 6, 7, 8,
2, 2, 3, 4, 5, 6, 7, 8,
3, 2, 3, 4, 5, 6, 7, 8,
4, 2, 3, 4, 5, 6, 7, 8,
5, 2, 3, 4, 5, 6, 7, 8,
6, 2, 3, 4, 5, 6, 7, 8,
as we put our fingers down. By the time we are done, we read our fingers and discover that we have 48 on our fingers.

X X X X

X X X O




O X

"Forty-eight"

For division, we count the number of times we subtract a certain number. For instance, 56 divided by 7. Start by pressing 56 with your fingers.

O O O O

X O O O




X X

"Fifty-six"

Then start removing fingers using groups of 7:
1, 2, 3, 4, 5, 6, 7,
2, 2, 3, 4, 5, 6, 7,
3, 2, 3, 4, 5, 6, 7,
4, 2, 3, 4, 5, 6, 7,
5, 2, 3, 4, 5, 6, 7,
6, 2, 3, 4, 5, 6, 7,
7, 2, 3, 4, 5, 6, 7,
8, 2, 3, 4, 5, 6, 7,
until you run out of fingers, keeping track of the number of groups of 7 you subtracted. If you have fingers left over, then that is your remainder.

As your child gets older, s/he will start remembering the simple stuff and won't bother with fingermath. Some will catch on to adding and subtracting 5 just by raising and lowering the thumb, without counting through all 5 fingers. Soon they will realize how easy it is to add 10 without going through the complete counting. Eventually they will remember all the math facts if they use them enough. And if they don't? Hey, they still have their fingers! Do you still remember 15 - 8 instantly? 6 x 7? You are never too old to use Fingermath!

For practice worksheets, you can download a program called "Candy Math", which creates worksheets for you. I started with easy worksheets for my kindergartner and she uses fingermath to solve the problems on each sheet. There are two columns, so I have her do one column the first day and the other column the next day. Then I increase the difficulty level by one and print off a new worksheet for her to do. I do a mix of addition and subtraction problems.

                                                     

FINGER MATH

Elements of Finger Computation

People have used their fingers not only for counting but also for computing--that is doing all sorts of mathematical operations.

A simple multiplication problem for example: 7 x 8  ---baby finger and fourth are held down, thumb, index finger, and middle finger remain held up on the right hand.  The thumb and index finger on the left hand are held up on the left hand. The three fingers on the right hand represent 7 and the two fingers on the left hand represent 8.

One can also spell using digital numerics (finger math)     Combining our numbers and the Roman alphabet, we come up with a simple phrase like "Be Careful". The numbers 3 1 20 19 5 1 7 5 represent the letters (Roman) C A U T E A G E

When doing finger math, the only instruments needed are your two hands You will start with your right hand, because units (ones) always appear on the right.  Regardless to how you learned to do math, you quickly realized that the units (ones) are done in the right column .  On the right hand, the thumb indicates five or five units.  It will always represent five. Your thumb represents five and the other fingers represent the other units which means on the right hand, you will have counted up to number nine.  The left hand represents the tens ; the thumb represents the number fifty and the other fingers represent tens .Therefore ,on the left hand, one will have counted up to 90.  The calculation is always with both hands or one of both hands in a suspended ready position.  Hands are placed flat on the table lightly touching the surface. The same method is used for Clearing.  A command to Clear fingers will be accomplished when the first finger moves forward slightly on the table.  Press 1 " push finger forward slightly" Clear "push first two fingers forward slightly on the surface of the table" The best age to begin learning finger math is when the child can read, write, and say the numbers 1 to 9.  READY!!!!! 1-----Say one as you press 1 by moving your first finger forward slightly.^ The other fingers remain up.    CLEAR YOUR FINGERS---Index finger moves forward slightly.       2---First, PRESS 1 (SAY ONE) then press 1 once again and keep your index finger down  ^ v.  Now CLEAR YOUR FINGERS, AND GET READY FOR THE NEXT NUMBER.  This time both index finger and second finger move forward slightly. ^^     3 First, press 1 (first finger downward slightly) and move second finger forward slightly at the same time and say three as you push the third finger forward lightly (ALL THREE FINGERS MOVE FORWARD TOGETHER) ^ ^ ^    CLEAR YOUR FINGERS by pushing all three of your fingers forward in a downward motion.  As you continue to count, the entire hand is used.  to CLEAR YOUR FINGERS, your entire hand is pushed forward.                      

Numerics

There are many children who have severe problems doing and comprehending the functions involved in solving math problems.  I am not solely referring to children considered disabled and/or handicapped; I am referring to children in general who just can't do math and become totally afraid at just the thought of the word !  Fingermath is a wonderful vehicle to stimulate interest in solving math problems and encouraging the students of any age to want to be involved in math classes.

An exciting activity which will provide students with practice in collecting data in order to find the answer to a simple question is the Finger Maze Activity.   Purpose is to determine whether practice has an effect on learning

               A stated hypothesis is "I think that practice has an effect on learning because.." (the student will write this statement to begin the activity)

               Materials:  Finger Maze Puzzle and a Timer

               Procedure:  

  1. Select a partner
  2. Place a finger maze puzzle sheet face down between you and your partner
  3. When your partner says "go", turn the sheet over and touch each number consecutively (1-20) while saying the number out loud.
  4. Your partner will keep time (in seconds) needed to complete the task and record the time it takes to complete the task on the data table.
  5. Repeat steps 3 and 4 at least three times

                  Results:

STUDENT                                          TIME (IN SECONDS)    

Average

Trial 1

Trial 2

Trial 3

       
       
       

 

 

                                                           FINGER MAZE

             Trials in Seconds

60            
55            
50            
45            
40            
35            
30            
25            
20            
15            
10            
5            

                                     1                           2                                3

                                           TRIALS

 THE MAZE

The Maze can be made in the classroom by the instructor by using a plain sheet of white construction paper and placing number 1 - 20 all over the page with dots beside each number.  The students who finish in the least amount of time are the winners and should be given a prize.

 

ASSESSMENT:

1.  How many fingers are used to form the number ten?

2    When counting 11 - 8 which fingers are used?

3   What fingers are used to spell the word Chocolate?

4.   Using your digits, count to forty-five.

5.   The palm plays what role in finger math?

6.   The three digits on the right thumb equals what number?

7.   The number "fifteen" is found on which digits?

8.   Which fingers are used to spell the word "flag"?

9.    The number uses which digits in multiplication?

10.   Divide the number 81 by 3 using your digits.

                    ENJOY YOUR DIGITS!


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