the stored-ten method of subtraction

The Stored-Ten Method of SubtractionAuthor(s): Audrey FergusonSource: The Arithmetic Teacher, Vol. 29, No. 4 (December 1981), pp. 15-18Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41190019 .

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The Stored-Ten Method of Subtraction

By Audrey Ferguson

Have you ever met a subtraction- resistant student? Have you asked yourself that agelong question, How do I help students develop the skill to perform subtraction problems at a rate that allows them to keep pace with their regular class?

In our many years of working with young remedial mathematics students, it has not been uncommon to find a student who is doing quite well with addition, yet the same student is stopped cold and stalemated by the process of subtraction. In many cas- es, once students like this are given a method for obtaining correct answers for subtraction, they are freed to go on learning more difficult arithmetical operations, some of which depend on the students' mastery of subtraction.

A classroom teacher needs a pock- etful of ideas to keep subtraction- resistant students turned-on and moti- vated to achieve. What works for one student may not be the answer for another. Thus the search for new alternative methods for teaching subtraction is an ongoing task for many of us. With this in mind, I would like to share a finger method for subtraction that has proved most successful with many of our young subtraction-trou- bled mathematics students. We call this the "stored-ten" method of finger

Audrey Ferguson is a Title I remedial mathematics specialist for the St. Louis Public Schools. As the head of one of two mathematics improvement teams at her school, she pro- vides diagnostic mathematics remediation for eligible and identified Title I students. In this capacity, she is also responsible for inservice programs for parents and classroom teachers through team meetings and demonstration les- sons.

December 1981

subtraction. It is especially good for use with students who have difficulty memorizing the harder "teen" subtraction facts.

The Stored-Ten Method The first part of the stored-ten

method is familiar to many teachers, but its explanation is a vital part of the explanation of the method as a whole. We start by telling our students that the top or first number in a subtraction example tells the number of fin-

gers to put up. The second number, which we refer to as the "take-away number," tells us the number of fingers we will be dropping down. Figure 1 shows the example 5-2.

I am sure that you have found that most children have little trouble using this method - many discover its use on their own initiative. The method works fine when a child is solving problems with minuends of 10 or less. Higher minuends present a problem because the child lacks the number of fingers needed to represent numbers greater than 10. Minuends of 11 to 18 require a method for showing a ten plus the ones number - hence the cre- ation of the stored-ten finger method. To "store a ten," a child merely crosses her or his wrists. This allows children to continue adding on and

Fig. 1

Showing 5 - 2

jíte Л

Five fingers go up Two fingers will drop down

The three fingers still standing give the answer.

15



^'9- 2 Г' П Twelve МП QtnrfiH япН 9 ип'

Nineteen (10 stored and 9 up)

Fig.3 This is ten

(You have 10 fingers stored away) Uncross your wrists to "pop".

(This releases your stored ten and all 10 fingers pop up to be counted)

Fig. 4

The Problem: 13 - 7 = ?

Step 1. Put up 13 fingers (10 stored Step 2. Take away the 3 standing and 3 up) fingers with a take-away count of 1 , 2,

3.

Step 3. "Pop" and quickly release the Step 4. Count the number of fingers stored-ten and continue taking away still standing to determine the answer. until you have taken away a total of 7 fingers with a continuing count of 4, 5, 6, i: 13 - 7 = j6_

*A continuous take-away count will not be hindered by the "pop-release" action when the count is rhythmical and the release action is performed quickly.

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they can thereby show 11, 12, and other teen numbers on their fingers. They can show as much as 20 using their crossed wrists as a stored ten and all ten of their fingers to depict 1 1 through 20. Figure 2 shows the differ- ences between 2 and 12 and between 9 and 19 when these numbers are repre- sented by the stored-ten system.

The crossed wrists means you have stored ten fingers away. When you uncross your wrists, all ten of the stored fingers will "pop"; all ten of them pop up quickly just like a jack- in-the-box. The process of "pop and release," which is illustrated in figure 3, should be practiced by students until they can perform the action smoothly and quickly.

The steps in the stored-ten method for solving subtraction problems in which the minuend is greater than 10 are illustrated in figure 4. Classroom teachers have found that the stored- ten subtraction method is easy to teach and that the learning process itself is enjoyable for young students. Children in the primary grades appear to genuinely enjoy the "pop-release" action, and once the technique is learned, students are able to use it quickly, independently, and with very accurate results.

Teaching Suggestions In teaching the stored-ten method to children in a remedial setting, our experience indicates that initially the teacher should work along with the student to ensure the development of "take-away count" conconcentration and to aid in the development of smooth finger action. The teacher should actively demonstrate the finger actions as he or she voices the take- away-count numbers along with the student. It is essential that students practice reciting the count numbers aloud in a smooth rhythmical manner as they perform the finger actions, and that when they "pop and release", they should continue the count. At first the teacher may also wish to voice the "pop" while the children perform the release action. Students, however, should refrain from voicing the pop; but they should practice performing a quick release

Arithmetic Teacher



Fig. 5

Chest-level hand action

One Ten (stored) Eleven

(10 stored plus 1 up)

Fifteen Twenty

(10 stored plus 5 up) (10 stored plus 10 up)

Fig. 6 An adaptation for use in addition The problem: 9 + 2 = ? (Nine is the starting number; two is the add-on count number.)

Step 1 . Start with 9 fingers Step 3. Convert that 10 up up. to a stored ten by crossing

your wrist. m ft ̂^ Step 2. Add on 1 finger. Step 4. Continue adding on That makes 10 up and time fingers to the stored-ten to store, so I can continue until you have reached your counting. The add-on count add-on count number, (in is 1 . this case, when I add on

one more finger, I reach my add-on count of 2.)

fifí £y# The answer shown is 11 (a stored-ten plus 1 finger up).

action when given the pop signal by the teacher. In this way students learn to concentrate on the take-away count, rather than on the pop-release action itself. With such practices, the pops and releases will soon become natural, smooth, automatic responses that do not interfere with the continu- ity of the take-away count.

As the practice session continues, gradually the teacher's voicing of the of the "Pop," should be discontinued, although teachers may still wish to demonstrate the finger actions along with the students. Then greater em- phasis should be placed on the student's performing the count and the release action idependently. You will find that most students will have the technique mastered in a relatively short period of time.

Many children find finger mathematics so natural that they develop techniques of their own, without help from anyone else. Other children, although they would benefit greatly from finger calculations, seem to lack the finger-count coordination to perform the actions without some in-

December 1981

struction. When this is the case, it may be necessary for the teacher of finger mathematics to demonstrate and help the student perfect the up- and-down techniques of finger addition and subtraction. This can easily be done in the initial teaching session when the teacher and pupil perform add-on and take-away finger actions together. A good activity might in- clude an add-on count that starts with zero and goes to twenty, followed by a reverse, take-away count from twenty to zero.

For the beginning stored-ten teaching and practice sessions, we have found it helpful to have both the teacher and the students perform the finger actions at the chest level, as illustrated in figure 5. Some children may continue this way, but others will become more sophisticated and lower their hands to the table or knee level. Whichever position the students pre- fer is acceptable. Initially, however, it is easier for the teacher to demonstrate and observe students' actions when both are working at the chest level.

It does not matter which hand the student selects first to start taking fingers away for the stored-ten method of subtraction. It is important, however, that the student continue to take away all fingers and the thumb on one hand before using fingers from the other hand. The rule: Use all fingers on one hand, then switch to your other hand. When all fingers on both hands are gone, pop quickly and continue the take-away count smoothly.

Stored-Ten Addition Stored-ten finger mathematics was

developed primarily to aid students who were having difficulty with subtraction facts. This method, however, has been used successfully by some students for addition as well. Figure 6 shows an example of how that works.

Summary Although stored-ten finger mathematics may not be for every student, it is an alternative approach for teaching subtraction that has been the answer for many of our young primary-grade remedial mathematics students. It has

17



served also as a means for helping normal classroom students, who are having difficulty learning subtraction facts, keep afloat. This technique is easily taught to and quickly learned by young children. And once it is learned, it enables the student to func- tion in subtraction proficiently and independently.

If you have a subtraction-resistant student this term, I invite you to try the stored-ten method. It may be just the "subtraction support system" that keeps that mathematics student going, m

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