| The abacus has been around in various forms for | | | | simple process. Begin by representing the first |
| over 2300 years. It was used for various counting | | | | number. Add the value of each place value in the |
| and operational tasks. One might even call it the | | | | second and subsequent numbers one at a time |
| original math manipulative (unless you count | | | | beginning with the lowest place value and regroup |
| fingers and stones). In my younger years, abaci | | | | as necessary. |
| were relegated to the bottom shelf or used as a | | | | Consider this simple example, 178 + 255. The |
| toy for the kinesthetic kids. These days, abaci can | | | | student would represent 178 on the abacus to |
| meet the same fate that the abaci of my youth | | | | begin. She would then add five to the ones row. |
| did. The first known abacus, the Salamis tablet, | | | | Since there aren't five more beads to add, this |
| collected dust for over 2100 years. For all those | | | | first move would also involve regrouping. The |
| lonely and banished abaci on dusty shelves | | | | student would move the two remaining ones, |
| everywhere, I dedicate this article on how to | | | | then regroup by sliding all ten ones back and |
| represent, add and subtract whole and decimal | | | | replacing them with a ten. She would then move |
| numbers. | | | | three more beads since she already moved two |
| As most teachers know, the use of manipulatives | | | | of them for a total of five. Since there was some |
| by younger elementary students helps them to | | | | regrouping, there would now be eight tens. The |
| understand the concepts of place value and | | | | students needs to add five more, so there would |
| operations later on. In my search for a variety of | | | | be another regrouping, this time of ten tens to |
| manipulatives to teach number sense, addition and | | | | make a hundred. Finally, the student moves two |
| subtraction, I came across a convenient tool in | | | | additional hundred beads; this time regrouping isn't |
| the abacus. I'm sure it was no coincidence that | | | | necessary. If everything was done correctly, the |
| each row on the abacus included exactly ten | | | | student would end up with four hundreds beads, |
| beads, but there was no operators manual with | | | | three tens beads and three ones beads. |
| the abacus I found. When I found an instruction | | | | A variation on addition is to add the second and |
| manual several years later, I found that the | | | | subsequent numbers from the highest place value |
| manufacturer of the abacus saw it as no more | | | | to the lowest place value. |
| than a counting device and had no idea of the | | | | Subtracting is much the same as addition, but it |
| place value power inherent in the design. | | | | involves "removing" beads. The procedure for |
| Representing Numbers With a Dusty Abacus | | | | subtracting is to represent the first number then |
| When I first started using an abacus as a | | | | to subtract the value of each place value in the |
| manipulative in math class, I was teaching grade | | | | second and subsequent numbers beginning with |
| six. In the grade six curriculum, students were | | | | the highest place value. |
| supposed to represent whole numbers greater | | | | Consider this example, 3.252 - 1.986. The student |
| that one million and decimal numbers to | | | | would first represent 3.252 using the abacus. He |
| thousandths. If you count the number of places | | | | would begin by subtracting one one. This is fairly |
| from one million down to thousandths, you get | | | | straight forward because there are enough ones |
| ten places. Coincidentally, the abacus had ten rods | | | | available. In the next step, though, the student |
| of ten beads each. I'm sure what I discovered | | | | has to subtract nine tenths from two tenths. He |
| was discovered long ago, and some | | | | begins by subtracting two of the nine tenths, but |
| manufacturers probably even send out better | | | | he then has to regroup one of the remaining ones |
| instruction manuals that make note of this, but at | | | | into ten tenths. Once he has ten more tenths, he |
| the time, it was a completely new discovery. | | | | can subtract the remaining seven tenths. He |
| To make a long story short, I assigned each row | | | | continues by subtracting eight hundredths from |
| a specific place value starting with millions at the | | | | five hundredths, and again, he has to regroup, this |
| top, and thousandths at the bottom. One could | | | | time, one of the tenths into ten hundredths. The |
| use a strip of tape or an indelible marker to label | | | | final step also involves regrouping since six |
| the rows. To represent a number, a student | | | | thousandths must be subtracted from two |
| would simply move the number of beads for the | | | | thousandths. In the end, the student hopefully |
| value of each place in the number they were | | | | ends up with one one, two tenths, six hundredths, |
| given. For example, the number 325,729 was | | | | and six thousandths (1.266). |
| represented by moving three of the hundred | | | | Subtraction could also be accomplished by |
| thousands beads, two of the ten thousands | | | | subtracting the lowest place value first, but this |
| beads, five of the thousands beads, seven of the | | | | sometimes means more manipulations of the |
| hundreds beads, two of the tens beads and nine | | | | beads which means more chance for error. |
| of the ones beads. | | | | Conclusion |
| I didn't have a class set of abaci, so I made up | | | | The use of the abacus takes a little bit of time to |
| little sketches of an abacus (six or so per page) | | | | master. It is important that the teacher and the |
| and students showed representations of numbers | | | | students use the correct place value terminology |
| using these. | | | | (e.g. "regroup ten hundreds to make one |
| Adding and Subtracting Numbers With a Polished | | | | thousand" instead of "turn ten green beads into |
| Abacus | | | | one blue bead"), so the concepts of place value, |
| Once students are familiar with representing | | | | addition, and subtraction can be transfered to |
| numbers using an abacus, they can move onto | | | | mental strategies and paper/pencil algorithms. |
| adding and subtracting numbers. The idea of | | | | Remember, the best way to dust and polish an |
| adding using an abacus and place value is quite a | | | | abacus is with little fingers! |