Therefore we will place our first quotient digit, 3, on the second rod left from the quotient unit rod. Here we should make clear how we are maintaining correct place value for the quotient as we work through the dividend.
Our dividend has 3 digits so the largest our quotient can be is 3 digits. However, in this problem since we could not divide 8 into the 2, the first dividend digit, we moved 1 more digit to the right on the dividend.
Therefore we also have to move 1 digit to the right on the quotient. This is why we placed the first quotient digit 3 on the second rod of the quotient, not the third rod from the quotient unit rod. So we know already our answer will only have 2 digits. Next we repeat the entire division process by moving 1 more digit to the right on the dividend.
We now consider dividing 8 into 40 because our dividend pointer is now on the dividend unit rod. Now that we have zeroed out the dividend our problem is complete and the quotient answer is Your child or student can get plenty of practice with both kinds of division word problems with Math Mammoth Division 1 worktext , or in grade 3 of the Light Blue series curriculum. Once the concepts of quotative division and sharing division are clear, the next step is to spend some time studying the connection between multiplication and division , because that is what students need to learn to use in order to solve simple division problems mentally — not manipulatives or pictures.
Video lessons on basic division concept. Two ways of thinking of division. Meanings and Relationships of the Operations: Division. Confused about the different options? Take a virtual email tour around Math Mammoth! You'll receive:. This is a little "virtual" 2-week course, where you will receive emails on important topics on teaching math, including:. I tend to send out these tips about once monthly, near the beginning of the month, but occasionally you may hear from me twice per month and sometimes less often.
Kindergarten math High school math. The concept of division, and how to use a bead abacus to teach it This post explains how to use a school abacus bead abacus to teach the basic concept of division, in particular, the measurement division as studied in 3rd grade math.
You may already know that there are TWO basic interpretations for the concept of division: Sharing division — the name tells you what it means. Quotative or measurement division. You think how many groups of the same size you can form. Or, you think, "how many times does the divisor fit into the dividend? Take 20 beads: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Group them in groups of 4: 00 00 Note that the red group is formed from 2 beads on one bar and 2 on the other.
Input your first number. Say you've got to add and Enter on the abacus by pushing up four beads in the ones place, three in the tens place, two in the hundreds place, and one in the thousands place.
Start adding from the left. The first numbers you'll add are the 1 and the 5 from the thousands place, in this case moving the single bead from the top row of that column down to add the 5, and leaving the lower bead up for a total of 6. Likewise, to add 6 in the hundreds place, move the top bead in the hundreds place down and one bead from the bottom row up to get a total of 8.
Complete an exchange. Since adding the two numbers in the tens place will result in 10, you'll carry over a 1 to the hundred place, making it a 9 in that column. Next, put all the beads down in the tens place, leaving it zero.
In the ones column, you'll do essentially the same thing. Eight plus 4 equals 12, so you'll carry the one over to the tens place, making it 1. This leaves you with 2 in the ones place. Count your beads to get the answer. Subtract by doing the addition process in reverse. Borrow digits from the previous column instead of carrying them over. Say you're subtracting from After entering into the abacus, start subtracting column-by-column starting on your left. Eight from nine is one, so you'll leave a single bead up in the hundreds place.
In the tens place, you can't subtract 6 from 3, so you'll borrow the 1 in the hundreds place leaving it zero and subtract 6 from 13, making it 7 in the tens place the upper bead up and two lower beads. Do the same thing in the ones place, "borrowing" a bead from the tens place making it 6 to subtract 7 from 12 instead of 2.
Part 3. Record the problem on the abacus. Start at the farthest left column of the abacus. Say you're multiplying 34 and Leave the rest of the columns to the right open for your product.
The abacus should have 3 beads up in the farthest column left, four up in the next farthest, a blank column, a column with one bead up, two beads up in the next, and another blank column. The rest of the columns are open. Multiply by alternating columns. The order here is critical. You need to multiply the first column by the first column after the break, then the first column by the second column after the break. Next, you'll multiply the second column before the break by the first column after the break, then the second column before the break by the second column after the break.
Record the products in the correct order. You will keep moving beads on the right hand portion of the abacus as you multiply the individual digits. For the problem 34 x [8] X Research source First, multiply 3 and 1, recording their product in the first answer column.
Push three beads up in that seventh column. Next, multiply the 3 and the 2, recording their product in the eighth column. Push one bead from the upper section down, and one bead from the lower section up.
When you multiply the 4 and the 1, add that product 4 to the eighth column, the second of the answer columns. Since you're adding a 4 to a 6 in that column, carry one bead over to the first answer column, making a 4 in the seventh column four beads from the bottom section pushed up to center bar and a 0 in the eighth all beads in their original starting position: the top section bead pushed up, bottom section beads pushed down.
Record the product of the last two digits 4 and 2 8 , in the last of the answer columns. They should now read 4, blank, and 8, making your answer Part 4. Leave space for your answer to the right of the divisor and the dividend. When dividing on an abacus, you will put the divisor in the left-most column s. Leave a couple blank columns to the right, then put the dividend in the columns next to those.
The remaining columns to the right will be used to do the work leading to the answer. Leave those blank for now. Leave the other columns blank for the answer section. To do this, push two lower beads from the bottom portion up in the left-most column. Leave the next two columns alone. In the fourth column, push three beads from the bottom portion up.
In the fifth column from the left, push four beads from the bottom portion up. The blank columns between the divisor and the dividend are just to visually separate the numbers so you don't lose track of what's what.
Record the quotient. Divide the first number in the dividend 3 by the divisor 2 , and put it in the first blank column in the answer section.
Two goes into 3 once, so record a 1 there. To do this, push one bead from the bottom portion up in the first column of the answer section. If you like, you can skip a column leave it blank between the dividend and the columns you want to use for the answer section. This can help you distinguish between the dividend and the work you do as you calculate.
Determine the remainder. Next, you need to multiply the quotient in the first answer section column 1 by the dividend in column one 2 to determine the remainder.
This product 2 needs to be subtracted from the first column of the dividend. The dividend should now read To make the dividend read 14, push two of the bottom portion beads currently pushed up to the center bar at the fifth column back down to their starting position.
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