Thursday, April 12, 2012

Dump and Divide

When working with fractions, my remedial math college students are never quite sure which number to divide by.  This same thing often occurred when I taught middle school and high school.  So the question I had to answer was, "How can I help my students remember what number goes where?"

First, the student must understand and know the vocabulary for the three parts of a division problem. As illustrated above, each part is correctly named and identified.

Side Note:  The symbol separating the dividend from the divisor in a long division problem is a straight vertical bar with an attached vinculum (you might have to look this word up) extending to the left, but it seems to have no established name of its own. Therefore, it can simply be called the "long division symbol" or  the division bracket.  I wish it were named something fancier, but sometimes plain and straight forward is the best!
Now let's look at a fraction that the student is asked to rewrite as a decimal.  The fraction on your right is two-fifths and is read from top to bottom as two divided by five.  That's easy enough, but when my students enter this into their calculators, many will put in the 5 first, and then press the division sign, followed by the 2. Of course, they get the wrong answer. Now let's look at the dump and divide method.


First, dump the 2 into the calculator.  Then press the division sign; then divide by 5.  The answer is 0.4.

I am aware that many of students are not allowed to use calculators; so, let's look at how this method would work using the division bracket. We will use the same fraction of 2/5 and the same phrase, dump and divide.


First, take the numerator and dump it inside the division bracket.  (Note: Use N side instead of inside so that numerator and N side both start with "N".)  Now place the 5 outside of the long division bracket and divide. The answer is still .4.

Dump and Divide will also work when a division problem is written horizontally as a number sentence such as:  15 ÷ 3.  First, reading left to right, dump 15 into the division bracket. Now place the 3 on the outside. Ask, "How many groups of three are in 15?"  The answer is 5.
Try using Dump and Divide with your students, and then let me know how it works.  You can e-mail by clicking on the page entitled Contact Me or just leave a comment.






Since many students do not know their multiplication tables, reducing fractions is almost an impossible task. The divisibility rules, if learned and understood, can be an excellent math tool.  The resource, Using Digital Root to Reduce Fractions, contains four easy to understand divisibility rules as well as the digital root rules for 3, 6, and 9.  A clarification of what digital root is and how to find it is explained. Also contained in the resource is a dividing check off list for the student. Download the preview to view the first divisibility rule plus three samples from the student check off list.

1 comment :

Adrienne said...

I am your newest follower!

Adrienne
Unless Teaching