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Different Ideas on How to Teach Long Division

As presented in an earlier posting, there is another way to approach long division.  However, since many of you are required to present it the long way, here are a couple of ideas to make it easier for your students.

First of all, have the students use graph paper.  The squares help to keep the numbers aligned which seems to be a problem for many students.  If you don't have graph paper, you can download free templates at Donna Young's Free Graph Paper and make your own.  I like the idea of separating the problems with lines to ensure there is no cross over from one problem to another.


Secondly, try using the acronym (a mnemonic device) of Does McDonald's Sell Cheese Burgers.  I have see this acronym many times on Pinterest, but usually the C is omitted.

Check means that after the student has subtracted, they should check to see if the remainder is smaller than the divisor.  If it is equal to or larger than the divisor, then enough was not taken out of the dividend.  This is a step often skipped when long division is taught; yet, if the student doesn't check and make the needed correction, the answer (quotient) will be wrong.

In order to learn division, the student must first have a good understanding of multiplication. Students don’t need to perfectly know all of the times tables, but a majority of the facts or having a reasonably quick strategy to figure out the answer is necessary.

Start by practicing division using the number series the students can easily skip count such as 2 and 5. Then gradually move up to nine. After that, move to division by double digit numbers using 10 since most students know how to skip count by 10. Once the concept is understood, teaching division will become more about guided practice to help your child to become comfortable with the division operation which, in reality, is a different kind of multiplication practice.

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The Long and Short of It - Two different ways to do long Division

My remedial college math class is currently working on fractions. (Yes, even many college students don't understand them!) When we discussed how to change an improper fraction to a mixed numeral, long division came up. I showed the class a shortcut I was taught many years ago (approximately when the earth was cooling) and none, no not even one student, had seen it before. I wonder how many of you are unfamiliar with it as well? First let's look at long division and how most students are taught today. We will use 534 divided by 3.

Now if that doesn't make your head swim, I don't know what will. Everything written in the third column is what the student must mentally do to solve this problem. Then we wonder why students have trouble with this process. There is another way, and it is called short division for a reason. This is the way I learned it.......

I don't know about you, but I would rather have my students doing mental math to solve division problems than writing everything out in the long form. And the paper and frustration you will save will be astounding! So what will it be.....long division or short division?

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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. This resource contains four easy to understand divisibility rules and includes the rules for 1, 5, and 10 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 use by the student. If you are interested, just click under the resource title page.