Division Debate

I was just having a conversation with two sixth grade teachers this morning and the topic of long division came up.  We had been talking about multiplication and how it would help children if we said, “groups of” instead of “times” when discussing multiplication.  I made the comment that the same could be said for division, since multiplication and division are the inverse of each other.  One of the teachers told me that she found it difficult to know exactly how to phrase a division problem when talking to her class.  She wondered, in the problem 108 divided by 8 if she should say,  “108 divided into 8 groups” or “108 divided into groups of 8″.

I think the confusion about division comes from the fact that there truly are two types of division but you don’t realize it in the “naked number” problem 108 divided by 8. It becomes apparent however, when we put the division into context. For example: We could be saying that 108 people will be divided onto 8 teams, which is a division partitive problem.  When given this problem a child who is a direct modeler will  make 8 groups and fair share out the 108 people onto those teams. In that instance we have divided the 108 people into 8 groups.

However, if the problem was 108 cookies were being distributed to people in packages containing 8 cookies and we were trying to determine how many people we could feed, then we have a division measurement problem. In that case, a child who is a direct modeler would take the 108 cookies and break them into groups of 8 and count the groups. Either way, you would arrive at the same answer, but the actions would be different.
The type of division problem that can be used to  help students with base ten understanding is the division measurement problem.  When the divisor is ten, or a power of ten,  students can remove groups of ten from the dividend.

Just “Sum”thing to think about…

Hi, I am Renee' Smith and I began teaching math in, of all places, a maximum security prison. “I was 21 years old and 99 lbs. soaking wet. Some of my students were convicted murderers and as scary as it sounds, it was incredibly sad. Many of those men had failed in the school system and then turned to crime.” That early experience with public school dropouts, cemented my resolve to help future students understand and succeed in the area of mathematics. To that end I dedicated 16 years to the classroom, teaching 5th grade math through algebra. After obtaining my Masters in Education from Baker University, I joined the ESSDACK team in 2007. I have presented at the local, state, and national levels but my most worthwhile experience at ESSDACK has been working to take the fear out of math for teachers and students alike. Although my primary focus has been providing professional development in mathematics, I also devote time to podcasting and creating materials for teachers to use in their classrooms. My podcasts include, By the Numbers, Just Desserts and Math Snacks. Working at ESSDACK has provided me the opportunity to do many of the things I love. “I have the time to research current educational practices, I get to be creative, collaborative, and I meet tons of new people."

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