In a previous post, I mentioned that, according to the "new math" folks, 5th graders are not able to learn division of fractions. These 5th graders are just not supposed to be able to grasp that concept!!

Now, this is almost funny to me, yet it's sad. Talk about "dumbing-down". That's exactly what this is. Why, I've taught division of fractions for 17 years in 5th grade and students are able to learn division of fractions. They understand it too. And since I rather suspect that "understanding" division of fractions is what the "new math" people really mean, I want to share with you how to be sure that your student understands. It is a procedure that I have used for the last 8 years very successfully. And it is important to "hang" division of fractions to something the student already understands.

If your student is entering 5th grade, he/she may or may not be expected to learn division of fractions. Some curricula (fuzzy, new-math types) will wait until 6th grade because that's when your child can learn it!!

Here's how to guarantee that your child learns and understands division of fractions, whether they are learning it in 5th or 6th grade. Remember it must be "tied" to a previous concept, and that concept is division of whole numbers. If you are helping your child review or relearn "division of fractions" here is what you must do.

Teach your child to reread or (more properly) reword every division problem -- I'm speaking of division of whole numbers.

Example: 12 divided by 4 (Write the problem sideways using the division sign. Or teach your child to rewrite the division problem using the division sign if it is written another way.)

Your child needs to reread/reword that problem as follows: "How many 4's are in 12?" because that is what we are really trying to discover. I show the students that we are almost reading the problem backwards (and we are indeed mentioning the numbers in reverse order). But do not rewrite the problem. It is important that your student see the problem written as a proper division problem as he/she rewords it.

Have your student repeat this activity early on as he/she is learning division of whole numbers. Write a problem. Ask the question, "What are we trying to discover?" Then ask your student to reword the problem. ("How many 6's are in 24?" or "How many 9's are in 63?") Use craft sticks, pennies, or other small manipulative items to work on this if your student needs to "see" it. This rewording of the problem needs to become second nature to your child before division of fractions is introduced.

Using manipulatives can be helpful indeed, but as soon as the student learns multiplication facts, the manipulatives should be used less and less. And the facts need to be learned before division is taught. Remember, Division is the process of searching for the missing factor. So students must know the two factors for 63 (9 and 7), hence learning the multiplication facts from memory is so important.

Do not assume because you have your student reword a division problem a few times that he/she will do it automatically. Practice, practice, practice it. This needs to become a part of your child's thought process every time he/she works a division problem. It will be invaluable later.

Now, when it's time to learn, or review/relearn division of fractions, the student will be used to seeing the division sign in the problem 3 divided by 1/2 and the rewording will come easily. Have your student read the problem "How many one halves are in 3?" Remind your child: "That's what we are really trying to find out, how many 1/2's are in 3." Starting with whole numbers is really smart. Ask your child, "What are we trying to find out?" (how many 1/2's are in 3, or how many 1/3's are in 2)

[Later on you can try 1/2 divided by 1/4 or 2/3 divided by 1/6. Have the student read "how many 1/4's are in 1/2?" or "how many 1/6's are in 2/3's?" ]

Now, hopefully you have some fractional pieces, so that your child can use manipulatives to determine how many 1/2's are in 3 or how many 1/3s are in 2 [or later, how many 1/4's are in 1/2 or how many 1/6's are in 2/3].

Remember the important thing is that students learn to think "how many ----'s are in ----?"

There are so many (real life) problems that we could generate which will show students how we are going to use division of fractions, but I will save that for another post. And it will come shortly. (And by the way, you will notice that we can use real life situations in a traditional classroom without getting bogged down for hours or days.)

## Wednesday, July 23, 2008

### Teaching division of fractions

Posted by Concerned Teacher (Happily Retired) at 1:24 PM

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## 12 comments:

thanks you explain it well

I have been teaching division of fractions for years and could never find a way to explain it satisfactorily. When I asked the math gurus they reverted to complicated algorithms but ended up tripping over their own explanations when trying to apply it.

Thank you. Thank you.

I only recently began teaching math and this is the simplest I've ever seen division of fractions explained. Thank you soo much!!!

I am a new teacher and have been looking for the easiest way to explain dividing fractions. This is so simple! Thank you!

THANK YOU! I am getting ready to teach division of fractions to my high math kids and I was having such a hard time understanding MYSELF the difference between dividing by 1/2 and multiplying (which is really dividing something in half.) I had just been taught the rule and asked not to question it! I knew my kids would need more of an explanation than that! It is so clear to me now!

Thank you from a homeschooling mother whose 5th grader WAS in tears over division of fractions. Teaching her rewording of the problem helped so much!

This is a great way to explain division of fractions. So clear and easy to understand. Thank you for sharing!!!

Thank you so very much. Your explanation is simple and direct and has made such a difference for me. I am now eager to enter the classroom and teach division of fractions. Thank you, thank you and may God bless you tremendously

I like the explanation and I "get" it; however, not all problems would be solved so easily in one's head. I see that 1/2 divided by 1/4 (reworded as how many 1/4th are in 1/2) is clearly 2; however, when physically can't use manipulatives or drawings to "see" it, how do you solve for it?

I have been looking for an easy way I could explain division of fractions. I am so glad I came across this. I feel confident when I teach my kids this week, they will understand. THANK YOU!!!

Me too....am so glad you chose to share this piece of information. Many many thanks to you.

This rewording is excellent. I have the montessori fraction material for my child, however, I was still struggling a bit on introducing the skittles - may be because I haven't done a course either.

But this method is just about RIGHT for me. For instance I can easily ask how many 1/4 ths are there in a 1/2. And, the child can easily get the point that it will be 2.

I am a high school math teacher (22 years and counting) and have been faced with the reality that most students do not UNDERSTAND fractions and don't know why the "tricks" work. I am currently teaching a class of 9th graders who are at a fourth through sixth grade level.

I am faced with teaching elementary topics to teenagers. This is challenging and has made me look at my practice completely differently. The first half of every class is now a hands on activity involving the topic at hand (dividing fractions in this post). At the same time I have to make sure that I'm not talking down to these students, just because their math level is at the fifth grade they are not fifth graders.

This is how I have been teaching division to them and have done some research and found a good and pretty straight forward way to tackle the harder problems ( 2/5 divided by 1/7 for instance). How many groups of 1/7 are in 2/5? It's actually the same concept as when you want to combine fractions using addition or subtraction, make the parts the same size, get a common denominator!

2/5 and 1/7 have a common denominator of 35. 2/5 is equivalent to 14/35 and 1/7 is equivalent to 5/35. (how many 5/35 are in 14/35?) 14/35 divided by 5/35 is 14/5 or 2 4/5.

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