Teaching division of fractions

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.)