Teaching How To Divide Fractions

Teaching How To Divide Fractions – Welcome to this free guide to fractional distribution. This tutorial will teach you how to use a simple three-step method called Keep-Change-Flip to easily divide by fractions (as well as fractions of whole numbers).

Below you will find several examples of dividing fractions using the Keep-Change-Flip method along with an explanation of why the method works for any math problem that involves dividing fractions. Plus, this free guide includes animated video lessons and free practice sheets with answers!

Teaching How To Divide Fractions

Teaching How To Divide Fractions

Before you learn how to divide fractions using the Keep-Change-Flip method, you need to make sure you understand how to multiply fractions (which is easier than dividing!).

How To Teach Dividing Fractions With Models

Since multiplying fractions is usually learned before dividing fractions, you probably already know how to multiply two fractions together. If so, you can skip to the next section.

Teaching How To Divide Fractions

Rule of Multiplying Fractions: Every time you add the fractions, multiply the numerator, and then multiply the whole number as follows…

Now that you know how to multiply fractions, you’re ready to learn how to divide fractions using the simple 3-step Save-Change-Flip method.

Teaching How To Divide Fractions

How To Divide Fractions By Fractions: 12 Steps (with Pictures)

To solve this example (and all problems where you have to split parts, use the Keep-Change-Flip method)

If we think about 1/2 ÷ 1/4 in the form of a question: How many 1/4 are there in 1/2?

Teaching How To Divide Fractions

And then if we imagine 1/4 and 1/2, we clearly see that there are 2 1/4 in 1/2, which is why 2 is the final answer.

Multiply & Divide Fractions With Whole Numbers

As in example 01, you can solve this problem by using the variable change method as follows:

Teaching How To Divide Fractions

What if you have to divide a fraction of a whole number? The process appears to be exactly the same as the previous example!

Note that in this example, you are dividing by a fraction of a whole number. But it is actually very easy to convert a whole number into a fraction. All you have to do is rewrite the number as a fraction where the numerator is the number and the denominator is 1.

Teaching How To Divide Fractions

Dividing Fractions: Using The Shortcut

Now that you have rewritten the whole number as a fraction, you can use the Keep-Change-Flip method to solve the problem.

Watch the video lesson below to learn more about dividing fractions by fractions and fractions of whole numbers:

Teaching How To Divide Fractions

Looking for some extra fractions practice? Click on the link below to download your free worksheet and answer key: Few subjects in arithmetic are as difficult as dividing fractions. And while this subject is difficult for our students, teaching fractions can be even more challenging for teachers.

Using Subtraction To Divide Fractions

It’s no wonder that many of us teach our students to ‘take care, change and reverse.’

Teaching How To Divide Fractions

But although these tactics seem to make our lives easier in the short term, they create hidden problems for us and for the students.

Looking for resources to help your students develop the basics of fractions? Download the free QuickStart guide Getting started Why focus on the segmentation view?

Teaching How To Divide Fractions

Education Resources For Teachers, Schools & Students

Research on learning and the brain has found many benefits related to understanding concepts in mathematics. When students learn mathematics by rote methods, many of these benefits are lost.

A cognitive approach to mathematics has been shown to increase retention, or a student’s ability to remember what they have learned.

Teaching How To Divide Fractions

We often think of ‘forgetting’ as good, and ‘forgetting’ as bad. But if we remember everything, our brain will quickly become cluttered and unable to think.

Dividing Fractions: 3/5 ÷ 1/2 (video)

The brain works like a master gardener, weeding out useless memories so we can use the important ones.

Teaching How To Divide Fractions

So how does the brain decide what is important? By looking at the relationship. Isolated pieces of information are picked up and discarded like weeds, but information that forms a web of connected understanding is valued and preserved.

Conceptual understanding is also important for application, or students’ ability to use what they learn in new situations. This includes applying their understanding outside the classroom, or to increasingly complex concepts they face in future classes.

Teaching How To Divide Fractions

Fractions For Kids Explained: How To Teach Your Child Fractions At Home

Building conceptual understanding is like building a house. If you want to build a skyscraper, you start by digging deep and pouring a solid foundation of concrete. Each level must be strong enough to support all the levels that will eventually be built on top of it.

Relying on tricks is like building a house of cards. It doesn’t require much grounding, and we may feel like we can move quickly from one level to the next. But such a system is not meant to last. They might support a story or two, but sooner or later things will go haywire.

Teaching How To Divide Fractions

Lesson Plans and Class Activities Converting fractions to percentage| Interactive Digital Visual Models $ 3.00 Add to Cart Lesson Plans and Classroom Activities Share Word Work Problems – Complete Digital and Print Lessons $ 5.00 Add to Cart. Lesson Plans and Classroom Activities Fundamentals of Parts Visual Models and Digital Manipulations | Interactive Google Slides $3.00 Add to Cart

Dividing Fractions: From Annoying To Fun!

So if you think you appreciate the importance of teaching the concepts behind sharing, the next question is ‘how’.

Teaching How To Divide Fractions

In fact, most textbooks are not designed to build conceptual understanding. They are built on the content coverage model of instruction, where a teacher moves students through uniform content, at a constant pace.

There are certainly benefits to exposing students to grade-appropriate content. But to foster deep understanding, students need to engage in inquiry-based learning (IBL). In order to learn through inquiry, we present students with questions rather than answers. By struggling productively, and building on what they already know, students develop a deep and lasting understanding of mathematical concepts.

Teaching How To Divide Fractions

Th Grade Divide Fractions Task Cards

With the number of standards revised every year, it can be difficult to come up with new ones

Number penalty: Expressions and equations are good alternatives to ‘stacking’ algorithms. Number sentences provide more flexibility and help students develop conceptual understanding.

Teaching How To Divide Fractions

Storytelling: Connecting math concepts to real-world situations (or word problems) helps students attach meaning to math and apply what they’ve learned outside of school.

Multiplying And Dividing Fractions Powerpoint For Ks3 Maths

I often use scale models to introduce new math concepts, as this is often the most effective way for students to understand the true meaning of numbers or operations. Next, I teach them to translate into symbolic / abstract representations using number sentences.

Teaching How To Divide Fractions

Finally, we will look at historical issues related to the new concept. Visual modeling and number sentences become useful strategies for solving story problems.

The ultimate goal is for students to be able to translate correctly in all 3 vehicles. This is a definite sign that they have mastered the subject.

Teaching How To Divide Fractions

Relationship Of Division And Fractions

For more information on planning inquiry-based lessons with this approach, see my previous posts on The Three Vehicles of Conceptual Mathematics and Lesson Plans That Promote Student Engagement.

The biggest challenge in teaching fractions is that many students do not have the basic concepts needed to understand fractions. Many have been exposed to a ‘trick-based’ method of teaching mathematics for years, and have a shaky, or non-existent, understanding of fractions and divisions.

Teaching How To Divide Fractions

When students have a good understanding of the basic concepts, they can understand the division of fractions by combining what they know about division, and what they know about division.

Scaffolded Math And Science: Dividing Fractions By Fractions Using Visual Models

But when I tried to teach my students to divide fractions for the first time, I began to realize that they did not have a basic understanding of division. In fact, I taught math for several years before I learned the difference between partial and fractional division.

Teaching How To Divide Fractions

The difference depends on the meaning of the divisor and the quotient. In partial division, the divisor tells us the number of units, leaving the quotient to determine the size of each unit.

In the quotational clause the meaning is reversed. The divisor determines the size of each unit, allowing the quotient to tell us how many units there are.

Teaching How To Divide Fractions

Th Grade: Dividing Fractions By Fractions

Most of us understand division as division: dividing in three ways to divide it into 3 groups, but it often makes more sense to use a quotation mark when dividing parts. After all, how do you divide something into ⅓ of a group?

As we go through the process of splitting, I recommend introducing each step using a partial split or quote. For most of us, it is enough to focus on one or the other at each stage. But it might be a fun challenge for you to consider how you will use these two types at each stage.

Teaching How To Divide Fractions

I think there are two reasons why it is particularly difficult to divide parts. The first is that division is a complex operation, requiring algebraic measurement. (Think ‘unknown’.)

Literacy & Math Ideas: Three Ways To Divide Fractions

The second reason is that fractions are a classification problem. So, when we are split in two, we are ‘divided in two.’ So what?

Teaching How To Divide Fractions

This is why it is important that students master the concept of fractional parts before dividing fractions. In most states, fractional quotients are 5th degree

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