How to Teach Dividing Fractions With Models | FREE Practice

Looking for a meaningful way to teach dividing fractions by fractions? This FREE digital activity for google slides uses area models to make sense of dividing fractions so your students understand the standard algorithm.

Dividing fractions is probably one of the trickiest standards to teach in sixth grade. Then add using models on top of that and it is easy to feel overwhelmed! We so often skim or skip over using and teaching models with our students because they can be confusing to not only our students but to us too! When we teach division of fractions through models, it is a powerful and useful tool that when used correctly can deepen our students’ understanding. 

Visual Models: Why They Matter

The purpose behind visual models is to help our students understand the why. Have you ever heard the phrase “Don’t ask why, just invert and multiply”? Our teachers often taught math this way to us, simple procedures with little to no deeper understanding.

Fortunately, we have discovered that real learning comes from helping children understand the reason behind procedures. Possibly even “discovering” the procedures for themselves. This kind of math learning leads to real understanding and is less likely to be memorized and then forgotten by our students. 

This may be especially true when dividing fractions by fractions.

Understanding and Using Fractional Models

Understanding Division of Fractions

Before we can help our students understand fractional models, we must understand them ourselves. When we are dividing a fraction by a fraction, we are essentially saying I am taking a fraction and creating groups the size of another fraction.

For example ½ ÷ ⅓ is saying how many groups of size ⅓ can I make from ½. The answer is 3/2 or 1 ½ groups.

In some division of fraction problems you can only make a partial group; ⅓ ÷ ½ = ⅔ of a group or I can make ⅔ of a group when ½ is my new whole and ⅓ is what I have.

Understanding the Models to Teach Dividing Fractions

When you are dividing the fraction ½ by ⅓, you take your dividend fraction, or what is being divided, ½, and then split it into thirds horizontally. This now allows you to easily see ⅓ of the whole while also making a common denominator. You then count the number of pieces it takes to make ⅓ which is your new whole.

In this case it is 2 which is why when you invert and multiply the 2 becomes your denominator. You then count the number of pieces you had originally from the ½. In this example it is 3, which is why it becomes your numerator. 

If you go in and circle the number of groups you can make with your new denominator, 2, from your numerator, 3, you find that you can make 1 group of 2 or one whole and then you are left with 1 of 2 pieces or 1 ½. This is the number you find when simplifying your improper fraction found from inverting and multiplying your expression.

Dividing Fractions by Fractions Task

In this digital resource, there are two parts. First, students will create the fractional model by dragging and overlaying the two fractional pieces. They then count the number of pieces used to make up their new denominator and numerator.

They will finish the first slide by finding and circling the number of groups they can find with their new whole.

On the second slide, students will invert and multiply the original problem. Then they simplify that answer if necessary to connect their thinking to the model

Helping Students who Struggle

If you have students who are still struggling to understand the models, having them draw the models themselves can be a powerful tool. If needed, draw the models with them so that they have the extra scaffolding they need while still putting pencil to paper.

It can also help if you start with more familiar fractions like the ones used above. As the students become more confident with their models using familiar fractions, you can begin adding in more complex fractions to deepen their understanding. 

Models Make the Difference!

I know teaching with models can be intimidating.  As a second year teacher moving to sixth grade, I wanted to just skip over them. Don’t do it! Models are powerful tools and there is a reason they are in the Common Core Math Standards. It may take some time and practice for both you and your students.

But the “aha” moment students have when they connect the standard algorithm to invert and multiply to their models makes it totally worth it! 

Free Resource to Teach Dividing Fractions!

I’m excited to share this free resource to help you teach dividing fractions using models in your classroom. It is an easy and effective tool that is already for you to copy and share with your students!

You can use this as a springboard for more in depth teaching of fractional models or as a practice/review. Regardless of how you use it, you’ll love this specially curated resource for you and your sixth graders!

{Click HERE to go to my shop and grab the FREE Digital Activity to Teach Dividing Fractions!}

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