Easily Teach How to Adding Mixed Numbers in 3 Different Ways -

Has your elementary student or class of students finally become successful with adding fractions but just the thought of adding mixed numbers frightens them a little or maybe you get frightened a little? You might wonder…”do I really have to teach them and talk about how to adding mixed numbers?”

Well…it’s not as bad as you think.

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Watch the video that goes along with this post: Add Mixed Numbers with Like Denominators.

Get your own visual pdf guide to adding mixed numbers similar to this article and the video by clicking here.

How to Adding Mixed Numbers with Like Denominators?

In this article, I am going to share with you three ways in which you can teach your students the process of adding mixed numbers. Since this is a new concept for them, we’ll focus on the how to adding mixed numbers with like denominators.

This will be done by using the CRA Model on the given word problem below.

Using an example, we’re going to look at a problem in context. Here we have a word problem:

Karla wanted to make cupcakes and brownies for her dinner party tomorrow. The cupcakes would need 2 3/10 cups of sugar and the brownies would need 3 5/10 cups of sugar. How much sugar will Karla need to make the cupcakes and brownies for her dinner party?

This skill aligns with the common core state standards:

Common Core Standards for Math

Teach these Common Core Math Standards together in order to give students context when adding mixed numbers together.

Generally, with the given problem we will be adding 2 3/10 + 3 5/10.

Misconceptions

Before we start, let’s first look at a common misconception that students might have when they are practicing how to adding mixed numbers.

One misconception students may have is that after adding the numerators together, they believe that they will need to add the denominators as well.

A common student misconception when adding fractions is to add both the numerators together and the denominators together.

Some Things to Consider

This will show you that your students don’t have a full understanding of what a fraction is. In the book, The Common Core Mathematics Companion: The Standards Decoded, by Gojak and Miles, they emphasize the meaning of the numerator and the denominator when referring to misconceptions with adding fractions.

“….the numerator tells the count, or how many, and the denominator describes the piece.” Many students, and some adults, don’t fully understand that the denominator, in these cases, is a descriptive word that describes the size of the pieces, not the number of pieces.

To clarify, when adding mixed numbers, or the fraction pars of the mixed numbers, we need to add the amounts, not the descriptions.

The purpose of the numerator and the denominator in a fraction.

Clarify with an Example

They give a great example in the book. “Since the pieces are the same size, the numerator, or count, is added and the description of the pieces does not change. When I add 2 pieces that are thirds to 3 pieces that are thirds, I will get 5 pieces that are thirds.”

Thinking about it this way can cause you to focus on the denominator as a description and not just a number or digit.

Once students really grasp this then teaching them how to adding mixed numbers becomes much easier.

How to add fractions together explained.

I highly suggest thinking about possible student misconceptions before teaching a specific lesson to students so you can plan for what they may possibly do.

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Using the CRA Model

Teach How to Adding Mixed Numbers Using a Concrete Model

Let’s keep learning by looking at a concrete model of our problem.

Cuisenaire Rods are great math manipulatives to use when solving problems involving fractions such as adding mixed numbers with like denominators.

For this example, I am going to use cuisenaire rods to represent both mixed numbers. The orange rods will represent the wholes and the white rods will represent the tenth-sized pieces.

Firstly, let’s show our first mixed number, 2 wholes and 3 tenth-sized pieces, or 3 tenths. The white rods are tenth-sized pieces in this scenario because it takes ten of them to be equal to the one whole represented by the orange rods. Next we’re going to join that together with, or add on, our second mixed number, 3 wholes and 5 tenth-sized pieces, or 5 tenths.

How to add mixed numbers with like denominators: 2 and 3/10 + 3 and 5/10 represent orange and white cuisenaire rods.

Starting with the whole numbers when it comes to adding mixed numbers, you can first join all of the whole numbers together. 2 plus 3 equals 5. There are 5 wholes in all.

How to add mixed numbers with like denominators: Join the orange cuisenaire rods together to represent adding the whole numbers together.

Next, combine the 3 tenths with the 5 tenths. 3 tenth-sized pieces plus 5 tenth-sized pieces equals 8 tenth-sized pieces or 8 tenths.

How to add mixed numbers with like denominators: Join the white cuisenaire rods together to represent adding the fractions with the same denominator together.

Last, let’s join the 5 wholes together with the 8 tenths. 5 wholes plus 8 tenths equals 5 and 8 tenths.

So returning to the word problem, Karla will need 5 and 8 tenths cups of sugar.

After joining the orange cuisenaire rods that represent the whole numbers with the white cuisenaire rods that represent the tenths, the sum is 5 8/10.

Teach How to Adding Mixed Numbers Using a Picture Representation

Once students are ready, move them along to drawing their own picture models to represent the actions that took place with the concrete model.

The next step in the CRA Model is to have students draw picture representations of the concrete models that show how to add mixed numbers together.

This can be done on paper, or a small whiteboard. Here I am drawing it out digitally for those who have students working remotely. I’m using the drawing tools in PowerPoint but you can use any online program that has a whiteboard or a blank white space.

Use the drawing tools in PowerPoint or on a whiteboard in any online digit platform for students that work remotely to practice drawing models when adding mixed numbers.

To begin, let’s represent the 2 wholes and and a third whole that is partitioned into tenths. There is no specific model that has to be done.

I find that it is typically easier to draw square or rectangle models than circular models. Whichever type of area models the students are exposed to more is the type of model that they are more likely to draw themselves.

Remember to emphasize that each whole must be the same size.

Remind students that the goal is not to draw perfect picture models. Encourage them to do their best to draw and represent the actions that took place with the concrete models.

After drawing the 2 wholes and shading them in, shade in three tenths to represent the fraction part of the mixed number.

Then do the same with the second mixed number. Draw 3 wholes and shade them in. Draw a fourth whole to partition into 10 equal parts.

The models drawn for the second mixed number should be the same as the first mixed number. Shade in five tenths to represent the fraction part of the mixed number.

Picture models drawn for both mixed numbers should be the same shape and size.

Next, circle the picture of the wholes in both mixed numbers. When joined together, 2 wholes and 3 wholes equals 5 wholes. Write a 5 after an equal sign somewhere under your picture model.

When adding mixed numbers, add the whole numbers together first.

Now we can add the fractions together. This would be a great time to remind students, or better, ask them, if you are able to add the two fractions together. Are the parts of the wholes the same size?

Consequently, due to drawing the pictures by hand, some students may stare at the pieces and analyze if they were drawn exactly equal to each other. If this happens, refer to the fraction numerals, or the denominators. Do both fractions have tenth-sized pieces? Yes.

Next, add the fraction parts together. When adding mixed numbers, they can join together because they have like denominators.

As a result of adding 3 pieces that are tenths to 5 pieces that are tenths, we now have 8 pieces that are tenths. We can also say 8 tenths.

Lastly, don’t forget about that whole number! When we add 5 wholes to 8 tenths, we finally get the sum, 5 wholes and 8 tenths, or 5 and 8 tenths.

Last, when adding mixed numbers, join the whole numbers and the fraction parts together.

Abstract: Teach How to Adding Mixed Numbers by Making Connections to an Equation

Following the demonstration of those models, let’s now connect what solving this problem looks like visually to an equation.

The final step in the CRA Model is to make connections between the concrete and/or the picture model with the equation.

Firstly, we can see from the end of the picture model that we circled the 2 wholes and the 3 wholes. With the equation, we can rewrite it with the two whole numbers next to each other and the two fractions next to each other.

Have students rewrite the equation with the whole numbers together and the fractions together.

Two plus three plus three tenths plus five tenths.

Then add the wholes together to get a sum of 5.

With the fractions, explicitly show to students how the model of 3 tenths and 5 tenths is written in the equation. Also explain that we know the parts are the same size because the denominator for both fractions is tenths (written as 10).

When adding mixed numbers, emphasize to students that the fractions can be joined together because they have the like denominators, or the parts are the same size.

Again we can restate here that when we add 3 pieces that are tenths to 5 pieces that are tenths, we now have 8 pieces that are tenths, or 8 tenths.

Last, combine the 5 wholes with the 8 tenths and the sum is 5 and 8 tenths.

Again, remember to join the whole numbers and the fraction parts back together in order to find the sum when showing students how to add mixed numbers.

To sum up, teaching your students how to add mixed numbers can seem difficult but it shouldn’t be.

Spend more time on firming up their understanding of fractions and what mixed numbers are and look like through concrete and picture models. As a result, this will clear up the misconception of wanting to add the denominators together once they are ready to use the equation.

Don’t become scared when its time to teach how to add mixed numbers. You can do it!

Extra Support

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Book Reference

This book that I mentioned earlier in the video on how to adding mixed numbers is The Common Core Mathematics Companion: The Standards Decoded, by Gojak and Miles.

It is an amazing resource. Firstly, it breaks down each Math Common Core State Standard into terms easily to understand. Secondly, it provides suggestion and examples on how you can teach them.

Even if your state doesn’t use Common Core, many state’s standards are very closely aligned with them. They just may be in a different grade level or domain.

Definitely check this great resource out.

Math Manipulatives

And if you don’t already have a set of some type of Math Manipulatives, or a class set, to work out problems involving fractions, like Cuisenaire Rods or Fraction Tiles, please don’t hesitate on getting your hands on some.

They are so beneficial to your students’ overall understanding of fractions and learning how to adding mixed numbers. There are so many options for you to choose from!

What ToolsShould I Use When Teaching How to Adding Mixed Numbers?

1. Cuisenaire Rods (Plastic Set)

2. Cuisenaire Rods (Foam Set)

3. Cuisenaire Rods (Small Group Set)

4. Rainbow Fraction Tiles (Plastic Set)

5. Rainbow Fraction Tiles (Foam Set)

6. Rainbow Fraction Tiles (Class Set)

7. Rainbow Fraction Tiles (Blank Set)

8. Rainbow Fraction Squares (Blank Set)

9. Rainbow Fraction Circles (Plastic)

10. Fraction Manipulatives Resource Kit

11. Small Group Fraction Kit (Grade 4)