How to Teach Adding and Subtracting Fractions with Like Denominators

 

Looking for how to introduce and teach adding and subtracting fractions with like denominators?

Let’s talk about using manipulatives, pictures, number lines, and equations. In addition, I’m sharing how to differentiate instruction for students when they add and subtract fractions.

What to look for in this post:

• The progression of adding and subtracting fractions
• Manipulatives for teaching fractions
• Introducing adding fractions to students with concrete manipulatives
• Representational modeling of adding and subtracting fractions
• Differentiation for adding and subtracting fractions with like denominators

If you prefer to hear me talk through this, here is a video featuring all of this content:

[0:40] The progression of adding and subtracting fractions

In many states, third grade is the year that students are first introduced to fractions. In fourth grade, they learn to add and subtract fractions with like denominators only. Then, in fifth grade they learn to add and subtract fractions and mixed numbers with unlike denominators.

When it comes to teaching math, research tells us that we need to provide students with concrete, representational, and abstract models for the skill. When we talk about concrete modeling for adding and subtracting fractions with like denominators, this includes using pattern blocks and fraction bars. For representational modeling, we are going to talk about drawing pictures and using number lines. Written equations with no additional help falls under abstract modeling.

I am going to go through these concrete, representational, and abstract models for teaching adding and subtracting fractions with like denominators.

[2:36] Manipulatives for teaching fractions

I want to discuss my favorite manipulatives to use when teaching fractions.

[2:46] Fraction bars or fraction tiles

Fraction bars are my favorite manipulatives for teaching fractions - whether we are introducing them or adding and subtracting them. These fraction bars or tiles show each fraction in proportion to the whole. Everything fits together just as the fractions should, and they provide a great concrete model for students to learn about fractions.

[3:21] Pattern blocks

Pattern blocks are also great manipulatives to use when teaching fractions. You are more limited to halves, thirds, and sixths, but they are often readily available in elementary classrooms.

[4:18] Introducing adding fractions to students with concrete manipulatives

When I introduce adding fractions to students, I actually don’t start with fractions. Instead, I have a conversation with them about everyday objects. I’ll ask them how many erasers I have if I have two erasers and get three more, and they will tell me that I would have five. I’ll ask them how many paperclips I have if I have one paper clip and then I get two more, and they will say three. If I have one paper clip and one eraser, those don’t combine into anything that we can do something with. The same is true for fractions.

I tell my students that if the fractions have the same denominator, I can do something with those. If I have one sixth and one sixth, just like erasers, I can add those and get two sixths. I find that framing things that way to students is really helpful.

[6:53] Using fraction bars to add fractions

I do, however, also want manipulatives in their hands as soon as we start talking about this. They can get out their fraction bars and show three eights plus four eighths.

During this time, I also like to have the one whole available as well. I won’t tell them this in the beginning, but sometimes we will have fractions that will add together to be greater than one whole. When we start adding, I have them line up the three eighths and add the four eighths. Then they can count the seven eighths and visually see that it does not equal one whole.

[7:43] Using pattern blocks to add fractions

If you don’t have fraction bars, you can use pattern blocks instead. Once we have established the different fractions, we can do a similar problem. Maybe this time we present two thirds plus two thirds, and as it stands we would see that we have four thirds. The blocks show us that they fit together to make a whole plus an extra third. I then want them to move the blocks to show that we can trade in three thirds for one whole, and then have three thirds left - totaling one and one third.

[9:26] Representational modeling of adding and subtracting fractions

Representational modeling can begin with pictures. Thankfully, you do not have to be a great artist to draw with fractions. What we want to do is have students begin by tracing the manipulatives that you have already been using. If they are ready for it, you can also jump to different pictures to represent the fractions.

In addition to drawing pictures, a number line is another pictorial representation that the standards call for students to be able to use. Kids can really have difficulty drawing number lines, so you can start by letting them trace fraction bars. A number line can show the range between zero and one, and hopefully this is not the first time your students have ever seen a number line. We can then place fractions along the number line, and show the representation of one fourth plus one fourth, etc.

For many students in your class, you can explain that when we add or subtract fractions with the same denominator, the denominator stays the same and we add or subtract the numerators. For some students, however, it will be difficult to make sense of this if they have not seen it depicted in these visual ways first. Hopefully, they can go back to the erasers and the paper clips in their minds as well.

[14:46] Differentiation for adding and subtracting fractions with like denominators

Adding and subtracting fractions with like denominators is not a difficult concept for most students, and they will catch on quickly. We want to make sure they can add and subtract the numerators, and that they understand simplest form.

If you have students who are not successful with those milestones, then they may need remediation in basic fraction skills. They would probably benefit from more time with manipulatives. If they are having trouble with simplest form, they are likely struggling with equivalent fractions. You can review with them and fill in the gaps in their knowledge, so they can move forward with adding and subtracting fractions.

If you need to challenge some students, you can work with them on sums that are greater than one whole. You can also work with them on mixed numbers with like denominators or subtracting fractions from a whole number so they have to regroup that whole number into a fraction.

Looking for more resources for teaching how to add and subtract fractions with like denominators?

I have put together a bundle of some of my favorite activities for adding and subtracting fractions with like denominators. It includes five activities:

• Two maze worksheets
• A matching game
• Two BINGO games

All of these are easy to put together and your students are really going to enjoy them.

The Activities Bundle is available on Teachers Pay Teachers.

You can also grab this free download, which includes everything we talked about today: the progression of the standards, the strategies that we went through, the milestones, and differentiation tips.

Check out these related posts:
How to Teach Metric Measurement for Third Grade
How to Teach Metric Conversions for Fourth and Fifth Grades


Check out these related YouTube videos:
How to Teach Adding and Subtracting Fractions with Unlike Denominators
How to Teach Adding and Subtracting Mixed Numbers
How to Teach Third Grade Measurement
How to Teach Converting Measurements for Fourth and Fifth Grades
How to Teach Polygons and Quadrilaterals for Third Grade