When I first started teaching, I assumed that teaching students adding like fractions would be a breeze. After all, you just add the numerators and keep the denominator the same—simple, right? But I quickly realized that while the algorithm is easy, students who don’t have a strong conceptual foundation often struggle. They mix up numerators and denominators, don’t understand why the denominator stays the same, or have no idea how fraction addition connects to real-world math.
That’s why I recommend using the CRA (Concrete-Representational-Abstract) approach when teaching students to add like fractions. By starting with hands-on models and visual representations, students build a solid understanding of what it actually means to combine fractions. This makes the transition to abstract computation smoother and more meaningful—setting them up for success when they move on to more complex fraction operations.
What is the CRA Method?
CRA stands for Concrete-Representational-Abstract. This is the process students should move through in order to build conceptual knowledge, which can be applied across multiple mathematical concepts. Ultimately, this is what we want! We don’t want students who know a formula but can’t figure out how or when to apply it. We want them to use it in real life across multiple situations and scenarios!
Here’s an overview of CRA:
- Concrete – In this stage, students use objects to model problems. For example, using base ten blocks or fraction bars.
- Representational – Students move from manipulatives to drawings in this stage. Students can use tallies, dots, circles, etc. to represent the concrete models.
- Abstract – This is the stage people typically think of with math: algorithms and equations! Here the actual mathematical symbols, notation, and algorithm will be used.
Introducing the Concept of Adding Like Fractions
First things first, before you begin teaching students how to add fractions, they need to have a strong understanding of unit fractions. Unit fractions are a single part of the whole (for example, ¼, ½, ⅓, and so on). To help build a strong foundation, fraction manipulatives are key to helping students visualize and understand fractions. You can use manipulatives like fraction tiles or strips to explore how unit fractions combine to form larger fractions. Students must also practice decomposing fractions into unit fractions. You can also make connections to real-world examples, such as cutting a pizza or folding paper into equal parts.
Another basic understanding that students need is how to represent and change fractions that are greater than one. Fractions greater than one can be represented with either improper fractions or mixed numbers. Students should have many opportunities to use fraction manipulatives to build fractions greater than one, representing them as both improper fractions and mixed numbers. Eventually, you would like for students to come up with a process they can use to change fractions without having to build them. But they must have a lot of practice building them first.
Building this solid foundation will help students once they begin adding fractions. They’ll have a better understanding of why they aren’t supposed to add the denominators. Students will also know what to do when they get an improper fraction as their answer and need to change it to a mixed number. They’ll even have an understanding of how to add mixed numbers together efficiently!
Adding Fractions with Concrete Models
The concrete stage is the “doing” stage of math where students are showing exactly what is happening with objects or manipulatives. There are plenty of manipulatives out there to use–fraction tiles, fraction circles, or even just paper to fold!
When adding like fractions, my favorite concrete models are fraction tiles or fraction bars (also known as linear models). Having students build each addend and combine them helps them to see that the numerators combine, but the denominator never changes. That’s because each fraction is made up of unit fractions!
Let’s take a look at an example: Brittany used 2/4 cup of milk for breakfast and another ¼ cup of milk to make cupcakes. How many cups of milk did she use?
This seems like a simple way to model it–and it is! It is tempting to rush through this step (or skip it altogether), but you can’t! If students don’t gain this conceptual understanding, they will make silly mistakes later, such as adding the denominators.
Another way to model adding fractions with like denominators is by folding paper. Paper folding is great way for students to see connections between equivalent fractions, and it also looks very similar to models that they will draw when they are ready for the representational phase.
Here is how students could solve the example above using paper folding:
As students add like fractions with manipulatives, make sure you are having frequent conversations about why the denominator is not changing. This will help them make connections to the algorithm later!
Once students have had enough practice with concrete models, they would begin to create their own “mental models”–that’s when they’re ready to start representing fraction addition with their own drawn models!
Using Drawn Representations to Add Fractions
When students are ready, start modeling problems using representations, or drawings. This is the “seeing” stage where students show what is happening with pictures or diagrams. Some helpful representations for adding like fractions are area models and number lines.
My favorite drawn model for fractions is the area model. Area models allow students to practice representing fractions by partitioning a rectangle.
Let’s take a look at an example: Ryan ate ⅜ of a pizza on Monday and 2/8 of the same pizza on Tuesday. How much pizza did he eat during those two days?
This simple model allows students to show that they are combining fractions. It also helps them see why the denominator doesn’t change!
Another way to model adding like fractions is on a number line. Number lines are a great model because it can be used for so many different concepts! Students can mark fractions on a number line to visualize the process of adding like fractions.
Here is how students could solve the example above using a number line:
Number lines are especially useful when students are solving for the distance or time. This type of model fits perfectly with those contexts!
Once students have had enough practice with drawn models, they are ready to start thinking abstractly about adding like fractions!
Adding Like Fractions using Abstract Thinking
Now that students understand how to add like fractions with concrete and representational models, you can move to the abstract–using an algorithm! I like to have students “discover” the algorithm using their understanding of their models.
When having students discover the algorithm, you might start by writing an equation on the board. For example, with the pizza scenario, you could write 2/8 + ⅜ = ⅝ on the board . Then, ask students about the relationship between the addition expression and the product. Hopefully, you’ll have some students who recognize that 2 + 3 = 5!
Now, I want to be realistic. Some students won’t be ready to add fractions with the algorithm just yet. Some students will need to stick with the concrete or representational models – and that is a-okay. There will also be students who need to move back and forth between the different stages, depending on the problem!
Helpful Resources
If you’re feeling overwhelmed with teaching multiplying fractions, try out some of these resources. They are filled with examples, guided practice, and more to help students master multiplying fractions.
#1 Guided Notes: These Guided Notes will help you easily scaffold students’ learning. The notes go over adding and subtracting like fractions, decomposing fractions, and adding and subtracting like mixed numbers. The notes really come in handy when reinforcing the representational and abstract portion of the CRA method, and you can use the problems in the notes to introduce the concrete stage.
If you love these guided notes, you can grab the entire 4th Grade Math Guided Notes Bundle.
#2 Interactive Worksheets: If you have students that are struggling with adding fractions or need extra help, the 4th Grade Fraction Interactive Worksheets make it a breeze. Each worksheet includes a QR code that links to a mini-lesson video. Plus, you can choose between worksheets with a word problem, just the algorithm, or the algorithm and the model to fit the stage your students are at.
#3 Math Riddles: Add a bit of fun to adding fractions with Adding and Subtracting Fractions Math Riddles. Each worksheet reviews adding and subtracting like fractions, decomposing fractions, or adding and subtracting like mixed numbers – plus includes a zoo themed riddle! As students solve the algorithms, they will fill in the blanks to answer the riddle. This makes for great morning work, early-finisher practice, and independent work.
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