When I first started teaching, I thought that teaching how to multiply fractions would be super easy. Walk in the park level easy. All you have to do is multiply the numerators and multiply the denominators, and you are done. Simple, right? While that is a pretty easy algorithm, jumping right into the how-to of multiplying fractions will leave your students with no conceptual understanding. And they will flounder.
Instead, I recommend using the CRA (Concrete-Representational-Abstract) approach to teaching multiplying fractions. It will help your students have a deeper understanding of what exactly fractions are (which goes a long way in application), not just a simple algorithm.
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 Multiplying Fractions
It might come as a surprise, but word problems are the best place to start with mathematical concepts. Typically, we see word problems as the “end game” or what our students will achieve when they master the algorithm. But CRA has the algorithm or abstract as the last part of the learning process.
Basically, starting with the word problem is all about creating context. Word problems give a context to multiplying fractions, which helps multiplying fractions make more sense and helps students model the scenarios.
Multiplying 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–counters, fraction tiles, fraction circles, or even just paper to fold!
When working on multiplying a whole number by a fraction, I like to use counters and a tape diagram. You can have students draw the tape model on a whiteboard, and using red and yellow counters, visually modeling the problem. Let’s take a look at an example:
Allie had 6 cups of sugar to use while making cookies. After baking all of the cookies, she only used ⅔ of the sugar. How many cups of sugar did Allie use?
As you can see in the model, students would draw three boxes, each to present ⅓ of the sugar used. The counters in this scenario represent the six cups. When the counters are laid out across the table, there are two counters in each box. To figure out how many ⅔ would be, students would look at two of the boxes and add up how many counters there were in total.
Now, let’s take a look at a word problem multiplying two fractions together:
Branda made lasagna for her family. After eating dinner, there was ½ of the lasagna left. The next day, Branda’s husband ate ¼ of the leftover lasagna. What fraction of the original lasagna did he eat?
The paper-folding method works really well in this scenario. The piece of paper would be folded in half to represent ½. Then, the paper can be folded or sectioned into fourths. If we look at ¼ of the leftover ½, students can see that it was actually ⅛ of the original lasagna.
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 multiplying fractions with their own drawn models!
Representation of Multiplying Fractions
When students are ready, start modeling problems using representations. This is the “seeing” stage where students show what is happening with pictures or diagrams.
Let’s think back to the example of Allie and the sugar scenario (multiply a fraction by a whole number). Now, instead of using manipulatives, students will actually draw the problem. They can still use a tape diagram, but instead of placing counters, they can draw dots into the boxes. If students are good at dividing, they can also write numbers in the boxes!
It’s very similar to the word problem with Branda’s lasagna (multiplying two fractions together). Instead of physically folding a paper, students will draw a square, and then begin creating the sections. First, they will draw a line down the middle to present ½. Then, they will section the square into fourths.
The key is to make sure students understand the concrete model before you move to representation. They cannot master multiplying fractions if they are moving on before they are ready!
Multiplying Fractions with the Abstract
Now that students understand how to multiply 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 lasagna scenario, you could write ¼ x ½ = ⅛ . Then, ask students about the relationship between the multiplication expression and the product. Hopefully, you’ll have some students who recognize that 4 x 2 = 8.
Now, I want to be realistic. Some students won’t be ready to multiply 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 5th Grade Guided Notes will help you easily scaffold students’ learning. The notes go over multiplying fractions, whole numbers, and 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 5th Grade Math Guided Notes Bundle.
#2 Interactive Worksheets: If you have students that are struggling with multiplying fractions or need extra help, the 5th 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 multiplying fractions with Multiplying Fractions Math Riddles. Each worksheet reviews multiplying fractions, whole numbers, and/or 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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