Adding fractions with common denominators (printable included)
Adding fractions is one of the most essential yet complex skills that students will have to master in grades 4 and 5. The process consists of multiple steps, and teachers have to make sure that students go through each one carefully before moving on to a more advanced stage.
First, students understand how to add fractions with common denominators, referring to simple models. They gradually become ready to expand their knowledge and work with mixed numbers and fractions with different denominators.
Adding fractions with common denominators using concrete models
A good start is to explain to students what adding fractions with common denominators means in the first place. We recommend using simple analogies, such as pies cut into equal numbers of pieces.
Once students get the idea of counting parts of similar objects to add them, teachers can move to relating these objects to numbers and fractions. Continue using concrete models, like slices of pizzas and pies. These objects, when they’re divided into pieces, seem to be the most relatable representation of fractions. That’s why Happy Numbers uses them to explain the concept behind adding fractions.
See how easy it is to learn how to add fractions with common denominators by adding one fifth of a strawberry pie with three fifths of a blueberry pie!
We at Happy Numbers recommend starting with the simplest examples of addition of fractions within 1. Soon, after apples and pies, students can move to a bit more abstract representations, like a number line model.
Using this model, teachers can show students that addition of fractions can be represented in the form of movement on the number line. On Happy Numbers, students can even model such cases by themselves by dragging a slider from one point to another. To see more, check out our curriculum.
Teachers are free to incorporate their own ideas, for example, fraction bars or fraction walls instead of the number line.
Based on multiple tasks with visual representations, finally, teachers can help students master the main rule: adding fractions with common denominators is all about adding numerators (or, if we refer to familiar terms, adding parts of the whole, while denominators stay the same).
This is the part where teachers provide fluency practice with and without visual support for their students. Happy Numbers provides free printables on fraction addition that can be used for independent practice.
The example below includes the number line model to support students in solving equations.
In addition, we like to reward students with game-like activities - the idea, which teachers can also benefit from.
Adding fractions and mixed numbers
Relying on students’ knowledge of mixed numbers and the associative property of addition, we slowly progress to adding fractions and mixed numbers. This won’t be a problem for students, since they’ve already built a firm foundation of adding fractions with common denominators within 1. Here, additionally, they’ll have to apply the knowledge of the associative property.
First, remind students that mixed numbers represent the sum of a whole number and a fraction, which will make it easier for them to perform the addition using the associative property.
This way, students can visualize each step they need to perform in order to find the correct answer of the equation: represent the mixed number as the sum of its parts, and add the fractions first, leaving the whole part outside the parentheses.
To see the full exercise, follow this link.
After reminding students of the associative property, we recommend introducing more complex cases, where addition of two fractions results in a whole number.
As always, teachers can start with models to explain the concept behind the equation and to show that students can also add a fraction and a mixed number by completing a whole.
On Happy Numbers, we go further by letting students restructure the model by themselves: in the example below, they’re asked to drag part of the second fraction to complete the whole of the first fraction.
It’s crucial to create constant connections between models and numbers representing them, so it’s always a good idea to ask students to record their actions using math symbols while they work with models.
Teachers should include as many examples as students need to practice their new skill on a mental level. After training on models, students are ready to add fractions and mixed numbers by making a whole with no visual support, and at this stage Happy Numbers makes sure to introduce as many practical tasks as needed.
Adding mixed numbers
Only after learning how to add fractions and mixed numbers are students ready to move to adding two mixed numbers together. Once again, remind students to apply the associative property and start by adding the wholes of mixed numbers separately from the fractional parts.
Relying on the prior knowledge that a mixed number represents the sum of its parts, teachers can ask students to calculate the final answer by adding the wholes and the fractional parts together.
Finally, it’s time to introduce students to more complex cases, where they’re asked to convert resultant fractions into mixed numbers. Just like in the example below, teachers are free to include various tasks for practice: adding fractions and whole numbers, fractions and mixed numbers, two mixed numbers, etc.
As we’ve illustrated, Happy Numbers helps students build their skills step by step from learning how to add fractions within 1 to mastering the skill of adding fractions that result in a mixed number, and practicing even more complex cases with mixed numbers.
Adding fractions involves more than just knowledge of the addition concept: students should also be ready to apply the associative property of addition, transform improper fractions to mixed ones, and more.
Once students have mastered these foundational skills of adding fractions, they’re ready to progress to the next level of complexity - adding fractions with different denominators.