Grade 3 Overview: Introducing Fractions

Grade 3 is an amazing time of huge discoveries in math! After comprehensive practiсe with addition and subtraction in previous grades, students now encounter multiplication and division, get a first taste of fractions and area measurement, delve deeply into arrays, and even touch on algebra.

Such a wide and varied agenda inspired Happy Numbers to create a curriculum that will both develop deep conceptual understanding and meet strict educational standards, enabling future academic success.

Because all critical areas of Grade 3 require work with arrays, Happy Numbers supplied the course with a large variety of visual models. Plenty of elements contribute to both the clarity of mathematical operations and students’ consistent immersion in new math themes with a smooth transition from concrete to abstract.

Let’s go ahead and take a look at how Happy Numbers can strengthen your math lessons for Grade 3 students!


All exercises mentioned below are part of the Happy Numbers course for Grade 3. Visit to explore our full curriculum and sign up for a free trial.



The Grade 3 curriculum is mostly devoted to multiplication. Happy Numbers reveals it through addition models with concrete objects learned in previous grades. This clearly demonstrates that multiplication is basically the same as repeated addition. Also, the use of models with concrete objects helps to develop deep understanding of the process and helps students grasp basic principles.

First, students simply count the objects. The exercise appears familiar at first…


… but it turns out to be counting of equal groups, which leads to the real meaning of multiplication.

Then, they learn that an object itself and a group of objects have different meanings and can be represented numerically.




The flip side of multiplication is division, and it is the second important theme in Grade 3. Students first encounter division by dealing out apples, used as manipulatives, into equal groups. The algorithm is the same: we start with familiar, tangible items to show the process.


Even those who never tried Happy Numbers before will easily navigate these exercises, as the items used here are based on real objects. The ability to interact with objects on the screen engages students and gives them a basic understanding of mathematical operations at the application level.


Properties of Multiplication and Division

After the sneak peek at multiplication and division, students advance to the study of their properties. They make a smooth transition to more abstract models. Look how we do so with a help of Tape Diagrams.

We start with familiar items, such as lightbulbs…


… which finally form a mathematical model.


Happy Numbers gradually raises the level of abstraction in tasks, so students will also encounter Tape Diagrams with number notation in unit form.


This classic instrument for learning commutative and distributive properties of multiplication and division becomes much more engaging with the ability to drag items and magically manage construction of the math model.


Students progress to models with only abstract items, like beads or tiles. It is the last step before we ask students to count numerically. Mathematical thinking starts here, when students can understand computation without tangible items.


We reinforce properties and build the connection between the visual model and numbers.


Finally, students transition from manipulatives with real objects to abstract diagrams, which model the pattern for solving real-life problems.



Multiplication Table

Now that students have mastered abstract models, they can move to numerical equations and the multiplication table. Memorizing the multiplication table without understanding the concepts behind it will not allow students to move forward and effectively accumulate knowledge.

Happy Numbers divides learning of the multiplication table into two parts. In Module 1, students learn basic properties of multiplication and practice them with numbers from 1 to 5 using visual models, with both concrete and abstract objects. After they gain an understanding of the multiplication concept, they continue to learn the table with abstract models and numerical equations.

After these exercises, students can confidently determine multiples in a multiplication chart because they perfectly understand what is going on!


Even if they get lost, Happy Numbers will support them with immediate feedback.


The diversity of tasks leads students to fact fluency and confident work with the multiplication table.





Area Models

Multiplication goes hand in hand with the concept of area. In Grade 3, students discover area as a numerical characteristic of the two-dimensional space occupied by a figure. But first, they must grasp the idea of the surface itself. That’s why Happy Numbers starts with game-like model-building tasks.


Through exercises about construction, we simply and clearly explain how the area of a rectangular figure is measured.


This is how students gradually come to understand area units. We ask them to draw a figure representing a square centimeter because through tangible experience they will develop a deep understanding of its measurement.


Surprisingly, the area model looks pretty much the same as the exercise with tiles students completed before! This is how they discover the connection between multiplication and area and learn area-finding methods. This is a great foundation for Grade 4, where they will step into a wide world of geometry and encounter Metric Measurement, Angle Measure, Plane Figures, etc.

The entire learning process is supported by vivid, illustrative examples.


In this grade, we conclude by finding area using side lengths. It’s amazing to learn the applications of area through animation! It is easy and accessible for every student.




Learning fractions is the logical culmination of Grade 3, where we give students the first formal introduction to this theme. The Happy Numbers fraction syllabus starts with working on fractional strips, learning the names of common fractional parts, and naming fractions on other models.


Fractions are absolutely clear when it comes to pie, aren’t they?


With immediate feedback, students will learn from their mistakes and build a strong foundation before going on.

In Topic B, we make a smooth transition from the visual model to the numerical and introduce the theme of unit fractions.


Happy Numbers consolidates knowledge through multiple representations, which helps to develop mathematical mindset.




Visual models continue to be essential when Happy Numbers introduces ways to compare fractions. Through the sequence of manipulative activities, students come to an understanding of the rule of how to compare fractions with the same numerators or denominators.


Besides using pictures and models, students naturally extend their understanding of both proper and improper fractions as points on a number line. They see that fractions have a place on the number line, just like whole numbers do!



Finally, students will not only understand the place value of any fraction less than one, but will also have the ability to find equivalent fractions and compare those which have the same numerator or the same denominator.



Knowledge (that Grows)

Math thinking is not something that can just be given. It is a complex skill that can be developed by diverse, consistent, and comprehensive learning. That’s why Happy Numbers created the Grade 3 program taking into account students’ prior knowledge and the knowledge that they will need in the next grades. Heavily grounded in pedagogy, Happy Numbers helps teachers to provide their students with personalized learning pathways and build meaning behind math for each student in the class. Start now, and get your personal AI-assistant, based on the latest technologies for education!


How can you enhance your instruction with Happy Numbers?

It’s incredibly easy to bring Happy Numbers to your class, and you can do so at any point in the school year. Sign up now or watch a 1-minute video that will guide you through the setup:


If you have any additional questions, our support team is always here to assist you. Click the blue messenger icon at the bottom right corner of this page to start a conversation with them.