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# 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 HappyNumbers.com to explore our full curriculum and sign up for a free trial.

## Multiplication

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.

## Division

The flip side of multiplication is division, and it is the second important theme in Grade 3. Students first encounter division by dealing out badges, used as manipulatives, into equal groups. The algorithm is the same: we start with 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  and be a part of a narrative story 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 the help of Tape Diagrams. … 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. 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 understand what is going on perfectly! 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.   ## Problem Solving with Units of Measure

### Weight units

Weighing objects using Balance Scales is an excellent introduction to measuring the weight of various objects. To introduce the concept of Pan Balance students can firstly compare the weight of different objects without using units of mass. In 3rd grade students progress to weigh objects using grams and kilograms as standard units of measurement. The visual representation of the Balance Scale helps to show the interrelation between kilograms and grams. Once students grasp the idea of units of measurements they can start weighing objects using pan balances and scales. Using interactive cards Happy Numbers helps to diversify the topic and make it more exciting for students as in the real classroom, it’s impossible to weigh a squirrel or a lion. Now that students have mastered measuring weight using different units of mass, they can move on to problem solving.

### Liquid units

Measuring liquids starts with explaining the concept of capacity and comparing containers with different volumes. Moving further students start to realize that in order to compare different volumes they also need to refer to some concrete units of measurements. Before introducing them, it’s best to show the practical purpose of common units of measurement. It may be difficult to keep measuring things with random objects like cups if each of them is different.

It’s crucial for the 3rd grade students to learn how to estimate and measure liquid volumes and masses of objects using standard units. Happy Numbers cards may come in handy while practicing and mastering these skills. ## Two- and Three-Digit Measurement Addition and Subtraction Using the Standard Algorithm

Once students are comfortable with measurement units, in the next module, they can combine that knowledge with already mastered addition and subtraction skills. They practice both skills while solving word problems. Here, we support students by using tape diagrams and charts to represent the activities.  Thus students lay the groundwork to move onto more difficult problems with two- and three-digit column subtraction and addition. Happy Numbers provides students with a large number and variety of tasks for practicing and developing fluency.

## Rounding

Rounding is a practical topic. To interest students, we start with explaining the practical purpose of it in real life. Again, familiar cosmic narratives will help engage the students in the topic:

As hard as it may seem to understand the concept of rounding for students, it's crucial to make sure that they get the main principles of the rule. Memorizing the numbers that round up or down is not enough. Instead, students should visualize the concept with the help of a number line and identify which tens are the nearest to the given number. Once students have mastered the concept of the nearest tens, it’s time to introduce rounding up and down, casually mentioning cases with fives in the middle of the number.

By making it visual students will gain a better understanding of how rounding works and when we need to round up and down. When students have learned the concept, they can move to a more abstract level by using a clear algorithm introduced by Happy Numbers.

In order to practice new skills while also keeping students interested and engaged, the Happy Numbers curriculum includes multiple interactive activities in which students can round real life objects up or down, like for example, the height of the Statue of Liberty or the Grand Canyon's depth. ## 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 have already completed! 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 Measurement, Plane Figures, etc.

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

Finally, in this grade, we conclude the topic by learning how to find an area using side lengths. A playful visual explanation of that concept is easy to understand and accessible for every student.

And it’s exciting to learn the applications of the area through animation!

## Fractions

Learning fractions is the logical culmination of Grade 3, where we give students the first formal introduction to this topic. 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 a 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 must 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?

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