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# How to Teach Multiplication to 3rd Grade: Introducing the Concept

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One of the main concepts of the 3rd grade is definitely multiplication. This basic knowledge is as crucial as addition and subtraction because all future skills are built on these foundations. That's why it's so important to form a conceptual understanding rather than just to memorize facts. Students should go beyond learning math facts by heart and grasp the concept of multiplication itself, thus stimulating their own math flexibility skills.

An effective way to introduce the idea of multiplication is step by step, progressively referring to math skills students already have. It’s better to start with invoking concrete and more familiar associations, for example, learning to manipulate and add groups of objects with natural structure. Happy Numbers uses common groups of objects to introduce multiplication as repeated addition and connect it with students’ personal experience: candles in a candleholder, bananas in bunches, wheels on a bicycle, etc.

The next step is manipulating groups of more abstract objects. In this step, students should be able to see and understand that a certain number of objects can be collected into a certain number of groups. Then, students learn to describe these pictures in groups. For example, 3 groups of 4 objects make 12 objects.

Students calculate the repeated addition sums by adding on to the previous addends, step by step, or by grouping the addends into pairs and adding. Now they see that there are two ways of showing the same fact: 4 groups of 3 make 12 or 3 + 3+ 3 + 3 = 12. With this understanding, it’s time to introduce the signs of multiplication and equation instead of words “groups” and “make” to shorten the multiplication fact.

It’s crucial for students to understand that multiplication is all about equal groups. That’s why Happy Numbers tries to make sure of this by providing relevant examples of flash cards where students are able to test themselves and  practice multiplication facts through visualizations.

Now when students begin to grasp the idea of multiplication, it’s time to slowly introduce arrays or tile models. This, being a more abstract level of representation of multiplication, also visually demonstrates the commutative property and explains the principles of calculating the area of a rectangle.

Let’s take a look at the models below and see that the order in which tiles are arranged doesn’t change the product.