Learning the times tables by rote with traditional flash cards can be a frustrating activity for children. Without any tangible or visual model to help them make a meaningful connection, multiplication facts in isolation are too abstract for many children to grasp. Array cards offer a better, more natural way to learn multiplication facts, building on what students already know about arrays. Children gain a deeper understanding as they learn multiplication through concrete, hands-on experience.
What is an Array Card?
An array card is a rectangle divided into squares. Its shape and size depend on the numbers being multiplied. For example, a 2x9 array card will be long and skinny. A 5x5 card will be square in shape. One side of the card shows the array with its dimensions written as a factor pair. The other side shows the product. Array cards are easy to make, or they can be purchased from educational suppliers.
At the simplest level, array cards can be used in place of flash cards to practice multiplication facts. The shape and size of the cards serve as contextual clues to help children recall the products. If they can't recall a product straight away, children can count the squares in the array. Even better, they can skip-count by rows, reinforcing their understanding of multiples.
Understanding Multiplication and Division
While children are using array cards to learn basic facts, they are also gaining an understanding of the properties of multiplication. They quickly see that a 3x4 card can be turned on its side to show 4x3, and that changing the order of factors does not change the product (commutative property). Also, they can illustrate the distributive property by covering a 6x4 card with two 3x4 cards. The array cards make it easy to see how the distributive property can be expressed as an equation: 6x4 = (3x4) + (3x4).
With a minor adjustment, array cards make the relationship between multiplication and division easy to see and understand. Flip the cards over so that the products are showing and pencil in one of the dimensions. For example, the back of a 3x4 card would show the product 12 and one dimension of the array (either 3 or 4). Looking at the product side of the card, students try to guess the missing factor (3 x ? = 12) or they can treat it as a division problem (12 / 3 = ?). Children can use the shape of the card as a clue to help them recall the multiplication or division fact.
Learning Math Through Play
Array cards can be used to play a variety of math games that reinforce multiplication skills and concepts. Several tried-and-true games have have been developed by TERC, an educational research group. Alternatively, teachers and students can design their own games.
Array cards work because they teach in the way that children learn. Through hands-on exploration and play, children progress naturally from a concrete level of understanding to a mastery of abstract concepts. Array cards take the mystery out of multiplication and keep it firmly grounded in the real world.
Resources
TERC. Investigations in Number, Data and Space: "What are Array Cards?" 2007.
Mark Giffen - Mark holds a BA in English and a master's degree in elementary education from the University of Chicago. He taught school for 19 years in ...
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