Introducing Multiplication Using Arrays in Everyday Objects

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You might be wondering how you can teach your students to master multiplying single-digit numbers and have even heard of multiplication using arrays. Suppose you were asked by your student what multiplication is; you can explain that it is one of the four basic mathematical operations wherein you repeatedly combine the same values until you reach the final repetition. However, as simple as the sentence can sound, the idea may still be puzzling to your students. 

It can lead to even more questions such as: What is that value being repeated? How do you combine repeated values? How many times do you repeat combining those values? When does the repetition stop?

These words, thoughts, concepts, and ideas are all abstract to a young learner. While it’s essential to learn the vocabulary associated with multiplication, a verbal explanation for an abstract concept can lead to more confusion; this is where teaching multiplication using arrays is a convenient visual tool. 

In this article, we’re going to give you ideas on how to explain what an array is to your students, how it is found in everyday objects, and how it can be used for teaching multiplication. We’ll also give you a free lesson plan plus activities and tools to download and use with this lesson, so keep reading for more. 

Explaining Arrays to Kids

We see arrays in ordinary things around us, which is a great entry point into explaining what an array is. These common visual examples can help your students begin to understand how multiplication works. A dozen eggs are arranged in a tray with two rows having six eggs in each row. Imagine being in a grocery store and notice how an equal number of canned goods can be stored in the rows of shelves. Even app icons on a smartphone or tablet are in a grid arrangement. We can also use tiles on the floor to show columns and rows.

With this as an entry point, explain that arrays are simply objects structured in rows and columns. Rows are arranged horizontally, while columns are arranged vertically (it helps to remember columns like pillars). This can be demonstrated visually by drawing numbers from 1 to 3 in different orientations.

Write the numbers 1 to 3 from left to right. This shows the number of columns you can make.

When teaching multiplication using arrays, students need to understand the concept of a column

There are 3 columns because you can draw 3 vertical lines. You can tell your students that counting rows start from the top to the bottom.

Write the numbers 1 to 3 from top to bottom. This shows the number of rows you can make.

When teaching multiplication using arrays, students need to know the basic concept of rows

There are 3 rows because you can draw 3 horizontal lines. You can tell your students that counting rows start from left to right.

Now that navigating the rows and columns of an array has been visually explained, you can give a real-life example.

For instance, a dozen eggs placed in a 2 by 6 tray can be interpreted as 2 rows of 6 eggs. Thus, 2 rows and 6 columns can be written as 2 x 6.

With this representation, we can count from left to right until 6, and we can count from top to bottom until 2. This means that there are 2 rows of 6 columns. Two rows of 6 eggs are the same as 2 x 6. Hence, when counting all the eggs in the array, there are 12 eggs all in all. We should also note that each row should have the same number of objects inside to represent an array model.

Similarly, if using a smartphone as an example, have students count how many icons are in a row and how many are in a column and have them write down the numerical representation of ____(rows) x _____ (columns). 

Arrays are Similar to Equal Groups

Let’s recall representations of objects enclosed in equal groups. Since each row contains an equal number of objects inside, a row can also be considered a grouping. Therefore, we can parallel the number of groups as the number of rows and the number of objects in each group as the number of objects in each row.

Imagine 3 containers and each container has 4 marbles. Therefore, there are 3 groups of 4 marbles.

If we arrange the marbles in rows and columns, there will be 3 rows and each row has 4 marbles in it.

Rearranging the representation of equal groups into an array model clarifies that each row contains the same number of items. This also explains the earlier questions:

What is that value being repeated? For this case, we are repeating 4 marbles 3 times in a row.
How do you combine repeated values? You combine them in rows and columns.
How many times do you repeat combining those values? There are 4 marbles in each row. There are 3 rows. Therefore, we are repeating 4 three times.
When does the repetition stop? The repetition stops when we reach the maximum number of rows. In the example above, we stop once we’ve repeated the value 4 three times.

An Array is a Table

Another application of array models is drawing a table. No, not the table used for furniture. We are talking about a table made for data. An array is also a table because a table shows rows and columns.

Consider the game tic-tac-toe. To play this game, you first have to draw a grid that is 3 squares by 3 squares (or as we describe arrays, 3 rows of 3 columns). Because the table or grid is 3 by 3, there are 9 empty spaces wherein you can put the X and the O alternately. If all the spaces are occupied, no one wins, but we can see 3 rows of 3 items in each row.

This visualization can help students acknowledge that any drawing partitioned into a table can show an array model. To add to this knowledge, you can also easily integrate the concept of a multiplication table with your students. We can draw the multiplication table using 10 rows and 10 columns. The top leftmost corner is 1, and the bottom rightmost corner is 100.

Because you have taught your student how to read arrays, your student may understand the navigation of a multiplication table easier. For example, what is the product if you have 5 rows of 4, the student can count 5 times downward, then 4 times to the right to get 20.

To end, the total number of objects arranged in an array is the product of the multiplication expression. The numbers of rows and the numbers of objects in each row are called the factors; wherein there is a multiplicand and a multiplier. Array models can be applied to different visualizations.

Remember that arrays are all around us. Engage your students to look for different arrays in everyday objects!

Free Lesson for Multiplication Using Arrays

When you’re ready to move on from explaining arrays, it’s time to turn to using them in a lesson to explain multiplication. One of the ways we like to teach the use of arrays is to present an introductory word problem to your students. Try something like this:

Your school is holding a science fair! The students will display their projects in their classrooms. How many displays will be in each classroom if there are four rows of desks and each row has four desks?  

Feel free to tweak the word problem to something that your students can relate to or have a particular interest in. Invite them to come up with ideas of how they can solve the problem quickly.

You can demonstrate that you can count the desks as 4 + 4 + 4 + 4 = 16, but there’s an easier way by drawing an array, e.g., 4 x 4 = 16.

With the introduction and the basics of an array explained, ask your students another word problem. You can try something like this:

It’s your birthday, and you’ve baked cupcakes to give to your friends. You want to put two Hershey’s kisses on top of each cupcake, and you have 6 cupcakes. How many chocolates will you need?

FREE Multiplication Using Arrays Worksheets and Resources

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