Arrays of Multiplication
Basics on the topic Arrays of Multiplication
Multiplication with Arrays
Arrays are a useful way to simplify multiplication. They can help you visualize multiplication. In this lesson, we are teaching multiplication using arrays.
An array is a model that can be used to find the product, or total, of a multiplication problem. We use arrays to lay out multiplication problems in rows and columns. Then, we count the number of marks to find the product. This is how to multiply using arrays.
You may see arrays in textbooks, worksheets and websites that are illustrated with symbols or pictures. But, when drawing your own array, it's normal to use x’s, dots, or circles.
Displaying Multiplication Facts Using Arrays
In theory, any multiplication fact can be found using arrays! However, you may be limited by the space required to draw out all the rows and columns depending on the fact. You find multiplication facts using arrays by looking at the expression. To start, look at the first factor in the expression and neatly draw the same number of rows. Then, look at the second factor and neatly put that number of marks on each rows Finally, count the total number of marks drawn to calculate the product. You can repeat this process of using arrays to show multiplication concepts.
Using Arrays in Multiplication
Using arrays to teach multiplication is simple. Pick a multiplication fact to model using arrays. We will use the fact two times three. To start, look at the first factor, two. Neatly draw two rows.
Then, look at the second factor, three, and neatly make three circles on each of the two rows.
Finally, count the total number of circles made to calculate the product. There are six circles in total. This means the multiplication fact two times three has a product of six. You can use this concept to solve multiplication worksheets using arrays.
Using Arrays to Solve Multiplication Problems – Summary of Steps
These are the necessary steps you need to follow using arrays to solve multiplication problems:
Steps  What to do 

1  Looking at the expression, begin by identifying the first factor. 
2  Neatly draw that same number of rows. 
3  Look at the second factor and neatly put that number of marks on each row. 
4  Count the total number of marks drawn to calculate the product. 
Have you practiced yet? On this website, you can also find examples of multiplication using arrays on worksheets, activities, and exercises.
Frequently Asked Questions regarding Multiplication with Arrays
Transcript Arrays of Multiplication
Mr. Squeak's workshop has gotten very messy from all of his recent projects. It's time for him to organize his materials so that he knows where everything is. Luckily, Imani has volunteered to help out. She can scan the room to locate the scattered items and represent the amount with a multiplication expression. But, they will need our help to organize with "Arrays of Multiplication!” An array is a model that can be used to find the product, or total, of a multiplication problem. We use arrays to lay out multiplication problems in rows and columns, then count the number of marks to find the product. When drawing your own array, it's common to use exes, dots, or circles. Let's try this out with the example two times three. To start, look at the first factor. This tells us how many rows we need, so here we need two rows. Neatly mark the two rows accordingly. Then, look at the second factor and neatly make three circles on each of the rows. Finally, count the total number of circles made to calculate the product: two times three equals six. Let's use this knowledge to help Mr. Squeaks and Imani. First, Mr. Squeaks holds up a wrench. Imani scans the rooms to locate all the scattered wrenches. She comes back with the expression three times six. Let's use an array to determine how many wrenches Mr. Squeaks has and how he should organize them. The first factor in this expression is three. This tells us to mark three rows. The second factor, six, tells us how many marks to put on each row. Finally, we count each mark to calculate the product. There are eighteen marks, so the product of three times six equals eighteen. Mr. Squeaks can hang all of his wrenchs in three rows of six! Second, Mr. Squeaks holds up sandpaper. Imani scans the rooms to locate all the scattered pieces of sandpaper. She comes back with the expression eight times seven. Let's use an array again to determine how many pieces of sandpaper Mr. Squeaks has and how he should organize them. But, they will need our help to organize with... This tells us we mark eight rows. The second factor, seven, tells us how many marks to put on each row. Finally, we count each mark to calculate the product. There are fiftysix marks so the product of eight times seven equals fiftysix. Mr. Squeaks can organize his sandpaper in a cabinet with eight rows of seven! Lastly, Mr. Squeaks shows Imani a nail. Iman scans the rooms to locate all the lost nails. She comes up with the expression ten times five. How can we solve this? We can use an array to determine how many nails Mr. Squeaks has and how he should organize them. The first factor in this expression is ten. So how many rows should we draw? We should draw ten rows. What does the second factor tell us? The second factor, five, tells us how many marks to put on each of the ten rows. What is the final step? The final step is to count each mark to calculate the product. How many nails does Mr. Squeaks have? He has fifty nails so the product of ten times five equals fifty. Mr. Squeaks can organize his nails in ten rows of five on a piece of wood! Wow! Mr. Squeaks workshop looks tidy now, thanks to all our hard work! When using arrays with multiplication, remember: Arrays are models of rows(...) and columns that are used to lay out the product of a multiplication problem. To draw an array, look at the first factor in the expression and neatly draw the same number of rows. Then, look at the second factor and neatly put that number of marks on each row. Finally, count the total number of marks drawn... to calculate the product. "Wow, I can see where everything is now!" "Hey, what's this?!" “I was wondering where my giant magnet went!”
Arrays of Multiplication exercise

Help Mr. Squeaks and Imani choose the best array container for the screws.
HintsMultiply the number of rows by the number of columns to get the total number of compartments in each box.
There is more than one correct answer.
One of the containers will not work to organize the screws.
SolutionMr. Squeaks and Imani can organize the 24 screws into arrays of 4 x 6, 2 x 12, and 3 x 8. He cannot organize the screws into an array of 5 x 5, since 5 x 5 = 25.

Can you find the rows and columns in this array?
HintsRows are horizontal, or go across.
Columns are vertical, or go up and down.
SolutionRows are horizontal, or go across.
Columns are vertical, or go up and down. 
Which expression does each array belong with?
Hints*In a multiplication expression:
The first factor tells us the number of rows
The second factor tells the number of columns.
Here is an array representing 3 x 8.
SolutionHow many rows are there? How many columns are there?
Example:
3 rows with 5 tiles each. The expression is 3 x 5

What is the product of each expression?
HintsMore than one expression belongs to each product.
Expressions with the same factors have the same product.
Try drawing an array with rows and columns to help you find the answer.
SolutionHere you can see which expressions belong to which product.

Which array below shows the expression 4 x 6?
HintsIn a multiplication expression:
The first factor tells us the number of rows.
The second factor tells the number of columns.
Here is an array representing the expression 2 x 12.
SolutionIn this array, there are 4 rows with 6 tiles each. This array represents the expression 4 x 6.

Can you help decide if Mr. Squeaks made an array?
HintsAn array is made up of rows and columns containing equal groups of items.
Not all terms will be used.
SolutionImani is correct in saying the organized tools are not in an array. An array is a formation made of rows with an equal number of objects. Mr. Squeaks did not create an array, because there are not an equal number of tools in each row.
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