how to do array math problems

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Teaching Multiplication with Arrays in Math

Students in Grades 3+ can more readily develop an understanding of multiplication when they see it visually. For example, they can picture a marching band arranged in equal rows or chairs set up evenly in an auditorium. In both cases, they are visualizing rows and columns. An arrangement of objects, pictures, or numbers in rows and columns is called an array . Arrays are useful representations of multiplication concepts (among other ideas in mathematics).

This array has 4 rows and 3 columns. It can also be described as a 4 by 3 array. The word "by" is often represented with a multiplication cross: 4 × 3.

This array has 5 rows and 4 columns. It is a 5 by 4 array.

Notice that the rows in each array are equal in length. Think of the rows as equal groups. Your students should have already used equal groups to multiply (2.OA.C.4).

If you arrange the equal groups in rows, you form an array.

When you show students the connection between equal groups and arrays, students can visualize how to use arrays to multiply. They will use arrays again later to divide.

Look at the multiplication sentence that describes the array below. The numbers in multiplication sentences have special names.

The numbers that are multiplied are called factors . The result of multiplying the factors is called the product .

Now look at what happens to the factors and product in the multiplication sentence when the array is turned on its side.

The order of the factors changed, but the product stayed the same. This is in fact always the case and a feature that has piqued the interest of mathematicians for centuries. You can change the order of factors, but the product stays the same, a mathematical property known as the Commutative Property of Multiplication . Students should be familiar with the commutative property because they have already seen it applied to addition (1.OA.B.3).

Help students realize that by applying the commutative property, they know twice as many multiplication facts. For example, if they know 8 × 5 = 40, then they also know 5 × 8 = 40.

Looking for more free math lessons and activities for elementary school students? Be sure to explore our Free Teaching Resources portal .

Get our FREE guide "Optimizing the Math Classroom: 6 Best Practices."

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How to Use a Multiplication Array to Help Your Child Master the Times Tables

What multiplication arrays are, why they’re so helpful for teaching the concept of multiplication, and how to use a multiplication array to help your child master the times tables. Includes a free printable multiplication array that you can use to model multiplication problems from 1×1 up to 10×10.  

Hands-on manipulatives help children make sense of math. They make math concrete and help children understand math at a deeper level.

But, when it comes to memorizing the multiplication facts, hands-on materials can become pretty cumbersome. After all, counting out 8 groups of 7 may take your whole math lesson! And, all that time spent counting won’t really help your child remember that 8 times 7 equals 56, either.

That’s why multiplication arrays are so helpful. Instead of counting out piles and piles of little plastic objects, you can model multiplication problems by simply sliding a piece of paper. Even better, multiplication arrays provide an simple visual model that not only helps kids understand the concept of multiplication– it helps kids memorize the times tables faster , too.

What’s a multiplication array?

An array is any arrangement in rows or columns. Cards laid out into rows to play Memory, seats arranged in rows for a recital, or numbers arranged in an Excel spreadsheet are all examples of arrays.

A multiplication array is simply an arrangement of rows or columns that matches a multiplication equation. You can make arrays out of objects or pictures, and you can use any sort of shape. For example, here are 3 different arrays that all show 3 × 4.

(Generally, the first number refers to the number of rows, and the second number refers to the number of columns. So, all of the above arrays are considered 3 × 4 arrays, not 4 × 3, even though the total number (12) would be the same either way.)

What are the benefits of a multiplication array?

1. multiplication arrays make it easy to visualize multiplication problems..

Hands-on objects are great for introducing multiplication, but they can be a bit of a pain when you’re doing a lot of problems or working with larger numbers. With a paper dot array, you can slide an L-shaped cover over the top of the array and show any multiplication fact you want from 1×1 up to 10×10. Here’s what the dot array and L-cover look like.

Here’s how you use them. For example, let’s say we wanted to help your child understand what 6 × 8 looks like. 6 × 8 means “6 groups of 8,” so slide the L-cover so that the dot array looks like this.

Each of the 6 rows has 8 dots, so there are 6 groups of 8 dots. So, the total number of dots in the array is the answer to 6 × 8. There are 48 dots showing, so 6 × 8 = 48.

2. Multiplication arrays help kids use strategies–not rote memorization–to find answers.

Let’s take 6 × 8. It’s one of the toughest facts for kids to memorize, but most children find it quite easy when they use 5 × 8 as a stepping stone.

Here’s how you teach your child to do this:

5 × 8 is 40. (5 × 8 makes a nice stepping stone, since children’s familiarity with 5s from their early years of arithmetic usually make the ×5 facts easy to learn.)

6 × 8 is just one more group of 8 than 5 × 8.

So, you can just add 40 + 8 to find the answer: 6 × 8 = 48.

This strategy works for all of the ×6 facts. And the good news is that there are similar strategies for all the multiplication facts!

• Related: Multiplication Strategies That Will Help Your Kids Master the Times Tables

3. Multiplication arrays make it easy for kids to see the commutative property in action.

The commutative property says that you can multiply numbers in any order and still get the same answer. For example, 2 × 7 and 7 ×2 both equal the same answer: 14.

To show your child this fact, use the dot array to show a multiplication fact. Then, turn the array 90 degrees. Now, the dot array shows the related multiplication fact–but the total number of dots didn’t change.

For more help using multiplication arrays to teach the times tables, check out Multiplication Facts That Stick .

12 thoughts on “how to use a multiplication array to help your child master the times tables”.

Very helpful so much.

This is wonderful. Thank you

I was wondering if you have any thoughts on how RightStart teaches multiplication as arrays. It teaches the opposite, that 3 x 4 should be represented as 4 rows of 3 apples. This seems different from the way that every other program teaches. I understand Dr. Cotter’s reasoning, but it bothers me that it deviates from the generally agreed on way of teaching arrays. Do you recommend teaching arrays the way you have them here, or sticking with RightStart if that’s the program we’re using? I don’t know how long we will be homeschooling so I worry about confusion if we transition to public school down the road.

Like you, I respect Dr. Cotter’s reasoning, but I find it a curious decision. (In Third Grade Math with Confidence, I’ll be using the more usual definition.) But I don’t think it’s anything to worry about, either. The beauty of arrays is that they show children that you can interchange the factors and still get the same product, so I’d suggest simply emphasizing that rather than the specific RS definition. Even if your child switches to a bricks-and-mortar school next year, I don’t expect it would cause much confusion. Kids are pretty adaptable, and any standardized test wouldn’t assume that kids know one definition rather than another for defining arrays.

Happy Math! Kate

Thank you for your quick reply! Truthfully I wish I could switch her to Math With Confidence. I like that it has fewer manipulatives, that it’s mastery-oriented, and that it still has the strong focus on conceptual understanding. She is in 2nd grade now so she is right in between what is available currently and what will be released in the spring. Is there any possible way to get my hands on the 2nd grade level early?

Wish I could get it to you, but I’m not able to distribute it while it’s in production. Sorry that the timing doesn’t work out for your daughter!

That makes sense. I just wanted to share with you that since I left these comments I purchased First Grade Math With Confidence for my younger daughter and it’s going great! She is having a blast with math and it’s so parent-friendly. Thank you for writing such an awesome curriculum!

Glad to hear that it’s going well, Grace!

Hello Kate, Thank you so much! I have a 8 yr old High Functioning Autistic child and this method is AWESOME and he’s getting it!! Thank you, thank you very much for what you are doing to help others. Can’t wait to get my PDF by email.

That’s wonderful that it’s clicking for him! Thanks for taking the time to let me know, and happy math!

Thank you for sharing…very helpful

thank you so much

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Arrays, Multiplication and Division

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Arrays hooray

In this unit students are given the opportunity to explore multiplication concepts using arrays. The use of multiple strategies and the sharing of strategies is encouraged, in group and whole class situations.

• Solve multiplication problems by using skip counting or additive strategies.
• Interpret and solve multiplication story problems.

In this unit the students use arrays to solve multiplication problems. Arrays are an arrangement of objects in rows and columns. For example, chocolate blocks are made up of an array of smaller pieces. The block below has two rows and five columns.

Orchards’ layouts are also arrays where the fruit trees are grown in rows and columns to make them easier to look after and easier to pick fruit from.

Arrays are strongly advocated by researchers in mathematics education because they model the binary (two factors) nature of multiplication. Therefore, this unit can be used as an introduction to multiplication. The number of rows and columns gives the factors by which the total number can be found, e.g. 2 x 5 or 5 x 2 for the chocolate block above. Arrays are also used extensively in the measurement of area, in finding all outcomes of a probability situation (Cartesian product), in grid systems on maps, and in spreadsheets and other digital tools. Recognising the multiplicative structure of arrays can be challenging for students, especially those who have little experience with equal sets.

Estimation is also an important component of this unit. Students are encouraged to use their number knowledge to anticipate approximate products when given two factors.

This unit can be differentiated by varying the scaffolding provided or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:

• supporting students to solve problems by counting, if that is their most sophisticated strategy. Encourage the use of skip-counting where possible
• modelling the effective use of the arrays on Copymasters 3 and 4, showing students how to partition the arrays using known number facts
• allowing students to use counters or other materials to create arrays
• reducing the numbers in the problems so that students are working with smaller arrays.

The contexts in this unit can be adapted to recognise diversity and student interests to encourage engagement. For example:

• lines of students in kapa haka groups, groups of people travelling in a bus or van, or planting seedlings in rows can be used as alternative contexts for arrays.
• te reo Māori kupu that could be introduced within these sessions include row (kapa) and column (tīwai), as well as words related to the fruits grown in the orchard problems and the numbers tahi (1) to rua tekau (20).

Consider how these contexts could provide links to other areas of current learning (e.g. about community gardens, school trips, planting out the school garden).

• Large pieces of paper for recording
• Counters and cubes
• Copymaster 1
• Copymaster 2  (made into cards for group station work)
• Copymaster 3
• Copymaster 4
• Copymaster 5
• PowerPoint 1
• PowerPoint 2
• PowerPoint 3

This series of lessons provides different contexts to explore multiplication concepts using arrays such as the one below. This array has 5 rows and 10 columns.

Session One: Getting started

The start of PowerPoint 1  shows the whole array. Show the complete array. Ask your students to open their eyes and take a mind picture of what they see. Click once to remove all the trees and ask your students to draw what their mind picture looks like.  One child could draw their picture on the whiteboard. This could then be referred back to throughout the rest of the lesson.

Look to see if they attend to the rows and columns layout even if the numbers of trees have errors. Discuss the layout.

• Have a pile of counters in the middle of the mat. Ask a volunteer to come and show what the first row of trees might look like. Or get 6 individuals to come forward and act like trees and organise themselves into what they think a row is. Alternatively click again in the PowerPoint so it’s easy for all to see what the first row of apple trees will look like. Ask your students to improve their picture if they can. What will the second row look like?  It’s important for students to understand what a row is so they can make sense of the problem. It is also important for them to notice that all rows have the same number of trees.
• Arrange the class into small mixed ability groups with 3 or 4 students in each. Give each group a large sheet of paper. Ask them to fold their piece of paper so it makes 4 boxes (fold in half one way and then in half the other way).
• How could you count the trees in groups rather than one at a time?
• What facts do you know that might help you?
• What sets of numbers do you know that might help you?
• What is the most efficient way of working out the total number of trees?
•  Ask the groups to cut up the 4 boxes on their large sheet of paper and then come to the mat. Gather the class in a circle and ask the groups to share what they think is their most interesting strategy. Place each group’s strategy in the middle of the circle as they are being shared. Once each group has contributed, ask the students to offer strategies that no one has shared yet. 

The shared strategies can be put into similar groups. Who used a strategy like this one?

• Show students PowerPoint 2 . The PowerPoint encourages students to disembed a given smaller array of trees from within a larger array. They are also asked to use their knowledge of the smaller array to work out the total number of trees in the larger array. This is a significant ability for finding the totals of arrays using the distributive property of multiplication.
• Provide your students with Copymaster 1 . The challenge is to find the total number of trees in each orchard. Challenge your students to find efficient strategies that do not involve counting by ones.
• As a class, share the different ways that students used to solve the Orchard Problems. You might model on the Copymaster to show how various students partitioned the arrays.

Sessions Two and Three: Exploring through work stations

The picture book Hooray! Arrays! by Jason Powe could be used to ignite interest in this learning.  In the next two sessions students work in pairs or threes to solve the problems on Copymaster 2 . Consider choosing these pairs to encourage tuakana teina through the pairing of more knowledgeable and less knowledgeable students.  Enlarge the problem cards and place them at each station. Provide students with access to copies of Copymaster 3  and Copymaster 4  (arrays students can draw on), and physical equipment such as counters, cubes, and the Slavonic Abacus.

Read the problems from Copymaster 2 to the class one at a time to clarify the wording. You may need to revisit the meaning of rows and columns by creating simple examples. As students work on a station activity, ask them to create a record of their thinking and solutions. The record might be a recording sheet or in their workbook. Note that Part 2 of each problem is open and requires a longer period of investigation.

As the students work watch for the following:

• Can they interpret the problem wording either as a physical representation or as symbolic equations?
• Do they create arrays of equal rows and columns?
• Are they able to use skip counting, additive or multiplicative strategies to find the total number of trees?
• Do they begin to see properties of whole numbers under multiplication? (for example, Apple Orchard Part 2 deals with the commutative property)

At times during both sessions you might bring the class together to discuss confusions or misconceptions, clarify language and share efficient strategies and ways of representing the problems.

Below are specific details related to each problem set.

Orange Orchard

Orange Orchard (Part 1) involves 6 x 8 (or 8 x 6). Students might use their knowledge of 6 x 6 = 36 and add on 12 more (two columns of six). That would indicate a strong understanding of the multiplicative structure of arrays.

Most students will use strategies that involve visualising the array and partitioning the array into manageable chunks (dis-embedding). For example, they might split rows of eight into two fours (6 x 8 = 6 x 4 + 6 x 4), or into fives and threes (6 x 8 = 6 x 5 + 6 x 3). Other students will use less sophisticated strategies such as counting in twos and fives, or a combination of skip counting and counting by ones.

Part 2 is an open task which requires students to identify the factor pairs of 24.

Encourage capable students to be systematic in finding all the possibilities (1 x 24, 2 x 12, 3 x 8, 4 x 6).

Kiwifruit Orchard

Part 1 requires students to coordinate three factors as the problem can be written as 3 x (4 x 5). Multiplication is a binary operation so only two factors can be multiplied at once. Do your student recognise the structure of a single orchard (4 x 5) and realise that the total is consists of three arrays of that size?

Similarly, in Part 2 students must restructure 36 plants into two sets. Do they partition 36 into two numbers, preferably that have many factors? The problem does not say that the two orchards must contain the same number of plants though 18 and 18 is a nice first solution. Once the two sets of plants are formed can your students find appropriate numbers of rows and columns that equal the parts of 36?

Strawberry Patch

Part 1 is a single array (5 x 12). Students might use the distributive property and solve the problem or 5 x 10 + 5 x 2 (partitioning 12) or 5 x 6 + 5 x 6. Some may re-unitise two fives as ten to create 6 x 10. These strategies are strongly multiplicative. Most students will use smaller units such as fives or two and apply a combination of repeated addition (5 + 5 = 10, 10 + 10 = 20, etc.) or skip counting (2, 4, 6, 8, …).

Part 2 is about factors that have the same product (24). This gives students a chance to recognise that some numbers have many factors and the expressions of those factors have patterns. For example, 6 x 4 and 3 x 8 are related by doubling and halving. The logic behind the relationship may be accessible for some students. If the rows are halved in length, then twice as many rows can be made with the same number of plants.

Apple Orchard

Part 1 gives students a chance to ‘discover’ the commutative property, the order of factors does not affect the product. In this case 5 x 10 = 10 x 5.

Part 2 applies the distributive property of multiplication though many students will physically solve the problem with objects. Look for students to notice that 12 extra trees shared among six rows results in two extra per row. So, the number of rows stays the same, but the rows increase in length to six trees. Similarly, if more rows are made the 12 trees are formed into three rows of four. The number of rows would then be 9. 6 x 6 and 9 x 4 are the possible options.

Sessions Four and Five

Sessions Four and Five give students an opportunity to recognise the application of arrays in other contexts.

The chocolate block problem involves visualising the total number of pieces in a block even though the wrapping is only partially removed. PowerPoint 3  provides some examples of partially revealed chocolate blocks. For each block ask:

• How many pieces are in this block?
• How do you know?

Look for students to apply two types of strategies, both of which are important in measurement:

Iteration: That is when they take one column or row and see how many times it maps into the whole block.

Partitioning: That is when they imagine the lines that cut up the block, particularly halving lines. They look to find a partitioning that fits the row or column that is given.

Copymaster 5  provides students with further examples of visualising the masked array.

The Kapa Haka problem is designed around the array structure of seating arrangements for Kapa Haka performances at school.

Begin by role playing the Kapa Haka problem. Use chairs to make a simulated arrangement of seats. You might like to include grid references used to locate specific seats.

Try questions like:

• How many rows are there? How many columns are there?
• How many audience members could be seated altogether?
• If the performance needed 24 seats what could they do?

Use different arrangements of columns and rows.

Give the students counters, cubes or square grid paper to design possible seat layouts with 40 seats. Encourage them to be systematic and to look for patterns in the arrangements. Some students will find efficient ways to record the arrangements such as:

2 rows of 20 seats                4 rows of 10 seats                5 rows of 8 seats

Record these possibilities as multiplication expressions on rectangles of card. Put pairs of cards together to see if students notice patterns, like doubling and halving.

It is important to also note what length rows do not work.

• Could we make rows of 11 sets? 9 seats? Why not? (40 is not divisible by 11 or 9 as there would be remaining seats left over)

If students show competence with finding factors, you could challenge them to find seating arrangements with a prime number of seats such as 17 or 23. They should find that only one arrangement works; 1 x 17 and 1 x 23 respectively.

As a final task for the unit, ask the students to make up their own array-based multiplication problems for their partner to solve.

• Tell the students that they are to pretend to be kūmara growers. They decide how many rows of kūmara plants they want in each row and how many rows they will have altogether.  As part of this learning, you could look into how early Maori people grew kūmara. This plant arrived in New Zealand with Polynesian settlers in the 13th Century. However, the climate here was much colder than the Polynesian islands. As a result, the kūmara had to be stored until the weather was warm enough for it to grow. The kūmara plant became even more important once settlers discovered that some of their other food plants would not grow at all in New Zealand’s climate. These kūmara were different to the ones we eat today - which came to us from North America. The books Haumia and his Kumara: A Story of Manukau by Ron Bacon , and Kumara Mash Forever by Calico McClintock could be used to engage students in this context.
• Then they challenge their partner to see if the partner can work out how many kūmara plants they will have altogether.
• Tell the students to create a record of their problem with the solution on the back. The problems could be made into a book and other students could write other solution strategies on the back of each problem page.
• Conclude the session by talking about the types of problems we have explored and solved over the week. Tell them that the problems were based on arrays. Let them know that there are many ways of solving these problems, tough multiplication is the most efficient method. Ask students where else in daily life they might find arrays.

Dear family and whānau,

This week we have been looking at arrays in class. Arrays have rows and columns like orchards. We have found it easy to figure out the number of things that are in arrays.

Ask your child to find some arrays in your home or neighbourhood. These could include a supermarket car park or an orchard, or an egg box, or the bus seats. Use these arrays to count the number of things in those arrays. You can also help your child to draw a sketch of the arrays showing the columns and rows. 

Figure it Out Links

Some links from the Figure It Out series which you may find useful are:

• Level 2-3, Number, High Flyers, page 14.
• Level 2, Number, Book One, Cooking Up a Storm, page 20.
• Level 2, Number, Book Two: It’s a Magic Mishmash, page 6; To Market, to Market, page 16; The Dinosaur Dig, page 19.
• Levels 2-3, Multiplicative Thinking: Sushi Surgery, pages 8-9; Fiordland Holiday, pages 16-17.
• Link, Number, Book One, Fives and Tens, page 4.
• Link, Number, Book Two: Table Tricks, page 2; Planting with the Whānau, page 6.

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Course: 3rd grade   >   Unit 1

Multiplication with arrays.

• Understand multiplication with arrays
• Multiply with arrays

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Video transcript

Multiplication Array – Definition with Examples

What is a multiplication array, how do we represent a multiplication array, what are factors and products in a multiplication array, solved examples, practice problems, frequently asked questions.

To understand the concept of multiplication array, let’s first break the concept into two words and understand them separately.

Multiplication is the concept of mathematics that allows us to multiply one number with another. For example, 3 x 5 is three times five, which is 15 .

An array is a table-like arrangement representing numbers or data in the form of columns and rows.

A multiplication array creates an arrangement where we display data in the form of an array to find the product of any multiplication question. The array is usually created using small objects or shapes or dots to make it interactive.

For example, to multiply 3 x 5, the same example as above, we will create the following multiplication array.

Tip: While you can use any number of objects in a row or column, use one method for every problem in the beginning to avoid confusion. So, we will represent the first number in the form of rows and the second in the form of columns.

In the above multiplication array, we can find the answer by counting the number of circles, which is 15.

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Let’s use the example of 2 x 7, also referred to as 2 by 7.

This means that we have 2 rows and 7 columns.

In this array, every row and column has an equal number of objects.

Another way of looking at it is that we have equal groups in the form of rows or columns. When you take these equal groups and arrange them as columns or rows, we get arrays.

For example, equal groups of two arranged in columns created the above array of stars.  

Related Worksheets

We use specific terms for numbers involved in multiplication:

• Factors are the numbers being multiplied
• Product is the result gained from the activity, which is the multiplication

What happens if we change the order of factors in the multiplication equation?

In the above example,  we had 2 rows and 7 columns. What if we make 2 columns and 7 rows?

The answer remains the same; it is still 14.

The situation is identical whether you keep the first number as a row or column, and this is true for every mathematical equation.

If more than two factors are involved in the problem, we can change the order but still receive the exact same answer. This is referred to as Commutative Multiplication Property.  

Example 1: We need to create a multiplication array for 5 by 6. How will we create it?

Let’s take 5 as rows and 6 as columns.

This means we need to make 5 rows horizontally and 6 columns vertically.

When you count these objects, you will get the following:

Example 2: Find out the multiplication factors in the given multiplication array:

First, we count the number of rows: 2

Then, we count the number of columns: 4

So, the multiplication factors are 2 x 4, which can also be written as 4 x 2.

Example 3: Find the answer or product for the given multiplication array:

First, we will count the objects across each row, which will give us the product = 12.

If we also need to find the factors, then we count the rows (3) and columns (4).

Multiplication Array

Attend this Quiz & Test your knowledge.

Which of the following figures is a multiplication array?

How will we create a multiplication array for the following equation? 3 x 5

Find the product for the given multiplication array:

How can we use arrays for multiplication?

To use a multiplication array, we need to assign factors to rows and columns, draw them and then count them. This is the easiest method for using a multiplication array.

Do you need to have a fixed array length in a multiplication array?

No. We can’t have a fixed length for the multiplication array before making the array.

But, once it is created, its length is fixed, and every column has the same length.

Is it necessary to have an array with even rows and columns?

We can have even rows and columns, but it is not necessary or mandatory. For example, 4 x 4 may form an even array, but 4 x 5 may not.

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Multiplication Arrays with Real-life Examples

What is a Multiplication array ? Isn’t it simply a faster method of addition? So, when you are multiplying a number by another number, you will add a number the same amount of times as the other number calls. Multiplication can be made easier than ever if you learn multiplication array . They are useful representations of multiplication concepts. Chairs arranged evenly in an auditorium or a marching troop depict arrays.

You can easily calculate the participating members if you visualize them in rows and columns. So, what is an array in multiplication? How can arrays help solve multiplication problems faster? Learn all about multiplication array in the article below.

Here is what we’ll cover:

• What is an array in multiplication?
• How to write multiplication array equations?
• How to perform multiplication array with skip counting?
• What are the benefits of a model multiplication array?
• Real-life examples of multiplication array

What is a Multiplication Array?

Visually seeing things can help develop a concrete understanding of important math concepts. Array employs visualizing multiplication members in rows and columns. An array is an arrangement of numbers, objects, or pictures in the form of rows and columns. A row is horizontal (from left to right), while a column (up and down) is vertical. 

Each column must contain the same number of objects in an array, and the same applies to each row. They must have the same number of objects as the other rows.

How to write Multiplication Array Equations?

To write an array multiplication equation, you first consider the number of rows and then the number of columns. Let us look at a few examples below to understand multiplication array.

In the following figure, the array has 2 rows and 4 columns of smileys. It can also be described as a 2 by 4 array. The word “by” can be represented with a multiplication cross. 

Hence, mathematically, you write an array as 2 × 4. And two times four equals eight, so the equation will be: 2 × 4 = 8

This array has 3 rows and 4 columns. It is a 3 by 4 array, and you can write it as 3 × 4. The multiplication equation will be: 3 × 4 = 12

So, you can see from the above examples that the first number represents the number of rows, and the second number represents the number of columns. So, the second array is 3 × 4, not 4 × 3, even though the calculated product, i.e. 12, will be the same either way.

How to Perform Multiplication Array with Skip Counting?

What is skip counting? Skip counting is a method of counting forward by numbers other than 1. So, if you have to skip-count by a number, you will keep adding the same number in every step to the previously obtained number. It is just like repeated addition. Suppose you have to skip count by 2, so your answers will be 4, 6, 8, 10, 12, 14, and so on. So, every time you add 2 to the previous number, i.e. add 2 to 4 to get 6, add 2 to 6 to get 8, and so on. 

Let us take the following donuts array example to understand how to skip count for array multiplication . 

The above array has three rows, and each row has five donuts. So, there are five columns of donuts. To calculate the total number of donuts, you can simply count them. But employing skip counting speeds up the process and makes it much easier. 

Here, you can skip count by 5 for every row to calculate the number of donuts. The first row has five donuts, so when you skip count by 5, the end of the second row amounts to ten, and that of the third row will give fifteen, which is your answer. It is the same as 3 × 5 =15

In the above image, you can also skip count column-wise. You will have to skip count by three as each column has three donuts. So, for five columns, the skip counting by three would go like 3, 6, 9, 12, and 15. 

So, interestingly one array can have two equations: one for columns and the other for rows. In the above example, the multiplication equations are:

For rows: 3 × 5 = 15

For columns: 5 × 3 = 15

What are the Benefits of Model Multiplication Array?

Array multiplication has several benefits in understanding and solving mathematical problems. Not just Math, computer languages such as Python use NumPy array multiplication to multiply an array. Some of the key benefits of array model multiplication in mathematics are as follows:

1. Array multiplication makes it easy to visualize problems

It can be a great way to introduce multiplication with hands-on objects, but it can be tedious when working with larger numbers or doing several problems. You can use a paper dot array to slide an L-shaped cover over the top of the array. This way, you can show any multiplication fact you want. The following image represents the dot array and L-cover.

You can use the dot array and L-cover as follows. Suppose you want to explain what 6 × 8 looks like, i.e. 6 groups of 8. Slide the L-cover on the dot array as shown below.  

Now, there are six rows, and each row has eight dots. You can easily calculate the total number of dots in the array by 6 × 8 = 48.

2. Array multiplication allows the use of strategies instead of rote memorization

Let us take the example of 6 × 7 to understand this. It gets tough for students to memorize answers for multiplications like this one, but they find it easier when they use 5 × 7 as a stepping stone. Students are mostly familiar with multiples of five from an early age. So, it gets much simpler when they see 6 × 7 as just one more group of 7 than 5 × 7. They will just have to add 35 + 7 to find the answer: 6 × 7 = 42. 

3. Array multiplication allows students to see the commutative property in action

According to the commutative property, you will get the same answer on multiplying the same numbers in any order. For instance, whether you multiply 4 × 7 or 7 × 4, both equal the same answer: 28.

Using dot array multiplication , you can explain the multiplication facts. To explain the commutative property, turn the array 90 degrees. The dot array will show the multiplication fact, and the total number of dots won’t change.

A multiplication sentence has several numbers, and each has a special name. The numbers that you multiply are called factors. The answer obtained by multiplying the factors is called the product. 

6 × 7 = 42 

Here, 6 is a factor that represents the number of rows, factor 7 represents objects in each row, and product 42 represents the total number of objects. 

When the array is turned on its side, things change as follows.

Here, factor 7 represents the number of rows, factor 6 represents objects in each row, and the product 42 is the total number of objects.  

The order of the factors changes, but the product stays the same, exhibiting a mathematical property known as the Commutative Property of Multiplication. 

4. Using arrays for large numbers

Using arrays, students can easily explore calculations on large numbers such as 12 x 5. The array can be split into useful chunks. For instance, 12 x 5 can be broken down to work out calculations.

12 x 5 = (10 x 5) + (2 x 5).

Although drawing dots is a good technique for beginners, it can get tedious. The blank array method helps solve complex multiplications by adopting an informal way. They teach students how to adopt other strategies, such as compensating, for the process of multiplication.  

The following example shows the blank array method for multiplication. Here, for calculating 34 x 9, the student decided to do 34 x 10. Next, he takes off the 34 x 1, simplifying the process.

So, 34 x 10 = 340 

340 – 34 = 306

You can also break down 34 as 30 and 4. Then, you will subtract 30 from 340, followed by 4 from the 310.  

5. Multiplication arrays worksheets allow students to practice equations

Multiplication array worksheets are a great way to practice equations. Students are generally given to complete the equation to describe the array, as shown in the image below. 

Real-Life Examples of Multiplication Array

You can practice array multiplication whenever and wherever you come across arrays. They are present all around you.

Following are some common real-life examples of arrays for multiplication:

• A tray of eggs
• A muffin baking tin
• A chocolate box
• Blister packs of medicines
• Water bottles in cartons
• Checkerboard
• Matrices are also arrays 
• Contacts on a cell phone
• A restaurant menu
• A question paper is an array of numbered questions, where each question is assigned some marks.

Frequently Asked Questions

1. how to multiply all values in an array.

The easiest way to multiply all values in an array is to first convert the array into a list.

Then, you can use the map function to multiply every value in the list.

The code below will multiply every value in the array:

a = [1,2,3] l = list(a) l * 2

2. What does an array mean in math?

 An array is a way of organizing numbers so that they can be easily sorted and searched. It’s like an Excel spreadsheet, but much more advanced.

3. What multiplication number sentence does the array represent?

 The array represents the multiplication sentence 5 × 3 = 15

4. How do you solve multiplication problems?

To solve a multiplication problem, you need to multiply the numbers in the first set of parentheses by the numbers in the second set of parentheses. For example, if you want to know how much 8 x 7 is, you would put down an 8 and then multiply it by 7. You would get 56 as your answer.

5. What is an array in Math 4th grade?

 An array is a set of numbers that have been organized in a particular way. In 4th grade Maths, arrays are used to solve problems. In an array, all of the numbers are listed in order. The first number is called the index number and it tells you how many numbers there are in the array. You use an index number when you want to tell your teacher what number goes where in a problem.

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