What is a good arrays math definition and ways to use them? Arrays are a great way to represent a multiplication equation, and several hands-on ways exist to explore them. Going on a scavenger hunt looking for real-world images of arrays helps students see math in their lives. Plus, assisting students in using the correct language helps them see the connection between repeated addition and multiplication.
☀Download this BONUS Guide with everything you need to create a growth mindset classroom and positive classroom community.
➕Includes definitions, lesson ideas, mindset surveys for students and teachers, and printable posters.
🧠💪Research shows a link between a growth mindset and math success. Kids with a growth mindset about their abilities perform better and are more engaged in the classroom.
👉Includes everything you need to start cultivating a more positive math classroom and students who love math. Download and get started today! Click here to download the Mindset Guide & Survey.
Last year, I had the opportunity to work with a group of 2nd graders at the end of the year. We had so much fun using tiles to build arrays and then write equations to represent our arrays. We then created a math bulletin board with our monster array project and a large multiplication table. Since it was an enrichment group, we exceeded the 2nd-grade standard of 25.
Multiplication Arrays Math Definition
An array is a way to represent multiplication and division using rows and columns. Rows represent the number of groups. Columns represent the number in each group or the size of each group.
Array Multiplication Definition
An arrays math definition is a number of mathematical elements that are arranged in rows and columns.
What is an Array in Math Multiplication Example?
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.
3 rows of 5 or 3 X 5= 15
Explain Arrays With Examples
An array is any arrangement in rows or columns:
- Cards laid out into rows to play Memory
- seats arranged in rows for a recital
- numbers arranged in an Excel spreadsheet are all examples of arrays
Reasons to Use Multiplication Arrays
Multiplication arrays make it easy to visualize multiplication problems.
Arrays show a number of objects in rows and columns. Then, they can use the array and repeated addition to come up with the total. ______ rows of _______.
Multiplication arrays make it easy for kids to see the commutative property.
The commutative property says you can multiply numbers in any order and still get the same answer. For example, 2 × 7 and 7 × 2 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. The dot array shows the related multiplication fact, but the number of dots didn’t change.
Arrays in Multiplication Standards
The learning of multiplication begins in 2nd grade when students are introduced to arrays. Then, the
Arrays in Math 2nd Grade
2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
Second graders begin to extend their understanding of addition to equal groups and use repeated addition to determine the total number of items in a rectangular array with up to 5 groups and up to 5 items in a group.
A rectangular array is an arrangement of objects in rows and columns. Students build arrays with concrete objects and pictures and determine the number of objects in a given array to prepare them for 3rd Grade.
- Provide students with concrete and pictorial representations of rectangular arrays and ask them to determine the number of objects shown.
- Ask students to describe the pictures ( X columns and y rows). Students explain how they determined the number of objects (counting, skip counting, repeated addition).
- Provide students with materials such as tiles, cubs, and counters to have them build arrays. Have them explore different configurations. For example, ask them to make an array with 8 objects.
- Use models to represent arrays with up to 5 rows and 5 columns and determine the total number of objects in the array.
- Students are given a number (up to 25) and build arrays using objects. Then, describe the array and explain how they know the array has that number of objects.
- Given the dimensions of an array, students construct the array.
Arrays Multiplication 3rd Grade
Starting in 3rd grade, students learn about the concept of multiplication and begin to solve problems using multiplication with concrete materials.
3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 X 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 X 7.
Students develop an initial understanding of the multiplication of whole numbers by modeling situations and understanding the meaning of the numbers (factors) and total (product).
The symbol X means groups of (or times).
Teachers should provide students with a variety of multiplication situations to model using concrete materials. Ask students to identify the number of groups, the number of items in each group, and the total number of items. Next, introduce students to numerical representations by writing equations representing their models.
Check out this Repeated Addition to Multiplication Resource.
Multiplication Word Problems
As students learn about multiplication and division, they can be introduced to word problems to act out.
3. OA. A. 3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Students need many opportunities to use concrete materials to model the situations and identify the number of groups and items in a group. Then, once students have an understanding, they can begin to draw pictures.
Teach Word Problems Division and Multiplication with these 160 Google Slides and 160 Worksheets. Use the counters to represent the word problems for multiplication and division on the slides. Then, fill in the equations and solve the multiplication and division word problems.
Using Equal Groups to Teach Multiplication
Another way to represent a multiplication equation is with equal groups. You have 3 plates. Each plate has 5 cookies. So 5 + 5= 5= 15 or 3 groups of 5= 15.
Images to Use to Teach Equal Groups
What Are Arrays in Multiplication Activities?
I like to have students use tiles to build arrays. I tell them to build 3 rows of 5 tiles. Then, we write it as 5 + 5 + 5 = 15, 3 rows of 5= 15, and 3 X 5= 15. We can also discuss what it would look like to change it to 5 rows of 3 tiles. Next, we start to draw arrays.
Using digital counters is another way to build arrays.
Multiplication Arrays Worksheets and Slides
Understand Multiplication with Equal Groups or Arrays with these 200 Slides and 150 Printable Worksheets. Use the counters to represent the multiplication problems equal group or use the multiplication arrays worksheet.
Then, fill in the addition and multiplication equation for each repeated addition leading to a multiplication problem.
Number Talks with Arrays
Display these real world images of arrays and discuss the equations you can use to represent the picture. Then, go on a scavenger hunt around the school to look for other real-world arrays.
Use Repeated Addition to Multiply
Repeated Addition and Multiplication Worksheets And Slides
Teach Repeated Addition to multiplication with these 50 Google Slides and Printable Worksheets. Use the counters to represent the multiplication problems equal group or use the multiplication arrays worksheet.
Then, fill in the addition and multiplication equation for each repeated addition leading to a multiplication problem. These activities will help students develop an arrays math definition and connect it to repeated addition.
Ideas for Teaching Arrays in Multiplication
Using Literature
There are so many great books to use to teach multiplication and division. Books help students understand what is happening with numbers and connect them to the real world. Two great books to use are:
- Amanda Bean’s Amazing Dream by Cindy Neuschwander is another fun book that will help kids see the importance of multiplication. Amanda Bean loves to count but isn’t sure why she needs to learn multiplication. Until she has a crazy dream full of sheep on bicycles, knitting grannies, and more, she can’t count them fast enough. This book focuses on repeated addition (and why multiplication is a “faster way to count”). The pictures also include lots of examples of arrays.
- The Doorbell Rang by Pat Hutchins is an excellent book for introducing division as sharing equally. Sam and Victoria are just about to sit down and enjoy fresh cookies when two friends arrive, and the four children divide the cookies four ways. Soon, the doorbell rings repeatedly, and the number of cookies per person dwindles each time.
Click here for a list of books to teach multiplication and division.
Acting it Out or Modeling
Using concrete materials to act out or model problems is essential. For example, after reading a book or giving students a situation, give them materials to act out the problem. For instance, after reading The Doorbell Rang, you could provide students with plates and cookies to act out the situation.
Eventually, students can begin to draw pictures and write equations to represent the problems.
Arrays Project
Use this Arrays Project with students to help them see the connection between repeated addition and multiplication. Students build multiplication arrays with tiles and then color on the multiplication with arrays worksheets.
You can have students roll dice to determine their factors or allow students to pick their factors for the multiplication problems using arrays.
This project can be done independently, in pairs, in small groups, or as a whole class arrays project. It is more engaging than a multiplication arrays worksheet. Have students build the arrays with tiles, color the array on the multiplication arrays worksheet, and write the repeated addition and multiplication problem. Cut and glue onto a large piece of paper and color in the background to create a Monster World.
Multiplication Arrays Worksheets and Google Slides
Understand Multiplication with Equal Groups or Arrays with these 200 Slides and 150 Printable Worksheets. Use the counters to represent the multiplication problems equal group or use the multiplication arrays worksheet. Building arrays will help students with the arrays math definition and an understanding of multiplication.
Then, fill in the addition and multiplication equation for each repeated addition leading to a multiplication problem. Click here to see the Multiplication Arrays Worksheets and Slides.
Addition Resource for Teaching Multiplication
- How to Successfully and Easily Teach Word Problems in Multiplication and Division
- Do You Need Exciting and Fun Online Multiplication Fact Practice Ideas and Games?
Using Arrays in Multiplication
Introducing arrays in 2nd grade and providing opportunities to build and write equations for them sets the foundation for multiplication in 3rd grade. Students must see the connections between repeated addition and equal groups and arrays.
☀Download this BONUS Guide with everything you need to create a growth mindset classroom and positive classroom community.
👉Includes everything you need to start cultivating a more positive math classroom and students who love math. Download and get started today! Click here to download the Mindset Guide & Survey.
Using the language of “groups of” and “ rows of “ with concrete examples helps students see the connection. Then, they will be able to draw arrays. Finding examples in books and their environments allows them to understand multiplication’s importance. Take some time to help students build a conceptual understanding of a multiplication arrays math definition.
