"Multiplication and Repeated Addition With Arrays" is a worksheet that is designed to help students visualize and better understand the operation behind multiplication problems.

Each worksheet page contains six different problems. Each one features an array of boxes that represent a multiplication problem, like 5x3, which features 5 columns and 3 rows. The first problem on the page fills in the blanks for the number of columns and rows to show students how to do it. Then, students fill in how many columns and rows are in the problems on the rest of the page.

At the bottom is the multiplication problem and matching repeated addition problem for the array displayed above. The first problem has the answers filled in. Students must fill in the factors and addends. Students fill in the factors, addends, and the answer in subsequent problems. The example for the array mentioned above is "___x___=___" and "___+___+___=."

In order for students to become proficient in multiplication, they must develop a deep understanding of how it works. Using visual arrays and repeated addition are both great ways to help students expand their thinking around multiplication.

You can start with manipulatives like base ten blocks, having students stack them in order to count the number of columns and rows before filling in the numbers in a multiplication problem. This is an especially effective strategy as students are making the transition away from one-to-one correspondence and learning to group numbers together when counting.

Students can also use counters or single manipulatives to create a repeated addition problem. Then, they could write the subsequent multiplication problem. For example, they could make five piles of two counters to equal 10.

As students become more proficient, they can complete the same types of problems on worksheets, where each multiplication problem is displayed as an array of squares or pictures.