Multiplication Using Arrays, Number Lines, and Repeated Additions

Arrays, number lines, and repeated addition can help students visualize multiplication.

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It is important for students to memorize their multiplication facts, however, it is also necessary for them to understand the significance of what they are doing. When students are in the process of learning about multiplication, the use of arrays, repeated addition, and number lines are helpful tools you can use to help students visualize this concept. If students are given the opportunity to practice different methods of visualizing multiplication, they will probably find one that best helps them internalize the concept. Each of the methods described below employ the use of hands-on learning and/or manipulatives.

Arrays: An array uses symbols to create rows and columns. For example, 4x5 would be 4 rows of 5, or 5 rows of 4. When showing students arrays, a few examples of 4 rows of 5 using a variety of symbols and tools can be helpful. Students can create 4 rows of 5 using hearts, circles or X's on paper. Then, students should also be given the opportunity to create arrays using manipulatives such as counters, M&Ms, or blocks. In doing so, students should be able to see that 4 rows of 5 are 20, and arranging 5 rows of 4 also equals 20 counters.  

Repeated Addition: The example of 4x5 could also be used with repeated addition. Students should understand that multiplication is actually repeated addition. Multiplication is a more efficient way to solve problems of repeated addition. Furthermore, in the early stages of learning multiplication, repeated addition is a helpful tool in better understanding this concept. For example,  4+4+4+4+4=20, or 4x5=20, and 5+5+5+5=20, or 5x4=20. With these two examples, the idea is to help students understand that repeating the number 4 five times or the value 5 four times is what equals 20.

Number Lines: The use of a number line is a helpful tool in understanding multiplication. With a number line, a visual representing the given multiplication sentence is created using “jumps” along a number line. For example, by using the example above, 4x5 would be 4 “jumps” of 5 along a number line. The point where the pencil stops after creating the appropriate number of “jumps” is the product, 20 in this case.

Multiplication Worksheets:

Multiplication with Arrays

This worksheet has students create an array based on each multiplication fact given. It also gives a simple explanation at the top of the worksheet about arrays.

Multiplication: Arrays

This worksheet has arrays with a variety of different symbols. Students are asked to come up with two multiplication sentences based on the visual given.

Multiplication: Repeated Addition

Students solve multiplication problems using repeated addition. Students may also use a number line to help them understand repeated addition.

Concept of Multiplication: Repeated Addition

Students solve problems using repeated addition. This worksheet also has word problems to be solved using repeated addition.

Concept of Multiplication: Number Lines

Students are asked to write the correct multiplication sentences for each number line and solve to find its product.