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The relationship between multiplication and addition

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Teachers should know and understand the relationship between addition and multiplication because this understanding will translate well into teaching students to understand the concept of multiplication. The relationship of these two operations is very close so it is especially important to ensure each student fully comprehends the rules of addition before proceeding to multiplication. Addition is the process of combining a number of individual items together to form a new total. Multiplication, however, is the process of using repeated addition and combining the total number of items that make up equal-sized groups. This means that in multiplication, groups are created to represent the numbers being multiplied, and then the groups are added together to produce a total.

Relating addition to multiplication is relatively simple. In fact, instruction on multiplication often begins in kindergarten as children develop ideas about numbers, addition, and groups. These experiences provide the basis of understanding for multiplication. Because addition is a precursor for multiplication, a student must be able to count items in groups and count the number of groups, which will then help them to be able to multiply them. Through the addition principles of skip counting, repeated addition, grouping, and number lines students can attain a deeper, broader understanding of multiplication. When students finally understand that multiplication and addition function under many of the same rules or properties, they will understand that addition and multiplication work under the same conditions.

The strategy called skip counting will benefit students who know how to count by two's, five's or ten's. Drill exercises using skip counting...

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... are computing using the distributive property will get them using the language of math, help them to see where they are making errors, and help them by having a peer agree or disagree with their answer. If the pair has different answers, they can re-work the problem using the distributive property to see who is correct. Sharing answers with the rest of the class will reinforce the correct procedure, thus reinforcing the property.

Teaching multiplication can be made less confusing for the students when the relationship between addition and multiplication is communicated and explained. Building upon prior knowledge of the use of addition strategies and incorporating the properties of multiplication, the students can reach a depth of knowledge about multiplication that will make it possible for them to discover the correct product and reinforce both concepts.
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