Array division, in the context described by the provided reference, refers to a model for understanding division where you divide to find the number of counters in each group. This model emphasizes the relationship between division and multiplication, highlighting how one "undoes" the other.
Understanding Array Division
The array division model helps to visualize division as the process of splitting a total number of items into equal groups. The goal is to determine the size of each group when you know the total and the number of groups (or, alternatively, determine the number of groups when you know the total and the size of each group).
Key Concepts:
- Relationship to Multiplication: The array division model underscores the inverse relationship between multiplication and division. Recognizing this connection allows students to leverage multiplication facts to solve division problems and vice versa.
- Same Three Numbers: The same three numbers are used in both the related multiplication and division facts, further demonstrating the inverse operation concept.
Example:
Imagine you have 12 counters and you want to divide them into 3 equal groups.
- Division Problem: 12 ÷ 3 = ?
- Array Division Model: You would arrange the 12 counters into 3 rows (groups) and then count how many counters are in each row.
- Solution: There are 4 counters in each group. Therefore, 12 ÷ 3 = 4.
- Related Multiplication Fact: This also shows that 3 x 4 = 12.
How Array Division "Undoes" Multiplication:
Let's consider the multiplication fact 3 x 4 = 12. Array division allows us to "undo" this multiplication in two ways:
- Finding the number in each group: If we divide 12 by 3 (the number of groups), we find that there are 4 in each group. (12 ÷ 3 = 4)
- Finding the number of groups: If we divide 12 by 4 (the number in each group), we find that there are 3 groups. (12 ÷ 4 = 3)
Benefits of the Array Division Model:
- Visual Representation: Provides a visual and concrete way to understand division.
- Connection to Multiplication: Reinforces the inverse relationship between multiplication and division.
- Fact Fluency: Encourages the use of related multiplication facts to solve division problems.
- Conceptual Understanding: Helps build a deeper understanding of the meaning of division, rather than just memorizing rules.
In summary, array division is a valuable tool for teaching and understanding the concept of division, particularly its relationship to multiplication. It allows for a visual representation and emphasizes the "undoing" aspect of division, strengthening the understanding of inverse operations.
