Array
An array is a rectangular arrangement of objects in equal rows and columns that visually represents multiplication. In Grade 4 math from Saxon Math Intermediate 4 Chapter 3, a 3×4 array of stars shows that 3 × 4 = 12 and reveals that 3 and 4 are both factors of 12. Arrays make multiplication concrete, connect it to area, and provide an intuitive model for the Commutative Property (a 3×4 array and a 4×3 array contain the same total number of objects).
Key Concepts
Property An array is a rectangular arrangement of numbers or symbols in columns and rows. It shows that the number of rows times the number of columns equals the total.
Examples A 3x4 array of stars shows the multiplication fact: $3 \times 4 = 12$. A 2x6 array of chairs illustrates the multiplication fact: $2 \times 6 = 12$. A 5x3 array shows that 5 and 3 are factors of 15.
Explanation Think of an array as organizing things, like cookies on a baking sheet, into neat rows and columns. It's a visual way to see a multiplication problem in action! The number of rows times the number of columns gives the total count and also reveals the factors of that total.
Common Questions
What is a multiplication array?
An array is a rectangular arrangement of objects in rows and columns. A 4×6 array has 4 rows and 6 columns, showing 4 × 6 = 24 objects in total.
How does an array show a multiplication fact?
Count the rows (first factor), count the columns (second factor), and multiply to get the total (product). Every array directly illustrates one multiplication equation.
How do arrays demonstrate the Commutative Property?
A 3×5 array (3 rows, 5 columns) and a 5×3 array (5 rows, 3 columns) each contain 15 objects, showing that 3×5 = 5×3.
When do Grade 4 students work with arrays?
Arrays are used in Chapter 3 of Saxon Math Intermediate 4 to build a visual foundation for multiplication facts and to connect multiplication to area.
How do arrays relate to area?
The area of a rectangle equals length × width, which is exactly what an array models. A 6×4 grid of unit squares represents both the multiplication fact 6×4=24 and an area of 24 square units.
What factors can you identify from an array?
Any array with r rows and c columns shows that r and c are both factors of the total r×c. A 2×6 array reveals that 2 and 6 are factors of 12.