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M.3 Write multiplication sentences for arrays

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What are arrays in multiplication?

Arrays are orderly arrangements of objects in rows and columns that help us understand multiplication. Each row has the same number of objects, and each column has the same number of objects.

Examples:
  • A tray of cupcakes arranged in 3 rows with 4 cupcakes in each row
  • A classroom desk arrangement with 5 rows and 6 desks in each row
  • A sheet of stamps with 2 rows and 8 stamps in each row
Note

Arrays help us see multiplication as equal groups organized in rows and columns. This visual model makes multiplication easier to understand.

How do we read arrays?

To read an array, we count the number of rows and the number of objects in each row. We say: "number of rows" times "number in each row."

Steps:
  • Look at the array and count the number of rows
  • Count how many objects are in one row
  • The multiplication sentence becomes: (rows) × (objects in each row) = total
Note

Rows go across (left to right), and columns go up and down. In multiplication with arrays, we usually count rows first, then objects in each row.

Writing multiplication sentences for arrays

A multiplication sentence for an array shows the relationship between the number of rows, the number in each row, and the total number of objects.

Array Examples:
  • An array with 4 rows and 3 circles in each row → 4 × 3 = 12
  • An array with 2 rows and 5 stars in each row → 2 × 5 = 10
  • An array with 6 rows and 1 square in each row → 6 × 1 = 6
  • An array with 3 rows and 7 triangles in each row → 3 × 7 = 21
Note

The multiplication sign (×) means "groups of" or "rows of" when working with arrays. The equal sign (=) shows that both sides have the same value.

Arrays work both ways: The commutative property

Arrays can be read in two different ways because multiplication follows the commutative property. Turning an array sideways gives us a different multiplication sentence with the same total.

Examples:
  • 4 rows of 3 (4 × 3 = 12) is the same as 3 rows of 4 (3 × 4 = 12)
  • 5 rows of 2 (5 × 2 = 10) is the same as 2 rows of 5 (2 × 5 = 10)
  • 6 rows of 3 (6 × 3 = 18) is the same as 3 rows of 6 (3 × 6 = 18)
Note

The commutative property means that changing the order of the factors does not change the product. Both multiplication sentences are correct for the same array.

Finding the total number of objects in arrays

To find the total number of objects in an array, multiply the number of rows by the number of objects in each row. You can count by equal groups or use repeated addition to check your answer.

Examples:
  • 3 rows with 4 apples each: 3 × 4 = 12 (also 4 + 4 + 4 = 12)
  • 5 rows with 2 books each: 5 × 2 = 10 (also 2 + 2 + 2 + 2 + 2 = 10)
  • 7 rows with 3 buttons each: 7 × 3 = 21 (also 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21)
Note

Multiplication is a faster way to do repeated addition. If you're unsure about a multiplication fact, you can always add equal groups to find the total.

Real-world array situations

Arrays appear in many everyday situations. Recognizing these patterns helps us use multiplication to solve real problems quickly.

Real-life Examples:
  • A box of eggs with 2 rows and 6 eggs in each row: 2 × 6 = 12 eggs total
  • Calendar dates arranged in 5 rows and 7 columns: 5 × 7 = 35 days shown
  • Chocolate bar with 4 rows and 8 pieces each: 4 × 8 = 32 pieces total
  • Parking lot with 9 rows and 3 cars in each row: 9 × 3 = 27 parking spaces
Note

When you see objects arranged in equal rows and columns, you're looking at an array. This pattern helps us use multiplication in daily life.