Third Grade · Math · week 2

Arrays: rows and columns

Use rows-and-columns arrays to model multiplication and see that order does not change the product.

An array is a neat picture of multiplication: equal rows lined up like an egg carton. Count the rows, count how many are in each row, and multiply. A carton with 2 rows of 6 eggs is 2 × 6 = 12.

Arrays show a cool secret: 2 × 6 and 6 × 2 both make 12. Turn the array sideways and the rows become columns — the total never changes. That is called the commutative property (a fancy name for "order does not matter").

📋 For the teacher
Teach it (10–15 min):
  • Use an egg carton, a muffin tin, or a window pane — real arrays are everywhere.
  • Have them physically rotate the array a quarter turn to SEE that the total stays the same.
  • Introduce the word "commutative" lightly; the idea (order does not matter) is what sticks.
  • Point out that arrays make big facts feel organized — no more counting one dot at a time.
Talk about it:
  • What is the same about 6 × 2 and 2 × 6?
  • How do you read an array as a multiplication?
  • Where do you see arrays in real life?

Mastery looks like: They can build an array for a fact and explain why swapping the two numbers keeps the same product.

Common stumbles: Counting the whole array by ones instead of using rows; forgetting the rows must all be equal length.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

MultiplicationEqual groups and arrays make products finally click.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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