The Commutative Property

"I have a puzzle for you to solve today," said Mrs. Francis.

"A puzzle? Aren't we going to have math next?" asked Noah. "I like math."

"Well, Noah, this puzzle is a math puzzle," explained Mrs. Francis. "If you like math, you'll like my puzzle," she promised. Mrs. Francis went to the board. On it she wrote

Does the order of the numbers in a multiplication problem matter?

And then below that, she wrote

2 X 6 = ______

6 X 2 = ______

Mrs. Francis gave the class a moment to look at the problems and think about them. Then she said, "Emily, what do you think?"

Emily said, "No, I don't think the order of the numbers matter. The answer to both problems is 12. It doesn't matter if the 2 comes first or the 6 comes first."

Noah held up his hand. "Yes, Noah?" Mrs. Francis said.

"I think the order does matter. You told us that the "X" means "groups of" in a multiplication problem. Two groups of six things is NOT the same as six groups of two things," Noah said.

"That's very good, Noah," said Mrs. Francis. "Class, please raise your hand if you agree with Noah." Most of the class raised their hands.

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