Prove whether two groups are exactly equal by matching objects one to one, and see that spreading a group out does not change how many there are.
Two groups are equal only when they have the exact same number. Not close. Not almost. Exactly the same.
Here is a secret: if you spread a group out or squish it together, the number does not change. 6 pennies in a line is still 6 pennies in a pile.
The best way to check if two groups are equal is to match them up, one to one, like pairs of shoes.
Mastery looks like: They confirm equal groups by matching one to one and understand that rearranging a group never changes its count.
Common stumbles: Thinking a spread-out group has more just because it looks bigger; guessing equal without matching or counting.
See it visually
Interactive, spoken-aloud tools that show this idea in motion.