Making change requires understanding coin values and computing the difference between a price and amount paid. For example, if an item costs 37¢ and you pay 50¢, the change is 50 − 37 = 13¢. Real and modeled shopping contexts apply arithmetic skills.
You know the value of each coin and how to count a collection of money. Now you're applying those skills in a real transaction. When you buy something, two amounts meet: the price of the item and the amount you pay. If they match exactly, no change is needed. When you pay more than the price, the difference comes back to you as change — and computing that difference is the core skill here.
The calculation is subtraction: amount paid − price = change. If you pay 50¢ for something that costs 37¢, the change is 50 − 37 = 13¢. But there's a second strategy called counting up that many people find more natural at a register: start from the price (37¢) and count up to the amount paid (50¢). Add 3¢ to reach 40¢, then add 10¢ to reach 50¢. Total added: 13¢. Counting up is mathematically identical to subtraction — you're measuring the gap between two numbers — but the mental motion mirrors how change actually moves between hands.
Deciding *which coins* to return is its own mini-problem. To make 13¢ in change, the fewest coins is 1 dime + 3 pennies. You could also use 2 nickels + 3 pennies, but that's more coins for the same amount. The practical strategy: use the largest denominations that fit, working down to smaller ones for the remainder. This is the same left-to-right strategy you used for counting money, now run in reverse.
Word problems add a reading layer on top of the arithmetic. "Mia buys a notebook for 65¢ and pays with 3 quarters. How much change does she get?" You must first interpret "3 quarters" as 75¢, then compute 75 − 65 = 10¢. The arithmetic is simple; the real skill is translating a situation into a calculation — identifying what is known, what is unknown, and which operation connects them. This translation skill is the foundation of all applied math, and every money word problem is practice at it.