Making Change in Simple Transactions

Core Idea

Making change means finding the difference between the amount paid and the price. If an item costs 28¢ and you pay 50¢, the change is 22¢. This is subtraction applied to real situations.

How It's Best Learned

Use play money and role-play transactions. Have students physically count up from the price to the amount paid ('start at 28, count up to 50'). Also solve with subtraction (50 - 28 = 22).

Common Misconceptions

• Confusing change with the amount paid.
• Subtracting in the wrong direction (price - amount paid instead of amount paid - price).
• Not recognizing that coins can be exchanged for equivalent amounts.

Explainer

You already know how to count collections of coins, and you can subtract numbers within 100. Making change is where those two skills meet in a real-world situation with a clear purpose: making sure a transaction is fair. When a customer pays more than an item costs, the store owes the customer the difference back.

The core question is always: how much more than the price did the customer pay? If something costs 28¢ and the customer hands over 50¢, the change is 50 − 28 = 22¢. The structure is always the same: price is what you owe, payment is what you hand over, and change is the difference. The direction matters — you subtract the price from the payment, not the other way around, because the customer is receiving money back, not paying more.

There are two strategies for finding change, and both are worth knowing. The first is subtraction: write the equation directly and calculate. The second is counting up: start at the price and add amounts until you reach what was paid. Starting at 28¢, you might count up 2¢ to reach 30¢, then 20¢ more to reach 50¢ — so the change is 2 + 20 = 22¢. Counting up is how many experienced cashiers reason through it mentally, and it connects naturally to your prior work on number lines and "how much more" situations.

A common trap is confusing the amount of change with the amount paid. If you pay 50¢, the change is not 50¢ — the store keeps 28¢ and returns only the rest. Another trap is subtracting in the wrong direction. Keeping the story clear — who paid, what was the price, who gets the difference back — prevents both errors. Every time you buy something and count your change, you're doing exactly this arithmetic in the real world.