Making change means returning money after a transaction. If a purchase costs 15¢ and the customer pays 25¢, change is 10¢. Finding change involves subtracting cost from amount paid, a practical application of subtraction.
You already know the values of coins — a quarter is 25¢, a dime is 10¢, a nickel is 5¢, a penny is 1¢ — and how to count up a collection of coins to find a total. Making change uses both those skills together in a real-world transaction: someone pays more than something costs, and the cashier returns the difference.
The core calculation is subtraction. If a pencil costs 17¢ and you pay with a quarter (25¢), the change is 25 − 17 = 8¢. But in real life, people rarely calculate change by doing the subtraction on paper. Instead, they count up from the price to the amount paid. Starting at 17¢, you might say: "18¢ (one penny), 19¢, 20¢ (another penny and a nickel), 25¢ (a nickel)." That gives you 3 pennies and 1 nickel — which is 8¢. Counting up is often easier because you're working with physical coins that have specific values, and you can stop as soon as you reach the amount paid.
There's a strategy that makes this even smoother: use fewest coins. If change is 8¢, you could hand back 8 pennies — but a nickel and 3 pennies is much easier for everyone. Think of it as building to a nice number: go to the next 5¢ or 10¢ first, then keep going to the total paid. This is exactly the same thinking as rounding to a friendly number when you estimate.
The key question to ask yourself in any change problem is: "How much MORE does the customer need to go from the price to what they paid?" That reframes subtraction as an addition problem — and addition is often easier to think through with coins. Change = amount paid − price. Both ways of thinking lead to the same answer.
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