Coins (pennies, nickels, dimes, quarters) and bills (ones, fives, tens) have different values. Count coins starting with the largest value first for efficiency: quarters, dimes, nickels, pennies.
Money is a real-world application of everything you know about counting and number values. Each coin and bill is simply a physical token that stands for a number of cents or dollars. A penny equals 1 cent, a nickel equals 5 cents, a dime equals 10 cents, and a quarter equals 25 cents. Paper bills work the same way at the dollar level: a one-dollar bill = 100 cents, a five = 500 cents, a ten = 1,000 cents. Knowing these values by heart is the starting point for everything else in money math.
The most efficient way to count a mixed collection of coins is to sort by value and start with the largest. If you have 1 quarter, 2 dimes, 1 nickel, and 3 pennies, begin at 25, count on by 10s (35, 45), then by 5s (50), then by 1s (51, 52, 53). You arrive at 53 cents without losing track. Starting with pennies would force you to count 1 by 1 all the way, making errors more likely. The "largest first" strategy works because it minimizes the number of counting steps.
The same logic applies to bills. If you have a ten, two fives, and three ones, start at 10, count on 5 (15), 5 (20), 1 (21), 1 (22), 1 (23): twenty-three dollars. Notice this is the same as adding: 10 + 5 + 5 + 1 + 1 + 1 = 23. Counting money is just addition with named values instead of abstract numbers.
One key idea is that different combinations can represent the same total. Two dimes and a nickel equal a quarter; five nickels equal a quarter; ten pennies equal a dime. Recognizing these equivalences lets you make change — swapping one combination for another of equal value. This skill builds directly toward making change, where you figure out what coins to give back so that the amount paid plus the change equals the price.