Pennies, Nickels, Dimes, and Quarters - Second Grade Mathematics
Money is one of the most exciting and practical applications of mathematics in the real world: you use coins to buy a frozen treat, purchase a pencil at the school store, or save up in a piggy bank for a special toy. In the United States currency system, coins possess unique physical attributes—such as color, size, edge textures, and historical portraits—that help you tell them apart. Even more importantly, each coin possesses a distinct mathematical value measured in cents. In this chapter, you will master the identification, attributes, and numerical values of the four most common American coins: the penny, nickel, dime, and quarter.
The Four Common Coins: Attributes and Values
Let us examine the four workhorse coins of United States currency side by side.
United States Coin Guide:
Coin: Penny Nickel Dime Quarter
Value: 1 cent (1c) 5 cents (5c) 10 cents (10c) 25 cents (25c)
Color: Copper-Brown Silver Silver Silver
Size: Medium-Small Medium-Thick Smallest Largest
Edge: Smooth Smooth Grooved Grooved
Front Face: Lincoln Jefferson Roosevelt Washington
Back (Symbol):Shield/Memorial Monticello Torch/Branches Eagle/Park
The Penny (1 Cent)
The penny is the easiest coin to spot because it is the only common coin made with a reddish, copper-brown color. Its value is 1 cent (1c). On the front (obverse) is a profile of Abraham Lincoln, our 16th president. On the back (reverse) is the Union Shield. Because its value is 1, counting pennies is just like counting by ones: 1, 2, 3, 4, 5 cents.
The Nickel (5 Cents)
The nickel is a thick, silver-colored coin with a smooth edge. Its value is 5 cents (5c). On the front is Thomas Jefferson, the 3rd president. On the back is Monticello, his famous Virginia home. Because a nickel is worth 5 cents, counting nickels means skip-counting by fives: 5, 10, 15, 20, 25 cents. It takes 5 pennies to equal the value of 1 nickel.
The Dime (10 Cents)
The dime is a silver-colored coin with a ridged (grooved) edge. Here is a fascinating mathematical surprise: although the dime is the SMALLEST and thinnest of all coins in physical size, it is worth TWICE as much as a nickel! Its value is 10 cents (10c). On the front is Franklin D. Roosevelt, the 32nd president. On the back are a torch, an olive branch, and an oak branch. Counting dimes means skip-counting by tens: 10, 20, 30, 40, 50 cents. It takes 10 pennies or 2 nickels to equal 1 dime.
The Quarter (25 Cents)
The quarter dollar, commonly called the quarter, is the largest and heaviest of the four common coins. It has a grooved edge and a silver color. Its value is 25 cents (25c). It is called a quarter because four quarters equal one whole dollar (100 cents). On the front is George Washington, our 1st president. On the back is an eagle or a special state commemorative design. Counting quarters means using the 25-cent rhythm: 25, 50, 75, 100 cents.
Physical Size vs. Numerical Value Trap
One of the most common pitfalls for beginning coin counters is assuming that larger coins are always worth more money.
The Size vs. Value Comparison:
Coin: Nickel Dime
Physical Size: LARGER SMALLLER
Actual Value: 5 cents 10 cents (TWICE AS VALUABLE!)
The Dime and Nickel Comparison
Look closely at a nickel and a dime resting on a table: the nickel is thicker and wider than the dime, yet the tiny dime is worth 10 cents while the chunky nickel is worth only 5 cents! In money, you must never judge a coin by its physical size; you must identify the coin by its portrait and features to know its true mathematical value.
Coin Trades and Benchmark Values
Understanding how coins trade for one another builds a strong place value foundation.
Basic Coin Trades:
1 Nickel = 5 Pennies (5c = 5c)
1 Dime = 2 Nickels (10c = 5c + 5c)
1 Dime = 10 Pennies (10c = 10c)
1 Quarter = 5 Nickels (25c = 5 x 5c)
1 Quarter = 2 Dimes + 1 Nickel (25c = 10c + 10c + 5c)
Trading for Equivalent Values
Trading coins is identical to trading base-ten blocks. When you have a heavy handful of 10 pennies, you can trade them to a friend or bank for 1 light dime. If you have 2 nickels, you can trade them for 1 dime. Understanding trades makes your pocket lighter and your calculations faster.
Practice Exercises
Exercise 1: List the four common coins in order from least value to greatest value, stating the name and exact cent value of each coin.
Exercise 2: Look at a nickel and a dime. Describe two physical ways you can tell them apart, and state which coin has the greater mathematical value.
Exercise 3: How many nickels does it take to equal the exact value of one quarter? Show your reasoning using skip-counting by fives.
Exercise 4: Explain why a pile of 6 dimes is worth more than a pile of 6 nickels, even though both piles contain the exact same number of coins.
Solutions and Explanations
Solution to Exercise 1: In order from least to greatest value: Penny (1 cent), Nickel (5 cents), Dime (10 cents), Quarter (25 cents).
Solution to Exercise 2: You can tell a nickel and a dime apart in two ways: first, a dime is significantly smaller and thinner than a nickel; second, a dime has grooved ridges along its edge, while a nickel has a smooth edge (and they feature different portraits: Roosevelt on the dime, Jefferson on the nickel). The dime has the greater mathematical value (10 cents compared to 5 cents).
Solution to Exercise 3: A quarter is worth 25 cents and a nickel is worth 5 cents. Skip-count by fives to reach 25: 5, 10, 15, 20, 25. That required 5 counts. Therefore, it takes exactly 5 nickels to equal the value of 1 quarter.
Solution to Exercise 4: The value of a collection of coins depends on the denomination of each coin, not just the count of coins. Six dimes are worth 6 x 10 cents = 60 cents. Six nickels are worth 6 x 5 cents = 30 cents. Because each dime is worth twice as much as each nickel, 6 dimes have double the value of 6 nickels (60 cents is greater than 30 cents).