# The Value of Counting Coins

May 02, 2022

About ten years ago I asked a group of third graders how many of them had coins in their room at home that they could touch and play with.  Only about 1/3 of the class raised their hands.  Ten years before that, every kid in the class raised their hand. Think about the last time you used coins to pay for something.  Last week I used coins to pay for my parking meter but many parking meters even take credit cards now.

For adults its often easier for us to use payment methods such as credit cards or Apple Pay when we need to pay for something.  We don’t have to scramble for coins or worry that we might not have the right amount. Kids, however, are losing valuable math skills as coins disappear from our daily use.

## Coin Values as Landmark Numbers

Coins can be used to pay for things but they are also a great model for using landmark numbers to calculate.  In our base ten system, 1s, 5s, 10s, and 25s are all useful chunks.  We want students to think efficiently about a number such as 23 as being made up of 2 tens and 3 ones (or two dimes and three pennies).  At the very least we hope they see 23 as being made up of 4 fives and 3 ones (or five nickels and three pennies).  Our goal is to help students think in groups which is more efficient than thinking of 23 as 23 ones (or 23 pennies).

Practice with counting coins helps students use mental math to calculate.  If they are buying something that costs 79¢ how much change do they get from a dollar?  They might think they will get 1¢ to get to 80¢ and then 20¢ more to get to a dollar for a total of 21¢ change.  This same thinking is what we use when we are adding and subtracting on a number line.  Students use landmark numbers to navigate along the number line and count up or down.  Young students can easily practice adding up their purchases and figuring our change by pretending to buy things around the house and pay for them with their coins.

## Coins as Fractions of a Dollar

With middle school students we use the 1, 5, 10, and 25 anchors when thinking about fractions.  We can think of money when we think of ¼.  We know that ¼ of a dollar is 25¢ therefore ¼ is equivalent to 25%.  Adding some fractions becomes easy if we use money as our model.  ¼ + ½ is the same as 25¢ + 50¢ so our total is 75¢, which is ¾ of a dollar.  Even though we often think of work with coins as being part of the younger grades, that work develops strong landmarks that middle schoolers can use to calculate as well.

A large part of geometric thinking is thinking about attributes and sorting shapes into groups.  Coins provide some great practice with sorting by attributes.  Students can sort by color or size to start.  Then they can dig deeper and sort by date or mint mark.  In recent years quarters have had different states on them and then there are those Sacagawea Dollar Coins that are a different color from all the rest of our coins and feature the first Native American female on a coin.  These are all fun attributes to look for and think about when sorting.

## Coins for Measurement of Weight and Length

We can also use coins for thinking about weight.  Think for a second about something in your house that weighs one ounce.  We buy lots of things at the store in ounces but few of us have an idea of the weight of one ounce.  We can use coins to help us further develop our thinking about ounces.  Ten pennies weigh one ounce, so do five quarters.  Now that you know this you and your child can make a simple pan balance at home and figure out the weight of other household objects.

Kindergarten and first grade students work on measuring in nonstandard units.  Coins work really well for this too!  Students can measure items in pennies or dimes to see how long they are.

Empty your pockets, dig in the couch cushions, and round up the coins in your home.  Let your child keep the collection in their room and use the coins often for play and math tasks.  This simple tool will reap large math benefits for many years.