Show Me the Money!

When was the last time you tried to teach a young child to count coins? If you’re like me, you probably found this to be a daunting task, as many math and non-math related issues surface.

As a child, I remember making a deal with my little sister: I offered to trade my four big nickels for her three little dimes. She thought I was being so generous…and we made the trade right there in the backseat of our Ford Pinto.

This goes to show that value-counting coins is a complex skill. It includes

  • memorizing coin names and values,
  • understanding the difference between counting the number of coins and “counting” their combined values,
  • understanding the proportional relationships between the values of various coins,
  • skip counting by different denominations,
  • adding mentally,
  • seeing coin values as fractions as a whole,
  • and the list goes on.

It turns out that our traditional method, using coins as the teaching tool, just doesn’t cut it. Coins are concrete objects, but there is nothing about them that represents their proportional values. Today, I’d like to make a suggestion – let’s, instead, use the ten-frame to teach money!

Using the Ten-Frame to Represent Coin Values

The ten-frame, a visual organizer for numbers 0-10, can be extended and partitioned to represent multiple ten-frames and fractional parts. As you can see below, we can partition and/or combine ten-frames to represent coin values – 1, 5, 10, 25, 50, and 100.

         

Using the largest ten frame to represent $1.00, students can see that $1.00 is composed of 100 small squares – we’ll call those pennies. They can also see that there are 10 small ten frames – we’ll call those dimes. Then it’s a matter of partitioning and combining ten-frames to find the nickels, quarters, and half-dollars.

From Ten Frames to Money Boards

This visual model, pictured below as a KP Money Board and Coin-Value Cards, helps students see the proportional relationships between the various coin values. It also helps them explore the fractional values of the coins.

KP Dollar Board & Coin Cards for download

Using Money Boards and Coin-Value Cards for Problem Solving

Money Boards and Coin-Value Cards also provide a foundation for students to conceptualize a number of important money-related skills:

  1. Finding coin equivalences for $1.00 (4 quarters, 10 dimes, 20 nickels, 100 pennies)
  2. Comparing relative values of coins (e.g., 1 dime = 2 nickels; 1 nickel = 5 pennies)
  3. Value-counting a set of mixed coins
  4. Making change from $1.00
  5. Counting past $1.00 by counting in groups of $1.00
  6. Solving money-based word problems and story problems

One Final Thought – Bills Before Coins

At KP, we take the stance that since whole numbers are mastered before fractions, value-counting bills (whole numbers) should be taught before value-counting coins (fractions of bills). Several years ago, I conducted an action-research project to see if students would learn to value-count coins faster if they first learned to value-count bills. After all, the bills are uniform in size and clearly indicate their values. Guess what I found? Yep – the class that learned to value-count bills first subsequently learned to value-count coins in about half the time it took the class that began with coins. Furthermore, we used $1, $10 and $100 bills to connect to place-value concepts rather than pennies, dimes, and dollars. This was a huge eye-opener to me and my colleagues. Might you give it a try?

We hope you’ll consider using the KP Money Boards and Coin-Value Cards as you plan for your upcoming money units and problem-solving units. Click here for a downloadable version of the KP Money Board and Coin-Value Cards: KP Dollar Board & Coin Cards for download.

What do you think of these ideas? Do they resonate with you? Are they new for you, or have you thought of something similar in the past? If so, will you share with our readers what have you tried and how it has worked? Please join the conversation by leaving your comments below.

Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.

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