Reflections from a Third-Grade Classroom

In my classroom, we are currently studying money. This is very difficult! There is also a huge amount of variation between the children. Some (who have a fairly developed conception of our number system, are very capable of counting money, and are even to the point of making change! Others are struggling with the idea that the smallest coin does not have the lowest value. Also, counting coins is difficult and the fact that quarters are counted 25, 50, 75, 1 dollar is impossible to remember. Most of the class falls somewhere in the middle. They can remember the value of the coins they are dealing with and (although they struggle), they can make combinations to reach a certain amount. The problem for the majority of my class is using the smallest number of coins possible. For example, if when told to make 48 cents, most students will count out 4 dimes and 8 pennies (rather than 1 quarter, 2 dimes, and 3 pennies).

Today, at the request of my CT, I pulled aside a small group (4 students) to try and see if I could help them begin using more advanced ways of making change. The four students I pulled aside were from a range of ability. One counted her quarters “25, 36, 82, 100.” Another was at the level where he would be comfortable making change. (”I want to buy your pen, which costs $0.46; if I give you $0.76, what change will I get back from you?”) The other two students were in the middle. I was hoping that by taking a range of levels, I could create an environment where the students could learn from and help each other.

I began by counting quarters and identifying values with the group to make sure that the basics of money were understood. Three of the students were great, the fourth still needed some work. I proceeded to give each student a “wallet”–a bucket full of play coins. I had the students look through their wallets and gave them a minute or so to interact with the manipulatives. I then showed them a book, and said, “Hmmm…I want you all to buy this book, which is 36 cents [at this point I wrote 32 cents on the board]. Can you make 36 cents from your coins?  Think about it, and give me a thumbs up when you’re done.”

After the students were finished, I went around and had each child show the group how they counted their coins.  I recorded their responses using number lines.  I represented the coins with jumps on the number lines.

•  Student One made 36 cents using:  three dimes, six pennies.
•  Student Two made 36 cents using: one quarter, eleven pennies.
•  Student Three made 36 cents using:  one quarter, one nickel, six pennies.
•  Student Four made 36 cents using: one quarter, one dime, one penny.

After representing all of the number lines on the board, I asked the students to help me count the number of coins in each method.

• Student One:  9 coins
• Student Two:  12 coins
• Student Three:  8 coins
• Student Four:  3 coins

Since I wanted students to begin using more “efficient” ways of putting together money, I pointed out how Student Four’s method only used three coins.  “Wow!  How neat if we can find the way that uses the fewest amount of coins!  This would be very fast, if you were in a hurry, to count three coins instead of twelve!  Let’s practice this!”

I pulled out another book and told the students that this book cost 58 cents.  “Show me how you can use your coins to buy this,” I said, writing the number on the board.  I allowed the students to work for a few minutes and when it looked like they were all satisfied, I asked them if they had found the way that used the least amount of coins.  Many hadn’t, and had relied on their previous, penny-centric method.  I told them I would give them a hint, “I want you to try to find the way that uses just 6 coins.”  This presented a problem for the children.  Some protested that it was too hard, and so I told them to work together and see if they could figure it out using teamwork.

After some trial and error, one student realized that you had to start with the biggest number (the quarter).  The students used one quarter, but hadn’t yet thought to use two.  I let them keep working, but redirected when I saw them struggling with the math.  One girl in particular could not add and keep track of such numbers.  She would pull out a quarter and a two dimes and count 31 cents (25, 30, 31).  I continuously held up various coins to reestablish their value, and showed children how to add on ten repeatedly as well.

I was very proud when the children finally came to the conclusion that the solution was to select two quarters, one nickel, and three pennies.  I gave them additional examples and found that the main inhibitor to success was the students’ ability to add the amounts.  The main reason so many reverted to pennies was because that is how most of them are currently adding–by counting on units of one.  Skip counting, as money is counted, is not a mastered skill for most of these students.

My initial reaction is that these students are not ready to be dealing with money.  Without the ability to comfortably skip count by tens and fives, this is nearly impossible.  However, while writing this, I have come to think that maybe money could be another way for children to access this information.  It seems that often, our natural reaction is to simplify information when our children appear to be struggling with it.  But maybe this is the wrong approach.  My students could drill addition strategies from now until June  and perhaps learn them, perhaps not.  However, everything in my training says that we need to push children with authentic meaningful assignments if we hope to help them succeed.  Perhaps money should be introduced first, rather than second.  Maybe money is an authentic pathway towards skip counting, and more advanced mathematics.  This activity was very eye opening for me, as it forced me to reevaluate my initial instinct.