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DACTM conference – Money, Money, Money!!!

November 26, 2010

The title for the session at the Detroit Area Council of Teacher’s of Mathematics was inspired by the Pink Floyd song Money.  I wanted to share a unit I had done with my students with the objective to learn more about making change in a real world situation and  the concept of counting up.

Since I was presenting to teachers and future teachers some of the basics I didn’t go into but I did break down the information so they could see how to model it for their students.  So the following are suggestions on how to present it to young children (Kindergarten to 2nd grade) and older students (3rd and 4th graders).

Young Children – With young children I help them identify the different coins by doing:

  • Coin rubbings (using enlarged coins to rub with a crayon helps children really see the differences)
  • Sorting coins from cafeteria, UNICEF… (it can just be the change from your pocket or the money left for a tip at a restaurant)
  • Enlarge coins to wear or hold

    Enlarged coins for students to see the details easier.

    My enlarged coins that my students have been known to wear on occasion.

  • Give children lots of opportunities to: Hold coins and describe them

To prepare children for counting coins, counting by one’s. then ten’s and five’s will definitely make a difference.  Counting by 10’s and 5’s can be done through games, jumping, coloring in hundred’s charts.  I usually do ten’s before counting by 5’s.

There are lots of games you can play with children to reinforce the skills.  I have many listed through Amazon to make it easier for you to find them.  My students have liked playing Money Town on the computer, Money Bags and Cool Cash Bingo. There are also plenty of games you can make yourself like; bingo, Roll for Pennies and a coin chart.

  • Bingo – you can make it progressively harder as your child gets better at making change and identifying coins.  You can have just a coin and they have to match the coin with their name or value or you could have several coins together and they have to add them up.

    Bingo cards

    Money bingo cards made with a coin stamp.

  • Roll for Pennies – I made my own dice using a penny stamp.  On each side of the dice I had 1, 2, 3, 4, 5 and 1 again penny stamped.  Your child would have to roll the dice and collect that many pennies for how many they rolled.  When  they have collected 5 pennies, they have to trade them in for 1 nickel (great way for them to get  introduced to trading for addition with regrouping).  The goal is for them to reach a quarter, so they keep doing that until they have 5 nickels and they trade it in for 1 quarter.  When your child is ready, you can add the confusing coin, a dime!  Who’s big idea was it to have the dime higher in value to the nickel but it is smaller?
  • Another activity that works great is making a chart to show the coins and their relationship to each other.  This one my students helped make and I have used it for years.
    Coin chart.

    A coin chart going up to 100 pennies.

    The coin chart.

    Rolling the chart on the floor to figure out how much change to give is very fun and effective.

Modeling Counting Up – Only when they understand all the coins and their values do I suggest introducing counting up.  Explain that it is easier to count up when they start from a number ending with a zero.  Start with an example that ends with some number not with zero.   Then pose the question, “How many coins would we need to get to the next highest zero?” Then ask, “What way can we make change using the smallest amount of coins?”  Then you could model the whole process for example:

If we wanted to buy play dough for $4.21

  • How many pennies to 5 or 0?
  • Counting up from $4.21
  • One penny = $4.22
  • 1¢ = $4.231¢ = $4.24
  • 1¢ = $4.25

Then you can ask, “Is it $5.00 yet?”  Although there are many ways to make change, explain one of the goals is to use the fewest coins to reach $5.00.  For young children you may want to have them feel the weight of 4 quarters vs. 100 pennies.  Which one  would they want to have in their pocket?

So pose a suggestion, “Let’s try nickels.” and let them estimate how many it will take.

Nickels are worth .05 so if we add 1 to our $4.25 it would be…(let them pull out nickels for each one if your child needs something concrete).

  • $4.25 + .05 = 4.30
  • $4.30 + .05 = 4.35
  • $4.35 + .05 = 4.40
  • $4.40 + .05 = 4.45
  • $4.45 + .05 = 4.50
  • $4.50 + .05 = 4.55
  • $4.55 + .05 = 4.60
  • $4.60 + .05 = 4.65
  • $4.65 +.05 = 4.70
  • $4.70 +.05 = 4.75
  • $4.75 +.05 = 4.80
  • $4.80 +.05 = 4.85
  • $4.85 + .05= 4.90
  • $4.90 +.05 = 4.95
  • $4.95 +.05 = 5.00

That’s a lot of nickels! How many are there? Could we try something else?
How many do you think it will take to reach $5.00?

Dimes… are worth how much? Starting at $4.25 let’s add one dime or 10¢ = 4.35.

  • $4.35 + .10 = 4.45
  • $4.45 + .10 = 4.55
  • $4.55 + .10 = 4.65
  • $4.65 + .10 = 4.75
  • $4.75 + .10 = 4.85
  • $4.85 + .10 = 4.95

$4.95 isn’t $5.00 what should we do? Let your child come up with a solution but remind them, one of the goals is to use the least amount of coins.

How many dimes are used? Is it more or less than the nickels? Can we try any other coins? How many quarters will it take? Let’s find out:

  • $4.25 + .25 = 4.50
  • $4.50 + .25 = 4.75
  • $4.75 + .25 = 5.00

What coin did you use the fewest?  I do this a number of times, depending on the group using a variety of items.  Sometimes I change it up and let them choose an item and the amount (I give them a dollar amount to keep it within range – great way to show number sense too).

Story Problems – When they are comfortable with the activity, I have them make their own story problems.  They love making silly problems using their friends names.  They also have to come up with the answer for their problems.  It shows me understanding and they get to practice the skill twice.  Also incorporating writing uses both sides of the brain in processing the information!  Win – win! Then they trade the story problems and can work together to figure out the problems, using coins if they need to. The following is a worksheet I used to see individual progress on counting up each student was making with making change for $.50.

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These two worksheets were for my older students.  It was interesting to see that they wanted to just subtract the figures rather then count up.  So this sheet forced them to apply the skill.

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Pizza Group – One way New Morning School makes working with money real is we have Pizza Group.  Each week students are in charge of counting the money for all the pizza orders for the week, making change and tallying how many pizza’s and cheese bread have to be ordered for Friday’s lunch.  They take the responsibility seriously.  It also gives us the ability to challenge the students to make change in a variety of way.  For instance, if a student is really comfortable with counting out only dimes, we may ask them to try making the change using the fewest amount of coins or as them “How many nickels would that be the same as?”  The following are the forms that are used.  They are simple and can be adapted for other things you may want to order.

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Connecting money to Colonial America unit – I did all of this to get them ready to open the Log Cabin General Store.  We had just finished studying Colonial America and had  made a log cabin using carpet tubes.  We wanted to make using money real, so we came up with everyone would earn $5.00 for:

  • Coming to school on time
  • Having a cooperative spirit with everyone
  • Completing their work each day

I drew these silly bills taking into account our recent studies of Benjamin Franklin, George Washington and a variety of other people that made a difference in our nation’s history like Anne Bailey.

My students had many opportunities to:

  • making change
  • purchase items that they wanted
  • learning about saving
  • counting up
  • and having fun!

Let me know what you think!  It was fun doing it.

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