Math Investigations

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Chapter 14

Part 1: Home and School Investigation

Send the Letter to Family (PDF file) home with each child. Once all the children have brought in their pictures showing how they made 50¢ using more than one coin, look at the different ways with the whole class. Create an area to display the children's work. Have one child put his or her picture in the display area. Ask, Does anyone else have a way to make 50¢ that is different? Keep asking this question to get as many different ways as you can on display. If a child shows a way that is already on display, put that drawing on top of or underneath the drawing that is already there. Once you have put up all the different ways the children have created, ask, Can anyone think of a way that is not here?


Here are the different ways to make 50¢ without using any pennies.
  • two quarters
  • one quarter, one dime, three nickels
  • one quarter, two dimes, one nickel
  • one quarter, five nickels
  • five dimes
  • four dimes, two nickels
  • three dimes, four nickels
  • two dimes, six nickels
  • one dime, eight nickels
  • 10 nickels

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 3 on counting coins.


Introducing the Investigation

Tell the children that they are going to see how many different amounts of money they can make using two coins. They can choose from quarters, dimes, nickels, and pennies.

Put the children in pairs and give them the Investigator Worksheet and some play money. Demonstrate how they can use the rows in the table on the worksheet by filling in the number of coins of each type for each different way.

Doing the Investigation

As you observe the children, help them find an organized way to do the activity so they can find all the possible combinations. For example, have them start with a quarter and find all the combinations that contain at least one quarter. Then do the same for dimes, etc., making sure they do not count one of the ways they already counted.

Make sure the children understand how to record each way in the table on the worksheet.

These are the ten different possibilities for combining two coins.

two quarters 50¢
one quarter, one dime 35¢
one quarter, one nickel 30¢
one quarter, one penny 26¢
two dimes 20¢
one dime, one nickel 15¢
one dime, one penny 11¢
two nickels 10¢
one nickel, one penny
two pennies

Extending the Investigation

Have the children do the exercise using three coins instead of two.

These are the 17 different possibilities for combining three coins.

three quarters 75¢
two quarters, one dime 60¢
two quarters, one nickel 55¢
two quarters, one penny 51¢
one quarter, two dimes 45¢
one quarter, one dime, one nickel 40¢
one quarter, one dime, one penny 36¢
one quarter, two nickels 35¢
one quarter, one nickel, one penny 31¢
one quarter, two pennies 27¢
three dimes 30¢
two dimes, one nickel 25¢
two dimes, one penny 21¢
three nickels 15¢
two nickels, one penny 11¢
three pennies
one dime, two nickels 20¢

Houghton Mifflin Math Grade 2