Math Investigations

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Chapter 20

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 numbers from newspapers or magazines, put the children in groups of two. Ask them to talk about the two numbers and about what is alike and different about them. For example, they might talk about the fact that both numbers have three digits and that the digit in one of the places in both numbers is the same. They might also talk about how the digit in one of the places in both numbers is different. After the children have done this, have some of the partners share what they talked about with the whole class.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 8 on ordering three-digit numbers.


Introducing the Investigation

Put the digits 1, 7, and 9 on the board. Ask the children for different ways to write a three-digit number using those digits. Write two or three of their suggestions on the board.

Show the children the worksheet and tell them that they are going to find as many different ways as they can to use the digits 2, 3, and 8 to write a 3-digit number. Tell them that they can use each digit only one time in a number. Tell them when they are finished to write the numbers in order from least to greatest.

Put the children in groups of two for the investigation.

Doing the Investigation

This investigation provides an excellent opportunity for children to practice the strategy of making an organized list. For example, they could list all the three-digit numbers that have 2 in the hundreds place, then those that have 3 in the hundreds place, and finally those that have 8 in the hundreds place.

Have the children share their results when they are finished.


  • 238
  • 283
  • 328
  • 382
  • 823
  • 832

Numbers in order from least to greatest:

238, 283, 328, 382, 823, 832

Extending the Investigation

Have the children do the same investigation with a different set of three digits. For more of a challenge, give them a set of four digits and have them make as many three-digit numbers as they can.

Houghton Mifflin Math Grade 2