Math Background

Lesson: Comparing and Ordering Greater Numbers
Developing the Concept

When students have a good understanding of place value, they can proceed to comparing and ordering greater numbers.

Materials: transparency of place-value chart through hundred millions

Preparation: Make a place-value chart through hundred millions or use the place-value chart from the previous lesson.

place-value chart

Prerequisite Skills and Background: Students should know place value to hundred millions and know how to order numbers through thousands.

  • Say: When you compare numbers, it is important to line up the digits in the correct places.

    Write 9,886,705; 437,062,185; and 73,655,211 on the place-value chart with the digits lined up as shown below.

    place-value chart
  • Ask: Are the digits lined up correctly?
    Students should recognize that the digits are not lined up correctly. Have a volunteer explain how the digits should be lined up and make the corrections on the place-value chart.
    place-value chart
  • Say: We're going to put these numbers in order from greatest to least.
  • Ask: Where do you start when you compare numbers?
    Students should recall that you start with the greatest place.
  • Ask: What is the greatest place of these numbers?
    Students should recognize that the hundred millions place is the greatest place.
  • Ask: Do all of the numbers have a digit in the hundred millions place? (no) So what is the greatest number? (437,062,185)
    Wipe 437,062,185 off the transparency and write it on the board.
  • Ask: What is the greatest place of the two remaining numbers? (ten millions place)
  • Ask: Do both numbers have a digit in the ten millions place? (no) So what is the next greatest number? (73,655,211)
    Wipe 73,655,211 off the transparency and write it on the board after 437,062,185.
  • Ask: What number comes last? (9,886,705)
    Wipe 9,886,705 off the transparency and write it on the board after 73,655,211.
  • Ask: When you compare numbers that have different numbers of digits, which number is the greatest? (the number with the greatest number of digits) Which number is the least? (the number with the least number of digits)

    Erase the board and write 364,706,199; 354,785,293; and 365,999,253 on the place-value chart.

  • Say: We're going to put these numbers in order from least to greatest.
  • Ask: What is the greatest place of these numbers? (hundred millions place)
  • Ask: What do you notice about the digits in the hundred millions place?
    Students should observe that the digits are the same.
  • Ask: What is the next greatest place? (ten millions place)
  • Ask: Which digit in the ten millions place has the least value? (5) So what is the least number? (354,785,293)
    Wipe 354,785,293 off the transparency and write it on the board.
  • Ask: What do you notice about the digits in the ten millions place of the two remaining numbers?
    Students should observe that the digits are the same.
  • Ask: What is the next greatest place?
    (millions place)
  • Ask: Which digit in the millions place has the least value? (4) What is the next least number? (364,706,199)
    Wipe 364,706,199 off the transparency and write it on the board after 354,785,293.
  • Ask: What number comes last? (365,999,253)
    Wipe 365,999,253 off the transparency and write it on the board after 364,706,199.
  • Ask: Did the value of the digits in the hundred thousands place help us order these numbers? Why or why not?
    Students should realize that the numbers were ordered based on the value of the greatest places and that the value of the hundred thousands place wasn't needed to order the numbers.

    Repeat the steps above for 59,714,343; 58,714,344; and 59,715,588. Have students write the numbers in order from greatest to least.
    (59,715,588; 59,714,343; 58,714,344)

Wrap-Up and Assessment Hints
Remind students of the need to line up correctly the digits of the numbers they are comparing. Use the questioning strategies in this lesson to assess their understanding of the concept.


Houghton Mifflin Math Grade 4