Math Background

Lesson: Comparing and Ordering Greater Numbers:
Introducing the Concept

Before students compare and order greater numbers, use this lesson to reinforce their understanding of place value of greater numbers.

Materials: transparency of place-value chart through hundred thousands

Preparation: Make a place-value chart through hundred thousands. Leave space on the left side of the chart so the millions period can be added to it.

place-value chart

Prerequisite Skills and Background: Students should know place value to thousands.

Write 356,770 on the place-value chart.

  • Say: Each group of three digits in a number is called a period.
  • Ask: What symbol is used to separate periods? (comma)
  • Ask: What places are in the ones period?
    (hundreds, tens, and ones)
  • Point to each place in the ones period and ask, What is the value of this digit? (hundreds place: 7, value: 700; tens place: 7, value: 70; ones place: 0, value: 0)
  • Ask: What is the value of the ones period?
    (seven hundred seventy)
  • Ask: What places are in the thousands period?
    (hundred thousands, ten thousands, and thousands)
  • Point to each place in the thousands period and ask, What is the value of this digit?
    (hundred thousands place: 3, value: 300,000, ten thousands place: 5, value: 50,000; thousands place: 6, value: 6,000)
  • Ask: What is the value of the thousands period?
    (three hundred fifty-six thousand)

    Have students read the number aloud.
    three hundred fifty-six thousand, seven hundred seventy

    Extend the place-value chart to the millions period. Write 2 in the hundred millions place, 4 in the ten millions place, and 8 in the millions place.

    place-value chart
  • Say: This is the millions period.
  • Ask: What places are in the millions period?
    (hundred millions, ten millions, and millions)
  • Point to each place in the millions period and ask: What is the value of this digit? (hundred millions place: 2, value: 200,000,000; ten millions place: 4, value: 40,000,000; millions place: 8, value: 8,000,000)
  • Ask: What is the value of the millions period?
    (two hundred forty-eight million)
  • Say: Read the number aloud.
    (two hundred forty-eight million, three hundred fifty-six thousand, seven hundred seventy)
  • Ask: Which digit in 248,356,770 has the greatest value? (2) How do you know?
    Elicit from students that the greatest place is the hundred millions place, so 2 has the greatest value.
  • Ask: Is the value of the digit 8 greater than or less than the value of the digit 4?
    Students should realize that 8,000,000 is less than 40,000,000, so the value of the digit 8 is less than the value of the digit 4.
  • Ask: Which places have the same digit? (the hundreds and tens places) Do the digits have the same value?
    Students should realize that the digit 7 in the hundreds place has a value of 700 and the digit 7 in the tens place has a value of 70.
  • Ask: Since the value of the digit in the ones place is 0, could we just drop the 0? Why or why not?
    Lead students to discover that without the 0, the number would be 24,835,677.

    Replace 248,356,770 with 154,656,902. Ask questions similar to those above.


Houghton Mifflin Math Grade 4