Math Background

Place Value to 999,999: Overview

The foundation of our number system is the base-ten place-value system, which shows that the value of each place in a number is ten times the value of the place to its right. Your students learned place value to one thousand last year in Grade 2. See Place Value to 1,000. Look at the place value chart below.

place value chart

This year, your students will extend their understanding of place value to hundred thousands.

place value chart

Students begin third grade by reviewing numbers through 1,000, using base-ten blocks. This model shows 1,247.

place value chart

As students explore numbers through hundred thousands, they move away from concrete models.

place value chart

The number represented in the place-value chart above can be written in different ways.

  • The standard form is 324,098.
  • The word form is three hundred twenty-four thousand, ninety-eight.
  • The expanded form is 300,000 + 20,000 + 4,000 + 90 + 8.

Notice that the digit in the hundreds place is 0. Point out to students that 0 is a digit even though its value is 0. This concept is reinforced in the “Introducing the Concept” part of the lesson on this Web site.

When students have a good understanding of place value to hundred thousands, you can move on to comparing and ordering greater numbers. Emphasize the importance of starting with the greatest place to compare numbers. See the examples in the second question in “When Students Ask.”

Students will rely upon their place-value skills in later chapters when they use regrouping with addition, subtraction, multiplication, and division and when they learn to round numbers in this chapter. Several lessons are dedicated to rounding numbers. Those lessons provide your students with a step-by-step development of this concept. You can provide opportunities for students to round numbers by gathering data from newspapers or Web sites and having them round the numbers to specific places. This activity will help students learn key “rounding” words such as about, up to, and almost.


Houghton Mifflin Math Grade 3