Understanding Place Value

Place Value Chart
Megaminxwin/Wikimedia Commons/Public Domain

Place value in an extremely important concept that is taught as early as in kindergarten, and as students learn about larger numbers, the concept of place value continues throughout the middle grades. Place value refers to the value of the digit based on its position and can be a difficult concept for young learners to grasp, but understanding place value is essential for basic math computations.

The reason this can be difficult to grasp is that students often begin with rote counting — 1, 2, 3, 4 — before learning two-digit and three-digit numbers and to a child, the 1 in the numbers 1, 10, and 100 often mean the same thing, though place value dictates that these numbers are vastly different — the place value of 1 in the number 1 is one while the place value for 1 in 10 is a group of one ten while the place value for 1 in the number 100 is a group of ten tens or one group of one hundred.

To simplify this lesson, students need opportunities to experiment with these values. That way, students can gain a hands-on understanding of how place values function in the larger mathematical world.

What Helps Students to Better Understand Place Value?

Students need opportunities to see amounts in numbers to better grasp the concept of place values changing the quantities associated with each value. For instance, use base ten blocks or strips to ensure that students see the value of numbers with the place value of ten.

These place value blocks are most effective at showing the value of numbers because there are cubes to represent one, strips to represent ten, flats to represent 100 and blocks to represent 1,000. The students can easily see that 10 cubes fit into a 10 strip, 10 strips fit into the 100 flat and 10 100-flats fit into the 1000 block.

By spending time having students show numbers with the blocks and then writing the numbers, students will be able to practice building many numbers with the place value blocks or strips to solidify their understanding of the concept better.

Small Steps to Understanding Place Values

As time progresses, provide a chart like the image atop this article and ask questions about the placement of specific numbers. For instance, with numbers like 7,028,360,501 you may say, what does the 7 represent (billion) or what does the 0 next to the 7 represent (hundred million) or what number is in the hundred thousand's place (0).

However, take small steps and begin with two- and three-digit numbers. As children progress throughout the grades, move on to the thousands and ten thousands. Do not move to the other side of ones until students are at the point in their math that they're ready for decimals (tenths, hundredths, etc.)

You can usually tell when students have a good grasp of place value by their ability to round numbers. When a child understands place value, they are quick to be able to round numbers to a specific place.