Why is Place Value a Difficult Concept for Students?
Think about the way young learners learn about numbers. They begin with rote counting, 1,2,3,4... From there they get to two digit numbers, 11, 12, 13 and to three digit numbers 100, 101, 102... To a child the 1 in 1, 10 and 100 often mean the same thing. However, in place value, a 1 is one, a 10 is 1 group of ten, 100, is ten, tens or 1 group of 100. Therefore, the difficulty is understanding the place of the specific number and knowing that the placement changes the value of the digit.
What Helps Students to Better Understand Place Value?
Students need opportunities to see amounts in numbers. For instance, use base ten blocks or strips to ensure that students see the value of numbers. The place value blocks are most effective at showing the value of numbers. 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. Spend times having students show numbers with the blocks and then writing the numbers. Practice building many numbers with the place value blocks or strips to better solidify the concept. As time progresses, provide a chart like the image with this article and ask questions about the placement of specific numbers. For instance, with a numbers like 7,028,360,501 You may say, what does the 7 represent? (billion) what does the 0 next to the 7 represent? (hundred million) what number is in the hundred thousand's place?
However, take small steps. Begin with 2 and 3 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.
You may wish to print this worksheet and reproduce the place value strip on it for students.