Place value is one of the key concepts in mathematics. Understanding place value (or not understanding it) will follow students through their mathematics journey. Without this understanding, students often struggle with regrouping, adding and subtracting multi-digit numbers, and more difficult computations. However, being able to say that 635 is 600 + 30 + 5 does not, in and of itself, mean that a student understands place value. Place value encompasses not only position and value of digits but also decomposition of numbers and a number’s relationship to other numbers.
Place value is taught as early as in kindergarten, and as students learn about larger numbers, the concept of place value continues throughout the middle grades. It can be a difficult concept for young learners to grasp, the reason being 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 skill, students need opportunities to experiment. These experiments allow students to gain a hands-on understanding of how place values function in the larger mathematical world. In our second grade classroom, we have been experiencing a great many of these hand-on opportunities.
