*I know the title is corny, but the content below is great.”*
What happens to place value understanding between elementary and middle school? From my observations, when tricks are introduced, the need for place value understanding is no longer necessary. Why know they relative size of numbers when I can “add” zeros and move decimal points?
If you are a middle school teacher, there’s a chance you didn’t know that in 4th grade students recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. (4.NBT.1) and in 5th grade students recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left (5.NBT.1). Why is that important for you to know? In middle school, students begin to look at percentages and scientific notation, among other concept extensions, which are based in place value. If we decide to make explicit connections between concepts students already know and understand to new information, we have essentially cut the amount to commit to memory down. It makes me think of Van de Walle discussion on how understanding the commutative property cuts multiplication problems in half. Well, if students know as a digit shifts left it is getting ten times larger and as it shifts right it is getting ten times smaller, it can be applied to solving percentage problems and scientific notation problems. However, if that connections is not made, students now have to memorize in which direction the decimal point “moves” or how many zeros to “add” in addition to solving the problem. All new information that does not make sense, nor can the reasonableness of the answer be determined.
Here are some activities I have used to help make the explicit connection of place value with scientific notation and percentages: