Place Value

Place value is the idea that a digit's position in a number decides what it is worth, not just what it looks like. In 452, the 4 is not "four," it is four hundred, because it sits in the hundreds place. Move that same 4 one spot to the right and it is worth forty instead. Nothing about the digit changed. Only its position did.

What place value means

Every digit in a number sits in a place: ones, tens, hundreds, thousands, and so on, each one ten times bigger than the place to its right. Once a child can name the place a digit sits in, they can explain why 452 and 425 are different numbers even though they use the same three digits, and why lining up the ones, tens, and hundreds columns is what makes column addition and subtraction work at all.

Why it trips kids up

Place value is easy to recite and hard to really see, especially with regrouping: "borrowing" in subtraction or "carrying" in addition are both just place value in disguise, moving a group of ten from one column to the next. A child who has memorized the steps but not the reason can follow the recipe on an easy problem and get lost the moment the numbers do not cooperate.

That is the moment worth slowing down for. Ask what a specific digit is worth in the problem in front of you, not the whole number, just that one digit, and let your child reason it out loud. Picture a 3rd grader, call her Riya (an illustrative example, not a real student): she went from guessing at regrouping to explaining it herself once she started narrating what each digit was worth before she moved anything.

If you want to see this explained out loud, step by step, on a whiteboard rather than described in text, watch the free Explanova demo: a 75-second recording of Coach Nova working a problem step by step instead of handing over the answer.