Our orthodontist has an ongoing game where kids get to guess the number of items in a jar:
Although the jar shape and item type change each month, my kids use the same strategy every time: they count how many items are in the bottom layer, figure out how many layers are in the jar, and either add or multiply to find the total count. It’s fairly intuitive, and it’s a great introduction to the concept of volume.
My son was recently working on a spiral math review when he encountered a problem that required finding the volume of a square pyramid. “What’s the formula for that one, Mom?”
Instead of giving him the volume formula, I reminded my son of the orthodontist’s game and let the connections happen. I’m pretty sure he won’t find the need to “store” a volume formula in his brain anymore. When learned in isolation without connection to real objects, volume formulas (and formulas in general) can hinder intuition and common sense.
As much as my son enjoyed winning the guessing game at the orthodontist one month, the real prize was the opportunity to use his own powerful intuition to make mathematical connections.