This page comes from one of Sophie’s summer homework books. It’s just one of many practice exercises in adding and subtracting:

Well, sure! My first thought whenever it’s raining out side is: “I wonder what the difference between the number of puddles here and the number of rain boots might be.”

This sort of infuriating problem is what leads to math being incomprehensible at higher levels. Subtraction isn’t a magical and arbitrary branch of abstract mathematics. It’s a tangible, everyday concept.

Sophie understands that when she spends money and gets change she can calculate the difference with subtraction. It’s an understanding not just of how but why. That’s harder to teach with higher-level mathematics. It shouldn’t be a challenge with elementary arithmetic.