My first grader is very advanced in math. Rather than doing more and more math and making school math even more boring for him, I recently decided to start going "deeper" rather than "faster."
Some of the questions we've explored recently are:
- Why do we use a numbering system? (Because otherwise we'd need an infinite number of names)
- Why is multiplication commutative? (Because you could switch the number of items and the number of people and you'd still need the same number of items in the 'rectangle')
- What might math look like without the number 0?
- Why are 2, 5, and 10 the only numbers whose divisibility tests only need the last digit? (because they're the factors of 10)
- Why is a number divisible by 9 if its digit sum is divisible by 9? (becuase every power of 10 has remainder 1 when divided by 9)
Are there any resources I can use to find more questions/explorations like this?