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To refine your example, as it's hard to talk about powers to children, you must take caution to not introduce *how* to do something without illustrating the *why* of the necessity of it and the *what* it is they are actually doing.

I think when it comes to teaching the numbers, starting with unary (base-1, or a tally system) representations of real-world things, and the operations on them, and then talk about how the operations are isomorphic (without using that word) to those on a decimal system. Bring to context the utility of a representation, you can bring up binary as an example (and learning binary alongside the standard curricula definitely helped add missing context to Arabic numerals for my childhood), but when you teach how unary behaves the same as decimal, they can carry that reasoning over to whatever else they encounter.