Real World Mathematics

. Doing Mathematics involves wanting to know why

and how -- not just "what" and "how much".

How would this work in 3 rather than 2 dimensions?

Why is the Pythagorean Theorem true?

How does the derivative relate to average rates of change?

Why do roots of a polynomial tell us its factors?

Notice:

These pictures can't be (effectively) replaced with symbols

But an explanatory couple of sentences would help!

If student can't supply them, their understanding is not complete
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