On multiplication, it's better to not think of multiplication as being repeated additions, but instead to think of it in terms of areas. Taking that approach, i

On multiplication, it's better to not think of multiplication as being repeated additions, but instead to think of it in terms of areas. Taking that approach, it becomes easier to consider, e.g., (x² + 2x - 1)×(3x² -4x + c) since we can write the terms along the sides of a rectangle and divide the rectangle into the products of the terms. One of the things I did in my math for liberal arts majors class I used to teach was also to do a fictionalized version of the expansion of the concept of numbers from *N* to the whole numbers to integers to rationals to algebraic numbers to reals to complex numbers. I say fictionalized because whole numbers and negative integers historically come after (positive) rationals, algebraic numbers and transcendental reals, but for pedagogical purposes, its easier to go in order of increasing supersets.