The distributive property turns out to be central to a surprising variety of important mathematics. One of the most valuable is to use it to break products into two pieces to make them easier to compute. Thus 56+510 is easier to solve in your head than 5*16. Here again we take what is generally considered an abstract principle and make it a concrete spreadsheet picture made up of different rectangles.
Tag: properties
Commutativity
The symmetry of the multiplication table around the square numbers diagonal we call commutativity or the commutative property. It means that in a 12 by 12 multiplication table we need only learn 72 or so facts and not 144. It also means that the square numbers are not the only important diagonal patterns in the table. As with so many of the things we do on spreadsheets, we not only encourage students to explore, we encourage them to be look for the beauty in math.
Associativity
Parentheses are not only important in paper math, they are critical in spreadsheets. To make sure that terms are handled properly by spreadsheets, we have to be sure we use parentheses to write our formulas so that there is no ambiguity. Associativity gives us the principle behind this grouping, for we ask which terms do I associate with this other term?