We use rules to build new numberlines. For example we can start in the middle and go both forward or backward using adding and subtracting rules. You can even generate and experiment with negative numbers by subtracting below 0. As you build numberlines on spreadsheets you are building them in your mind. And by thinking of numberlines in terms of rules you are getting ready for algebra.
Category: Numbersense
Hundreds Table Patterns
We introduce students to more complex patterns and rules in hundreds tables. In particular, we have students look at diagonal patterns and develop rules to fill them. This spreadsheet hundreds table practice is designed to build numbersense, the primary building block for a strong math education. We encourage students and teachers to develop more spreadsheets like these to exercise and develop numbersense.
Distributivity
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.
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?