Spreadsheets always automatically perform the operations you ask them to do. But sometimes we want to see the process. We can make spreadsheets show us that in several ways. Here we show the factors and have students build a times table showing the factors by using a special formula called Concatenate which means join together. This enables us to create a table of factors that we can see with a single rule. Concatenate has a wide variety of uses and it is worth playing with both to visualize factors and to build interesting spreadsheets.
Author: Ryan McQuade
Factor Pairs
Multiplying creates products, factoring separates a product into the numbers that make it up. We thus start with the table and then look at the axes to find the factor pairs that make the product. Once again we focus on the patterns in the times table so that you can not only go from factors to their products but from products back to their factors. Factors and factoring become very important in algebra and in making headmath much easier.
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.
Counting By
Counting-By introduces multiplication. Counting-by or skip-counting is, we believe, the best way to help students build their multiplication facts, and though they will live in an age of ubiquitous spreadsheets and calculators, they still need to have mastered their multiplication facts to do any interesting math in their heads. Here they learn to build rules that count-by and in the process practice both counting-by and rule-making. Counting-by adds the same number again and again and their rule should do the same.
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.