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.
Category: Labs
Build a House
Spreadsheets with their natural grid make a great, though not entirely flexible, platform for architectural design and for working with shapes. Build a house introduces students to using spreadsheets to create floor plans and to measure area. Most spreadsheets have amazing graphic flexibility. You may want to encourage students to use spreadsheets for art. Here is an incredible example: http://www.spoon-tamago.com/2013/05/28/tatsuo-horiuchi-excel-spreadsheet-artist/
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?
Addition Table
From here on students can go in most any order they choose. They can start with addition or with multiplication. They should imagine themselves on an elevator able to go up or down anytime they want, to find interesting floors to explore. NOTE: The addition table, like the other tables, goes up and to the right to link their patterns with graphing and further work with functions. They thus have a horizontal and a vertical axis that they use to build their rules. The best rules needed to build this table requires the use of “absolute” addressing. Normal or “relative” addresses are patterns that copy from one area of a spreadsheet to another. Absolute or fixed addresses refer to a specific or fixed cells. You can fix an address by column in a rule by putting a $ sign in front of the letter or in a row by putting a $ sign in front of its number. For example: = $J15 or =J$15, or =$J$15.
Addition Patterns
Now that students can build addition tables, they should look for the patterns in them. We introduce them to a variety of things they might want to look for. We also suggest that some students may want to try to make a subtraction table. We have another Lab for making subtraction tables but this can provide some students with an interesting challenge. They should build these two tables side by side to compare their patterns.