Activities on importing (adding) and exporting (subtracting) in different bases using the Fair Lands blocks (multi-base arithmetic blocks for base 2 and base 3), Ten Land (base ten) blocks, and counters in order of difficulty with (1) no recording to (2) recording just the answers to (3) recording the answers and the trades made to get the answers.
- Addition is modeled as importing the blocks or counters for a particular "land" to a warehouse—a gameboard with columns designating where to store the items by kind. A truck loaded with blocks or counters arrives at the warehouse with a packing slip designating the number and kind of items on the truck. Students unload the truck and put the items in the designated columns on the gameboard in keeping with the Law of the Land for the land in question. For example, if the event is in Three Land and a truck arrives with 2 unit cubes and there is 1 unit cube already in the warehouse, all three unit cubes would be traded for a long, resulting in 1 more long in the warehouse. The addition problem thus modeled is the number and kind of items on the truck being added to the number and kind of items already in the warehouse.
- Subtraction, being the reverse of addition, is modeled as exporting the blocks or counters from the warehouse. An empty truck arrives at the warehouse with an invoice listing the items that are to be taken from it and put on the truck. If there aren't enough of a particular item to satisfy the invoice, the next larger item is traded for its equivalent of the smaller item so as to have enough. For example, if the event is in Three Land and a truck arrives with an invoice for 2 longs and there are no longs in the warehouse, a flat from the warehouse would be traded for 3 longs, 2 of which would be loaded onto the truck, leaving 1 long in the warehoiuse. The subtraction problem thus modeled is the number and kind of blocks in the warehouse less the number and kind of blocks indicated on the invoice.
In making "fair" trades up and down in importing and exporting in different lands or bases, students learn how a place value numeration system works irrespective of its base and thus how to add and subtract in any base with understanding, including base ten.
Grades K-6, 108 pages with permission to duplicate. Downloadable e-book.