Why Two Land and Three Land?
Adding and subtracting in any place value numeration system amounts to making and recording fair trades. For elementary school students to learn this with understanding, they must perform these operations in bases other than 10. Then what stays the same when the base numbers change stands out, namely, that adding and subtracting are about making and recording fair trades.
Two Land (base 2) and Three Land (base 3) were chosen as alternate bases because …
•Students do not need to know the addition and subtraction facts to add and subtract with just 0, 1, and 2.
•The smaller the base, the more practice making and recording fair trades.
•Place value in the systems could be represented with blocks out to seven places without the blocks getting too big.
These lands differ from most lands by the strictness of their laws. In these lands, if a trade can be made, it must be made. In Two Land, every two blocks the same must be traded for one of the next bigger block, and in Three Land, every three blocks the same must be traded for one of the next bigger block. In contrast, seven pennies in Five Land may be traded for a nickel and two pennies; 75 minutes in Sixty Land may be traded for an hour and 15 minutes; 30 inches in Twelve Land may be traded for 2 feet, 6 inches, and 3/2 may be traded for 1-1/2.
Fair Lands is a trading center for fair trades, particularly ones based on numbers like five pennies for a nickel, 60 minutes for an hour, 12 inches for a foot, and two halves for a whole. Since the numbers are backed by law or convention, the items traded are said to be in a land, and the land is named after the number that prescribes the trade. So for the trades mentioned, pennies and nickels are in Five Land because five pennies make a nickel; minutes and hours are in Sixty Land because 60 minutes make an hour; inches and feet are in Twelve Land because 12 inches make a foot; and halves and wholes are in Two Land because two halves make a whole.
Fair Lands Blocks
This booklet is about two exceptional lands made of specially designed blocks. One is called Two Land because . The other is called Three Land because . By clicking on their pictures, you can see how they are made.
Two Land Blocks
Three Land Blocks