Fair Land

A trading center for trades based on numbers and established exchange rates.

Fair Trade

What the Law of the Land dictates. In Two Land, the fair trades would be two Unit Cubes for a Long, two Longs for a Flat, two Flats for a Super Cube, and so on up to two Super Flats for a Mega Cube. In Three Land they would be three Unit Cubes for a Long, three Longs for a Flat, three Flats for a Super Cube, and so on up to three Super Flats for a Mega Cube. In Ten Land the fair trades up to a thousand would be ten ones for a ten, ten tens for a hundred, and ten hundreds for a thousand.


Modeling addition as a business transaction—a purchase—in Fair Lands. The blocks or counters already on a Fair Lands activity board show what is in inventory. Those on the purchase order show what is to be added to the inventory.


An acronym for “Keep it safe and simple, meaning keep your activity board safe and trades as simple as possible.


An indicator that the numbers governing a trade are sanctioned—that when a trade can be made, it must be made, not may be made.

Law of the Land

Used only with Two Land, Three Land, and other place value numeration systems like Ten Land where it’s required that trades be made, not lands like those for money, time, measurement, and fractions where trades are optional.

The Law of the Land in Two Land is “Never have two or more alike. That in Three Land “Never have three or more alike. That in Ten Land “Never have ten or more alike.


Not in violation of the Law of the Land. Being safe in Fair Lands acknowledges the number that is raised to consecutive powers to designate place value in a land. In Two Land or base 2, the number is two. In Three Land or base 3, it is three. In Ten Land or base 10, it is ten. In each case, the Law of the Land is that the base number cannot be equaled or exceeded by that many blocks or counters all the same, that is, in the same place (column) on a Fair Lands activity board.

Simple (as in “keep trades simple)

In importing and exporting, keeping trades simple means always trading the smallest and fewest blocks or counters possible. The smallest requirement forces working from right to left on a Fair Lands activity board. The fewest” one ensures working column by column and not skipping over columns.

Stage 1 Recording

Recording only the answer to an importing or exporting problem. This requires that students can represent a Two Land or Three Land numeral with blocks or counters. Once they can do this, they can be directed to centers where they can work from written instructions like 1012+112 or 100121102 for the Two Land blocks or 11103+2023 or 2013–123 for the Three Land blocks.

Stage 2 Recording

Recording each trade in an importing or exporting problem. Stage 2 recording models the algorithms—the step-by-step procedures by which we add or subtract. It means Show your work.

Trading “Down

Trading down is the reverse of trading up. It is exchanging big things for little things, like one Long for two Unit Cubes in Two Land, one Flat for three Longs in Three Land, or one hunded for ten tens in Ten Land (or a quarter for five nickels, a half hour for 30 minutes, one yard for three feet, or two thirds for four sixths).

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