Elementary school children in the middle grades and upper grades should also learn to add and subtract in Two Land and Three Land. They, too, need to become proficient at making fair trades in different lands because, as shown earlier, there are lots of lands besides Ten Land—like all the fraction lands—and Two Land and Three Land provide way more practice with making fair trades than Ten Land. Ten Land, in comparison, requires counting all the way to 10 to make a fair trade.
Let’s Get Started
To begin, download and save or print the free QUICK START ebook Fair Lands QUICK START—the Teacher’s Manual for how to import (add) and export (subtract) in Two Land (base 2) and Three Land (base 3) with the Fair Lands™ blocks. (To access it without downloading it, click .) Highlights include samples of two math games in progress, and . Fair Trades UP is about trading small blocks the same for one of the next bigger block and is a readiness activity for addition. Fair Trades DOWN is about the reverse and is a readiness activity for subtraction.
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Playing Fair Trades Up and Fair Trades Down to Prepare to Add and Subtract
Once familiar with the Fair Lands™ blocks and Ten Land blocks, have students play Fair Trades UP and Fair Trades DOWN. Have them play the games in all three lands represented by the blocks, first in Two Land, then Three Land, then Ten Land. To play the games in Two Land, they will need . . .
__ Two Land activity board with (then one with )
__ Set of (then , then )
__ Coin to toss
For Fair Trades Up, they will also need . . .
In playing the game, students are to “police” (help) one another make the activity board “safe” between plays. The policeman card is to remind them to do that. The law in Two Land is “Never have two or more the same.” In Three Land it is “Never have three or more the same.” In Ten Land it is “Never have ten or more the same.”
If you do not have the Fair Lands™ blocks, you can make paper models of them using the for such in the free QUICK START ebook. Alternatively, you can make the small blocks by gluing sugar cubes together. For Two Land made of sugar cubes, two cubes glued together make a Long, four cubes a Flat, and eight cubes a Super Cube. For the large blocks—the Super Long, Super Flat, and Mega Cube—use and make, say, two Super Cubes (made of sugar cubes) a fair trade for a green counter (as if it were a Super Long), two green counters a fair trade for a red counter (as if it were a Super Flat), and two red counters a fair trade for a blue counter (as if it were a Mega Cube). Note, however, the huge jump in abstraction in resorting to counters for the large blocks. Two counters of one color do not match up at all with one counter of another color.