To play, have students begin with the 4-column activity board and transition to the 7-column one. Have them play Fair Trades Up for a few days, then Fair Trades Down for a few days, then Fair Trades Up for a few days, and so on back and forth. The longer between switching from one game to the other, the harder it becomes for students to adjust their thinking to the reverse of what they were doing before. (A serious flaw in every textbook-based elementary school math program in America is the failure to teach addition and subtraction side-by-side as opposites.) Repeat for Three Land, then Ten Land, and optionally, where are used instead of blocks.
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The trading games in Ten Land are sluggish because of having to count all the way to 10 before making a fair trade, so have students play them just long enough to see that they are just like the games in Two Land and Three Land except that the blocks are bigger and they have to count a lot. Once students can play the games up or down in any of the lands with ease, they are ready to learn how to add and subtract in different lands.
Now Let’s Add and Subtract in Different Lands
In ALL KIDS CAN LEARN ARITHMETIC, addition is modeled as an importing event and subtraction as an exporting event with that cart blocks or counters to and from Fair Lands™ — the activity boards used in playing Fair Trades UP and Fair Trades DOWN. The following ebooks may be downloaded for less than $1 each to direct the hands-on activities:
, K-6, 108 pages
, K-6, 72 pages
If the thought of teaching addition and subtraction in bases other than ten intimidates you, please relax. You are in great company. Most elementary school teachers are intimidated at the thought. Truthfully, though, you will find it is easy to do with the activities in the ebooks. The activities, themselves, do the teaching. Your role is that of a facilitator. The hurdle is getting started. It is critical that you do.
Assuming your students are familiar with the Two Land, Three Land, and Ten Land blocks and are adept at playing the math game Fair Trades UP, the instructional sequence for teaching addition in any land is the same as the one below for importing (adding) in Two Land with blocks. Examples from the Fair Lands™ ebook above are given for each step in the sequence.
• Import in Two Land, no recording (because the answer is given), ,
• Import in Two Land, record just the answer, ,
• Import in Two Land, record trading and the answer column by column, ,
For importing, the truck arrives at Fair Lands™ (the activity board) with a load of blocks and a packing list. The job is to unload the truck and put the blocks in their designated columns on the activity board and make whatever trades are dictated by the law of the land that is in effect for the blocks. The addends are the blocks on the truck and the blocks already in Fair Lands™ (on the activity board) when the truck arrives. The sum is what is in Fair Lands™ after the blocks have been unloaded and stored properly, that is, after the activity board has been “legalized” or made “safe” by making whatever trades were dictated by the law of the land. (See for a sample problem. Hover the cursor over the packing list to enlarge it and click on any of the blocks to see how the sum was computed.)
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