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I actually prefer a manipulative like Digi-Blocks Each box can hold only ten units. Dumping the box to simulate “borrowing” makes the trade crystal clear. I have seen even junior high students incredulous that after dumping the box, the total number of packed and unpacked units did not change. These students have done trading activities with base ten flats, rods, and cubes without ever acquiring true conservation of number. I also like the use of the term “equivalent” as opposed to “equal” because the form of 3 tens 2 ones is not identical to the form 2 tens 12 ones. Carefully distinguishing the difference implicitly anticipates “equivalent” fractions, where two fractions of differing appearance are equivalent because the underlying value is equal. The use of “equivalent” helps build consistency, for example, in geometry, when students must differentiate equal measure as opposed to identical and/or congruent. Perhaps the “equal” sign should be renamed the “equivalent” sign because equivalent is what we usually mean. Another valuable way to exploit differing representations is to use different ways to record the model. What the authors call equivalent “representation” is actually equivalent variations of the model, in this case, base ten blocks.