Watch these two boys count small sets of blocks and then combine them to double the count. Sammy, in green, counts “Three, four, five, I got five.” Notice the emphasis he places, saying “five” even before he adds it to the row of four. He knows two things. He knows that this is the last block on the table and he knows, therefore, when he gives it a number name that it is both the fifth block and the total number of blocks (i.e. ordinal and cardinal value). Then, after his friend Golden, in red, counts out four, he says again, “I have five,” as if to say, “I have more.” Sammy retrieves just one more block to add to Golden’s row, so they both have five, a practical form of adding 4 + 1 = 5. But, at 00:59, he does not add 5 + 5 to get 10. Sammy counts each block and miscounts saying, “Eleven.” Saying “eleven” does not bother him because he has not deduced that a set of five combined with another set of five would have to be ten.

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