which students could answer with 5 + 7 = 12 = 8 + 4 = 22 — 10 etc., or with a picture
of a dozen
eggs in an
egg crate (two
equal rows = > even
number) or
of a 4 x 3 array
of counters (factors shown visually), if they had command
of syntax and symbols, understood the idea
of equivalence, and were actively making connections between multiple representations.