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Many teachers miss the moment. Certainly, a filled times table can prove useful. But it is a blank times table -- one that the students fill themselves -- that gives students the best opportunities.
For one, the students themselves see every product, since they have to complete the entire table. Then, they can start finding patterns. Many patterns are obvious, such as the zero product property, the multiplicative identity, and the commutative property of multiplication, for starters. But some patterns are revealed with just a little effort. In particular, the squares increase by "an increase of two"; the difference between consecutive squares increases by two with each successive square. This can be verified in numerous ways in the table itself, and can be proven with algebra.
I expect my middle school students to complete the table to 12x12, and my high school students to 20x20. And I always create this table so that the numbers increase moving upwards, and rightwards. (This is to deliberately duplicate "Quadrant I" of the Cartesian coordinate system.) I have found that most of my tutoring students benefit, simply by finding ways to verify or correct their own work. My adult students love this; in all my experience, none have ever reported filling in one previously. Often, my students request a second blank times table, just to ensure that they get it right!
Ask your students to "find the patterns". And tell me how it goes!