Watch this video for more discussionThe associative property of multiplication says that you can multiply 3 numbers in any order: (2x3)x4=2x(3x4). If you can break down one number into its factors, it can help you do mental multiplication.
Example: Because 28 = 3 x 5, and 22 = 2 x 11, I can figure out 15 x 22 this way:
15 x 22 = 3 x (5 x 2) x 11 = 10 x (3 x 11) = 10 x 33 = 330.
If one of the numbers you are multiplying is close to an easy number, you can round up or down and use the distributive law:
Example: Because 28 = 30 - 2, I can figure out 28 x 7 this way:
28 x 7 = (30 - 2) x 7 = 30 x 7 - 2 x 7 = 210 - 14 = 200 - 4 = 196
Actually, I'd be most likely to use both the associative and distributive laws and do it this way:
28 x 7 = 4 x 7 x 7 = 4 x 49 = 4 x (50-1) = 4 x 50 - 4 = 200 - 4 = 196
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Read the Bassarear (Mathematics for Elementary Teachers) discussion of mental math in multiplication. Edition 4, pages 175-176
A non-standard multiplication algorithm that has become more common in recent years is lattice multiplication. You should become familiar with this algorithm, and also be able to explain how it preserves correct place values.
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