"a student who fully understands what 3 x 5 means not
only realizes that it equals 15, but, at some point, understands all of the following
* It represents the amount in 3 equal groups of 5, no matter what is in
* It represents the sum of 5 5 5.
* It represents the area of a rectangle with dimensions 3 and 5.
* It represents the number of combinations of any 3 of one type of
item matched with any 5 of another type of item (e.g., 3 shirts and
5 pairs of pants 15 outfits).
* It represents the result when a rate of 5 is applied 3 times (e.g., going
5 km/h for 3 hours).
* It is half of 6 x 5, 5 more than 2 x 5, and 5 less than 4 x 5.
Because the student realizes what 3 x 5 means, he or she can use it to figure
out 6 x 5, 4 x 5, 3 x 6, etc., as well as multiply multi-digit numbers like
3 x 555 and solve a variety of problems involving multiplication of 3 by 5."
(c) Dr M. Small, one of the creators of the new Canadian school math