For the past five years I have been presenting a course called Multiple Ways to Multiply, an effort to improve the mental computational skills of students on the middle school level. My belief is that students can not only improve their comprehension of basic multiplication facts (the basic 100 fact grid that we have all used ourselves); they can master two-digit comprehension while gaining a true appreciation for many of the mathematical properties that allow them to complete these algorithms with greater speed and accuracy.
Let's consider the Rule of 11:
Kids can easily complete the multiplication of 11 and any one-digit number. What they often fail to realize is that, with only three steps, they can complete the multiplication of any two-digit number by 11. Let's take for example 11 x 32:
The Rule of 11 calls for three steps: 1) Estimate (11 is close to 10 and 32 is close to 30, and 10 x 30 = 300)
2) Split (the 3 goes in the hundreds' place while the 2 goes in the units' place)
11 x 32 _______ 3 _ 2
3)Add (by adding the digits 3 and 2, we get 5; the 5 is placed in the tens' place)
11 x 32 _______ 3 5 2
We have just successfully multiplied 11 and 32. Please let me know if this was helpful.