LOIF

We should be familiar with multiplying two binomials using the FOIL method
(X+4)*(X+5)
First: X*X
Outside: 5*X
Inside: 4*X
Last: 4*5
Answer = X^2 + 9X + 20
In Number Sense, we can do the same when multiplying two 2-digit numbers using a similar method, LOIF.
*Example*
43x27
Last: Multiply the last 2 digits and write down a single digit in the one's place(Carry if necessary)
          3x7 = 21
     Write down the 1 and remember the 2
Outside: Multiply the outside digits but don't write anything else down yet.
          4x7 = 28
     Remember the 28
Inside: Multiply the inside digits and then add to what you got from the outside digits (add any numbers carried from the last digits). Write down a single digit in the ten's place and carry if necessary.
          3x2 = 6
          6+28 = 34
          34+2 = 36
     Write down the 6, carry the 3  
 First: Multiply the first digits and then add any numbers that were carried from the previous step. Write down the number in the hundred's place.
          4x2 = 8
          8+3 = 11
     Write down the 11
Answer = 1161