This morning, while working with an adult student, we made a mnemonic clue to help her remember how to change mixed numbers into improper fractions.  This student has a number of challenges and difficulty remembering: 1)   the times tables, 2)  the steps in arithmetic operations, 3)  which direction to complete operations, and 4)  when to do what.  She becomes very frustrated because she can complete the operations of fractions when she is prompted, and then, for that class or tutoring session, she can remember what to do.  However, later that day or the next day, she does not remember what to do or how to begin.  The following mnemonic clue provides her with a way to remember how to change mixed number into improper fractions.  Additionally, she has learned how to use Tic Tac Toe Math for reducing and changing fractions. 

 The following are examples that demonstrate the student’s errors that cause confusion.  This operation involves changing 2 and ½ into five halves.  In the first example she would multiple the whole number with the denominator and add the whole number with the numerator.  In the second example, she would add the whole number to both the numerator and the denominator.  These errors were not consistent; sometimes she was able to complete the operation correctly.  The inconsistence is what caused her much frustration.  

This week’s mnemonic clue is a visual one that uses the location of the numbers and symbols to provide the person with a way to remember how to change mixed numbers into improper fractions.  First, the person places a multiplication sign between the whole number and the denominator, remembering that multiplication produces larger number, making the number heavy, therefore on the bottom.  Next he or she places an addition sign between the whole number and the numerator, remembering that adding produces smaller numbers than multiplication, making the number lighter, therefore, on top.  The student then draws or visualizes arrows as illustrated.  After a while many students will able to remember the operation without drawing the signs and arrows, but when, in doubt, they can always draw them.