“Keep Change Flip” vs. “Keep Change Change”

One of the benefits of tutoring students from dozens of different schools with different classroom teachers is that I hear, secondhand, a wide variety of tips, advice and devices that teachers pass along to their students. The most clever of these, two or three, I have kept and added to my own toolbox to increase my effectiveness as a tutor. A memorable tip or mnemonic device is a big help when guiding students through a new or tricky task, provided that they remember it correctly and know when it applies.

“Keep Change Flip” is one of the more common tips used in middle school math. It guides students through the process of dividing fractions. It’s a shorthand way of reminding them to take the following three steps: 1) Keep the first number as is, 2) Change the division sign to multiplication, 3) Flip the second fraction upside down (…then multiply the fractions). Multiplying fractions is always taught before dividing fractions, so these steps revert division problems back to multiplication, which presumably the student has mastered.

Keep Change Flip sounds very similar to another math mnemonic…

“Keep Change Change” is a memory aid used to teach students how to subtract signed numbers. This one, too, lets students convert a trickier operation back to something they already know. Specifically, it converts subtraction problems to addition problems. (This is around the time when many students are taught that subtracting is “adding the opposite.”) As an example, take a problem like -7 – (-5). The Keep would have you keep the -7 as is. The first Change refers to the operation symbol, a subtraction sign which becomes an addition sign. The second Change refers to the sign of the second number: if it’s negative make it positive; if positive make it negative. Following these steps would remake the problem into: -7 + 5.