Sorry if this has been said; I'm responding before reading the entire thread.
This is NOT how most clerks make change. It's how those of us over the age of 30 (give or take) were taught how to make change. THESE days, the clerks are taught to ring in the total given ($20.00) and give whatever the register tells them to give. Kids aren't taught to count back money anymore.
I teach math in the K-8 setting, both in one-on-one situations and as an in-class co-teacher, and requiring kids to learn all these different methods simply confuses them. As with so many things, I think we ask kids to learn to do things before they are cognitively able to both understand and accomplish the tasks. We are asking them to accomplish a variety of math skills without first solidifying the basic skill involved. This is the consequence of spiraling math programs and common core requirements that one be able to explain HOW they got the answer- in words, not mathematically. Math is pretty straightforward, but kids HATE math because we make it so difficult to learn what should be pretty basic stuff.
My husband teaches chemistry at the University level. He is constantly amazed by the number of freshmen who cannot do basic math. I am not talking solving equations; this fall a full third of his class couldn't MULTIPLY- asic multiplication, like 37X158, without their calculators. It's pathetic
but I think it's because we are spending so much time insisting on learning different ways and methods without first solidifying the basics, moving elementary kids forward too quickly by letting them use addition and multiplication charts so they can learn to do more advanced math topics without being held back by not knowing their multiplication facts. As a country, we are trying to improve math scores by NOT teaching basics. Many kids don't learn math anymore- they just learn how to do certain styles of problems, the ones that are going to be asked on the standardized tests, and then move on.
I gave up on Common Core when the "educator" providing the math training said, "Getting the correct answer is not what's important; KNOWING how you got the answer is what counts." Yeah, right
until you have to balance your checkbook because things are bouncing!