Though I've officially been out of schools for nearly 20 years, I still have an internal clock for the school year, so I know that this coming week most of the teachers in our area will be starting back with their beginning of the year meetings and classroom time. Next week most of the local students start.
This also brings the early fall SAT and ACT college level tests that most seniors take---and to that end I've begun tutoring a local girl who wants to improve her scores from last spring. She doesn't have much of a problem with actual calculations, it's determining what to do (aka deciphering the reading of the problem) that is her challenge. Here's an example from our last session:
A factory supervisor inspected 6 of 30 products to see if there were any defects. This will give them an idea of the number of defective ones they are producing. What is the ratio of inspected products to uninspected products?
See bottom of blog for answer!
This is a mildly tricky question believe it or not. They want the kids to just see the numbers 6 and 30 and choose b) 1:5 which is the reduction of the fraction 6/30.
The whole problem is really much more about reading than about the arithmetic needed. Congratulations if you chose a) 1:4. Six are inspected, twenty-four are not inspected. So the ratio of inspected to uninspected...which is what was asked, is 6/24 or 1/4.
They get a little more complicated than this for sure, but the bottom line is reading, drawing figures and understanding the words as much as doing the actual algebra/geometry involved.
I'll give you another one on Thursday--as in, Here's a chance to understand all the math. you didn't quite get in high school!