This week we've been focusing on rational expressions - simplifying, multiplying, and dividing them, along with word problems involving side lengths, etc. All these techniques make heavy use of factoring, which is difficult for many students, so teaching the material has been frustrating. I've gone over several mnemonic aids which can be employed to simplify factoring, and this has helped somewhat.
The other challenging aspect of these lessons is that the process of simplifying requires a solid grasp of order of operations and the way that numbers act when they are multiplied vs. added or subtracted. Many students don't seem to have a solid foundation in this, and as a result they split up factors, factor improperly, etc. This is something I would really want to address much earlier in the year, but I may have to conduct a review as things now stand.
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