Accelerated Math 7
Factoring is one of the most difficult concepts in algebra. I think it's a lot like tennis. It seems to take forever and an enormous amount of practice before you show even basic competency. I began this week by introducing my Accelerated Math 7 students problems involving factoring. I showed them examples of all three techniques they will be responsible for on their final exam. In my class we are going to refer to them as common factor, backwards foil, and the difference of two perfect squares. I have seen various textbooks use different names for these exact same techniques but the problems are all the same. This is going to be a slow process. It will take them a long while to recognize which technique they need to use for which problem. And then, sooner than they would like, we begin to combine techniques in one problem. Factoring is definitely a skill but I plan to be very patient while they develop it.

Accelerated Math 8
Sometimes we expect a lot from our teenagers. This week in Accelerated Math 8 is one of those times. This week I expect them to become comfortable with the irrational. To the best of my knowledge, all of their experiences to date have been with rational numbers but this week I introduced them to numbers they may never have heard of before. The definition is simple enough. Irrational numbers cannot be expressed as fractions. But when you tell them that these numbers go on forever with no repetition in their digits, their eyes light up. When you tell them that they have to stop rounding off their decimal answers because they are eliminating an infinite number of digits and changing the value of the answer, they glare at you and seem to be preparing for an argument. When you ask them to draw a square with 1 inch sides and you tell them that the diagonal is a length that can never be measured accurately, they all but jump out of their seats with their hands raised and their objections at the ready. It really is a pleasure to teach such a smart group of kids a topic as abstract as irrational numbers.