Accelerated Math 7
The first technique we learn in factoring you could call “common factor” because if you called it "factoring polynomials whose terms have a common monomial factor”, your students would be asleep before the end of your first sentence. My Accelerated Math 7 class has done very well with this first technique. We have just finished discussing the second technique of factoring or "the difference of two perfect squares." I would say it went well but not as well as common factor. Fortunately, I get to review both techniques when I start giving my students problems which combine both types of factoring. Then we can move on to our third technique called backwards FOIL. After that we start to combine all three techniques. And then the real fun begins.

Accelerated Math 8
We are now at the halfway point in Accelerated Math 8 this year. It's true that every class is about to close their books on the second quarter but in Math 8, it is a turning point. I hope to spend at least some part of every remaining class on review for the Regents exam. This will involve solving problems from previous Integrated Algebra exams. There are only so many topics to study and the New York State Regents can be a little repetitive in the way they ask questions. So I am going to take advantage of that trait and practice until my students become familiar and comfortable with the tone and style of each question. Meanwhile we will continue our study of radicals. Soon, I hope, we will be able to re-examine problems involving circles and the Pythagorean theory only now the answers may not always come out nicely as they have in the past. Discussing application problems becomes so much more realistic once we finish discussing radicals.

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.

Accelerated Math 7
I received an e-mail two days ago from a parent complimenting me on the amount of material my Accelerated Math 7 class had covered in a relatively short amount of time. I'm afraid I can't take much credit for our progress. I really do have an exceptional group of students this year. In the topic of simple equations, they have excelled. Although I'm willing to bet that most of them would argue with the term "simple" to describe the problems they've been solving. Our definition of simple equations simply means equations including a variable whose exponent is 1. But even given that simple restriction, they have been solving large and formidable looking problems for weeks now. At the present, we are hovering at the top of this particular mountain of a topic. I would like them to drill on these problems a little longer before we move on.

Accelerated Math 8
Our current topic in the Accelerated Math 8 is solving systems of equations. I wanted to begin by giving them a visual representation of their work. Therefore, they have drawn dozens of graphs in order to discover points of intersection. In the last few days we have moved on to the more difficult topic of solving those same problems without the use of pictures or graphs. We call this solving systems algebraically. It is a very difficult and abstract concept for young students but this class has made the transition beautifully. Sometimes I wish my high school math students could see this class in action. They get so excited about their work and in asking questions that they sometimes forget to show any class courtesy. But if my biggest problem with this group is that they're so excited to talk about math that they forget to raise their hands before they shout out their questions, and I think it's best I learned to live with it.