The week of Nov.7th - Nov. 11th, 2011

Math IA

We have an odd week ahead of us due to a conference day on November 8th.  I've decided that the best use of our time might be to spend Monday's class reviewing last week's work on adding and subtracting rational numbers.  That is, adding and subtracting numbers with decimal points, positive or negative signs, or even fractions.  Then Wednesday through Friday I hope to introduce new material on multiplying and dividing rational numbers, the distributor property, and the properties of numbers in general.  For those of you who read these entries, I'd like to give you a little head start on next week’s assignments.  They are as follows;

Multiplying/Dividing Rational Numbers

p73 1-30, 32-57, 63-66

Distributive property

p82 15-46

Properties of Numbers

p88 1-15, 44

The week of Oct.17th - Oct. 21th, 2011

Math IA

Scatter plots and number types are the big topics this week.  I am predicting that we will spend most of our time multiplying, dividing, adding, and subtracting fractions and mixed numbers.  In my experience, this is often one of the most challenging topics for algebra students.  But, hopefully, if we prepare a good foundation now then later, when we introduce variables with fractional coefficients, they are more likely to be successful.   I am planning to give a large exam at the end of this week.  Any time you can spend practicing with your son or daughter would be helpful.

The week of Oct.12th - Oct. 14th, 2011

Math IA

We will spend a short week exploring real numbers.  Whenever we cover this topic, I am reminded of an old proverb…

Don't be like the frog at the bottom of the well who looks up at that small circle of stars and thinks that is all there is to heaven.  

My job this week is to expand my students’ sense of what is a number.  They know how to count, and they understand zero, but do they know where to put the square root of five on a number line? Can they tell a rational number from an irrational number? And if we have time, we might even discover complex numbers.

The week of Oct.3rd - Oct. 7th, 2011

Math IA
It has been said that mathematics is the study of patterns.  Next week, we will be focusing on patterns and functions.  We'll begin with some classic puzzles which I hope my students will find interesting and then move on to problems from their textbook.  The handouts we will begin with are entitled patterns 1-6 and links to them can be found in the sidebar.

first week 2011_2012

Math IA

The handouts we will be using this week are Area problems and Carpets and Stripping problems.

Accelerated Math 7

Pool and miniature golf problems have been the focus of our studies in Accelerated Math 7. I have often wondered what went through the minds of anyone walking by my classroom and overhearing my instructions detailing how to put a cue ball in the pocket using a three cushion shot. Little do they know that our current topic is geometry or, more specifically, transformation geometry and that the focus of the lesson is line reflections.

We've also begun reviewing material from the beginning of the school year. This week we will finish discussing review sheet number two.

Accelerated Math 8

About a month ago, I gave each of my Accelerated Math 8 students their very own copy of the green book. The green book is a small paperback that contains the last seven Regents exams. This week we will finish discussing the August 2009 paper. Each night their homework is to complete a specific section of each paper and the next day we go over their answers.

Each of them has also been given a graphing calculator which they will be allowed to use during their Regents exams. Each day I choose several questions and instruct them on the use of their new calculators to solve the problems. My very intelligent Math 8 students often point out that they have discovered an easier way to solve the problem, but as I have pointed out repeatedly, some of the problems I have chosen are simply examples I have chosen to demonstrate the capabilities of their calculators. My goal is to give them several options they can choose from when the time comes to complete the real exam.

Accelerated Math 7
It can be very frustrating for algebra students when they don't get immediate feedback on their work. This week we made a transition from frustrating to satisfying, or at least I hope so. For the last few weeks, we have been practicing and practicing the various methods of factoring. This is a difficult topic for my seventh graders because they are never quite sure if they came up with the right answer. This week we took our factoring skills and applied them to solving equations. This may not sound exciting but it does give your son or daughter a chance to discover immediately if they are getting the right answers to the homework. When you're solving equations, you can always check your work. We have a quiz this Wednesday on factoring and solving equations and perhaps a review question or two. As we get closer to the end of the year, more and more I have been reviewing material from the beginning of the year. My students know that any review is fair game for their quizzes.

Accelerated Math 8
By the end of this week, all of my accelerated math 8 students will know how to add and subtract fractions that may or may not have common denominators. You may recall that this particular topic has already been presented and mastered in the fifth grade. However, by the ninth grade we find the need to reintroduce this topic because the fractions are now algebraic. I mention the ninth grade as a reminder of the level of work I expect from my accelerated students. They are studying algebra. They are studying the topic in math which has traditionally been reserved for high school freshman. Almost daily I remind them of some of my expectations because this is a ninth grade class they're in now. I expect that all their homework is complete if not all correct. I expect they will ask questions when they don't understand something and not sit quietly in ignorance and hope no one notices. And I expect that these eighth-graders will be very successful on the ninth grade algebra exam that they are preparing to take at the end of the year.

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.