Mr. Flanagan's Class

The week of Jan 9th-Jan 13th

2012-01-07T22:32:00.000-08:00

Math IA

If you assume wisdom depends on age, and wisdom is afunction of age. This week we will beginstudying the concept of graphs and functions. This topic will help students build on their knowledge of equations byrelating graph to the story it tells and to the equation whose solutions atpictures. Students will read and usefunctional notation as a model function rules with tables and graphs.

Some of the assignments we will be completing this weekinclude;

p2541-10, 18-21

p2591-23, 32-35

p2661-9, 15-23, 27-35

p2721-18, 27-29

The week of Jan. 3rd - Jan 6th, 2012

2012-01-02T18:21:00.000-08:00

Math IA

After the Christmas break, we will begin our work with inequalities. Until now all of our equations have been balanced. Now we begin to solve unbalanced equations and the number of solutions becomes infinite. This is going to be quite a change for most of my students. The assignments we will be completing this week include;
p202 1-32
p208 4-19, 67-72
p215 1-28
p222 1-9, 13-21

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

2011-11-05T18:27:00.000-07:00

Math IA

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

Multiplying/DividingRational Numbers

p731-30, 32-57, 63-66

Distributiveproperty

p8215-46

Properties of Numbers

p881-15, 44

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

2011-10-16T20:02:00.001-07:00

MathIA

Scatter plots andnumber 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 mostchallenging topics for algebra students. But, hopefully, if we prepare a good foundation now then later, when weintroduce variables with fractional coefficients, they are more likely to besuccessful. I am planning to give alarge exam at the end of this week. Anytime you can spend practicing with your son or daughter would be helpful.

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

2011-10-11T20:59:00.000-07:00

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

2011-09-11T09:27:00.001-07:00

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

2011-09-10T18:26:00.000-07:00

Math IA

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

2011-05-25T05:14:00.001-07:00

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.

2011-02-15T17:17:00.000-08:00

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.

2011-01-18T16:01:00.001-08:00

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.

2011-01-06T17:56:00.000-08:00

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.

2010-10-26T21:26:00.000-07:00

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.

2010-09-23T21:04:00.000-07:00

Accelerated Math 7
Every day this year I come face-to-face with my future and my past. In the morning, I see the mature educated confident faces of the ninth graders who were in my Accelerated Math 8 class last year. In the afternoon, I look into the eyes of the naïve but eager students who chose to join my current Accelerated Math 7 class, each of them armed with only a pencil and a dream.

After our current work on scientific notation, we will spend many weeks on solving simple equations.

Accelerated Math 8
We wasted no time in the first weeks of Accelerated Math 8 as we worked on several types of questions from the New York State Algebra Regents. I chose the topic of solving quadratic equations graphically and I think my math 8 students have already begun to feel more confident about their upcoming end of the year exam. This year I have the simple goal of preparing all of my eighth-graders to pass the state algebra exam. After a brief review of last year's material, we will focus on solving quadratic equations using a variety of methods. If you would like to hear an example of their work, ask them to sing "Pop goes the weasel."

2010-06-13T19:20:00.000-07:00

Accelerated Math 7
In Accelerated math 7 we will be spending our last weeks reviewing the material we have studied this year. The goal of my math 7 class has been to make my students proficient in at least 60% of the material they will need to know for their Integrated Algebra regents exam next year. Thanks to this year's very special and very intelligent seventh graders, we have surpassed that goal. I hope that all the students in my Accelerated math 7 class decide to continue their challenging work into math 8. Given their current level of maturity and discipline, I have no doubt they will do well.

Accelerated Math 8
The exam we have been preparing to take for the last two years is only a few days away now. We have done nothing but practice and review in the last month. I have run out of questions in their green review books and have chosen to move on to problems that are rarely on the exam because of their level of difficulty. Based on their recent grades and their behavior in class I am expecting a terrific result when these Accelerated math 8 students finally take their tests. Good Luck to you all.

2010-03-29T17:47:00.000-07:00

Accelerated Math 7
In Acc. Math 7 we have been spending a great deal of time on fractions. Or at least that's what I tell my students. We have actually been spending time on factoring polynomials. In order to simplify any of the answers they receive in their fraction problems they need to be able to separate a polynomial in two factors that can be used to simplify the fraction. To put it more plainly, they need algebra to finish the problem. Factoring takes an incredible amount practice because the problems can be very similar in solution but look very different in appearance. We will continue to practice factoring on almost every quiz for the rest of the year because I believe it is one of the most challenging topics will cover this year.

Accelerated Math 8
In Acc. Math 8 fractions have been the topic of review. There is an incredible amount of algebra needed to answer their fraction questions. But there are only three methods they need to answer any question.
1) common factor
2) difference of two perfect squares
3) backwards foil
I invite you to make a poster of these and hang it in your young students’ room. They will thank you for this later. Much later.

2010-01-15T23:55:00.000-08:00

Accelerated Math 7
The topic of circles is a large component of the Accelerated Math 7 curriculum. This week we began with a simple pizza problem using data from a local restaurant. Students were given the size and price of two different pizza selections. We began by simply calculating the area, in square inches, of each pizza. That immediately began a discussion about the nature of irrational numbers in the use of the number pi. After that we worked on a circle problem involving a Norwegian goat. If the goat was tied to the side of a barn using a 30 foot rope, then what is the area of land he can graze on? We finished our week with a short quiz consisting of questions similar to the problems we studied earlier this week.

Accelerated Math 8
We have reached a very interesting point in the Accelerated Math 8 curriculum. My students have completed about 75% of their preparation for the integrated algebra exam. It's appropriate at this point to begin reviewing material from last year or perhaps earlier this year. That is exactly what we did this week. Each day Math 8 students were given a question from a New York state Regents exam from years past. After a little discussion my students realized that they had not forgotten as much as they thought they had. We finished our week with the short quiz that coincidentally consisted of questions very similar to the questions we spent the week working on.

2010-01-03T19:36:00.000-08:00

Accelerated Math 7
From the “What kid of puzzles do your 7th graders do in class?” department…

1) There are 13 stepping stones across a stream. One of the stones is loose and anyone who steps on it will be swimming. As you stand and watch three young boys cross the stream safely. The first boy steps on the first stone, skips the second, steps on the third, and so on. The second boy steps on the first two stones, skips two, steps two, and so on. The third boy steps on the first four, skips four, and so on. Which stone is the loose one?

2) A log is cut into 4 pieces in 9 seconds. At that same rate, how long would it take to cut the log into 15 pieces?

Accelerated Math 8
From the “What kid of puzzles do your 8th graders do in class?” department…

1) If it takes Big Ben thirty seconds to chime six o’clock, how long does it take to chime twelve o’clock?

2) A woman is going to town to sell her eggs. On the way, she passes a man named Sam who buys half of her eggs plus half an egg.
The woman continues on and passes a second person named Alice who buys half of her remaining eggs plus half an egg.
Just outside of town, the woman meets her friend Harry who buys half of her eggs plus half an egg.
Just as she is entering town she meets Betty who buys half of her eggs plus half an egg.
In town, the woman again sells half of her eggs plus half an egg. This time to a person named Tom.
Also in town, she meets the minister of her church and gives the minister half of her eggs plus half an egg.
Finally the woman arrives at the market. She has exactly 1 egg.
She never broke an egg on her journey!
How many eggs did the woman start with?

2009-06-09T18:12:00.000-07:00

Accelerated Math 7
The last two weeks of school are all about review. We have revisited every topic we discussed and I plan to finish the year with a few practical labs so they can apply what they have learned. I look forward to seeing them all again in Accelerated Math 8.

Accelerated Math 8
The last four weeks of school have been all about review. We are working our way through previous Integrated Algebra regents exams and ending each week with a quiz on the week’s work. The quiz grades have gotten increasingly better along with their confidence. The regents exam will be on June 19th. Please remember to arrange for transportation from the high school to home on that day.

Thank you all for your support this year.

2009-05-04T19:30:00.000-07:00

Accelerated Math 7

This week started with my accelerated math 7 students working on the first part of an integrated math regents. Instead of doing all 30 part one problems, I selected problems that were based on topics we have covered in math seven. Tomorrow I plan to collect their answers and do an item analysis in order to find out which questions were incorrectly answered and how often. Experience has shown that this is an excellent way of demonstrating what my students have learned and what topics need to be reviewed. Wednesday I plan to pass back their squeeze lab quizzes. This lab is a terrific opening for any number of topics we need to cover this year. We will be able to discuss direct correlation, slope, y-intercepts, and move into the general equation of a straight line.

Accelerated Math 8

This week started with my accelerated math 8 students working on the first part of an integrated math regents. Tomorrow I plan to collect their answers and do an item analysis in order to find out which questions were incorrectly answered and how often. Experience has shown that this is an excellent way of demonstrating what my students have learned and what topics need to be reviewed. At this point in the year my accelerated math 8 students have covered all the topics they need for their upcoming regents exam. However, covering the material can be a far cry from learning it. So I plan on spending this week going over whatever topics I think need the most review.

2009-03-12T13:11:00.000-07:00

Hello class

2009-03-09T20:47:00.000-07:00

Accelerated Math 7
This week we are spending most of our class time preparing for the New York State grades 7 math assessments. I have already explained to my students that I have become very selfish with our class time and would prefer to spend it all preparing for their Math A Regents exam. The Regents exam is the goal of their accelerated program and will enable them to begin their high school work with a full year advantage over their classmates and leave the door open for pursuing calculus in high school. However, I have been able to find a number of questions on their assessment tests which make it a useful review for the Regents exams. Therefore, I have been spending class time on assessment questions that overlap their region's curriculum so my hope is they will be very successful on both.

Accelerated Math 8
This week we are spending most of our class time preparing for the New York State grades 8 math assessments. I have already explained to my students that I have become very selfish with our class time and would prefer to spend it all preparing for their Math A Regents exam. The Regents exam is the goal of their accelerated program and will enable them to begin their high school work with a full year advantage over their classmates and leave the door open for pursuing calculus in high school. However, I have been able to find a number of questions on their assessment tests which make it a useful review for the Regents exams. Therefore, I have been spending class time on assessment questions that overlap their region's curriculum so my hope is they will be very successful on both.

2009-02-03T16:04:00.000-08:00

Accelerated Math 7
Geometry is one of the most practical topics we will cover in accelerated math 7. Today we finished our review of basic geometric shapes and techniques in calculating the area of each shape. I decided to review coordinate geometry at the same time by asking my students to graph four points and tell me how to calculate the area of the shape. For homework, they were assigned about 20 problems and asked to find the area for each geometric figure.

Accelerated Math 8
Some of the questions on the upcoming math regents exam will give the student a choice of methods to be used to solve a given problem. We have spent quite a bit of time on graphing linear equations. Now we will spend time doing the same problems algebraically. There are two primary methods we use to solve systems of equations algebraically; substitution and elimination. Both techniques let us eliminate one variable and reduce the problem to a much simpler version. I gave my students seven problems to do using each technique out of 14 problems available on a hand out. Several of my students did all the problems because "I really get this stuff". So I decided to award extra credit to anyone who did all the problems and not just the ones aside.

2009-01-13T20:08:00.000-08:00

Accelerated Math 7
In statistics, we use several types of graphs to illustrate data. They say a picture is worth a thousand words. In class today the picture was worth about 20 data points that made no sense expressed as a list but made a very clear point when expressed as a box and whisker graph. Then we translated the data into stem and leaf graphs. Finally we drew an example of a histogram just like the ones they will need to do on their exams.

Accelerated Math 8
This year I have a math 8 class that actually gets very emotional and very opinionated about mathematics. It's usually a pleasure to argue with them and today was no exception. We discussed several problems from last night's homework which is a summary of our work in graphing straight lines. The class had many questions and I hope received satisfactory answers. But they didn't agree with everything. They're thinking. And that's great. I hope to finish our discussion of the homework tomorrow.

2009-01-09T20:35:00.000-08:00

Accelerated Math 7
Cows and feed were the topic today. The problem today was to take the number of pints produced by ten cows before and after feeding the cows a new feed. We created two Box-and-Whisker graphs to illustrate the difference in output. Then the kids took Quiz 12.

Accelerated Math 8
I wanted to give the class a quiz today but the scores on the last quiz were a little low for this class. I decided to give them a quiz next Friday (Jan 16) and count the larger of the two grades twice.
Today’s material was difficult. It involved using the point-slope form for the equation of a line. I’ve posted short demonstrations of some selected problems for review. Let me know if they help.

Using Point-Slope Formula prob 2
Using Point-Slope Formula prob 3
Using Point-Slope Formula prob 4
Using Point-Slope Formula prob 5
Using Point-Slope Formula prob 8
Using Point-Slope Formula prob 11