Welcome to Middle-School Mathematics!

The curriculum, more or less, follows the textbook table of contents, with supplemental problems that I shall add. Attached are the following documents:

(i) the (general) Guidelines for all middle-school math classes; and
(ii) the Homeroom procedures (specifically for the students in my "6S" 6th Grade homeroom class).
(iii) tutoring form (if your child is interested in being a tutor to help other students, or to be tutored by other students).

If your child is out sick, a good rule of thumb for your child to prepare for the next math class would be to read the next subsection in the math text and to do all the even-numbered "Check Your Understanding" and "Homework Exercise" problems at the end of the subchapter. (Pursuant to school policies, children who miss class due to illness are given extra class days to make up homework.)

Test dates:

6th Grade: Next test -- Final Exam (90 minutes) -- Friday, May 23

7th Grade: Next test -- Final Exam (90 minutes) -- Wednesday, May 21

Pre-Algebra: Next test -- Final Exam (90 minutes) -- Wednesday, May 21

Algebra: Next test -- Final Exam (90 minutes) -- Wednesday, May 21.


*As has been discussed in class, please note that all class math tests are cumulative.

Overview of Quarters Three and Four

6th Grade - Utilities related to the manipulation of fractions will be explored in the context of ratios, rates, proportions and percents, including applications in interest, tax and commission. A broad exploration of geometry will encompass fundamentals involving one dimension (points, lines, rays, etc.), two dimensions (planes, angles, polygons, etc.), and three dimension (spheres, cylinders, cones, polyhedrons, etc.), and applications related therein. Basic concepts related to the probability of an event will be analyzed, as well as solving practical problems involving mutually exclusive events and events that are dependent or independent. Some fundamentals related to algebra will also be explored, including deriving and solving basic equations arising out of story problems.

7th Grade - A more detailed analysis will be made related to geometry concepts, including the nomenclature of various polygons, polyhedrons and circles, including finding various related areas, surface areas and volumes, and related applications of such material, including story problems. A more thorough understanding of the number pi will be analyzed. There also will be more hands-on work, including the construction and duplication of various geometric configurations using a straight edge and compass. Fundamentals of identifying and working with arithmetic and geometric sequences will be analyzed. Preparing for more advanced algebra, basics related to function rules will be studied, including in the context of various statistical methods, as well as the fundamentals related to graphing linear and quadratic equations. There also will be basic concepts studied related to square roots and the Pythagorean Theorem. Finally, fundamentals in probability will be explored, including calculations and applications related to combinations and permutations.

Algebra - Taking linear equations and their related graphs to the next level, detailed analysis will be explored related to the algebraic and geometric interpretations and implications related to systems of equations and systems of inequalities, including methods for solving such problems, including strategies for deriving such systems from various story problems. Advanced rules related to exponents, including working with negative exponents will be studied. The fundamentals related to sequences will be related to story problems, including analyzing scientific functions involving growth and decay. Working with polynomials, including a variety of factoring techniques, will be examined, and application of those methods will be related to story problems. Quadratic functions will be analyzed, including various methods of solutions and applications. Detailed work with the manipulation of radical expressions will be done, including graphing square root functions. The relationship between geometry and the trigonometric ratios will be analyzed.

Pre-Algebra: - Expanding work done on solving linear equations, fundamental concepts related to inequalities and their graphs will be examined, and related applications will be studied. A comprehensive study of geometry concepts will include examining various two and three-dimensional constructions and related applications, including nets. Advanced analysis of graphs and data will be examined, including related to various statistical models and their applications. The fundamentals of probability will be taken further with the study of classifications of various events and resolving related story problems through combinations and permutations. The basics of linear functions and their graphing methods will be analyzed. Fundamentals of polynomials will be explored, including performing basic operations with two or more polynomials.


Postive Feedback Regarding Textbook's Website.

Several students have reported to me that they took my advice to check out the website linked to their math class's textbook, PHSchool.com, and they found the site to be useful, and even fun. The textbook provides a list of web codes that correspond to the website which allows you to access vocabulary quizzes, chapter tests, chapter projects and even video tutorials, all of which are specific to particular chapter subsections. While many codes appear in the beginning of the textbook, there are additional webcodes within many of the subchapters themselves. If you or your child are adept at utilizing the Internet, this may afford a good opportunity to get a change of pace with your child's math study and/or test preparation. The textbook pages where the main webcode listings appear for the respective classes are as follows: 6th Grade - Page xxiii; 7th Grade - Page xxiii; Algebra - xix; Pre-Algebra - Page xxiii. If you access the website, please let me know how the experience is for you.

If you or your child have questions or would like to set up a meeting with me, please contact me through my email address: mschiano@mpbdenver.org I usually can return email messages by early afternoon.

Or call me at school: 303-757-1279 (the best time to reach the office secretaries is usually between 8:00 a.m. and 4:00 p.m., or you can leave me a voicemail message).

Or call me at home: 303-758-5121 (at home -- the best time is about 6:00 p.m. -- 9 p.m. on weekdays or between 8:00 a.m. and 9 p.m. on Saturdays and Sundays).

Thanks for showing interest in your child's progress in Math!
Michael Schiano

A fundamental question/concept that is visited in class is:

What Are the Overall Goals of Math?

A typical answer to that question, which is accurate, yet incomplete, is that math comes up all the time in the form of arithmetic -- at the store, in sports, while measuring and building things, etc. However, that response does not do justice to the broad range of disciplines that math impacts, and even changes and shapes. Outside my room there is a bulletin board that uses a crossword puzzle design, and there also is a poster with a detailed table outlining where math arises; between the two of them, there are well over 100 different professions, trades and disciplines listed that connect with math, and even those listings are by no means complete. The bottom line is that math isn’t just about a couple of routine important things like balancing your checkbook, measuring out a ball field, and getting good grades on math tests. Math is about problem solving. It’s about finding solutions to an unlimited number and type of scenarios through data gathering, applications of theory and experience, creativity and perseverance. It’s about organization, discipline and believing in ideas that used to seem impossible.

You May Ask: What Distinguishes MPB’s Math Program?

As demonstrated by last year’s graduating class, if our students have interest in testing into honors math classes, they normally get their wish. Offering comprehensive materials and instruction is just the beginning. At MPB, we have a unified community in which we rely on each other. For example, many of our students are members of the Mentor Leadership Group, and as such, they offer their time after school as tutors to students at or below their class level. The only compensation these tutors receive is the knowledge that they were helpful, while testing and sharpening their own skills at the same time. The unified nature of our community is also demonstrated by the united efforts of our faculty. For example, our middle-school Science teacher plays a significant role in the math enrichment of the students by running the Math Counts weekly meetings and annual competition. When I am not teaching one of my six classes, coaching the middle school speech teams, or assisting the 7th Grade basketball coach, I am generally available in my room for one-on-one assistance with students from 6 a.m. until 6 p.m. every school day.

Individual Goals of Each Student in Connection with Math

I’d like to think that every student learns, if nothing more, that each course forms an integral part of their academic development, regardless of what interests the student may have while they are at MPB. Even when I was in college, I did not know if I wanted to be a teacher, a lawyer, an architect, etc. In 2002, after years of part-time teaching and working about two decades in the legal profession, I decided to teach full time. I was 43 years old! So even though some middle-school students feel that math is a “waste” of their time, because they never will use it, they might never make a bigger mistake. Regardless of where their precious dreams take them, studying math as rigorously as possible is time and effort well spent. Obviously, if a student has an interest in math, or realizes that seriously studying math will benefit their academic career, then the point (as lawyers always say) is moot. However, it is the student who does not think that math will be necessary is the one who is malnourishing him or herself. That’s because even if the “anti-math” student never needs math as a prerequisite for any other classes or the career that he/she selects, taking math seriously now, and making strides in it, is fantastic for him/her for various reasons. As a start, applying oneself to master various mathematical theories and concepts enhances ones problem-solving skills and develops character. I have no doubt that I made a much better lawyer, because of how much I advanced through math. That’s because math greatly developed my logic, organization and perseverance skills. It gave me confidence, humility and courage I never thought I’d have. But just as important, I learned about commitment, follow-through and accountability. By no means did I enjoy every moment of every math class that I attended, including many moments from the 17 math classes I took in college. Yet, I learned to wade through and take on material that was required, and how beneficial is that!? No matter what your child strives for, there will be the undesirable aspects – the bad with the good. And certainly, the sooner we learn to accept and even welcome the hard parts, the sooner we learn to deal with life’s curveballs, and appreciate what we truly have and love.

Approach for Splitting the 8th Grade Math Class into a Regular Class and an Advanced Class

In an effort to appropriately prepare each of our students for high school math, MPB has two different math classes for its 8th-Graders. The regular math class, Pre-Algebra, is a typical 8th-Grade level math class, and adequately prepares students for entry-level math classes in high school. Indeed, regarding the Class of 2007, even though Pre-Algebra is not an advanced-level math class, three of our Pre-Algebra students qualified for honors math classes when they entered high schools. The advanced MPB math class for 8th-Graders, Algebra, is geared for students who demonstrate both the aptitude and interest in a more complex math curriculum, as it covers material that is typically covered the first year of a regular high school freshman class.

The decision about who in 8th-Grade should take Pre-Algebra, and who is eligible to take Algebra, depends on the following student data: (1) their cumulative math average in 7th Grade; (2) their ITBS scores; (3) their MAPS scores; and (4) their average on two placement tests I give them. The most important of these scores is the first, their math average in 7th Grade, which not only reflects their abilities, but their incentive in connection with mathematics. Students who demonstrate the ability and interest in Algebra are then invited to attend that class the following year when they are 8th Graders. Thus, a student may qualify to take Algebra, but may choose not to do so.

The intent of this process is to place students in the 8th-Grade math class that best suits their abilities and interests so that they are as well-prepared as possible for high school. As such, every student is reviewed, and where necessary interviewed, individually about this process. The intent is to avoid discouraging the appropriate academic development of students by either placing students (i) in a regular math class (Pre-Algebra) that would be unchallenging; or (ii) in an accelerated class (Algebra) that would be overwhelming. In connection with that, high schools are happiest with students who took whichever math class in 8th Grade was most appropriate for their individual development and success.

For the Class of 2007, the split of the number of students in each class was about 50-50; for the class of 2008, it's anticpated that slightly less than half of the 7th-Graders will be invited to take Algebra, and that the rest are on course to take Pre-Algebra.

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