Math

March 13, 2013
By

Geometry Funnies!

February 26, 2013
By

2012 NJ ASK is just around the corner

March 4, 2012
By

NJ ASK3: May 7, 8, 9, 10, 2012 Regular Testing (Language Arts Literacy Days 1 and 2, Mathematics Days 1 and 2)

NJ ASK4: May 7, 8, 9, 10, 11, 2012 Regular Testing (Language Arts Literacy Days 1 and 2, Mathematics Days 1 and 2, Science Day 1)

NJ ASK5: Apr 30, 2012; May 1, 2, 3, 2012 Regular Testing (Language Arts Literacy Days 1 and 2, Mathematics Days 1 and 2)

NJ ASK6: Apr 30, 2012; May 1, 2, 3, 2012 Regular Testing (Language Arts Literacy Days 1 and 2, Mathematics Days 1 and 2)

NJ ASK7: Apr 23, 24, 25, 26, 2012 Regular Testing (Language Arts Literacy Days 1 and 2, Mathematics Days 1 and 2)

NJ ASK8: Apr 23, 24, 25, 26, 2012 Regular Testing (Language Arts Literacy Days 1 and 2, Mathematics, Science)

Happy Practice for Test Prep and Best Wishes!

Did you know that numbers have categories?

March 2, 2012
By

Each set of numbers includes the numbers of the nested sets.  For example, all natural numbers are whole numbers and all whole numbers are integers.

Natural Numbers:  1    2    3  4  etc (the numbers you count with)

Whole Numbers:  Includes all Natural numbers, but adds 0 (That's a zero!)  0  1  2  3  etc

Integers:  Includes all Natural numbers and all Whole numbers, but also adds negative numbers  …. -4   -3    -2    -1    0   1   2   3  etc

Rational Numbers:  Includes all of the above, but adds the fractions and decimals.  ALL fractions are included and decimals that can be written as ending or repeating decimals.  For example:  ¼ and ½ and 3.5 and 3.33

Irrational Numbers:  This is the first group that doesn't include the other numbers already defined.  This is the group that includes non-ending or non-repeating decimals.  Examples of this includes $\sqrt{x}\!\,$ where x is not a perfect square and π (pi)

Real Numbers:  Includes all of the above and doesn't add anything new, but it is the group that puts irrational numbers into the main group with the other numbers.

Now, the last group of numbers is called Complex or Imaginary Numbers.  The most famous of these is i otherwise known as the square root of -1.  There are a few others that are used in engineering and physics.  This group is outside of the other groups above and sits all alone.

Get a printable copy of the chart here

Upcoming SAT tests

January 1, 2012
By

The next SAT test is scheduled for January 28.  That is only 27 days away!  If you are registered to take this test it is time to buckle down and finish your preparation.

What should you be doing?

Sign up for word of the day by Dictionary.com  Pay attention to the derivatives of the word when you get each new word.  Don't worry so much about memorizing the word, although that is a good thing, but try to memorize the prefixes and suffixes of that word.

Review the most basic math formulas and practice using each one a few times.  This includes finding the area of squares, rectangles, parallelograms, trapezoids, circles and triangles.  You will also need perimeter of quadrilaterals and other polygons and the circumference of a circle.  Add to that finding the surface area of cones, cylinders, cubes and pyramids and the volume of those figures are well.  Yes you are provided these formulas at the beginning of each math section on the SAT, but you don't want to spend time shuffling through the pages to find them each time you need to use one and you certainly don't want to have to spend time staring at them to figure out what the letters in the formulas stand for.  The best way to do this is to put each formula on one side of an index card and put at least 2 examples on the other side of the card.

Don't complain about the critical reading.  Yes, everyone knows you aren't interested in the subject matter of each reading; they are boring; they use tough vocabulary.  Remember, the SAT is a measure of how well you will do in college and there will be many times in college when you will be required to read something that doesn't interest you, even in your major subject.

The night before the test don't study at all.  Do something you like to do, but don't go out partying; watch TV, listen to music, read for fun or play video games.  Gather your pencils and make sure they are sharpened.  Be certain you have fresh batteries in your calculator.  Get a good night's sleep and be sure to eat a good breakfast before you leave for the test.  Include some protein in that breakfast to provide you with long lasting energy.

Most of all, don't panic.  Enjoy the experience.  GOOD LUCK!!

Why do homework?

November 21, 2011
By

The movie “Those Magnificent Men in their Flying Machines” is about about a race from London to Paris in 1910. In the movie a German officer reads a book in order to learn how to fly. It doesn’t work too well for him though, because he crashes his plane into the English Channel.

Some students think that listening to a lecture and doing a few problems in school is enough. But the truth is, students need to practice what they have learned. The practicing serves two purposes. First, it cements the skill in that part of the brain that does things by rote. It makes those skills a habit. But just as important, it also exposes the questions or gaps in the skill, so that the student can go back to the teacher and get further instruction.

I have seen many articles and books written about the subject of homework. As a matter of fact, in the last few years there are many books that are clearly opposed to it. In my experience, students who do all of their homework get far better grades than students who don’t complete it all. And, in addition, the students who do all of their homework are able to study for the larger midterm or final tests in less than half the time of the students who hadn’t done their homework all along. So, the payoff for doing your homework is better grades and less time studying for tests. I think most kids would buy into that option for sure!

When I teach study skills, I work with students that have never put a priority on school or homework. They learn to keep a calendar, make a schedule, prioritize their activities, analyze notes, manage their projects and even how to spend LESS time doing their school work.

Students should be doing homework in every subject, every day. Just because the work isn’t being collected the next day, doesn’t mean it shouldn’t be worked on. Fifteen minutes per day, spent working on learning a new concept in science or some new vocabulary has far more worth than 3 hours spent on a project once every other week. Ask your student how they learn a new video game or how they learn to play on the football team. Neither of those things work when “crammed” into long lessons. They both require regular every day practice. Well, so do school subjects. Practice EVERY DAY!

Cramer’s Rule

November 10, 2011
By

Cramer’s Rule is a method of solving systems of equations. There are many methods including substitution and elimination. Sometimes though the coefficients of the equation are ugly. (Ugly isn’t my terminology, it is one given to me by a student.) To many students anything that isn’t a small whole number is ugly. So, when a system of equations includes fractions or decimal numbers, Cramer’s Rule has a way of simplifying what might be an otherwise cantankerous solution method.

Cramer’s Rule involves setting up something called a determinant using the coefficients (numbers before the variables).

Given the following system of equations:

Where x and y are variables and A, B, C, D, E, F are constants

Ax + By = E
Cx + Dy = F

The determinants are placed in a fraction to solve for each variable X and Y

It is written as

FOR X:

|E  B |
| F D |
_____
| A B |
| C D |

FOR Y:

| A E |

| C F |
_____
| A B |
| C D |

As you might have noticed, the denominators are the same and in alphabetical order for X and Y. That makes the denominator pretty easy to remember, but what about the numerators????

Well, mnemonic devices are memory techniques that utilizes acronyms or sentences or even music to help a student remember important items. One of my latest favorites is a method to remembering Cramer’s Rule.

My mnemonic for Cramer’s Rule is EVERY BOY FINDS DOGS for X and ALL ELEPHANTS CAN’T FORGET for Y. I had a student change the Y to ALL ELEPHANTS CAN’T FLY. Whatever works for you is the one to use.

Anyhow, so what does the alphabet soup tell you once you have remembered it???

Well, after you have set up the determinants, it is just arithmetic from here on in.

For X = (E*D – B*F) divided by (A*D – B*C)
And Y = (A*F – E*C) divided by (A*D – B*C)

Here is one example:

2x-3y = 9
x+5y =-2

FOR X

|9   -3|
|-2  5|                                      (9 * 5) – (-3 * -2)                           45 – 6               39
____         =                         ____________        =                        ______      =    __       =       3
|2  -3|                                      (2 * 5) – (-3 * 1)                            10 – -3               13
|1    5|

FOR Y

|2   9|
|1  -2|                                     (2 * -2) – (9 * 1)                                   -4 – 9                 -13
____          =                       ___________             =                           ____        =        __      =       -1
|2  -3|                                     (2 * 5) – (-3 * 1)                                  10 – -3                13
|1    5|

So, the solution set for the above example is (3, -1)