This Blog exists for the collective benefit of all 7th grade math students. While the posts are specific to Mr. Chamberlain's class, we welcome comments from everyone. The more specific your question (including your own attempts to answer it) the better.
EVEN MORE WELCOME ARE ANSWERS FROM FELLOW STUDENTS. BLOG ON!
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Friday, December 10, 2010
hw #3-9 Unit Review
pg 152-153
#1-30 Odd
pg 154
#1-11 (you've done these problems already, so get it right this time!)
#29-37
Any and all questions in the Chapter Review and the Chapter Test are FAIR GAME for your UNIT TEST!
Given a linear equation such as y = x+3, I will expect you to be able to make a table of ordered pairs (an x-y table a.k.a input-output table) and graph the ordered pairs in the coordinate plane.
I am SO HAPPY that there are no questions for the UNIT TEST. I must be the WORLD'S GREATEST MATH TEACHER! This will also make it much easier for me to grade your tests, since everyone will be handing in perfect papers with fully developed scrap work. A real WIN-WIN!!
Seriously folks, you've had since Tuesday to ask questions and I have received none. Please don't expect a homework review prior to the test on Monday. On the other hand, if you are as prepared and confident as your lack of questions indicate, more power to you!!
Feel free to skip to the end, where I'll tell you what JUST you need to know for the test.
BUT since you asked a GOOD QUESTION!!...
Real numbers are ALL numbers that can be graphed on a (real) number line (duh, that's helpful). Non-real numbers are called imaginary numbers... an example is the square root of a negative number, it does not exist in the real number system, it CANNOT be graphed on a real number line. The skills you will learn in pre-algebra and algebra deal only with real numbers... the only time we spend on imaginary numbers is to recognize that they do exist... you will study them in higher mathematics courses in the high school. Imaginary numbers have many applications in the engineering world.
What follows was a part our class discussion on Thursday:
Natural Numbers - aka counting number 1,2,3,...
Whole Numbers (the set of Natural numbers and zero) 0,1,2,3,...
Integers - the set of whole numbers AND their opposites ...,-3,-2,-1,0,1,2,3,...
Rational Numbers - Any number that can be expressed as a ratio of two integers (which includes all integers)
Irrational Numbers - Numbers such as the square root of non-perfect squares and pi are considered irrational. They can be graphed on a number line, but cannot be expressed accurately as a ratio of two integers. Pi is sometimes estimated as 3.14 or 22/7, but that is an estimate. Pi has an infinite number of non-repeating digits after the decimal point.
From the knowledge above, we can make the following statements:
a) The set of natural numbers is a subset of the set of whole numbers. b) The set of whole numbers is a subset of the set of integers c) The set of integers is a subset of the set of RATIONAL NUMBERS d) None of the sets mentioned in a-b-c above are members of the set of IRRATIONAL NUMBERS. e) The disjoint (mutually exclusive) sets of RATIONAL and IRRATIONAL numbers combine to form the set of REAL NUMBERS. f) Any single set of numbers mentioned in a-e above can be considered as a subset of the set of REAL NUMBERS.
The sets of Rational Numbers and Irrational Numbers are "disjoint" or "mutually exclusive" sets. That means that if a number is classified as rational, it is not irrational and vice versa.
To draw a metaphorical comparison, FMS has instrumental musicians. You can be a band musician or an orchestra musician, but you cannot be a member of both "sets."
The set of rational numbers and the set of irrational numbers combine to form the overall set of REAL NUMBERS.
The set of band musicians and the set of orchestra musicians combine to form the overall set of instrumental musicians at FMS.
Just to round out the whole discussion, the set of REAL NUMBERS and the set of IMAGINARY NUMBERS combine to form the set of COMPLEX NUMBERS. TA-DAAA!!
The ability to distinguish between rational and irrational numbers.
The only irrational numbers you need to recognize are a) the sqrt of a non perfect square b) pi c) a decimal number that is portrayed as non-repeating... the only tricky one I the book seems to throw at us is something like this:
6.121221222...
It has a pattern that seems to repeat, but really does not, which means that it is an irrational number.
Any mixed number, 6 2/7 is a rational number because it can be represented as a ratio of two integers.
Any terminating decimal is a rational number, such as .3458, can be represented as a ratio of two integers by simply using powers of 10... 3458/10000, right?
Any repeating decimal is a rational number because they can ALL be represented as ratios of two integers. We did not take a deep look at this at all, but I would expect you to know that 1/3 is represented as .3 repeating (the little bar "thingy" over the 3) and 2/3 is .6 repeating and 8/9 is .8 repeating and so on.
Another good question. Take heart... many algebra students are fuzzy on the same topic.
One thing you should notice about linear equations in the coordinate plane, is that they are either vertical lines, horizontal lines, or diagonal lines. When the linear equation involves both an x and y variable, it is a diagonal line.
What that means to you is that you can pick ANY x value as an input, and you will produce a y-value as an output.
As a general guideline ("rule of thumb"), mathematicians have decided that five input values make for a good sampling. In our class, we have decided that a couple of negative x values along with zero and a couple of positive x values, make for a good set of input values.
As you work more and more with linear equations over the next few years, you will become more comfortable with the process.
We will be spending more time with this topic later in the year.
linear equations are confusing!!!!
ReplyDeleteGiven a linear equation such as y = x+3, I will expect you to be able to make a table of ordered pairs (an x-y table a.k.a input-output table) and graph the ordered pairs in the coordinate plane.
ReplyDeleteNot to worry, we will review tomorrow in class.
I am SO HAPPY that there are no questions for the UNIT TEST. I must be the WORLD'S GREATEST MATH TEACHER! This will also make it much easier for me to grade your tests, since everyone will be handing in perfect papers with fully developed scrap work. A real WIN-WIN!!
ReplyDeleteSeriously folks, you've had since Tuesday to ask questions and I have received none. Please don't expect a homework review prior to the test on Monday. On the other hand, if you are as prepared and confident as your lack of questions indicate, more power to you!!
Im confused about what a real number is
ReplyDeleteFeel free to skip to the end, where I'll tell you what JUST you need to know for the test.
ReplyDeleteBUT since you asked a GOOD QUESTION!!...
Real numbers are ALL numbers that can be graphed on a (real) number line (duh, that's helpful). Non-real numbers are called imaginary numbers... an example is the square root of a negative number, it does not exist in the real number system, it CANNOT be graphed on a real number line. The skills you will learn in pre-algebra and algebra deal only with real numbers... the only time we spend on imaginary numbers is to recognize that they do exist... you will study them in higher mathematics courses in the high school. Imaginary numbers have many applications in the engineering world.
What follows was a part our class discussion on Thursday:
Natural Numbers - aka counting number
1,2,3,...
Whole Numbers (the set of Natural numbers and zero)
0,1,2,3,...
Integers - the set of whole numbers AND their opposites
...,-3,-2,-1,0,1,2,3,...
Rational Numbers - Any number that can be expressed as a ratio of two integers (which includes all integers)
Irrational Numbers - Numbers such as the square root of non-perfect squares and pi are considered irrational. They can be graphed on a number line, but cannot be expressed accurately as a ratio of two integers. Pi is sometimes estimated as 3.14 or 22/7, but that is an estimate. Pi has an infinite number of non-repeating digits after the decimal point.
From the knowledge above, we can make the following statements:
a) The set of natural numbers is a subset of the set of whole numbers.
b) The set of whole numbers is a subset of the set of integers
c) The set of integers is a subset of the set of RATIONAL NUMBERS
d) None of the sets mentioned in a-b-c above are members of the set of IRRATIONAL NUMBERS.
e) The disjoint (mutually exclusive) sets of RATIONAL and IRRATIONAL numbers combine to form the set of REAL NUMBERS.
f) Any single set of numbers mentioned in a-e above can be considered as a subset of the set of REAL NUMBERS.
The sets of Rational Numbers and Irrational Numbers are "disjoint" or "mutually exclusive" sets. That means that if a number is classified as rational, it is not irrational and vice versa.
To draw a metaphorical comparison, FMS has instrumental musicians. You can be a band musician or an orchestra musician, but you cannot be a member of both "sets."
The set of rational numbers and the set of irrational numbers combine to form the overall set of REAL NUMBERS.
The set of band musicians and the set of orchestra musicians combine to form the overall set of instrumental musicians at FMS.
Just to round out the whole discussion, the set of REAL NUMBERS and the set of IMAGINARY NUMBERS combine to form the set of COMPLEX NUMBERS. TA-DAAA!!
=======================================
NEWS FLASH!!!!!!!
ALL YOU NEED TO KNOW FOR THE TEST IS:
The ability to distinguish between rational and irrational numbers.
The only irrational numbers you need to recognize are
a) the sqrt of a non perfect square
b) pi
c) a decimal number that is portrayed as non-repeating... the only tricky one I the book seems to throw at us is something like this:
6.121221222...
It has a pattern that seems to repeat, but really does not, which means that it is an irrational number.
Any mixed number, 6 2/7 is a rational number because it can be represented as a ratio of two integers.
Any terminating decimal is a rational number, such as .3458, can be represented as a ratio of two integers by simply using powers of 10... 3458/10000, right?
Any repeating decimal is a rational number because they can ALL be represented as ratios of two integers. We did not take a deep look at this at all, but I would expect you to know that 1/3 is represented as .3 repeating (the little bar "thingy" over the 3) and 2/3 is .6 repeating and 8/9 is .8 repeating and so on.
Thanks for asking!
It would be helpful to me for anyone and everyone in the class to let me know if this was helpful to you...
ReplyDeleteAny other questions or are we a lock for those 100's for EVERYONE?!
Thiswas helpful.
ReplyDelete-Maggie
I'm still fuzzy on how to pick the numbers on the x,y chart, for linear equations.
ReplyDelete-Maggie
Another good question. Take heart... many algebra students are fuzzy on the same topic.
ReplyDeleteOne thing you should notice about linear equations in the coordinate plane, is that they are either vertical lines, horizontal lines, or diagonal lines. When the linear equation involves both an x and y variable, it is a diagonal line.
What that means to you is that you can pick ANY x value as an input, and you will produce a y-value as an output.
As a general guideline ("rule of thumb"), mathematicians have decided that five input values make for a good sampling. In our class, we have decided that a couple of negative x values along with zero and a couple of positive x values, make for a good set of input values.
As you work more and more with linear equations over the next few years, you will become more comfortable with the process.
We will be spending more time with this topic later in the year.
Hope that helps!