HELP IN: Middle School Mathematics
Have YOU ever dazed off in LA-LA-LAND? It's [reyyu fun, right? Yeah...until you fail the big math test! Do you need "HELP"? Well, here are a few pointers.
Lesson One: Types of Numbers
There are 3 MAIN types of numbers that have a lot to deal with in the middle school life of Math. Counting Numbers, Integers, and Whole Numbers.
Counting Numbers are all the numbers, NOT including Zer0.
Examples: 1, 2, 3, 4, 5, 6, 7, 8, ...............on and on and on...............................
Whole Numbers are all numbers that include Zer0.
Examples: 0, 1, 2, 3, 4, 5, 6, 7...................on and on and on...................
Integers are a little bit trickier to remember, but they are not that hard once you know them. Integers are numbers that include Zer0, are positive numbers AND negative numbers.
Examples:.......... -4, -3, -2, -1, 0, 1, 2, 3, 4..........
NOTE: If it is easier for you to remember the positive numbers, you can just write the numbers like this: .......-4, -3, -2, -1, 0, +1, +2, +3, +4......
Counting Numbers are all the numbers, NOT including Zer0.
Examples: 1, 2, 3, 4, 5, 6, 7, 8, ...............on and on and on...............................
Whole Numbers are all numbers that include Zer0.
Examples: 0, 1, 2, 3, 4, 5, 6, 7...................on and on and on...................
Integers are a little bit trickier to remember, but they are not that hard once you know them. Integers are numbers that include Zer0, are positive numbers AND negative numbers.
Examples:.......... -4, -3, -2, -1, 0, 1, 2, 3, 4..........
NOTE: If it is easier for you to remember the positive numbers, you can just write the numbers like this: .......-4, -3, -2, -1, 0, +1, +2, +3, +4......
Lesson Two: Decimal Places
Have you ever seen a number that looked like this: "958.237", and have you ever wondered what all of the numbers mean't? Well, here is an example that tells you where the numbers belong!
9 5 8 . 2 3 7
Hundreds Tens Ones AND Tenth Hundreths Thousanth
Do YOU want to know how to pronounce this number? Well, the correct way to say this number is:
CORRECT WAY: " Nine-Hundred Fifty-Eight AND Two-Hundred Thirty-Seven ThousanTHs."
The reason that the "AND" is so big, is to make sure that you know, when you are reading or speaking aloud a decimal number, you MUST include the AND when you read the decimal. In a moment, you will find out why the "TH" in Thousanth is big and in bold letters.
Here are some exampled of incorrect ways of saying decimals.
INCORRECT WAY: "Nine-Hundred Fifty-Eight Point Two-Hundred Thirty-Seven Thousanths."
INCORRECT WAY: "Nine-Hundred Fifty-Eight Dot Two-Hundred Thirty-Seven Thousanths."
INCORRECT WAY: "Nine-Hundred Fifty-Eight Period Two Hundred Thirty-Secen Thousanths."
The ONLY Correct way to say the decimal place when reading the number is "AND."
The reason that the "TH" is big and bold is because all numbers AFTER the decimal-place is "TH"s-i-fyed. Haha, Just joking around, but you DO have to add the "TH" after the decimal point.
9 5 8 . 2 3 7
Hundreds Tens Ones AND Tenth Hundreths Thousanth
Do YOU want to know how to pronounce this number? Well, the correct way to say this number is:
CORRECT WAY: " Nine-Hundred Fifty-Eight AND Two-Hundred Thirty-Seven ThousanTHs."
The reason that the "AND" is so big, is to make sure that you know, when you are reading or speaking aloud a decimal number, you MUST include the AND when you read the decimal. In a moment, you will find out why the "TH" in Thousanth is big and in bold letters.
Here are some exampled of incorrect ways of saying decimals.
INCORRECT WAY: "Nine-Hundred Fifty-Eight Point Two-Hundred Thirty-Seven Thousanths."
INCORRECT WAY: "Nine-Hundred Fifty-Eight Dot Two-Hundred Thirty-Seven Thousanths."
INCORRECT WAY: "Nine-Hundred Fifty-Eight Period Two Hundred Thirty-Secen Thousanths."
The ONLY Correct way to say the decimal place when reading the number is "AND."
The reason that the "TH" is big and bold is because all numbers AFTER the decimal-place is "TH"s-i-fyed. Haha, Just joking around, but you DO have to add the "TH" after the decimal point.
Lesson Three: Expanded Notation
Have you ever been confused about these two words: "EXPANDED NOTATION"? Well be confused no more! It is time that you learned expanded notation a simpler way!
For Examples:
Here is a number: "207,050".
Here is this number in EXPANDED NOTATION: (2 x 100,000) + (7 x 1,000) + (5 x 10)
You are EXPANDING this number. All you do...is find how many zeros the number has, put a "1" in frong of it, and multipy it by the number that is in the place.
In the number: "1,234,567", the "1" is in the MILLIONS place. The "2" is in the HUNDRED-THOUSANDS place. The "3" is in the TEN-Thousands place. The "4" is in the THOUSANDS place. The "5" is in the HUNDREDS place. The "6" is in the TENS place. The "7" is in the TENS place, and how would you put that number in EXPANDED NOTATION, you ask? Simple. You just:
1. Get the "1". And then find the "1" again and replace all of the numbers behind it with "0"s. Then you put them in parethisis and put the multiplication sign (x) between the two numbers. So the first part of the equation would be:
(1 x 1,000,000) + _______
2. You do the same for the rest of the numbers.
3. Put the numbers in the correct order.
4. You're answer should be:
vvvvvvvvvvvvvvTHE ANSWERvvvvvvvvvvvvvv
(1 x 1,000,000) + (2 x 100,000) + (3 x 10,000) + (4 x 1,000) + (5 x 100) + (6 x 10) + (7 x 1)
^^^^^^^^^^^^^THE ANSWER^^^^^^^^^^^^^^^^^
If you are still confused with this lesson, make up a few of your own problems just like these here. Ask a parent to help you.
For Examples:
Here is a number: "207,050".
Here is this number in EXPANDED NOTATION: (2 x 100,000) + (7 x 1,000) + (5 x 10)
You are EXPANDING this number. All you do...is find how many zeros the number has, put a "1" in frong of it, and multipy it by the number that is in the place.
In the number: "1,234,567", the "1" is in the MILLIONS place. The "2" is in the HUNDRED-THOUSANDS place. The "3" is in the TEN-Thousands place. The "4" is in the THOUSANDS place. The "5" is in the HUNDREDS place. The "6" is in the TENS place. The "7" is in the TENS place, and how would you put that number in EXPANDED NOTATION, you ask? Simple. You just:
1. Get the "1". And then find the "1" again and replace all of the numbers behind it with "0"s. Then you put them in parethisis and put the multiplication sign (x) between the two numbers. So the first part of the equation would be:
(1 x 1,000,000) + _______
2. You do the same for the rest of the numbers.
3. Put the numbers in the correct order.
4. You're answer should be:
vvvvvvvvvvvvvvTHE ANSWERvvvvvvvvvvvvvv
(1 x 1,000,000) + (2 x 100,000) + (3 x 10,000) + (4 x 1,000) + (5 x 100) + (6 x 10) + (7 x 1)
^^^^^^^^^^^^^THE ANSWER^^^^^^^^^^^^^^^^^
If you are still confused with this lesson, make up a few of your own problems just like these here. Ask a parent to help you.
Leasson Four: Simple Key Terms ("ADD" These Key Terms to Your Vocabulary!)
Have you ever wondered what the numbers were called when you're adding numbers together? Is the only word you can think of is "#Numbers#"? Well wonder no more!
The numbers being added together are called ADDENDS. The number that is the answer to the addition problem is called the SUM.
Here is an example:
25
42 } Addends
+ 31
_______
98 } Sum
Is this Math starting to make a little bit more sense? We sure hope so!
The numbers being added together are called ADDENDS. The number that is the answer to the addition problem is called the SUM.
Here is an example:
25
42 } Addends
+ 31
_______
98 } Sum
Is this Math starting to make a little bit more sense? We sure hope so!
Lesson Five: Number Line
Have you ever seen a number line before? You probably have...even if you don't realize what you are looking at. If you are SURE that you have seen on before...are you a little Iffy (or confused) about it?
Here is a little ryme to help you remember how to put the numbers on a number line in order.
"LEFT is LESS and RIGHT is MIGHT"
Here is an example of what this means:
<--|----|---|---|---|---|---|---|---|---|---|------->
...-5 -4 -3 -2 -1 0 1 2 3 4 5....
The left side of the number line is smaller, because it contains negative numbers. While, the right side is bigger because it contains whole numbers.
So, "Left is Less and Right is Might!" Is stated to be true.
This concludes this lesson.
Here is a little ryme to help you remember how to put the numbers on a number line in order.
"LEFT is LESS and RIGHT is MIGHT"
Here is an example of what this means:
<--|----|---|---|---|---|---|---|---|---|---|------->
...-5 -4 -3 -2 -1 0 1 2 3 4 5....
The left side of the number line is smaller, because it contains negative numbers. While, the right side is bigger because it contains whole numbers.
So, "Left is Less and Right is Might!" Is stated to be true.
This concludes this lesson.
Lesson Six: This Certain Type of Division
Here is a problem:
64
----- = 4
A
Are you a little bit confused on how to work it? Well, here is one easy step that helps you understand and solve this problem!
THE Step One: Divide 4 into 64.
1 6
------
4| 6 4
- 4
------
2 4
- 2 4
-------
0 0
The Answer is: A = 16
Let's Try one VERY Similar, but it is SLIGHTLY different!
A
--- = 15
3
Step One: Multiply 15 by 3 and you get the answer.
15
x 3
---------
4 5
So The answer is: A = 45!
64
----- = 4
A
Are you a little bit confused on how to work it? Well, here is one easy step that helps you understand and solve this problem!
THE Step One: Divide 4 into 64.
1 6
------
4| 6 4
- 4
------
2 4
- 2 4
-------
0 0
The Answer is: A = 16
Let's Try one VERY Similar, but it is SLIGHTLY different!
A
--- = 15
3
Step One: Multiply 15 by 3 and you get the answer.
15
x 3
---------
4 5
So The answer is: A = 45!