Chapter 1 Study Guide

HELLLLOOOOOOOOOO friends.

So... what's going to be on your Chapter 1 assessment? I've included a run-down below, categorized by section. Don't forget to use the Glencoe website for self-check quizzes, tutor videos, extra examples, and lots of great studying resources. If it's not already saved in your favorites, here's the link:
http://www.glencoe.com/sec/math/msmath/mac04/course1/self_check_quiz/index.php/

1-1: Basic problem-solving (remember to make a plan before you solve and to check your answer after you solve)

1-2: Divisibility Patterns (look back through your divisibility rules! They are posted on the blog if you've misplaced them)

1-3: Prime Factors
- Remember, to "find the prime factorization" of a number, make a factor tree. Your prime factors at the bottom are the answer.
- Always check your answer by multiplying the factors at the bottom of your tree to make sure you get the number at the top.

Example: Find the prime factorization of 42:

                         42
                     6   x   7
                  2x3    x     7 ---> Answer. Check: Does 2 x 3 x 7 = 42? Yes. The answer is correct. 

1-4: Powers and Exponents
Here are two previous blog posts that review powers and exponents. Be sure to check out the post that includes how to incorporate exponents into prime factorization.
http://tlsmath6.blogspot.com/2012/09/exponents.html
http://tlsmath6.blogspot.com/2012/09/expressing-prime-factorization-with.html

1-5: Everyone's favorite, ORDER OF OPERATIONS!!!!!!! AHHHHHH!!!!!!!!!
Two things I need you to remember about PEMDAS:
1. Multiplication and Division are on the same level and go LEFT to RIGHT
2. Please, please, PLEASE show your work line-by-line. Once you complete an operation, bring EVERYTHING ELSE DOWN exactly as it appears on the next line. This will help you keep track of what you've already done and will keep you from doing things out-of-order.

1-6 and 1-7: Algebra
These were the sections where we had to plug in a value for the variables and then solve the expressions. Then, we used mental math to solve equations.
Examples:

1. If a = 2 and b = 3, evaluate:
2a + 3b.
--- Remember, a number right next to a variable means multiply. Now, plug in the values:
2 x 2 + 3 x 3
---Now, be sure to use order of operations when you solve (multiply first, then add):
4 + 9
= 13

2. Solve the equation mentally: p + 2 = 9.
---Ask yourself, "What plus two would give me nine?"
---We can conclude that p = 7 because 7 + 2 would give us 9.

1-8: Area of Rectangles
Formula is length x width. Don't forget to include units squared.

Don't forget about your practice worksheets over the weekend. I suggest doing 10 problems Friday, 10 Saturday, and 10 Sunday. Study study study and you'll be good to go!

Homework Questions 9/22

Greetings Mathlings,

Here are some selected questions from your classmates. Please use the order of operations - line by line!!!!!!! - to find your answer.

1)    3 x 4 + (10 + 2) ÷ 2

2)    3³ – 7 + (14-13) + 8

3)    5 x 4 + 8  ÷ 2 + 11 + 5

4)    11 x 8 x (4  ÷ 2) + 5 

5)    (3 x 4) x 4  ÷ 4 + 40

Thursday, 9/4

Hey folks! Nice job today with your human factor trees! Here are some pics:

Now, onto exponents. Please read the following info to prepare for class tomorrow. Answer the four questions that appear throughout the reading.

EXPONENTS
(Question 1: Who sits at your table/desk cluster in class?)

Here is some basic info you can refer to when dealing with exponents. Remember, an exponent is that teeny little number floating above and to the right of a number (the base):

(Question 2: What's your favorite kind of pizza?)

This reads "two to the third power." I like to think these “powers” refer to some kind of alien power on a distant planet. (Question 3: What was the last movie you saw?) Aliens are VERY fussy about how their powers are used! :) When you see a number with an exponent like the one above, don't multiply the two numbers together, like this: 2 x 3. Your answer will be incorrect. Instead, the base number is multiplied by itself, and the power tells us how many times. (Question 4: What would you like to be when you grow up?) The problem above would be solved by multiplying two by itself, three times:

2 x 2 x 2 = 8

And voila! The aliens are happy :)

T.Math HW for 8/27

Greetings, Mathlings!

Here are the divisibility rules. Please copy them down in your "notes" section. 

source: posterenvy.com

Math Final

Hello all. Just wanted to give you a run-down of what's going to be on your final. Remember, we'll be taking a practice final next week as we review.

Please review the following in your notes (also, remember to use Glencoe's online Self-Check Quizzes to test your knowledge of each section in the book):

- Prime factorization
- Powers and exponents
- Order of operations
- Variables and expressions
- Area

- Graphing (Bar/Line graphs)
- Frequency tables & Stem and Leaf plots
- Measures of central tendency (Mean, Median, Mode, Range)

- Rounding, adding, subtracting, multiplying, and dividing decimals

- Adding, subtracting, multiplying, and dividing fractions
- GCF/LCM
- Turning fractions into decimals
- Turning decimals into fractions

- Comparing/ordering fractions and decimals

- Adding, subtracting, multiplying, and dividing integers
- The Coordinate Plane

Adding Integers

Hello all,
Just wanted to post a quick review for your assessment Tuesday. We'll be checking the practice quiz Monday so please remember to bring it with you to class for workshop.

On this assessment, we'll be covering 8-1 through 8-3 (adding/subtracting integers). For subtraction, please review the previous post about the KFC method. Remember, Keep, Flip, Change!!! :)

For addition:

First, remember that a negative plus a negative will always equal a negative. If you lose five bucks and then you lose three more, you've LOST a total of 8 bucks, and a loss is represented by a negative, so you'd have -8 dollars.

-5 + -3 = -8

The tricky part comes in when you need to add a negative and a positive together.

Let's review the 3 methods we can use to add negative and positive integers:

1. Use a number line. From your starting point, move to the right if adding a positive integer; move to the left if adding a negative integer.

2. Use the method you have in your notes:
     1. Ignore the signs. What numbers do you have?
     2. Find the difference of those two numbers.
     3. For your answer, keep the sign of the biggest number.
     
     -7 + 4 -----> What numbers do I have if I ignore the signs? 7 and 4.
       7 - 4 ----->  Now, I take the difference of the two numbers.
       = 3   -----> Since the number with the greatest absolute value was -7, the answer becomes negative.
       = - 3

3. Use counters! Place negative and positive symbols inside a shape of your choosing. Cancel out whatever you can. What you're left with is your answer. Example:

The following picture represents 4 + (-5):

Since 1 positive is cancelled out by one negative, we are left with this, which represents -1:

And voila! You have your answer :)

If you're having a hard time adding integers in your head, any of these 3 methods will help you out. Happy adding!

Subtraction and... Fried Chicken?!!

Scared of subtraction involving negative integers? Don't be - remember, it's just addition in disguise!

The rule for subtraction is:

Add the OpPoSiTe!


Who likes fried chicken? It's one of my all-time favorites. :)

Img: thebittenword.com

So... what does fried chicken have to do with subtracting integers? Check out this cool chart from passyworldofmathematics.com:


Then, solve your problem as an addition problem. Here are a few examples:

-5 - 3 = ?
-5 + (-3) = -8  ---> Both numbers are the same sign, so we can add like normal and keep the sign.

7 - (-2) = ?
7 + 2 = 9   ---> Again, both numbers are the same sign, so we can add like normal and keep the sign.

4 - 8 = ?
4 + (-8) = ?  ---> Now we've got addition with two different signs, so remember to use your absolute values!
The absolute values are 4 and 8. The difference between 4 and 8 is 4. Now, is it negative or positive? Look at the original number that had the greatest absolute value: -8. Since it's negative, we know the answer is -4.



1) a. -5
    b. -1
    c. -3

2) a. -4
    b. -6
    c. 5

3) a. 35
    b. -106
    c. -46

HaPpY SuBtRaCtInG!