Chapter 1 Study Guide

Hello everyone. Don't forget your Chapter 1 Assessment is Monday. Here's what will be on the test:

Variable Expressions
- You'll need to know how to write variable expressions for word phrases. For example:
Write a variable expression for a number n increased by 5.
Well, if we're starting with an unknown number (n) and we're increasing by 5, we must be adding. So n + 5 would be our variable expression.

Order of Operations
***Please remember that you should be using the correct order of operations for any math problem you complete - not just problems that specify that you need to "use order of operations to..."***
- Use PEMDAS
- Remember that MULTIPLICATION and DIVISION  are on the same level and are performed LEFT to RIGHT
- Remember that ADDITION and SUBTRACTION are also on the same level and are performed LEFT to RIGHT

Evaluating Expressions
- To evaluate an expression, substitute a number for each variable. Then solve using order of operations.
Example:
Evaluate 3x + 4 for x = 5. 
1. First, we plug the value in for x: 3 x 5 + 4
2. Next, we multiply: 15 + 4
3. Finally, we add: 19
And voila. We've evaluated the expression.

Integers, Integers, Errry'thang Integers
You'll need to know how to:
- Compare and order integers (remember, as we go further left on the number line, the values decrease; as we go further to the right, the values increase)
- Find the absolute value (remember, absolute values are ALWAYS POSITIVE and absolute value lines act as grouping symbols, just like parentheses)
- Add and subtract with integers
Quick review: Adding with the same sign - add like normal and keep the sign. 
                       Adding with different signs - find the difference of the absolute values and keep the 
                       sign of the "larger" number
                       Subracting: USE KFC (Keep, Flip, Change); then, use your addition rules.
- Multiply and divide with integers
Quick review: When multiplying OR dividing, if both numbers have the same sign, the answer is 
                        ALWAYS POSITIVE
                        If the numbers have different signs, the answer is ALWAYS NEGATIVE

Patterns & Reasoning
- Use inductive reasoning to find the pattern. Then write the rule. Remember, that's when we use the "Start with .... and then....." model.

The Coordinate Plane
- Coordinates are (x, y) --- Don't forget, you have to walk into the building before you can take the elevator
- Know your quadrants

Study, study, study your notes! See you Monday!

Subtracting Integers

*Please read the post below this one for tonight's KhanAcademy assignment*

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.

If you are self-checking subtraction of integers tonight, here are the answers to the Quick Checks from 1-6 (pgs. 30 & 31):

1) a. -5
    b. -1
    c. -3

2) a. -4
    b. -6
    c. 5

3) a. 35
    b. -106
    c. -46

HaPpY SuBtRaCtInG!

Assignment 1, September 2

Assignment 1

Hello all! Welcome to your very first assignment :)

1. Visit KhanAcademy.org.

2. Click the link below to watch your first video. If it does not take you to a video called "Introduction to Order of Operations," go to the search box at the top of the website and type "Introduction to Order of Operations" - then, select the video.

http://www.khanacademy.org/math/arithmetic/order-of-operations/v/introduction-to-order-of-operations

3. After the video, click the gray "Practice" button that appears on the screen. Try to earn as many energy points as you can! Please remember what we talked about in class:PLEASE EXCUSE MY DEAR AUNT SALLY. Remember that the numerator and denominator in a fraction are grouped together (as though they had parentheses).

*If your practice questions give you negative integers and you're not sure how to add/subtract them, just try your best.*