Chapter 1 Study Guide

Hello everyone. Don't forget your Chapter 1 Assessment is Tuesday. 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

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


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

Study Guide For Quiz WED

Hey guys, here are a few things to remember for your quiz tomorrow. The quiz will cover:

1) Order of operations (PEMDAS) - don't forget that multiplying and dividing are on the same level, and are completed from left to right; same thing for addition and subtraction - they're on the same level and are completed from left to right.

2) Evaluating expressions (just remember to substitute the given value for a variable and then use your order of operations to solve!)

3) Integers and absolute value
- Remember, as you go left on the number line, the value decreases; as you travel right, the value increases.
- Absolute values are always positive - remember, absolute value is the distance of a given number from zero (on the number line)

4) Adding and subtracting integers
- Study your notes for the rules!
- The tricky one for adding integers is when they have different signs. Just remember to find the difference of their absolute values and then keep the sign of the number with the greatest absolute value.
- When subtracting, use the KFC method (keep, flip, change) and remember that once you've turned that subtraction problem into an addition problem, the original subtraction problem disappears!

*You will also be given one question that will ask you to write a variable expression to represent a word phrase. Look back through section 1-1 to review!

Subtracting Integers

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!

Oh, Aunt Sally...

Check out Justin's rendition of what Aunt Sally did:

Homework for WED., 9/2

For tonight's homework, I'd like you to kick back, relax, and watch a video that will introduce you to the material we're covering tomorrow. Please visit the following link on Khan Academy:

https://www.khanacademy.org/math/pre-algebra/order-of-operations/order_of_operations/v/introduction-to-order-of-operations

After the video, there's an option to try some problems by clicking the "Practice this concept" button at the top right. You are not required to do them, but if you'd like to try them, go for it! Many of you are already familiar with the order of operations, and the acronym we use ("PEMDAS" or "Please Excuse my Dear Aunt Sally"). 

After you've watched the video (and mayyyybe tried some problems? :) jot down what you think "Aunt Sally" may have done that put her in a position in which she needs to be "excused." :) We'll share our theories on Aunt Sally tomorrow after the drill! (The drill will cover today's lesson on variables and variable expressions.)

See you tomorrow!