Martin+W

toc "Any journey of 1,000 miles starts with a first step." - Anonymous

Signed Numbers
Addition and Subtraction of Integers


 * __Goal__**: You need to rewrite any expression that has two signs in a row (called "sign-sign" by Mr. Vizza) into an equivalent expression with only one sign.
 * __Why__**: The writing that you will be required to do in Algebra will be made so much easier if you increase your literacy with regard to being able to fluently read these types of expressions.


 * __Steps__ **
 * 1) ** Rewrite any expressions that involve adding an negative or subtracting a negative so that the "sign-sign" phenomenon is eliminated. **
 * 2) ** Simplify by using the SAME OR DIFFERENT visualization method. **

PEMDAS

 * __Goal__**: Increase reading and writing level with regard to non-variable expressions.
 * __Why__**: Understanding the Order or Operations is the basis for algebraic literacy.


 * __ Steps: __**
 * 1) ** Simplify any expressions in the innermost set of parentheses grouping symbols .**
 * 2) ** Simplify any exponential expressions. **
 * 3) ** Simplify any multiplications or divisions (whichever you see first while working from left to right.) **
 * 4) ** Simplify any addition or subtractions (whichever you see first while working from left to right.) **

__**Worksheet(s**__):


 * Basic Level
 * More Challenging Level

Evaluation

 * __Goal__**: Develop ability to manipulate variable expressions when given values for the variables.
 * __Why__**: It is used in problem solving in math when you run into a "real-world" math problem. Also, it is essential for all of the math work you will be required to use in science class.


 * __Steps__: **
 * 1) ** Substitute in the given values for the variables into the expression. (MAKE SURE YOU USE PARENTHESES) **
 * 2) ** Apply PEMDAS to Simplify. **
 * 3) ** Check with your calculator. **

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__ **//Under Construction - I need to assess your ability on this. If you have this skill mastered great. If not, it is too essential to skip.//** __

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Distributive Property

 * __Goal__**: Gain fluency in ability to apply the distributive properties.
 * __Why__**: This often a step in SOLVING EQUATIONS IN ONE VARIABLE. It is often the first step of a multi-step equation that needs to be solved.


 * __Steps__**:


 * 1) **Multiply the term outside the parentheses by every term in the quantity. (The quantity is the expression in the parentheses.)**

__Worksheet__:



Collecting Like Terms

 * __Goal__**: Gain fluency in ability to recognize like terms in a variable expression as well as rewrite them in their simplest form.
 * __Why__**: This often a step in SOLVING EQUATIONS IN ONE VARIABLE. It is often the SECOND step of a multi-step equation that needs to be solved.

__**Steps:**__
 * 1) Identify terms that are like.
 * 2) Use the box strategy if necessary.
 * 3) Simplify.



Distribution and Collection of Like Terms
__**GOAL**__: Start to put together the previously learned skills with regard to Distribution and CLT. Practice here will help solidify each individual skill.
 * __Why__**: The combination of these two skills are often seen.

**__Steps__**:
 * 1) Distribute (Draw arches and be mindful of signs)
 * 2) Collect Like Terms (Draw boxes around the like terms and be mindful of signs)

__**Worksheet:**__

Simplifying Basic Variable Expressions
__**Goal**__: Fluency around the SUBTLE NUANCES between multiplication and division with variable expressions. __**Why**__: Multiplication of Variable Expressions is one skill. Addition of Variable Expressions is another skill. In and of themselves, they are not that hard. When you are asked to do problems that involve both they are easily confused with each other.

__Steps__: 1. Try to identify the basic model/property used below. 2. Apply the model/property to simplify the expressions.

Use the properties above as models to try to identify the property (or Properties) in the problems on the flashcards below.

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Solving Equations

 * __Goal__**: This is a goal in an of itself. Getting this skill nailed down and differentiating (and seeing how it is different from other skills) will help you grow as a math student and give you competency throughout the rest of high school math.

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 __ **//Under Construction - I need to assess your ability on this. If you have this skill mastered great. If not, it is too essential to skip.//** __

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__ **//Under Construction - I am not sure how to attack this just yet. It is a wide area and we need to drill down into some subtle areas.//** __

__%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%__  __%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%__ Use the following properties as model to try to identify the property (or Properties) in the problems on the flashcards below.