# The Language and Tools of Algebra

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The Language and Tools of Algebra
Chapter 1 The Language and Tools of Algebra

Frayer Foldable- fold the paper in half both width and length wise
Frayer Foldable- fold the paper in half both width and length wise. While folded into fours, fold down the corner that has all creases. Open the paper and it should look like shown:

1.1 Variables and Expressions
Addition Plus Increased by More than Sum of Subtraction Minus Decreased by Less than Fewer than Difference of

1.1 Variables and Expressions
Multiplication Multiplied by Times Product of # of # (usually fractions) Twice, etc. Exponents To the power Squared, cubed, etc Division Divided by Quotient of Into

1.1 Variables and Expressions
Write an algebraic expression for each verbal expression 13 less than a number 9 more than the quotient of b and 5 Write a verbal expression for each algebraic expression .

1.1 Variables and Expressions
Evaluate each expression .

1.2 Order of Operations P E M D A S Please Excuse My Dear Aunt Sally=
Parentheses Exponents Multiplication/Division Addition/Subtraction Evaluate all expressions inside grouping symbols Evaluate all the powers Multiply and/or divide in order from left to right Add and/or subtract in order from left to right

1.2 Order of Operations Evaluate:

1.2 Order of Operations Evaluate:

1.2 Order of Operations Evaluate:

1.3 Open Sentences Set up a chart/table with the replacement set and equation Fill in the chart to find which elements of the replacement set are solutions List the solution set

Find the solution set for 28=4(1+3d) if the replacement set is d={0, 1, 2, 3}
True or False 1 2 3 False 28=4(1+3(0)) 28=4(1) 28=4

1.3 Open Sentences Use the order of operations to solve the equation

1.3 Open Sentences An open sentence with <, >, is an inequality
Solve for the solution set the same way as a regular open sentence equation

Find the solution set for 19>2y-5 if the replacement set is n={5, 6, 7, 8, 9}
True or False 5 6 7 8 9

1. 4 Identity and Equality Properties 1. 5 Distributive Property 1
1.4 Identity and Equality Properties 1.5 Distributive Property 1.6 Commutative and Associative Properties See text for properties and examples and also use property chart from in class Property chart

1.8 Number Systems Positive Numbers: listed to the right of zero
Negative Numbers: listed to the left of zero Natural Numbers: 1, 2, 3, … Whole Numbers: 0, 1, 2, 3, … Includes natural numbers and zero Integers: -3, -2, -1, 0, 1, 2, 3, … Includes natural, whole, and negative numbers Rational Numbers: any numbers that can be written as a fraction Includes natural, whole, and negative numbers, and integers

1.8 Number Systems Square root: one of two equal factors of a number (what times itself equals the number?) Irrational Numbers: numbers that cannot be written as terminating decimals or as a fraction Real Numbers: all rational and irrational numbers

1.9 Functions and Graphs Frayer Foldable- fold the paper in half both width and length wise. While folded into fours, fold down the corner that has all creases. Open the paper and it should look like shown:

1.9 Functions and Graphs Function
A relationship between input and output- the output depends on the input A function is graphed using a coordinate system, formed by two intersecting number lines x-axis: horizontal line/axis y-axis: vertical line/axis origin: (0, 0) where the axes intersect (x, y): ordered pair

1.9 Functions and Graphs Independent variable: the variable in a function that is subject to choice (changes on its own) Such as- years, days, hours, etc. Dependent variable: the variable in a function that changes value based upon the independent variable

1.9 Functions and Graphs Relation: a set of ordered pairs
{(1, 29), (2, 58), (3, 58), (4,87), (5, 116)} Domain: all the x coordinates listed least to greatest {1, 2, 3, 4, 5} Range: all the y coordinates listed least to greatest {29, 58, 87, 116}

1.9 Functions and Graphs Discrete function: a graph that consists of points that are not connected Continuous function: a graph that has a line or smooth curve of connected points