1-1 Patterns and Expressions Algebra 2

Identifying Patterns Patterns can be represented using words, diagrams, numbers, or algebraic expressions. What is the next figure? Algebra 2

Look at the figures from right to left. What is the pattern? Algebra 2

Try this on your own. Draw the next figure. Algebra 2

Numerical Pattern What is the next number in the pattern 2, 4, 6, 8, …. 6, 3, 0, -3, …. Algebra 2

Variable- a symbol, usually a letter that represents one or more numbers ex: x or n Numerical Expression- mathematical phrase that contains numbers and operation symbols. ex: 3+5 Algebraic Expressions- mathematical phrase that contains one or more variables ex: 3n+5 What is the only difference between an algebraic and a numerical expression? Algebra 2

Using Tables to help identify patterns Input Process Column Output 1 2 3 4 5 n Algebra 2

Input Process Column Output 1 5 2 9 3 13 4 17 n Algebra 2

Expressing a Pattern with Algebra How many toothpicks are in the 20th figure? Figure Number (Input) Process Column Number of Toothpicks (output) 1 1(4) 4 2 2(4) 8 3 3(4) 12 n What is an expression that describes the number of toothpicks in the nth figure? You can use a table to look for a pattern that relates the figure number to the number of toothpicks Algebra 2

Patterns on Graphs What is the cost of purchasing 5 DVD’s? 10 DVD’s? 1 The graph shows the cost depending on the number of DVDs that you purchase. What is the cost of purchasing 5 DVD’s? 10 DVD’s? Input (x value) Process Column Output (y-value) 1 16 2 32 Algebra 2

Section 1-1 Overview Patterns- look at the figures or numbers from left to right and identify the pattern. Variables are used in math to represent an unknown number in equations and inequalities. Using Input/Output tables can help you find patterns. Algebra 2

Warm Up  

Properties of Real Numbers Section 1-2 Properties of Real Numbers

Commutative property Order doesn’t matter! Examples: Of Addition: Of Multiplication:

Order stays the same, but the terms are regrouped. associative property Order stays the same, but the terms are regrouped. Examples: Of Addition: Of Multiplication:

Additive identity Add zero to a term so the term does not change Example:

multiplicative identity Multiply by one so the term does not change Example:

Multiplicative property of zero Anything times zero equals zero! Example:

Distributive property Multiply to each term inside parenthesis Examples:

Substitution property of equality Replacing an expression by another expression of the same value Example:

Symmetric property of equality Switch sides! (do not change order of terms on each side) Examples: If then If then

Reflexive property of equality Same thing (same order) on each side of the equal sign Examples:

Transitive property of equality If , then Example: If , then

Addition property of equality Add the same thing on both sides of an equation. Example:

Subtraction property of equality Subtract the same thing on both sides of an equation. Example:

multiplication property of equality Multiply the same thing on both sides of an equation. Example:

division property of equality Divide the same thing on both sides of an equation. Example:

1-3 Algebraic Expressions

Modeling Words with an Algebraic Expression Seven fewer than t t+7 -7t t-7 7-t Think: What operation does ‘seven fewer than t’ suggest?

Key Words to Identify Operations Addition (+) Subtraction (-) Multiplication (x) Division (÷) Sum Difference Product Quotient More than Less than Times Divided by Increased by Fewer than of Total Subtracted by Added to minus

Practice The difference of a number p and 36 2. 15 more than the number q 3. The product of 10 and a number r 4. The total of a number y and 9

Modeling a Situation To model a situation with an algebraic expression do the following: Identify the actions that suggest operations Define one or more variables to represent the unknown (s). Represent the actions using the variables and the operations.

Determine which quantity is unknown. You start with $20 and save $6 each week. What algebraic expression models the total amount you save? Determine which quantity is unknown. Starting amount Amount saved Number of weeks plus times Let w = the number of weeks 20 6 w + x

Evaluating Algebraic Expressions To evaluate an algebraic expression, substitute a number for each variable in the expression. Then simplify using the order of operations. What is the value of the expression for the given values of the variables. for a = -4 and b = 5  

Evaluate:   For x=6 and y=-3

Important Vocab Term- a number, a variable, or the product of a number and one or more variables. -4ax + 7w - 6 Coefficient- the numerical factor of a term. Constant term- a term with no variables Constant term coefficient term

Combine like terms:  

Combine like terms: