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Identifying Patterns
Patterns can be represented using words, diagrams, numbers, or algebraic expressions.
Algebra 2 2
What is the next figure?
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
Algebra 2 6
Expressing a Pattern with Algebra
Algebra 2 9
Figure Number(Input)
Process Column Number of Toothpicks
(output)
1 1(4) 4
2 2(4) 8
3 3(4) 12
n
How many toothpicks are in the 20th figure?
Algebra 2 10
Patterns on GraphsThe 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)
0 0
1 16
2 32
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 11
associative property
• Order stays the same, but the terms are regrouped.Examples:
321321 Of Addition:
321321 Of Multiplication:
Substitution property of equality
• Replacing an expression by another expression of the same valueExample:
8148104
Symmetric property of equality
• Switch sides! (do not change order of terms on each side)Examples:
,1073 If then 7310 x7If then 7x
Reflexive property of equality
• Same thing (same order) on each side of the equal sign
Examples:
2525 aa
Addition property of equality
• Add the same thing on both sides of an equation.
Example:
13
103
x
x
Subtraction property of equality
• Subtract the same thing on both sides of an equation.Example:
7
103
x
x
multiplication property of equality
• Multiply the same thing on both sides of an equation.
Example:
30
103
x
x
division property of equality
• Divide the same thing on both sides of an equation.
Example:
4
123
x
x
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 OperationsAddition (+) 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
1. 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.
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 x w
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
Important Vocab
• Term- a number, a variable, or the product of a number and one or more variables.
-4ax + 7w - 6 Constant term
coefficientterm
• Coefficient- the numerical factor of a term.
• Constant term- a term with no variables