1-1 Patterns and Expressions

Algebra 2 1

Identifying Patterns

Patterns can be represented using words, diagrams, numbers, or algebraic expressions.

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What is the next figure?

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

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Try this on your own.

Draw the next figure.

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Numerical Pattern

What is the next number in the pattern

2, 4, 6, 8, ….

6, 3, 0, -3, ….

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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

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Input Process Column Output

1 0

2 1

3 2

4 3

5

n

Using Tables to help identify patterns

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Input Process Column Output

1 5

2 9

3 13

4 17

5

n

Expressing a Pattern with Algebra

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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?

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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.

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Warm Up

Section 1-2Properties of Real Numbers

Commutative property

• Order doesn’t matter!Examples:

4334 Of Addition:

4334 Of Multiplication:

associative property

• Order stays the same, but the terms are regrouped.Examples:

321321 Of Addition:

321321 Of Multiplication:

Additive identity

• Add zero to a term so the term does not change

Example: 303

multiplicative identity

• Multiply by one so the term does not change

Example: 313

Multiplicative property of zero

• Anything times zero equals zero!

Example: 303

Distributive property

• Multiply to each term inside parenthesisExamples:

8424 xx

8442 xx

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

Transitive property of equality

• If , then

cbba , ca

Example:

• If , then

236,624 2324

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

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 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

For x=6 and y=-3

Evaluate:

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

Combine like terms:

Combine like terms: