1. 1-1 Patterns and Expressions
Algebra 2

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

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

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

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

6. 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

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

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

9. 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

10. 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

11. 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

12. Warm Up

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

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

15. 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:

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

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

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

19. Distributive property
Multiply to each term inside parenthesis
Examples:

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

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

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

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

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

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

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

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

28. 1-3 Algebraic Expressions

29. 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?

30. 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

31. 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

32. 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.

33. 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

34. 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

35. Evaluate:
For x=6 and y=-3

36. 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

37. Combine like terms:

38. Combine like terms: