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1-1 Patterns and Expressions

1-1 Patterns and Expressions. Identifying Patterns. Patterns can be represented using words, diagrams, numbers, or algebraic expressions. What is the next figure?. Look at the figures from right to left. What is the pattern?. Try this on your own. Draw the next figure. Numerical Pattern.

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1-1 Patterns and Expressions

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  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 Algebra 2

  7. Using Tables to help identify patterns Algebra 2

  8. Algebra 2

  9. Expressing a Pattern with Algebra How many toothpicks are in the 20th figure? Algebra 2

  10. Patterns on Graphs 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? 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. Section 1-2 Properties of Real Numbers

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

  15. 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 If then 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-77-t Think: What operation does ‘seven fewer than t’ suggest?

  30. Key Words to Identify Operations

  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. 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:

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