Variables & Expressions

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Students are introduced to variables and basic expressions.

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Variables & Expressions

  1. 1. What You'll Learn Vocabulary 1) variables 2) algebraic expression 3) factors 4) product Variables and Expressions <ul><li>Write mathematical expressions for verbal expressions. </li></ul><ul><li>Write verbal expressions for mathematical expressions. </li></ul>5) power 6) base 7) exponent 8) evaluate
  2. 2. What algebraic expression can be used to find the perimeter of the triangle below? Variables and Expressions a b c
  3. 3. What algebraic expression can be used to find the perimeter of the triangle below? Perimeter = a + b + c Variables and Expressions a b c
  4. 4. What algebraic expression can be used to find the perimeter of the triangle below? Perimeter = a + b + c In this algebraic expression, the letters a, b, and c are called ________. Variables and Expressions a b c
  5. 5. What algebraic expression can be used to find the perimeter of the triangle below? Perimeter = a + b + c In this algebraic expression, the letters a, b, and c are called ________. variables Variables and Expressions a b c
  6. 6. What algebraic expression can be used to find the perimeter of the triangle below? Perimeter = a + b + c In this algebraic expression, the letters a, b, and c are called ________. variables In algebra, variables are symbols used to represent unspecified numbers or values. Variables and Expressions a b c
  7. 7. What algebraic expression can be used to find the perimeter of the triangle below? Perimeter = a + b + c In this algebraic expression, the letters a, b, and c are called ________. variables In algebra, variables are symbols used to represent unspecified numbers or values. NOTE: Any letter may be used as a variable. Variables and Expressions a b c
  8. 8. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Variables and Expressions
  9. 9. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions
  10. 10. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions
  11. 11. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions
  12. 12. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions
  13. 13. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: In algebraic expressions, we often use a dot or parentheses to indicate multiplication. This is so we don’t mistake the symbol X for the letter (variable) x . Variables and Expressions
  14. 14. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: In algebraic expressions, we often use a dot or parentheses to indicate multiplication. This is so we don’t mistake the symbol X for the letter (variable) x . Examples: Variables and Expressions
  15. 15. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: In algebraic expressions, we often use a dot or parentheses to indicate multiplication. This is so we don’t mistake the symbol X for the letter (variable) x . Examples: In each expression, the quantities being multiplied are called _______, and the result is called the _______. Variables and Expressions
  16. 16. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: In algebraic expressions, we often use a dot or parentheses to indicate multiplication. This is so we don’t mistake the symbol X for the letter (variable) x . Examples: In each expression, the quantities being multiplied are called _______, factors and the result is called the _______. Variables and Expressions
  17. 17. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: In algebraic expressions, we often use a dot or parentheses to indicate multiplication. This is so we don’t mistake the symbol X for the letter (variable) x . Examples: In each expression, the quantities being multiplied are called _______, factors and the result is called the _______. product Variables and Expressions
  18. 18. It is often necessary to translate verbal expressions into algebraic expressions. Variables and Expressions
  19. 19. It is often necessary to translate verbal expressions into algebraic expressions. more than Variables and Expressions Math Translation English word(s)
  20. 20. It is often necessary to translate verbal expressions into algebraic expressions. more than addition Variables and Expressions Math Translation English word(s)
  21. 21. It is often necessary to translate verbal expressions into algebraic expressions. more than less than addition Variables and Expressions Math Translation English word(s)
  22. 22. It is often necessary to translate verbal expressions into algebraic expressions. more than less than addition subtraction Variables and Expressions Math Translation English word(s)
  23. 23. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction Variables and Expressions Math Translation English word(s)
  24. 24. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication Variables and Expressions Math Translation English word(s)
  25. 25. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of Variables and Expressions Math Translation English word(s)
  26. 26. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient Variables and Expressions Math Translation English word(s)
  27. 27. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Variables and Expressions Math Translation English word(s)
  28. 28. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: Variables and Expressions Math Translation English word(s)
  29. 29. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: a) Eight more than a number n . Variables and Expressions Math Translation English word(s) translates to
  30. 30. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: a) Eight more than a number n . 8 + n Variables and Expressions Math Translation English word(s) translates to
  31. 31. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: a) Eight more than a number n . 8 + n b) Seven less the product of 4 and a number x . Variables and Expressions Math Translation English word(s) translates to translates to
  32. 32. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: a) Eight more than a number n . 8 + n b) Seven less the product of 4 and a number x . 7 – 4x c) One third of the size of the area a . Variables and Expressions Math Translation English word(s) translates to translates to translates to
  33. 33. It is often necessary to translate verbal expressions into algebraic expressions. more than less than product addition subtraction multiplication of multiplication quotient division Write an algebraic expression for each verbal expression: a) Eight more than a number n . 8 + n b) Seven less the product of 4 and a number x . 7 – 4x c) One third of the size of the area a . Variables and Expressions Math Translation English word(s) translates to translates to translates to
  34. 34. An expression like x n is called a ______, and is read, “ x to the n th power.” Variables and Expressions
  35. 35. An expression like x n is called a ______, power and is read, “ x to the n th power.” Variables and Expressions
  36. 36. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. Variables and Expressions
  37. 37. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent Variables and Expressions
  38. 38. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent The exponent indicates the number of times the _____ is used as a ______. Variables and Expressions
  39. 39. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent The exponent indicates the number of times the _____ is used as a ______. base factor Variables and Expressions
  40. 40. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent The exponent indicates the number of times the _____ is used as a ______. base factor Variables and Expressions exponent base 4 6 power 6 factors of 4
  41. 41. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent The exponent indicates the number of times the _____ is used as a ______. base factor NOTE: It is extremely important that you identify the base correctly. The base is exactly what the exponent is operating on (sitting on top of). Variables and Expressions exponent base 4 6 power 6 factors of 4
  42. 42. An expression like x n is called a ______, power and is read, “ x to the n th power.” The variable x is called the ____, and n is called the ________. base exponent The exponent indicates the number of times the _____ is used as a ______. base factor NOTE: It is extremely important that you identify the base correctly. The base is exactly what the exponent is operating on (sitting on top of). Variables and Expressions exponent base 4 6 power 6 factors of 4 base is only the x base is the ( ) and everything in it.
  43. 43. 4 1 4 2 4 3 4 4 3b 5 x n Variables and Expressions Meaning Words Symbols
  44. 44. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power Variables and Expressions Meaning Words Symbols
  45. 45. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power 4 to the second power or 4 squared Variables and Expressions Meaning Words Symbols
  46. 46. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power 4 to the second power or 4 squared 4 to the third power or 4 cubed Variables and Expressions Meaning Words Symbols
  47. 47. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power 4 to the second power or 4 squared 4 to the third power or 4 cubed 4 to the fourth power Variables and Expressions Meaning Words Symbols
  48. 48. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power 4 to the second power or 4 squared 4 to the third power or 4 cubed 4 to the fourth power 3 times b to the fifth power Variables and Expressions Meaning Words Symbols
  49. 49. 4 1 4 2 4 3 4 4 3b 5 x n 4 to the first power 4 to the second power or 4 squared 4 to the third power or 4 cubed 4 to the fourth power 3 times b to the fifth power x to the n th power Variables and Expressions Meaning Words Symbols
  50. 50. To evaluate an expression means to ____________. Variables and Expressions
  51. 51. To evaluate an expression means to ____________. find its value Variables and Expressions
  52. 52. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 Variables and Expressions
  53. 53. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 Variables and Expressions
  54. 54. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 = 4 = 25 = 64 = 121 Variables and Expressions
  55. 55. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 = 4 = 25 = 64 = 121 Variables and Expressions
  56. 56. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 = 4 = 9 = 25 = 36 = 64 = 81 = 121 = 144 Variables and Expressions
  57. 57. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 = 4 = 9 = 25 = 36 = 64 = 81 = 121 = 144 Variables and Expressions
  58. 58. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 = 4 = 9 = 16 = 25 = 36 = 49 = 64 = 81 = 100 = 121 = 144 = 169 Variables and Expressions
  59. 59. Find the perimeter of the triangle. The dimensions are in feet. a b c = 8 = 17 = 15 Variables and Expressions
  60. 60. Find the perimeter of the triangle. The dimensions are in feet. a b c Perimeter = a + b + c Write the expression. = 8 = 17 = 15 Variables and Expressions
  61. 61. Find the perimeter of the triangle. The dimensions are in feet. a b c Perimeter = a + b + c Write the expression. = 8 + 15 + 17 Substitute values. = 8 = 17 = 15 Variables and Expressions
  62. 62. Find the perimeter of the triangle. The dimensions are in feet. a b c Perimeter = a + b + c Write the expression. = 8 + 15 + 17 Substitute values. = 40 Simplify. = 8 = 17 = 15 Variables and Expressions
  63. 63. Find the perimeter of the triangle. The dimensions are in feet. a b c Perimeter = a + b + c Write the expression. = 8 + 15 + 17 Substitute values. = 40 Simplify. The triangle has a perimeter of 40 feet. = 8 = 17 = 15 Variables and Expressions
  64. 64. Exponents often are used in the formula for area and volume. In fact, the word squared comes from the formula for the area of a square. Variables and Expressions s s Area of a square: A = s 2 The word cubed comes from the formula for the volume of a cube. s s s Volume of Cube: V = s 3
  65. 65. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Variables and Expressions
  66. 66. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Variables and Expressions
  67. 67. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Variables and Expressions
  68. 68. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Each dimension of the cubical storage space inside a fireproof safe is 12 inches. What is the volume of the storage space? Variables and Expressions 12 in 12 in 12 in
  69. 69. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Each dimension of the cubical storage space inside a fireproof safe is 12 inches. What is the volume of the storage space? Variables and Expressions 12 in 12 in 12 in
  70. 70. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Each dimension of the cubical storage space inside a fireproof safe is 12 inches. What is the volume of the storage space? Variables and Expressions 12 in 12 in 12 in
  71. 71. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Each dimension of the cubical storage space inside a fireproof safe is 12 inches. What is the volume of the storage space? Variables and Expressions 12 in 12 in 12 in
  72. 72. End of Lesson!

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