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Variables & Expressions

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Students are introduced to variables and basic expressions.

Students are introduced to variables and basic expressions.

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  • 1. What You'll Learn Vocabulary 1) variables 2) algebraic expression 3) factors 4) product Variables and Expressions
    • Write mathematical expressions for verbal expressions.
    • Write verbal expressions for mathematical expressions.
    5) power 6) base 7) exponent 8) evaluate
  • 2. What algebraic expression can be used to find the perimeter of the triangle below? Variables and Expressions a b c
  • 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. 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. 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. 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. 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. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Variables and Expressions
  • 9. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions
  • 10. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions
  • 11. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions
  • 12. An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations. Examples: Variables and Expressions
  • 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. 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. 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. 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. 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. It is often necessary to translate verbal expressions into algebraic expressions. Variables and Expressions
  • 19. It is often necessary to translate verbal expressions into algebraic expressions. more than Variables and Expressions Math Translation English word(s)
  • 20. It is often necessary to translate verbal expressions into algebraic expressions. more than addition Variables and Expressions Math Translation English word(s)
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. An expression like x n is called a ______, and is read, “ x to the n th power.” Variables and Expressions
  • 35. An expression like x n is called a ______, power and is read, “ x to the n th power.” Variables and Expressions
  • 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. 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. 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. 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. 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. 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. 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. 4 1 4 2 4 3 4 4 3b 5 x n Variables and Expressions Meaning Words Symbols
  • 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. 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. 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. 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. 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. 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. To evaluate an expression means to ____________. Variables and Expressions
  • 51. To evaluate an expression means to ____________. find its value Variables and Expressions
  • 52. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 Variables and Expressions
  • 53. To evaluate an expression means to ____________. find its value Evaluate each expression: 2 4 = = 16 5 3 = = 125 Variables and Expressions
  • 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. 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. 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. 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. 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. Find the perimeter of the triangle. The dimensions are in feet. a b c = 8 = 17 = 15 Variables and Expressions
  • 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. 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. 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. 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. 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. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Variables and Expressions
  • 66. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Variables and Expressions
  • 67. Evaluate the expression for the given values of the variables. c 3 + d when c = 4 and d = 16 Variables and Expressions
  • 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. 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. 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. 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. End of Lesson!

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