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01 Writing Expressions and Equations.notebook September 04, 2013 Warm Up!! Evaluate: 2. 23 31 1. 17 9 Tap -8 8 Tap 4. 3. 42÷ 6 4Tap 7 Tap Today's Lesson: §1-1 Writing Expressions & Equations Variable: A letter that represents a number. Examples: x, y, z, etc. Algebraic Expression: Consists of one or more numbers and variables along with one or more arithmetic operations. Examples: a + 2 7x - 3 5mn/3k Numeric expression: contains only numbers and mathematical operations (+/-/*/ ÷) Examples: 6 + 2 ÷ 1 4x5x8 1 01 Writing Expressions and Equations.notebook September 04, 2013 Factors: the quantities being multiplied. Product: the result of factors multiplied together Examples: (2)(3) The factors are: 2, 3 The product is: 6 3(xy) The factors are: 3, x, y The product is: 3xy 2m(5x) The factors are: 2, m, 5, x The product is: 10mx Translating Words to Mathematics: Match! 2 01 Writing Expressions and Equations.notebook September 04, 2013 Translating Words to Mathematics: Match! Important Information to Remember: 3 01 Writing Expressions and Equations.notebook September 04, 2013 Write the Algebraic Expression for the given Verbal Expression Verbal Expression Algebraic Expression 7 less than the product of 3 and a number x 3x - 7 the product of 7 and a divided by the product of 8 and y 7s ÷ 8y four years younger than Sarah (Let "s" stand for Sarah's age) S - 4 half as big as last night's crowd (Let "c" stand for last night's crowd) A python eats 4 pounds of meat each month. 1. Write a numeric expression that represents how much meat a python eats in 5 months. 4x5 4 5 OR 4(5) 2. Write an algebraic expression that represents how much meat a python eats in "x" months. 4 x BETTER 4x 4 01 Writing Expressions and Equations.notebook September 04, 2013 Tips to remember: 1) Letters in algebra are called variables because their values can vary. 2) When multiplying a number and a variable, the number is written first . For example: x times 5 is 5x NOT x5. 3) Don't use subtraction in the wrong order! For example: "the difference of 5 and t" and: "5 decreased by t" are translated as 5 - t while: "5 less than t" and: "5 subtracted from t" are translated as t - 5 . Write the Verbal Expression for the given Algebraic Expression Verbal Expression Algebraic Expression x ÷8 g + 5 x - y 3y - 4 5 01 Writing Expressions and Equations.notebook September 04, 2013 Equation Expression 1. An expression is a sentence fragment or a phrase 1. An equation is a complete sentence 2. An equation can be simplified & solved 2. An expression can be simplified 3. An expression does NOT have an equal sign or an inequality symbol (no < or > symbol), therefore it cannot be solved! 3. An equation has an equal sign Translating Words to Mathematics: Match! Typo on Notes :( 6 01 Writing Expressions and Equations.notebook September 04, 2013 Write an algebraic equation for each sentence. 3 (mult) x = 21 3x = 21 1. Three times a number equals 21. (divide) x 8 = 20 2. The quotient of a number and 8 is 20. (minus & switch order) x (two times) = 31 3. Seven less than twice a number is equal to 31. 2x - 7 = 31 Grouping Symbols: • Parentheses are known as grouping symbols in algebra. • The words "the quantity" are interpreted algebraically as parenthesis. • For example: Three times the quantity six minus two is twelve. Means: 3(6 - 2) = 12 7 01 Writing Expressions and Equations.notebook September 04, 2013 Match the Sentence with the Algebraic Equation: 1. Two less than five times "d" is "r". 5d 2 = r 2. Twice the quantity five less than "d" is equal to "r". 2(d 5) = r 3. The product of two and "d" decreased by five equals "r". 2d 5 = r 4. The product of two and the quantity "d" less than five is "r". 2(d 5) = r 5. Five times the quantity "d" subtracted from two is "r". 5(2 d) = r 6. Two times five minus "d" is equal to "r". 2(5) d = r check Match the Sentence with the Algebraic Equation: 1. Two less than five times "d" is "r". 5d 2 = r 2. Twice the quantity five less than "d" is equal to "r". 2(d 5) = r 3. The product of two and "d" decreased by five equals "r". 2d 5 = r 4. The product of two and the quantity "d" less than five is "r". 2(d 5) = r 5. Five times the quantity "d" subtracted from two is "r". 5(2 d) = r 6. Two times five minus "d" is equal to "r". 2(5) d = r 8 01 Writing Expressions and Equations.notebook September 04, 2013 Today's Math Journal Questions Day 1 Question: ______________________ (Date) 1. Why did you (or your parents) choose to take Double Block Algebra this year? 2. What do you dislike about math? (“Everything” is not an acceptable answer) 3. What do you like about math? (“Nothing” is not an acceptable answer) 4. What grade(s) do you hope to earn this year in Double Block Algebra? 5. Is there anything special I can do to help make this class go as smoothly and least stressful as possible for you? 6. Circle when you have study hall this semester & list who your study hall teacher is Day 1 Day 2 Block 1 Block 2 Block 3 Block 4 1st half of the block 2nd half of the block Homework: Worksheet 1-1 9