Variablesand and Expressions Warm Up Lesson Presentation Lesson

Variablesand and. Expressions Warm Up Lesson Presentation Lesson Quiz Holt Mc. Dougal Algebra 1

Variables and Expressions Warm-Up Write at least FOUR SYNONYMS (words or phrases) for the four math operations (addition +, subtraction – , multiplication x, and division ÷). If you have a phone or other electronic device, you may look up synonyms on the internet. HAVE YOUR HOMEWORK OUT TO BE CHECKED!! Holt Mc. Dougal Algebra 1

Powers and Exponents 1. 12 x 6 2. 512 3. 7 x 3 4. 125 Orders of Operations 1. 17 2. 8 3. 18/7 or 2. 57 4. 27 Solving Equations Using Multiplication and Division 1. K = 7 2. X = - 4 3. Z = 60 4. Y = 8 Integers 1. 1. 5 2. 3/2 3. 2/3 4. 6. 3 Evaluating Algebraic Expressions 1. 19 2. 32 3. 300 4. 34 Solving Equations Using Addition and Subtration 1. X=15 2. Z= - 8 3. Y = 8 4. K = - 3 Comparing and Ordering Integers 1. -4, -2, 6 2. -1 3. -13, -5 4. -10 Adding Integers 1. – 3 2. – 6 3. 2 4. 5 Subtracting Integers 1. 9 Homework Solutions: 2. – 9 3. 2 4. – 17 Solving Equations Using Addition and Subtraction 1. N = 15 2. X = - 10 3. Y = 8 4. K = 11 Solving Equations Using Multiplication and Division 1. X = -6 2. Z = - 6 3. Y = - 33 4. H = - 45 Solving Inequalities Using Addition and Subtraction 1. X < 24 2. Y ≥ 16 3. K> 7 4. Z ≤ -2 Multiplying Integers 1. – 21 2. 48 3. – 35 4. 18 Dividing Integers 1. – 6 2. – 4 3. 9 4. – 7 Solving Inequalities Using Multiplication and Division 1. X > 8 2. B ≥ - 4 3. C ≥ - 8 4. Y > 9

Variables and Expressions Today’s Objectives Translate between words and algebra. Evaluate algebraic expressions. Holt Mc. Dougal Algebra 1

Variables and Expressions Vocabulary variable constant numerical expression algebraic expression evaluate Holt Mc. Dougal Algebra 1

Variables and Expressions A variable is a letter or a symbol used to represent a value that can change. (ie. X, y, a, n) A constant is a value that does not change. (ie. 5, -7, or 356) A numerical expression contains only constants and operations. (ie. 5+7 -12*35. 3) An algebraic expression may contain variables, constants, and operations. (5 x-7 a+3) To evaluate an expression is to find its value. To evaluate an algebraic expression, substitute numbers for the variables in the expression and then simplify the expression. Holt Mc. Dougal Algebra 1

Variables and Expressions You will need to translate between algebraic expressions and words to be successful in math. Copy this table into your notes. Leave extra space because we will add to these. + – Plus, sum, increased by Minus, difference, less than � � Times, product, Divided by, quotient equal groups of Holt Mc. Dougal Algebra 1

Variables and Expressions Writing Math These expressions all mean “ 2 times y”: 2 y 2(y) 2 • y (2)(y) 2 xy (2)y Holt Mc. Dougal Algebra 1

Variables and Expressions Notes: Example 1: Translating from Algebra to Words Give two ways to write each algebraic expression in words. A. 9 + r B. q – 3 the sum of 9 and r the difference of q and 3 9 increased by r 3 less than q C. 7 m D. j 6 the product of m and 7 the quotient of j and 6 m times 7 j divided by 6 Holt Mc. Dougal Algebra 1

Variables and Expressions Check It Out! Example 1 White boards! Give two ways to write each algebraic expression in words. 1 a. 4 - n 4 decreased by n n less than 4 1 c. 9 + q the sum of 9 and q q added to 9 Holt Mc. Dougal Algebra 1 1 b. the quotient of t and 5 t divided by 5 1 d. 3(h) the product of 3 and h 3 times h

Variables and Expressions To translate words into algebraic expressions, look for words that indicate the action that is taking place. Add Put together, combine Multiply Put together equal groups Holt Mc. Dougal Algebra 1 Subtract Find how much more or less Divide Separate into equal groups

Variables and Expressions Ditto Notes: Example 2 A: Translating from Words to Algebra John types 62 words per minute. Write an expression for the number of words he types in m minutes. m represents the number of minutes that John types. 62 · m or 62 m Holt Mc. Dougal Algebra 1 Think: m groups of 62 words

Variables and Expressions Ditto Notes: Example 2 B: Translating from Words to Algebra Roberto is 4 years older than Emily, who is y years old. Write an expression for Roberto’s age y represents Emily’s age. y+4 Think: “older than” means “greater than. ” Holt Mc. Dougal Algebra 1

Variables and Expressions Ditto Notes: Example 2 C: Translating from Words to Algebra Joey earns $5 for each car he washes. Write an expression for the number of cars Joey must wash to earn d dollars. d represents the total amount that Joey will earn. Think: How many groups of $5 are in d? Holt Mc. Dougal Algebra 1

Variables and Expressions White boads: Check It Out! Example 2 a Lou drives at 65 mi/h. Write an expression for the number of miles that Lou drives in t hours. t represents the number of hours that Lou drives. 65 t Think: number of hours times rate per hour. Holt Mc. Dougal Algebra 1

Variables and Expressions White boards: Check It Out! Example 2 b Miriam is 5 cm taller than her sister, than her sister who is m centimeters tall. Write an expression for Miriam’s height in centimeters. m represents Miriam’s sister's height in centimeters. m + 5 Think: Miriam's height is 5 added to her sister's height. Holt Mc. Dougal Algebra 1

Variables and Expressions White boards: Check It Out! Example 2 c Elaine earns $32 per day. Write an expression for the amount she earns in d days. d represents the amount of money Elaine will earn each day. 32 d Think: The number of days times the amount Elaine would earn each day. Holt Mc. Dougal Algebra 1

Variables and Expressions EVALUATING EXPRESSIONS Holt Mc. Dougal Algebra 1

Variables and Expressions Ditto Notes: Example 3: Evaluating Algebraic Expressions Evaluate each expression for a = 4, b =7, and c = 2. A. b – c b–c=7– 2 =5 B. ac ac = 4 · 2 =8 Holt Mc. Dougal Algebra 1 Substitute 7 for b and 2 for c. Simplify. Substitute 4 for a and 2 for c. Simplify.

Variables and Expressions Whitboards! Example 3 Evaluate each expression for m = 3, n = 2, and p = 9. a. mn mn = 3 · 2 =6 b. p – n p–n=9– 2 =7 c. p ÷ m p÷m=9÷ 3 =3 Holt Mc. Dougal Algebra 1 Substitute 3 for m and 2 for n. Simplify. Substitute 9 for p and 3 for m. Simplify.

Variables and Expressions Ditto Notes: Example 4 A: Recycling Application Approximately eighty-five 20 -ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag. Write an expression for the number of bottles needed to make s sleeping bags. The expression 85 s models the number of bottles to make s sleeping bags. Holt Mc. Dougal Algebra 1

Variables and Expressions Ditto Notes: Example 4 B: Recycling Application Continued Approximately eighty-five 20 -ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag. Find the number of bottles needed to make 20, 50, and 325 sleeping bags. Evaluate 85 s for s = 20, 50, and 325. s 85 s 20 85(20) = 1700 50 85(50) = 4250 325 85(325) = 27, 625 Holt Mc. Dougal Algebra 1 To make 20 sleeping bags, 1700 bottles are needed. To make 50 sleeping bags, 4250 bottles are needed. To make 325 sleeping bags, 27, 625 bottles are needed.

Variables and Expressions Writing Math A replacement set is a set of numbers that can be substituted for a variable. The replacement set in Example 4 is (20, 50, and 325). Holt Mc. Dougal Algebra 1

Variables and Expressions Whiteboards! Example 4 a To make one sweater, 63 twenty ounce plastic drink bottles must be recycled. Write an expression for the number of bottles needed to make s sweaters. The expression 63 s models the number of bottles to make s sweaters. Holt Mc. Dougal Algebra 1

Variables and Expressions Whiteboards! Example 4 b Continued To make one sweater, 63 twenty ounce plastic drink bottles must be recycled. Find the number of bottles needed to make 12, 25 and 50 sweaters. Evaluate 63 s for s = 12, 25, and 50. s 63 s 12 63(12) = 756 25 63(25) = 1575 50 63(50) = 3150 Holt Mc. Dougal Algebra 1 To make 12 sweaters, 756 bottles are needed. To make 25 sweaters, 1575 bottles are needed. To make 50 sweaters, 3150 bottles are needed.

Variables and Expressions White boards: Lesson Check: Part I Give two ways to write each algebraic expression in words. 1. j – 3 The difference of j and 3; 3 less than j. 2. 4 p 4 times p; The product of 4 and p. 3. Mark is 5 years older than Juan, who is y years old. Write an expression for Mark’s age. y+5 Holt Mc. Dougal Algebra 1

Variables and Expressions White boards: Lesson Check: Part II Evaluate each expression for c = 6, d = 5, and e = 10. d 4. e 1 5. c + d 11 2 Shemika practices basketball for 2 hours each day. 6. Write an expression for the number of hours she practices in d days. 2 d 7. Find the number of hours she practices in 5, 12, and 20 days. 10 hours; 24 hours; 40 hours Holt Mc. Dougal Algebra 1

Variables and Expressions Split: Cards or Extension • You will only be using the red and blue cards to begin with. Holt Mc. Dougal Algebra 1

Variables and Expressions Closing & HW Closing: Write two of your own algebraic expressions. Then, translate them in to words. HW: Review for Mastery 1 -1. Holt Mc. Dougal Algebra 1