Unit 2 Lesson 1 . Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up Evaluate each algebraic expression for the given value of the variables. 1. 7 x + 4 for x = 6 2. 8 y – 22 for y = 9 3. 12 x + for x = 7 and y = 4

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Warm Up

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Unit 2 Lesson 1 Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Evaluate each algebraic expression for the given value of the variables. 1.7x + 4 for x = 6 2. 8y – 22 for y = 9 3. 12x + for x = 7 and y = 4 4.y + 3z for y = 5 and z = 6 46 50 8 y 86 23

Problem of the Day A farmer sent his two children out to count the number of ducks and cows in the field. Jean counted 50 heads. Charles counted 154 legs. How many of each kind were counted? 23 ducks and 27 cows

Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua. An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua. When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.

• add 3 to a number • a number plus 3 + • the sum of a number and 3 n + 3 • 3 more than a number • a number increased by 3 • subtract 12 from a number • a number minus 12 • the difference of a number and 12 - x – 12 • 12 less than a number • a number decreased by 12 • take away 12 from a number • a number less than 12

a 6 or ÷ 6 a •2 times a number • 2 multiplied by a number 2m or 2 • m + • the product of 2 and a number • 6 divided into a number ÷ • a number divided by 6 • the quotient of a number and 6

n 4 Additional Example 1: Translating Verbal Expressions into Algebraic Expressions Write each phrase as an algebraic expression. A. the quotient of a number and 4 quotient means “divide” B. w increased by 5 increased by means “add” w + 5

4 n Additional Example 1: Translating Verbal Expressions into Algebraic Expressions Write each phrase as an algebraic expression. C. the difference of 3 times a number and 7 the difference of 3 times a number and 7 3 • x– 7 3x– 7 D. the quotient of 4 and a number, increased by 10 the quotient of 4 and a number, increased by 10 + 10

Check It Out: Example 1 Write each phrase as an algebraic expression. A. a number decreased by 10 decreased means “subtract” n – 10 B. r plus 20 plus means “add” r + 20

Check It Out: Example 1 Write each phrase as an algebraic expression. C. the product of a number and 5 the product of a number and 5 n• 5 5n D. 4 times the difference of y and 8 4 times the difference of y and 8 y– 8 4 • 4(y – 8)

Additional Example 2A: Translating Real-World Problems into Algebraic Expressions Mr. Campbell drives at 55 mi/h. Write an algebraic expression for how far he can drive in h hours. You need to put equal parts together. This involves multiplication. 55mi/h ·h hours = 55h miles

Additional Example 2B: Translating Real-World Problems into Algebraic Expressions On a history test Maritza scored 50 points on the essay. Besides the essay, each short-answer question was worth 2 points. Write an expression for her total points if she answered q short-answer questions correctly. The total points include 2 points for each short-answer question. Multiply to put equal parts together. 2q In addition to the points for short-answer questions, the total points included 50 points on the essay. Add to put the parts together: 50 + 2q

Check It Out: Example 2A Julie Ann works on an assembly line building computers. She can assemble 8 units an hour. Write an expression for the number of units she can produce in h hours. You need to put equal parts together. This involves multiplication. 8 units/h ·h hours = 8h

Check It Out: Example 2B At her job Julie Ann is paid $8 per hour. In addition, she is paid $2 for each unit she produces. Write an expression for her total hourly income if she produces u units per hour. Her total wage includes $2 for each unit produced. Multiply to put equal parts together. 2u In addition the pay per unit, her total income includes $8 per hour. Add to put the parts together: 2u + 8.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Write each phrase as an algebraic expression. 1. 18 less than a number 2. the quotient of a number and 21 3. 8 times the sum of x and 15 4. 7 less than the product of a number and 5 x – 18 x 21 8(x + 15) 5n – 7 5. The county fair charges an admission of $6 and then charges $2 for each ride. Write an algebraic expression to represent the total cost after r rides at the fair. 6 + 2r

Lesson Quiz for Student Response Systems 1. Which of the following is an algebraic expression that represents the phrase ‘15 less than a number’? A.x – 15 B.x + 15 C. 15 –x D. 15x

Lesson Quiz for Student Response Systems 2. Which of the following is an algebraic expression that represents the phrase ‘the product of a number and 36’? A. 36xC. B.D.x + 36 36 x x 36

Lesson Quiz for Student Response Systems 3. Which of the following is an algebraic expression that represents the phrase ‘5 times the sum of y and 17’? A. 5(y + 17) B.y + 17 C. 5y + 17 D. 5(y – 17)

Lesson Quiz for Student Response Systems 4. Which of the following is an algebraic expression that represents the phrase ‘9 less than the product of a number and 7’? A. 7x + 9 B. 7x – 9 C. 9x + 7 D. 9x – 7

Lesson Quiz for Student Response Systems 5. A painter charges $675 for labor and $30 per gallon of paint. Identify an algebraic expression that represents the total cost of painting, if the painter used x gallons of paint. A. 30 + 675x B. 675x C. 675 + 30x D. 30x

Unit 2 Lesson 2 Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Evaluate each expression for y = 3. 1. 3y + y 2. 7y 3. 10y – 4y 4. 9y 5. y + 5y + 6y 12 21 18 27 36

Problem of the Day Emilia saved nickels, dimes, and quarters in a jar. She had as many quarters as dimes, but twice as many nickels as dimes. If the jar had 844 coins, how much money had she saved? $94.95

In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by + and –. x 3 7x + 5 – 3y2 + y + term term term term term Coefficient Variable 7 In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. A variable by itself, like y, has a coefficient of 1. So y = 1y. x

Like terms are terms with the same variables raised to the same exponents. The coefficients do not have to be the same. Constants, like 5, , and 3.2, are also like terms. 1 2 w 7 3x and 2x w and 5 and 1.8 5x2 and 2x 6a and 6b 3.2 and n Only one term contains a variable The exponents are different. The variables are different

Helpful Hint Use different shapes or colors to indicate sets of like terms. Additional Example 1: Identifying Like Terms Identify like terms in the list. 3t 5w2 7t 9v 4w2 8v Look for like variables with like powers. 3t 5w2 7t 9v 4w2 8v Like terms: 3t and 7t 5w2 and 4w2 9v and 8v

Check It Out: Example 1 Identify like terms in the list. 2x 4y3 8x 5z 5y3 8z Look for like variables with like powers. 2x 4y3 8x 5z 5y3 8z Like terms: 2x and 8x 4y3 and 5y3 5z and 8z

Additional Example 2: Simplifying Algebraic Expressions Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 6t – 4t 6t and 4t are like terms. 6t– 4t 2t Subtract the coefficients. B. 45x – 37y + 87 In this expression, there are no like terms to combine.

Additional Example 2: Simplifying Algebraic Expressions Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6 Identify like terms. 3a2 + 5b+ 11b2 – 4b + 2a2 – 6 Group like terms. (3a2 + 2a2) + (5b – 4b)+ 11b2 – 6 5a2 + b + 11b2 – 6 Add or subtract the coefficients.

Check It Out: Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 5y + 3y 5y and 3y are like terms. 5y+ 3y 8y Add the coefficients.

Check It Out: Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 4x2 + 4y + 3x2 – 4y + 2x2 + 5 4x2 + 4y + 3x2 – 4y + 2x2 + 5 Identify like terms. (4x2 + 3x2 + 2x2)+ (4y – 4y) + 5 Group like terms. Add or subtract the coefficients. 9x2 + 5

Additional Example 3: Geometry Application Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 3 3x + 2 x Write an expression using the side lengths. 2x + 3 + 3x + 2 + x Identify and group like terms. (x+ 3x + 2x) + (2 + 3) 6x + 5 Add the coefficients.

Check It Out: Example 3 Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 1 2x + 1 x Write an expression using the side lengths. x + 2x + 1 + 2x + 1 (x + 2x + 2x) + (1 + 1) Identify and group like terms. 5x + 2 Add the coefficients.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz: Part I Identify like terms in the list. 1. 3n2 5n 2n3 8n 2. a5 2a2a3 3a 4a2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 3. 4a + 3b + 2a 4. x2 + 2y + 8x2 5n, 8n 2a2, 4a2 6a + 3b 9x2 + 2y

Lesson Quiz: Part II 5. Write an expression for the perimeter of the given figure. 2x + 3y x + y x + y 2x + 3y 6x + 8y

Lesson Quiz for Student Response Systems 1. Identify the like terms in the list. 6a, 5a2, 2a, 6a3, 7a A. 6a and 2a B. 6a, 5a2, and 6a3 C. 6a, 2a, and 7a D. 5a2 and 6a3

Lesson Quiz for Student Response Systems 2. Identify the like terms in the list. 16y6, 2y5, 4y2, 10y, 16y2 A. 16y6 and 16y2 B. 4y2 and 16y2 C. 16y6 and 2y2 D. 2y5 and 10y