Preview Warm Up California Standards Lesson Presentation

Term (list some from the examples) Warm Up Define and find in examples (not all examples can be used) Variable Constant Numerical Expression Algebraic Expression Term (list some from the examples) 3x -5 4x 4 + 5 = 9 5 4 + 25

California Standards Preparation for 4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x – 5) + 4(x – 2) = 12.

Vocabulary variable constant numerical expression algebraic expression evaluate replacement set

A variable is a letter or a symbol used to represent a value that can change. A constant is a value that does not change. A numerical expression contains only constants and/or operations. An algebraic expression contains variables, constants, and/or operations.

+ – x ÷ Plus, sum, Minus, difference, less than increased by You will need to translate between algebraic expressions and words to be successful in math. The diagram below shows some of the ways to write mathematical operations with words. + – x ÷ Plus, sum, increased by Minus, difference, less than Times, product, equal groups of Divided by, quotient

These expressions all mean “2 times y”: 2y 2(y) 2 • y (2)(y) 2 y (2)y Writing Math

Additional 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. 7m D. j  6 the product of m and 7 the quotient of j and 6 m times 7 j divided by 6

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

Multiply Divide Add Subtract Find how much more or less To translate words into algebraic expressions, read the problem to determine what actions are taking place. Add Subtract Multiply Divide Put together, combine Find how much more or less Put together equal groups Separate into equal groups

Additional Example 2A: 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 62m Think: m groups of 62 words

Additional Example 2B: 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.”

Additional Example 2C: 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?

Check It Out! Example 2 Miriam is 5 cm taller than Jan. Jan is m centimeters tall. Write an expression for Miriam’s height in centimeters. m represents Jan’s height in centimeters. m + 5 Think: Miriam's height is 5 added to Jan’s height.

To evaluate an expression is to find its value 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. A replacement set is a set of numbers that can be substituted for a variable.

One way to indicate a set is to use braces, { } One way to indicate a set is to use braces, { }. The items in a set are called elements. Writing Math

Additional Example 3A: Evaluating Algebraic Expressions Substitute and Solve Evaluate the expression for the replacement set {6, 7, 2}. b – 1 Substitute each value in the replacement set for b and simplify (solve). b – 1 b – 1 b – 1 (6) – 1 (7) – 1 (2) – 1 5 6 1

Additional Example 3B: Evaluating Algebraic Expressions Evaluate the expression for the replacement set {6, 7, 2}. 3b Substitute each value in the replacement set for b and simplify. 3(b) 3(b) 3(b) 3(6) 3(7) 3(2) 18 21 6

Check It Out! Example 3a Evaluate the expression for the replacement set {2, 3, 9} . n Substitute each value in the replacement set for n and simplify. n n n (2) (3) (9)

Check It Out! Example 3b Evaluate the expression for the replacement set {2, 3, 9} . 15 – n Substitute each value in the replacement set for n and simplify. 15 – n 15 – n 15 – n 15 – 2 15 – 3 15 – 9 13 12 6

Check It Out! Example 3c Evaluate the expression for the replacement set {2, 3, 9} . n + 0.15 Substitute each value in the replacement set for n and simplify. n + 0.15 n + 0.15 n + 0.15 2 + 0.15 3 + 0.15 9 + 0.15 2.15 3.15 9.15

Additional Example 4A: 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 85s models the number of bottles to make s sleeping bags.

Additional Example 4B: Recycling Application 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 85s for s = 20, 50, and 325. s 85s 20 50 325 To make 20 sleeping bags, 1700 bottles are needed. 85(20) = 1700 To make 50 sleeping bags, 4250 bottles are needed. 85(50) = 4250 To make 325 sleeping bags, 27,625 bottles are needed. 85(325) = 27,625

Check It Out! Example 4a To make one sweater, sixty-three 20-ounce plastic drink bottles must be recycled. Write an expression for the number of bottles needed to make s sweaters. The expression 63s models the number of bottles to make s sweaters.

To make one sweater, sixty-three 20-ounce Check It Out! Example 4b To make one sweater, sixty-three 20-ounce plastic drink bottles must be recycled. Find the number of bottles needed to make 12, 25, and 50 sweaters. Evaluate 63s for s = 12, 25, and 50. s 63s 12 25 50 To make 12 sweaters, 756 bottles are needed. 63(12) = 756 To make 25 sweaters, 1575 bottles are needed. 63(25) = 1575 To make 50 sweaters, 3150 bottles are needed. 63(50) = 3150

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

Lesson Quiz: Part II Evaluate each expression for the replacement set {5, 8, 12}. 4. 5. 6 + d Shemika practices basketball for 2 hours each day. d 2 5 2 ; 4; 6 11; 14; 18 6. Write an expression for the number of hours she practices in d days. 7. Find the number of hours she practices in 5, 12, and 20 days. 2d 10 hours; 24 hours; 40 hours