Order of Operations and Evaluating Expressions Section 1

Order of Operations and Evaluating Expressions Section 1 -2 Part 2

Goals Goal Rubric • To use the order of operations to evaluate expressions. Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

Vocabulary • Evaluate

Evaluating Expressions • In Part 1 of this lesson, we simplified numerical expressions with exponents and learned the order of operations. • Now, we will evaluate algebraic expressions for given values of the variable.

Definition • Evaluate – 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.

Example: 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 Substitute 7 for b and 2 for c. Simplify. Substitute 4 for a and 2 for c. Simplify.

Your Turn: 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 Substitute 3 for m and 2 for n. Simplify. Substitute 9 for p and 3 for m. Simplify.

Example: Evaluating Algebraic Expressions Evaluate the expression for the given value of x. 10 – x · 6 for x = 3 10 – x · 6 First substitute 3 for x. 10 – 3 · 6 Multiply. Subtract. 10 – 18 – 8

Example: Evaluating Algebraic Expressions Evaluate the expression for the given value of x. 42(x + 3) for x = – 2 42(x + 3) 42(– 2 + 3) First substitute – 2 for x. 42(1) Perform the operation inside the parentheses. 16(1) Evaluate powers. 16 Multiply.

Your Turn: Evaluate the expression for the given value of x. 14 + x 2 ÷ 4 for x = 2 14 + x 2 ÷ 4 14 + 22 ÷ 4 First substitute 2 for x. 14 + 4 ÷ 4 Square 2. 14 + 1 15 Divide. Add.

Your Turn: Evaluate the expression for the given value of x. (x · 22) ÷ (2 + 6) for x = 6 (x · 22) ÷ (2 + 6) (6 · 4) ÷ (2 + 6) (24) ÷ (8) 3 First substitute 6 for x. Square two. Perform the operations inside the parentheses. Divide.

Your Turn: What is the value of -10 – 4 x if x = -13? 1. 2. 3. 4. -62 -42 42 52

Your Turn: What is the value of 5 k 3 if k = -4? 1. 2. 3. 4. -8000 -320 -60 320

Your Turn: What is the value of if n = -8, m = 4, and t = 2 ? 1. 2. 3. 4. 10 -6 6

Example: Application A shop offers gift-wrapping services at three price levels. The amount of money collected for wrapping gifts on a given day can be found by using the expression 2 B + 4 S + 7 D. On Friday the shop wrapped 10 Basic packages B, 6 Super packages S, and 5 Deluxe packages D. Use the expression to find the amount of money collected for gift wrapping on Friday.

Example - Solution: 2 B + 4 S + 7 D 2(10) + 4(6) + 7(5) 20 + 24 + 35 44 + 35 79 First substitute the value for each variable. Multiply. Add from left to right. Add. The shop collected $79 for gift wrapping on Friday.

Your Turn: Another formula for a player's total number of bases is Hits + D + 2 T + 3 H. Use this expression to find Hank Aaron's total bases for 1959, when he had 223 hits, 46 doubles, 7 triples, and 39 home runs. Hits + D + 2 T + 3 H = total number of bases 223 + 46 + 2(7) + 3(39) 223 + 46 + 14 + 117 400 First substitute values for each variable. Multiply. Add. Hank Aaron’s total number of bases for 1959 was 400.

USING A VERBAL MODEL Writing algebraic expressions that represent real-life situations is called modeling. The expression is a mathematical model. Use three steps to write a mathematical model. WRITE A ASSIGN WRITE AN VERBAL MODEL. LABELS. ALGEBRAIC MODEL.

Writing an Algebraic Model A PROBLEM SOLVING PLAN USING MODELS VERBAL MODEL Ask yourself what you need to know to solve the problem. Then write a verbal model that will give you what you need to know. LABELS Assign labels to each part of your verbal problem. ALGEBRAIC Use the labels to write an algebraic model based on MODEL your verbal model.

Example: 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.

Example: 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 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.

Your Turn: 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.

Your Turn: 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 To make 12 sweaters 756 bottles are needed. To make 25 sweaters 1575 bottles are needed. To make 50 sweaters 3150 bottles are needed.

Joke Time • What do you call a blind deer? • No eye deer. • What did the fish say when it swam into a wall? • Damn. • What's a cat’s favorite color? • Puuuuuurrrrrple!!!!

Assignment • 1. 2 Pt 2 Exercises Pg. 17 – 18: #6 – 17