Lesson Menu Main Idea and New Vocabulary NGSSS Example 1:Translate Phrases into Algebraic Expressions Example 2:Translate Phrases into Algebraic Expressions Example 3:Evaluate Algebraic Expressions Example 4:Evaluate Algebraic Expressions Example 5:Evaluate Algebraic Expressions Example 6:Real-World Example: Use Expressions to Solve Problems Five-Minute Check

Main Idea/Vocabulary Translate verbal phrases into algebraic expressions. Evaluate algebraic expressions. variable algebra algebraic expression defining a variable

NGSSS MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear functions. MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems.

Example 1 Translate Phrases into Algebraic Expressions Translate seven dollars more than John has into an algebraic expression. Answer: 7 + d

Example 1 CYP Translate nine more books than Maria has into an algebraic expression. A.9b B.9 + b C.9 – b D.9b + 1

Example 2 Translate Mrs. Ruiz had 50 pens and gave 2 to each of her students into an algebraic expression. Translate Phrases into Algebraic Expressions Answer: 50 – 2s

Example 2 CYP Translate Mark had 20 guitar picks and gave 3 to each of his friends into an algebraic expression. A.20 + f B f C.20 – f D.20 – 3f

Example 3 Evaluate Algebraic Expressions Evaluate (x – y) + 3 ● (–2) if x = –4 and y = 5. (x – y) + 3 ● (–2)=(–4 – 5) + 3 ● (–2) Replace x with –4 and y with 5. =–9 + 3 ● (–2) Perform operations in the parentheses first. =–9 + –6 or –15 Multiply 3 and –2. Then add. Answer: –15

Example 3 CYP Evaluate (x + y) + 2 ● (–4) if x = 3 and y = –6. A.–32 B.–11 C.–5 D.4

Example 4 Evaluate 3(a – b) ÷ 2 if a = 8 and b = 4. Evaluate Algebraic Expressions 3(a – b) ÷ 2 =3(8 – 4) ÷ 2 Replace a with 8 and b with 4. =3(4) ÷ 2 Perform operations in the parentheses first. =12 ÷ 2 or 6 Multiply 3 and 4. Then divide. Answer: 6

Example 4 CYP Evaluate 5(a – b) ÷ 4 if a = 7 and b = 3. A.4 B.5 C.6 D.10

Example 5 Evaluate Algebraic Expressions Evaluate if c = 2 and d = 6. Replace c with 2 and d with 6. Simplify. Evaluate the numerator and denominator. Then divide. Answer: 2

Example 5 CYP Evaluate if c = 9 and d = –6. A.–1 B. C.1 D.

Example 6 KAYAKS River Rentals rents kayaks. They charge a $10 service charge plus $3 per hour. Write an expression that can be used to find the total cost to rent a kayak for any number of hours. Answer: The expression is h. Use Expressions to Solve Problems

Example 6 CYP KAYAKS River Rentals rents kayaks. They charge a $10 service charge plus $3 per hour. What is the total cost to rent a kayak for 3 hours? A.$13 B.$16 C.$19 D.$33

Five Minute Check 1 Translate the phrase into an algebraic expression. the number of ounces of water divided among ten beakers A.w – 10 B.10w C. D.

Translate the phrase into an algebraic expression. Sarah has thirty pencils and gives two to each of her friends. Five Minute Check 2 A.30 ÷ f B.30 – 2f C.30 – f D.30  2f

Translate the phrase into an algebraic expression. Tommy earns twenty-five dollars for each lawn he mows. Five Minute Check 3 A.25n B.25 + n C. D.20  5n

Evaluate 4(c – 2b) + 5 if a = 3, b = –1, c = 4, and d = 0. Five Minute Check 4 A.8 B.20 C.29 D.–36

Five Minute Check 5 Evaluate if a = 3, b = –1, c = 4, and d = 0. A.12 B.3 C.0 D.–3

A moving company rents its trucks for $36 per day. There is an additional charge of $1.20 for each mile the truck is driven. Jared rents a truck for two days. The total rental cost is $252. How many miles did Jared drive the truck? Five Minute Check 6 A.120 B.150 C.180 D.216