Homework: P. 13/15-35 odd; 36, 46, 49, 52

Lesson 1-2 Warm Up P. 15/69-71, 76, 77-31 odd

The area of a trapezoid is one half of the product of the height h and the sum of the bases b1 and b2 of the trapezoid. Write an expression that gives the area of a trapezoid. A. B. C. D. 5-Minute Check 6

CCSS Content Standards A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. A.SSE.2 Use the structure of an expression to identify ways to rewrite it. Mathematical Practices 7 Look for and make use of structure.

Evaluate—to find a numerical answer for Vocabulary Evaluate—to find a numerical answer for Order of Operations—please excuse my dear Aunt Sally(PEMDAS)

Order of Operations. Parentheses Exponents Multiplication And Division in order from left to right Addition and Subtraction in order from left to right.

Example 1 Evaluate Expressions Evaluate 26. 26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 Use 2 as a factor 6 times. = 64 Multiply. Answer: 64

Example 1 Evaluate 44. A. 64 B. 128 C. 192 D. 256

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Example 2 Use Order of Operations Evaluate 48 ÷ 23 ● 3 + 5. 48 ÷ 23 ● 3 + 5 = 48 ÷ 8 ● 3 + 5 Evaluate powers. = 6 ● 3 + 5 Divide 48 by 8. = 18 + 5 Multiply 6 and 3. = 23 Add 18 and 5. Answer: 23

Example 2 Evaluate [(92 – 9) ÷ 12]5. A. 6 B. 15 C. 30 D. 45

Example 3 A. Evaluate (8 – 3) ● 3(3 + 2). Expressions with Grouping Symbols A. Evaluate (8 – 3) ● 3(3 + 2). (8 – 3) ● 3(3 + 2) = 5 ● 3(5) Evaluate inside parentheses. = 5 ● 15 Multiply 3 by 5. = 75 Multiply 5 by 15. Answer: 75

Example 3 B. Evaluate 4[12 ÷ (6 – 2)]2. Expressions with Grouping Symbols B. Evaluate 4[12 ÷ (6 – 2)]2. 4[12 ÷ (6 – 2)]2 = 4(12 ÷ 4)2 Evaluate innermost expression first. = 4(3)2 Evaluate expression in grouping symbol. = 4(9) Evaluate power. = 36 Multiply. Answer: 36

Example 3 C. Evaluate the power in the numerator. Expressions with Grouping Symbols C. Evaluate the power in the numerator. Multiply 6 and 2 in the numerator. Subtract 32 and 12 in the numerator.

Example 3 Evaluate the power in the denominator. Expressions with Grouping Symbols Evaluate the power in the denominator. Multiply 5 and 3 in the denominator. Subtract from left to right in the denominator. Answer: 2

Example 3 A. Evaluate the expression 2(4 + 7) ● (9 – 5). A. –60 B. 66 C. 88 D. 68

Example 4 Evaluate 2(x2 – y) + z2 if x = 4, y = 3, and z = 2. Evaluate an Algebraic Expression Evaluate 2(x2 – y) + z2 if x = 4, y = 3, and z = 2. 2(x2 – y) +z2 = 2(42 – 3) + 22 Replace x with 4, y with 3 and z with 2. = 2(16 – 3) + 22 Evaluate 42. = 2(13) + 22 Subtract 3 from 16. = 2(13) + 4 Evaluate 22. = 26 + 4 Multiply 2 and 13. = 30 Add. Answer: 30

Example 4 Evaluate x3 – y2 + z, if x = 3, y = 2, and z = 5. A. 6 B. 28 C. 36 D. 10

Example 5 Write and Evaluate an Expression ARCHITECTURE Each side of the Great Pyramid at Giza, Egypt, is a triangle. The base of each triangle once measured 230 meters. The height of each triangle once measured 187 meters. The area of a triangle is one-half the product of the base b and its height h.

Example 5 Write and Evaluate an Expression A. Write an expression that represents the area of one side of the Great Pyramid.

Example 5 B. Find the area of one side of the Great Pyramid. Write and Evaluate an Expression B. Find the area of one side of the Great Pyramid. Replace b with 230 and h with 187. Multiply 230 by 187. Multiply by 43,010. Answer: The area of one side of the Great Pyramid is 21,505 m2.

Example 5 Find the area of a triangle with a base of 123 feet and a height of 62 feet. A. 3813 ft2 B. 7626 ft2 C. 15,252 ft2 D. 32 ft2