1. Course 2 1-8 Translate Words into Math Do Now 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 86 8y8y 23 Hwk: p 6 & 8 due Wednesday, test on chap 1 sec1-5

2. Course 2 1-8 Translate Words into Math EQ: How do I translate words into numbers, variables, and operations and use properties to solve algebraic expressions? M7A1a Translate verbal phrases to algebraic expression M7P1c Adapt and apply a variety of appropriate strategies to solve problems

3. Course 2 1-8 Translate Words into Math

4. Course 2 1-8 Translate Words into Math OperationVerbal Expressions Algebraic Expressions add 3 to a number a number plus 3 the sum of a number and 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 12 less than a number a number decreased by 12 take away 12 from a number a number less than 12 n + 3 x – 12

5. Course 2 1-8 Translate Words into Math OperationVerbal Expressions Algebraic Expressions 2 times a number 2 multiplied by a number the product of 2 and a number 6 divided into a number a number divided by 6 the quotient of a number and 6 2m or 2 m ÷ a6a6 ÷ 6 or a

6. Course 2 1-8 Translate Words into Math 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 n4n4

7. Course 2 1-8 Translate Words into Math Write each phrase as an algebraic expression. Additional Example 1: Translating Verbal Expressions into Algebraic Expressions C. the difference of 3 times a number and 7 the difference of 3 times a number and 7 D. the quotient of 4 and a number, increased by 10 3 x – 7 the quotient of 4 and a number, increased by 10 4n4n + 10

8. Course 2 1-8 Translate Words into Math Check It Out: Example 1 A. a number decreased by 10 decreased means “subtract” B. r plus 20 plus means “add” r + 20 n – 10 Write each phrase as an algebraic expression.

9. Course 2 1-8 Translate Words into Math Check It Out: Example 1 Write each phrase as an algebraic expression. C. the product of a number and 5 D. 4 times the difference of y and 8 y – 8 n 5 the product of a number and 5 5n5n 4 times the difference of y and 8 4(y – 8) 4

10. Course 2 1-8 Translate Words into Math When solving real-world problems, you may need to determine the action to know which operation to use. ActionOperation Put parts together Put equal parts together Find how much more Separate into equal parts Add Multiply Subtract Divide

11. Course 2 1-8 Translate Words into Math Mr. Campbell drives at 55 mi/h. Write an algebraic expression for how far he can drive in h hours. Additional Example 2A: Translating Real-World Problems into Algebraic Expressions You need to put equal parts together. This involves multiplication. 55mi/h · h hours = 55h miles

12. Course 2 1-8 Translate Words into Math 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. Additional Example 2B: Translating Real-World Problems into Algebraic Expressions The total points include 2 points for each short- answer question. Multiply to put equal parts together. 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 2q2q

13. Course 2 1-8 Translate Words into Math 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

14. Course 2 1-8 Translate Words into Math 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. In addition the pay per unit, her total income includes $8 per hour. Add to put the parts together: 2u + 8. 2u2u

15. Course 2 1-8 Translate Words into Math Vocabulary Commutative Property Associative Property Identity Property Distributive Property

16. Course 2 1-8 Translate Words into Math

17. Course 2 1-8 Translate Words into Math

18. Course 2 1-8 Translate Words into Math

19. Course 2 1-8 Translate Words into Math Additional Example 1: Identifying Properties of Addition and Multiplication Tell which property is represented. A. (2  6)  1 = 2  (6  1) B. 3 + 0 = 3 C. 7 + 9 = 9 + 7 Associative Property Identity Property Commutative Property

20. Course 2 1-8 Translate Words into Math Check It Out: Example 1 Tell which property is represented. A. 7  1 = 7 B. 3 + 4 = 4 + 3 C. (5  1)  2 = 5  (1  2) Identity Property Commutative Property Associative Property

21. Course 2 1-8 Translate Words into Math Additional Example 2: Using Properties to Simplify Expressions Simplify each expression. Justify each step. A. 21 + 16 + 9 B. 20  9  5 21 + 16 + 9 = 16 + 9 + 21 Commutative Property. = 16 + (9 + 21) = 16 + 30 Associative Property. = 46 Add. 20  9  5 = 20  5  9 Commutative Property. = 20  (5  9) = 20  45 Associative Property. = 900 Multiply.

22. Course 2 1-8 Translate Words into Math Check It Out: Example 2A & B Simplify each expression. Justify each step. A. 17 + 14 + 3 B. 12  3  5 17 + 14 + 3 = 14 + 17 + 3 Commutative Property. = 14 + (17 + 3) = 14 + 20 Associative Property. = 34 Add. 12  3  5 = 3  5  12 Commutative Property. = 3  (5  12) = 3  60 Associative Property. = 180 Multiply.

23. Course 2 1-8 Translate Words into Math You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

24. Course 2 1-8 Translate Words into Math Additional Example 3: Using the Distributive Property to Multiply Mentally Use the Distributive Property to find 6(54). Method 1: Method 2: = (6  50) + (6  4) Rewrite 54 as 50 + 4. = 300 + 24 = 324 Use the Distributive Property. Multiply. 6(54) = 6(60 – 6) Rewrite 54 as 60 – 6. = (6  60) – (6  6) = 360 - 36 Use the Distributive Property. Multiply. = 324 Subtract. Add. 6(54) = 6(50 + 4)

25. Course 2 1-8 Translate Words into Math Check It Out: Example 3 Use the Distributive Property to find 8(19). Method 1: Method 2: = (8  10) + (8  9) Rewrite 19 as 10 + 9. = 80 + 72 = 152 Use the Distributive Property. Multiply. 8(19) = 8(20 – 1) Rewrite 19 as 20 – 1. = (8  20) – (8  1) = 160 – 8 Use the Distributive Property. Multiply. = 152 Subtract. Add. 8(19) = 8(10 + 9)

26. Course 2 1-8 Translate Words into Math TOTD Write each phrase as an algebraic expression. 1. 18 less than an 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 21 x – 18 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

27. Course 2 1-8 Translate Words into Math TOTD Tell which property is represented. 1. 17  1 = 17 2. (12 + 14) + 5 = 12 + (14 + 5) 3. 2  16 = 16  2 Simplify each expression. Justify each step. 4. 4  12  25 5. 48 + (15 + 2) Use the Distributive Property to find each product. 6. 6  (12 + 5) 7. (20 – 7)  9 Identity Property Associative Property Commutative Property 1,200 65 102 117

28. Course 2 1-8 Translate Words into Math Problem of the Day Daniel usually buys 6 bottles of water and 3 apples when he goes to the grocery store. Next time he goes, he will buy three times as many of each. How many items will Daniel buy? 27