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NameClassDate10.1 Independent PracticeCOMMONCOREPersonalMath Trainer6.EE.2a, 6.EE.2b, 6.EE.4, 6.EE.2.610. Write an algebraic expression with theconstant 7 and the variable y.my.hrw.comOnlineAssessment andInterventionSarah and Noah work at Read On Bookstoreand get paid the same hourly wage. The tableshows their work schedule for last week.Read On Bookstore Work Schedule (hours)Write each phrase as an algebraic expression.11. n divided by 8Sarah12. p multiplied by 4NoahMondayTuesday53Wednesday813. b plus 1414. 90 times x15. a take away 1616. k less than 2417. 3 groups of w18. the sum of 1 and q19. the quotient of 13 and z20. c added to 4530. Write an expression that represents Sarah’stotal pay last week. Represent her hourlywage with w.31. Write an expression that represents Noah’stotal pay last week. Represent his hourlywage with w.32. Are the expressions equivalent? Did Sarahand Noah earn the same amount lastweek? Use models to justify your answer.Write a phrase in words for each algebraicexpression.22. m 8323. 42s24. 9d25. t 2926. 2 g27. 11xh28.1229. 5 k266Unit 433. Mia buys 3 gallons of gas that costs ddollars per gallon. Bob buys g gallons ofgas that costs 3 per gallon.a. Write an expression for the amountMia pays for gas.b. Write an expression for the amountBob pays for gas.c. What do the numeral and the variablerepresent in each expression? Houghton Mifflin Harcourt Publishing Company21. 8 less than w

34. The student council is asking people to donate money for thenew park outside the school. Everyone who makes the suggesteddonation amount will be given a bracelet. If everyone donates thesuggested amount, and b bracelets are given away, what algebraicexpression represents the total amount collected in donations?35. Mr. Delgado has some young orange trees. He wants to plant themin 46 rows. If t is the total number of orange trees, write an algebraicexpression to represent how many trees he can plant in each row.36. There are 15 violinists in the orchestra this year. Next year, two violinistswill leave and some new violinists will join the orchestra. If v is thenumber of violinists who will join the orchestra, write an expression torepresent the number of violinists in the orchestra next year.37. Jill, Meg, and Beth are sisters. Jill is 2 years younger than Meg. Beth ishalf as old as Meg. Let m represent Meg’s age. Write two other algebraicexpressions based on this situation. Tell what each expression represents,and what the variable stands for in each expression.38. Multistep Will, Hector, and Lydia volunteered at the animal shelter inMarch and April. The table shows the number of hours Will and Hectorvolunteered in March. Let x represent the number of hours Lydiavolunteered in March. Houghton Mifflin Harcourt Publishing CompanyMarch VolunteeringWill3 hoursHector5 hoursa. Will’s volunteer hours in April were equal to his March volunteerhours plus Lydia’s March volunteer hours. Write an expression torepresent Will’s volunteer hours in April.b. Hector’s volunteer hours in April were equal to 2 hours less than hisMarch volunteer hours plus Lydia’s March volunteer hours. Write anexpression to represent Hector’s volunteer hours in April.c. Did Will and Hector volunteer the same number of hours in April?Explain.39. The town of Rayburn received 6 more inches of snow than the town ofGreenville. Let g represent the amount of snow in Greenville. Write analgebraic expression to represent the amount of snow in Rayburn.Lesson 10.1267

40. Abby baked 48 dinner rolls and divided them evenly into bags. Let brepresent the number of bags. Write an algebraic expression torepresent the number of dinner rolls in each bag.41. Eli is driving at a speed of 55 miles per hour. Let h represent the numberof hours that Eli drives at this speed. Write an algebraic expression torepresent the number of miles that Eli travels during this time.FOCUS ON HIGHER ORDER THINKING42. Multistep Bob’s Bagels offers two breakfast options, as shown.a. Let x represent the number of customers who order coffee and abagel. How much money will Bob’s Bagels make from these orders?b. Let y represent the number of customers who order tea and abreakfast sandwich. How much money will Bob’s Bagels make fromthese orders?c. Write an algebraic expression for the total amount Bob’s Bagels willmake from all the coffee and bagel orders and from all the tea andbreakfast sandwich orders.43. Represent Real-World Problems The number of shoes in a closet is s.Work Areaa. How many pairs of shoes are in the closet? Explain.b. What If? Suppose one of the pairs is missing a shoe. How many44. Problem Solving Write an expression that has three terms, two differentvariables, and one constant.45. Represent Real-World Problems Describe a situation that can bemodeled by the expression x 8.46. Critique Reasoning Ricardo says that the expression y 4 is equivalentto the expression 1y 4. Is he correct? Explain.268Unit 4 Houghton Mifflin Harcourt Publishing Companyshoes are in the closet?

LESSON10.2?EvaluatingExpressionsESSENTIAL QUESTIONCOMMONCORE6.EE.2cEvaluate expressions atspecific values of theirvariables.How can you use the order of operations to evaluate algebraicexpressions?Evaluating ExpressionsRecall that an algebraic expression contains one or more variables. You cansubstitute a number for that variable and then find the value of the expression.This is called evaluating the expression.Math On the Spotmy.hrw.comEXAMPL 1EXAMPLECOMMONCOREEvaluate each expression for the given value of the variable.6.EE.2cMy NotesA x - 9; x 1515 - 9Substitute 15 for x.6Subtract.When x 15, x - 9 6.16Bn ;n 8168Substitute 8 for n.2Divide. Houghton Mifflin Harcourt Publishing Company16When n 8,n 2.C 0.5y; y 1.40.5(1.4)Substitute 1.4 for y.0.7Multiply.When y 1.4, 0.5y 0.7.D 6k; k 136.HINT: Think of 6 as1()6 131 for k.Substitute32Multiply.When k 13, 6k 2.Lesson 10.2269

YOUR TURNPersonalMath TrainerEvaluate each expression for the given value of the variable.Online Assessmentand Intervention1. 4x; x 82. 6.5 - n; n 1.8m; m 183.6my.hrw.comUsing the Order of OperationsMath On the Spotmy.hrw.comExpressions may have more than one operation or more than one variable.To evaluate these expressions, substitute the given value for each variable andthen use the order of operations.EXAMPLE 2COMMONCORE6.EE.2cEvaluate each expression for the given value of the variable.A 4(x - 4); x 74(7 - 4)Substitute 7 for x.4(3)Subtract inside the parentheses.12Multiply.When x 7, 4(x - 4) 12.B 4x - 4; x 74(7) - 4Substitute 7 for x.28 - 4Multiply.24Subtract.C w - x y; w 6, x 5, y 3Math TalkMathematical PracticesIs w - x y equivalentto w - y x? Explain anydifference in the orderthe math operationsare performed.(6) - (5) (3)Substitute 6 for w, 5 for x, and 3 for y.1 3Subtract.4Add.When w 6, x 5, y 3, w - x y 4.D x2 - x; x 9(9)2 - (9)Substitute 9 for each x.81 - 9Evaluate exponents.72Subtract.When x 9, x2 - x 72.270Unit 4 Houghton Mifflin Harcourt Publishing CompanyWhen x 7, 4x - 4 24.

YOUR TURNEvaluate each expression for n 5.4. 3(n 1)5. 4 (n - 4) 14PersonalMath Trainer6. 6n n2Online Assessmentand InterventionEvaluate each expression for a 3, b 4, and c 6.7. ab - c8. bc 5amy.hrw.com9. a - (b c)3Evaluating Real-World ExpressionsYou can evaluate expressions to solve real-world problems.EXAMPL 3EXAMPLECOMMONCORE6.EE.2cThe expression 1.8c 32 gives the temperature in degrees Fahrenheit fora given temperature in degrees Celsius c. Find the temperature in degreesFahrenheit that is equivalent to 30 C.STEP 1Math On the Spotmy.hrw.comFind the value of c.c 30 CSTEP 2Substitute the value into the expression.1.8c 321.8(30) 32Substitute 30 for c.54 32Multiply.86Add. Houghton Mifflin Harcourt Publishing Company86 F is equivalent to 30 C.YOUR TURN10. The expression 6x2 gives the surface area of a cube, and the expressionx3 gives the volume of a cube, where x is the length of one side ofthe cube. Find the surface area and the volume of a cube with a sidelength of 2 m.S m2; V m311. The expression 60m gives the number of seconds in m minutes.How many seconds are there in 7 minutes?secondsPersonalMath TrainerOnline Assessmentand Interventionmy.hrw.comLesson 10.2271

Guided PracticeEvaluate each expression for the given value(s) of the variable(s).(Examples 1 and 2)1. x - 7; x 232. 3a - b; a 4, b 63. 8t ; t 44. 9 m; m 1.55. 12 w 2; w 196. 5(6.2 z); z 3.87. The table shows the prices for games in Bella’s soccer league.Her parents and grandmother attended a soccer game. Howmuch did they spend if they all went together in one car?(Example 3)Women’s Soccer Game Pricesa. Write an expression that represents the cost of onecarful of nonstudent soccer fans. Use x as the numberof people who rode in the car and attended the game.Student tickets 6Nonstudent tickets 12Parking 5is an expression that represents the costof one carful of nonstudent soccer fans.b. Since there are three attendees, evaluate the expression12x 5 for x 3.12() 5 The family spent 5 to attend the game.8. Stan wants to add trim all around the edge of a rectangular tablecloththat measures 5 feet long by 7 feet wide. The perimeter of the rectangulartablecloth is twice the length added to twice the width. How much trimdoes Stan need to buy? (Example 3)represent its width. The expression would be.b. Evaluate the expression P 2w 2l for l 5 and w 7.2() 2(Stan bought?) 14 of trim to sew onto the tablecloth.ESSENTIAL QUESTION CHECK-IN9. How do you know the correct order in which to evaluate algebraicexpressions?272Unit 4 Houghton Mifflin Harcourt Publishing Companya. Write an expression that represents the perimeter of the rectangulartablecloth. Let l represent the length of the tablecloth and w

NameClassDate10.2 Independent PracticeCOMMONCOREPersonalMath Trainer6.EE.2cOnlineAssessment andInterventionmy.hrw.com10. The table shows ticket prices at the Movie 16theater. Let a represent the number of adulttickets, c the number of children’s tickets,and s the number of senior citizen tickets.Movie 16 Ticket PricesAdults 8.75Children 6.50Seniors 6.5013. Look for a Pattern Evaluate theexpression 6x - x2 for x 0, 1, 2, 3, 4, 5,and 6. Use your results to fill in the tableand describe any pattern that you see.x6x - x01234562a. Write an expression for the total costof the three types of tickets. Houghton Mifflin Harcourt Publishing Companyb. The Andrews family bought 2 adulttickets, 3 children’s tickets, and 1 seniorticket. Evaluate your expression in parta to find the total cost of the tickets.c. The Spencer family bought 4 adulttickets and 2 children’s tickets. Did theyspend the same as the Andrews family?Explain.11. The area of a triangular sail is given by theexpression 12 bh, where b is the length ofthe base and h is the height. What is thearea of a triangular sail in a model sailboatwhen b 12 inches and h 7 inches?A in.214. The kinetic energy (in joules) of a movingobject can be calculated from theexpression 12 mv2, where m is the mass ofthe object in kilograms and v is its speed inmeters per second. Find the kinetic energyof a 0.145-kg baseball that is thrown at aspeed of 40 meters per second.E joules15. The area of a square is given by x2, wherex is the length of one side. Mary’s originalgarden was in the shape of a square. Shehas decided to double the area of hergarden. Write an expression that representsthe area of Mary’s new garden. Evaluatethe expression if the side length of Mary’soriginal garden was 8 feet.12. Ramon wants to balance his checkingaccount. He has 2,340 in the account. Hewrites a check for 140. He deposits a checkfor 268. How much does Ramon have leftin his checking account?Lesson 10.2273

16. The volume of a pyramid with a square baseis given by the expression 13 s2h, where s is thelength of a side of the base and h is the height.Find the volume of a pyramid with a squarebase of side length 24 feet and a heightof 30 feet.FOCUS ON HIGHER ORDER THINKINGWork Area17. Draw Conclusions Consider the expressions 3x(x - 2) 2 and2x2 3x - 12.a. Evaluate each expression for x 2 and for x 7. Based on yourresults, do you know whether the two expressions are equivalent?Explain.18. Critique Reasoning Marjorie evaluated the expression 3x 2 for x 5as shown:3x 2 35 2 37What was Marjorie’s mistake? What is the correct value of 3x 2for x 5?274Unit 4 Houghton Mifflin Harcourt Publishing Companyb. Evaluate each expression for x 5. Based on your results, do youknow whether the two expressions are equivalent? Explain.

RE6.EE.3Apply the properties ofoperations to generateequivalent expressions. Also6.EE.2b, 6.EE.4ESSENTIAL QUESTIONHow can you identify and write equivalent expressions?EXPLORE ACTIVITY 1COMMONCORE6.EE.4Identifying Equivalent ExpressionsOne way to test whether two expressions might be equivalent is to evaluatethem for the same value of the variable.Match the expressions in List A with their equivalent expressions in List B.List AList B5x 655x 15(x 1)5x 51 5x5(13 x)A Evaluate each of the expressions in the lists for x 3. Houghton Mifflin Harcourt Publishing CompanyList AList B5(3) 65 5(3) 1 5(3 1) 5(3) 5 1 5(3) 5(13 3) B Which pair(s) of expressions have the same value for x 3?C How could you further test whether the expressions in each pair areequivalent?D Do you think the expressions in each pair are equivalent? Why or why not?Lesson 10.3275

EXPLORE ACTIVITY 1 (cont’d)Reflect1.Error Analysis Lisa evaluated the expressions 2x and x2 for x 2 andfound that both expressions were equal to 4. Lisa concluded that 2xand x2 are equivalent expressions. How could you show Lisa that sheis incorrect?EXPLORE ACTIVITY 2COMMONCORE6.EE.3Modeling Equivalent ExpressionsAlgebra TilesYou can also use models to determineif two expressions are equivalent.Algebra tiles are one way to modelexpressions. 1 xDetermine if the expression 3(x 2) is equivalent to 3x 6.A Model each expression using algebra tiles.B The model for 3(x 2) hasThe model for 3x 6 has3x 6x tiles andx tiles and1 tiles.1 tiles.C Is the expression 3(x 2) equivalent to 3x 6? Explain.Reflect2.276Use algebra tiles to determine if 2(x 3) is equivalent to 2x 3. Explainyour answer.Unit 4 Houghton Mifflin Harcourt Publishing Company3(x 2)

Writing Equivalent ExpressionsUsing PropertiesProperties of operations can be used to identifyequivalent expressions.my.hrw.comProperties of OperationsExamplesCommutative Property of Addition: When adding,changing the order of the numbers does notchange the sum.3 4 4 3Commutative Property of Multiplication: Whenmultiplying, changing the order of the numbersdoes not change the product.2 4 4 2Associative Property of Addition: When addingmore than two numbers, the grouping of thenumbers does not change the sum.(3 4) 5 3 (4 5)Associative Property of Multiplication: Whenmultiplying more than two numbers, the groupingof the numbers does not change the product.(2 4) 3 2 (4 3)Distributive Property: Multiplying a number bya sum or difference is the same as multiplying byeach number in the sum or difference and thenadding or subtracting.6(2 4) 6(2) 6(4)8(5 - 3) 8(5) - 8(3)Identity Property of Addition: Adding zero to anumber does not change its value.9 0 9Identity Property of Multiplication: Multiplying anumber by one does not change its value.1 7 7EXAMPL 1EXAMPLE Houghton Mifflin Harcourt Publishing CompanyMath On the SpotCOMMONCORE6.EE.3Use a property to write an expression that is equivalent to x 3.The operation in the expression is addition.You can use the Commutative Property of Addition to write an equivalentexpression: x 3 3 x.YOUR TURNFor each expression, use a property to write an equivalent expression.Tell which property you used.3. (ab)c 4. 3y 4y 5. 6 7PersonalMath TrainerOnline Assessmentand Interventionmy.hrw.comLesson 10.3277

Identifying Equivalent ExpressionsUsing PropertiesMath On the Spotmy.hrw.comEXAMPLE 2COMMONCORE6.EE.3Use the properties of operations to determine if theexpressions are equivalent.A 3(x - 2); 3x - 63(x - 2) 3x - 6AnimatedMathDistributive Property3(x - 2) and 3x - 6 are equivalent expressions.my.hrw.com1 (4 x)B 2 x;21x 21 (x 4) 221x 2 21 x.2 x does not equal 2 2They are not equivalent expressions.Distributive PropertyCommutative PropertyYOUR TURNUse the properties of operations to determine if the expressions areequivalent.PersonalMath TrainerOnline Assessmentand Interventionmy.hrw.com278Unit 46x - 8; 2(3x - 5)7.2 - 2 5x; 5x8.Jamal bought 2 packs of stickers and 8 individual stickers. Use x torepresent the number of stickers in a pack of stickers and write anexpression to represent the number of stickers Jamal bought. Is theexpression equivalent to 2(4 x)? Check your answer with algebratile models. Houghton Mifflin Harcourt Publishing Company6.

Generating Equivalent ExpressionsParts of an algebraic expressionThe parts of the expression thatare separated by or - signsNumbers that are multiplied byat least one variableTerms with the same variable(s)raised to the same power(s)termscoefficientslike terms12 3y2 4x 2y2 412 3y2 4x 2y2 4Math On the Spotmy.hrw.com12 3y2 4x 2y2 4When an expression contains like terms, you can use properties to combine thelike terms and write an equivalent expression.EXAMPL 3EXAMPLECOMMONCORE6.EE.3, 6.EE.2bCombine like terms.A 6x2 - 4x26x2 and 4x2 are like terms.6x2 - 4x2 x2 (6 - 4) x2(2)Distributive PropertySubtract inside the parentheses. 2x 2Commutative Property ofMultiplication6x2 - 4x2 2x2Math TalkMathematical PracticesWrite 2 terms that can becombined with 7y4.B 3a 2(b 5a) Houghton Mifflin Harcourt Publishing Company3a 2(b 5a) 3a 2b 2(5a)Distributive Property 3a 2b (2 · 5)aAssociative Property ofMultiplication 3a 2b 10aMultiply 2 and 5. 3a 10a 2bCommutative Property of Addition (3 10)a 2bDistributive Property 13a 2bAdd inside the parentheses.3a 2(b 5a) 13a 2bC y 11x 7y - 7xy 11x 7y - 7x y 7y 11x - 7xy and 7y are like terms;11x and 7x are like terms.Commutative Property (1 7)y (11 - 7)xDistributive Property 8y 4xSimplify inside parentheses.y 11x 7y - 7x 8y 4xLesson 10.3279

YOUR TURNPersonalMath TrainerOnline Assessmentand Interventionmy.hrw.comCombine like terms.9. 8y - 3y 10. 6x2 4(x2 - 1) 11. 4a5 - 2a5 4b b 12. 8m 14 - 12 4n Guided Practice1. Evaluate each of the expressions in the list for y 5. Then, draw lines tomatch the expressions in List A with their equivalent expressions in List B.(Explore Activity 1)List B4 4y 4y 4 4(y 1) 4(y 1) 4y 1 1 4y 2. Determine if the expressions are equivalent by comparingthe models. (Explore Activity 2) x 4For each expression, use a property to write an equivalentexp

Math Trainer Online Assessment and Intervention Personal my.hrw.com Math On the Spot my.hrw.com x 5 x -5 x 32x - 3 - 2 Draw a bar model to represent each expression. 7. t - 2 8. 4y YOUR TURN Comparing Expressions Using Models Algebraic expressions are equivalent if they are equal for all val