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# Lessons 18 29 quiz review with answers

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1. 1. Name ____________________________________ Date ________________________ Mrs. Labuski / Mrs. Portsmore Period ________ Module 4 Lessons 18-29 Qz Review Module 4 Lesson 18 Writing and Evaluating Expressions – Addition and Subtraction Read the story problem. Identify the unknown quantity and write an addition or subtraction expression that is described. Then evaluate your expression given the further information. Story Problem Description with Units Expression Evaluate the Expression if: Show your Work and Evaluate Robby has two more basketballs than his brother Michael. Let 𝒆 = the number of balls Michael has 𝒆 + 𝟐 Michael has 𝟕 basketballs. 𝒆 + 𝟐 𝟕 + 𝟐 𝟗 Robby has 𝟗 basketballs. Ella baked 𝟖 more cupcakes than Anna in the sixth grade. Anna baked 𝟏𝟎 cupcakes in the sixth grade. Lisa has been surfing for 𝟑 more years than Danika. Danika has been surfing for 𝟗 years. Mrs. Labuski went running yesterday. Now she has run 5 more miles than Bob. Write an expression to represent the number of miles Bob ran. Let m = the number of miles Mrs. Labuski ran. Write an expression to represent the number of miles Mrs. Labuski ran. Let b = the number of miles Bob ran. If Mrs. Labuski ran 8 miles, how many miles did Bob run?
2. 2. Module 4 Lesson 19 Substituting to Evaluate Addition and Subtraction Expressions Sara and Tiffany are in 6th grade and both take drum lessons at School of Rock Music Store. This is Sara’s first year, while this is Tiffany’s fifth year. Both girls plan to continue taking lessons throughout high school. a. Complete the table showing the number of years the girls will have been drumming at the music store. Grade Sara’s Years of Experience With Drums Tiffany’s Years of Experience With Drums Sixth Seventh Eighth Ninth Tenth Eleventh Twelfth b. If Sara has been taking drum lessons for 𝑦 years, what expression could represent how many years has Tiffany been taking lessons? c. If Tiffany has been taking drum lessons for x years, what expression could represent the number of years Sara has been taking lessons? 3. The elementary school Writer’s Club has 15 poets this year. The Writing Club instructor insists that there are to be 5 more essay writers than poets at all times. a. How many essay writers are in the Writer’s Club this year? b. Write two expressions that describes the relationship of the number of poets (𝑝) and the number of essay writers (𝑒). c. If there are only 12 essay writers interested in joining the Writer’s Club next year, how many poets will the Writing Club instructor want in the club?
3. 3. Module 4 Lesson 20 Writing and Evaluating Expressions – Multiplication and Division Joe earns \$75.00 per day. Create a table of values that shows the relationship between the number of days that Joe worked , d, and the amount of money that he earned, e. a. If we let d represent the number of days that Joe worked, what is the expression that shows how much money Joe earned. b. Use your expression to determine how much Joe earned if he worked 12 days. c. If let e represent how much money Joe earned, what is the expression that shows how many days he worked. d. Use your expression to determine how many days Joe worked if he earned \$600.00.
4. 4. Module 4 Lesson 21 Writing and Evaluating Expressions – Multiplication and Addition The PTA is planning a weekend field trip for its graduating seniors. The cost of the bus is \$350.00 for the weekend. In addition, each student will have to pay \$5 for the price of the trip. Complete the table below to calculate the amount of money the PTA will pay if ten seniors go on the trip. a. Write an expression that shows the amount of money the PTA collects if s number of students attend the trip. b. Use your expression to determine the amount of money the PTA would collect if 60 students attend the trip. Module 4 Lesson 22 Writing and Evaluating Expressions – Exponents Judah had two children. When those children grew up, each one also had two children, who later each had two children as well. If this pattern continues, how many children are there in the 5th generation? Generation Number of Children Number of Children written as a power of 2 a. Write an expression for how many children would be born after g generations. b. Use your expression to determine how many children would be born after 10 generations.
5. 5. Module 4 Lesson 23 True or False Number Sentences Substitute the value for the variable and state in a complete sentence whether the resulting number sentence is true or false. If true, find a value that would result in a false number sentence. If false, find a value that would result in a true number sentence. 18b ≥ 54. Substitute 3 for b. 28 + c = 35. Substitute 8 for c. 18 ≥ 33 – t. Substitute 15 for t. Module 4 Lesson 24 True of False Number Sentences. State whether the sentence is true or false. 56 – 14 < 48 33 ≥ 13 + 23 State when the following equations and inequalities will be true and when they will be false. 6r > 36 15 = 6 + d 32 – t < 18
6. 6. Module 4 Lesson 26 One Step Equations – Addition & Subtraction Find the solution of the equations using a tape diagram. Check your answer. p + 5 = 11 f – 8 = 10 Find the solution of the equations below algebraically. Check your answer. k – 29 = 54 46 + m = 100 46 = t – 4 n + 5 = 17 Module 4 Lesson 27 One Step Equations – Multiplication & Division Find the solution of the equations using a tape diagram. Check your answer. 4x = 20 3 m = 9
7. 7. Find the solution of the equation below algebraically. Check your answer. 7x = 35 12y = 60 5 h = 6 7 k = 2 Module 4 Lesson 28 Two-Step Problems – All Operations Find the solution of the equation below algebraically. Check your answer. x + 15 − 6 = 18 y + 9 +12 = 40 x + x =12 n + 2n = 9 Barry had 𝟓𝟎 doubles last season which is 𝟏𝟎 more than his best season. Willy had 8 more doubles than Derek last season. Willy had the same number of as Barry’s best season. Let 𝑏 represent the number of doubles Barry had during his best season, 𝑑 represent the number of Derek’s doubles last season, and 𝑤 represent the number of Willy’s doubles last season. How many doubles did Derek have last season?
8. 8. Lesson 29 Multi-Step Problems – All Operations Solve the problem using tables and equations, and then check your answer with the word problem. Try to find the answer only using two rows of numbers on your table. 1. The PE teachers are organizing supplies for this year’s field day. In order to have enough materials for all of the students, they need twice as many hula hoops as Frisbees. The number of flags required is ten times more than the number of hula hoops. The number of cones that is needed is half as many flags. If they have a total of 396 supplies, how many cones do they have? ANSWER: Flags Cones Frisbees Hula hoops total
9. 9. Name ____________________________________ Date ________________________ Mrs. Labuski / Mrs. Portsmore Period ________ Module 4 Lessons 18-29 Qz Review Module 4 Lesson 18 Writing and Evaluating Expressions – Addition and Subtraction Read the story problem. Identify the unknown quantity and write an addition or subtraction expression that is described. Then evaluate your expression given the further information. Story Problem Description with Units Expression Evaluate the Expression if: Show your Work and Evaluate Robby has two more basketballs than his brother Michael. Let 𝒆 = the number of balls Michael has 𝒆 + 𝟐 Michael has 𝟕 basketballs. 𝒆 + 𝟐 𝟕 + 𝟐 𝟗 Robby has 𝟗 basketballs. Ella baked 𝟖 more cupcakes than Anna in the sixth grade. Let c = the number of cupcakes Anna has c + 8 Anna baked 𝟏𝟎 cupcakes in the sixth grade. c + 8 10 + 8 18 Ella bakes 18 cupcakes Lisa has been surfing for 𝟑 more years than Danika. Let d = number of years Danika has been surfing d + 3 Danika has been surfing for 𝟗 years. d + 3 9 + 3 12 Lisa has been surfing for 12 years. Mrs. Labuski went running yesterday. Now she has run 5 more miles than Bob. Write an expression to represent the number of miles Bob ran. Let m = the number of miles Mrs. Labuski ran. m - 5 Write an expression to represent the number of miles Mrs. Labuski ran. Let b = the number of miles Bob ran. b + 5 If Mrs. Labuski ran 8 miles, how many miles did Bob run? m – 5 8-5 3 Bob ran 3 miles
10. 10. Module 4 Lesson 19 Substituting to Evaluate Addition and Subtraction Expressions Sara and Tiffany are in 6th grade and both take drum lessons at School of Rock Music Store. This is Sara’s first year, while this is Tiffany’s fifth year. Both girls plan to continue taking lessons throughout high school. a. Complete the table showing the number of years the girls will have been drumming at the music store. Grade Sara’s Years of Experience With Drums Tiffany’s Years of Experience With Drums Sixth 1 5 Seventh 2 6 Eighth 3 7 Ninth 4 8 Tenth 5 9 Eleventh 6 10 Twelfth 7 11 b. If Sara has been taking drum lessons for 𝑦 years, what expression could represent how many years has Tiffany been taking lessons? y + 4 c. If Tiffany has been taking drum lessons for x years, what expression could represent the number of years Sara has been taking lessons? x - 4 3. The elementary school Writer’s Club has 15 poets this year. The Writing Club instructor insists that there are to be 5 more essay writers than poets at all times. a. How many essay writers are in the Writer’s Club this year? 15 + 5 = 20 b. Write two expressions that describes the relationship of the number of poets (𝑝) and the number of essay writers (𝑒). p + 5 = e e – 5 = p c. If there are only 12 essay writers interested in joining the Writer’s Club next year, how many poets will the Writing Club instructor want in the club? e - 5 = p 12 - 5 = p 7 = p The instructor will want 7 poets.
11. 11. Module 4 Lesson 20 Writing and Evaluating Expressions – Multiplication and Division Joe earns \$75.00 per day. Create a table of values that shows the relationship between the number of days that Joe worked , d, and the amount of money that he earned, e. Number of Days Joe Worked, d Amount Earned, e, in Dollars 1 75 2 150 3 225 4 300 a. If we let d represent the number of days that Joe worked, what is the expression that shows how much money Joe earned. 75d b. Use your expression to determine how much Joe earned if he worked 12 days. 75d 75  12 900 Joe will earn \$900 if he works 12 days. c. If let e represent how much money Joe earned, what is the expression that shows how many days he worked. e ÷ 75 d. Use your expression to determine how many days Joe worked if he earned \$600.00. e ÷ 75 600 ÷ 75 8 Joe worked 8 days.
12. 12. Module 4 Lesson 21 Writing and Evaluating Expressions – Multiplication and Addition The PTA is planning a weekend field trip for its graduating seniors. The cost of the bus is \$350.00 for the weekend. In addition, each student will have to pay \$5 for the price of the trip. Complete the table below to calculate the amount of money the PTA will pay if ten seniors go on the trip. Number of Students on the Trip (s) Total Cost in Dollars (d) 1 355 2 360 3 365 4 370 5 375 6 380 7 385 8 390 9 395 10 400 a. Write an expression that shows the amount of money the PTA collects if s number of students attend the trip. 350 + 5s b. Use your expression to determine the amount of money the PTA would collect if 60 students attend the trip. 350 + 5s
13. 13. Module 4 Lesson 22 Writing and Evaluating Expressions – Exponents Judah had two children. When those children grew up, each one also had two children, who later each had two children as well. If this pattern continues, how many children are there in the 5th generation? Generation Number of Children Number of Children written as a power of 2 1 2 21 2 4 22 3 8 23 4 16 24 5 32 25 a. Write an expression for how many children would be born after g generations. 2g b. Use your expression to determine how many children would be born after 10 generations. 2g 210 1024 Module 4 Lesson 23 True or False Number Sentences Substitute the value for the variable and state in a complete sentence whether the resulting number sentence is true or false. If true, find a value that would result in a false number sentence. If false, find a value that would result in a true number sentence. 18b ≥ 54. Substitute 3 for b. True. Any value less than 3 will result in a false statement 28 + c = 35. Substitute 8 for c. False. The number 7 is the only value that will result in a true number sentence. 18 ≥ 33 – t. Substitute 15 for t. True. Any value 18 or greater will result in a true sentence. Module 4 Lesson 24 True of False Number Sentences. State whether the sentence is true or false. 56 – 14 < 48 True 33 ≥ 13 + 23 False
14. 14. State when the following equations and inequalities will be true and when they will be false. 6r > 36 This inequality is true for any value that is greater than 6 and false then the value is less than or equal to 6. 15 = 6 + d This equation is true when the value of d is 9 and false when the value is any other number. 32 – t < 18 This inequality is true for any value that is less than 14 and false then the value is greather than or equal to 14. Module 4 Lesson 26 One Step Equations – Addition & Subtraction Find the solution of the equations using a tape diagram. Check your answer. p + 5 = 11 f – 8 = 10 p = 6 p + 5 = 11 f – 8 = 10 6 + 5 = 11 18 – 8 = 10 11 + 11  10 = 10  𝒑 𝟓 𝟏𝟏 𝟔 𝟓 𝟏𝟏 𝟔 𝟓 𝒑 𝟓 𝒑 𝟔 𝒇 𝟖 𝟏𝟎 𝒇 𝟏𝟖 𝟖 𝟏𝟎 f = 18
15. 15. Find the solution of the equations below algebraically. Check your answer. k – 29 = 54 46 + m = 100 k – 29 + 29 = 54 + 29 46 + m – 46 = 100 – 46 k = 83 m = 54 check check k – 29 = 54 46 + m = 100 83 – 29 = 54 46 + 54 = 100 54 = 54  100 = 100  46 = t – 4 n + 5 = 17 46 + 4 = t – 4 + 4 n + 5 – 5 = 17 – 5 50 = t n = 12 check check 46 = t – 4 n + 5 = 17 46 = 50 – 4 12 + 5 = 17 46 = 46 17 = 17 Module 4 Lesson 27 One Step Equations – Multiplication & Division Find the solution of the equations using a tape diagram. Check your answer. 4x = 20 3 m = 9 x = 5 check check 4x = 20 3 m = 9 4(5) = 20 27 ÷ 3 = 9 20 = 20 9 = 9 𝒙 𝟓𝟓 𝟓𝟓 𝟐𝟎 𝒙𝒙 𝒙𝒙 𝟐𝟕 𝒎 𝒎 ÷ 𝟑 𝟗 𝒎 ÷ 𝟑𝒎 ÷ 𝟑 𝒎 ÷ 𝟑 𝟗𝟗 𝟗 𝒎
16. 16. Find the solution of the equation below algebraically. Check your answer. 7x = 35 12y = 60 7x ÷ 7 = 35÷ 7 12y ÷ 12 = 60 ÷ 12 x = 5 y = 5 check check 7x = 35 12y = 60 7(5) = 35 12(5) = 60 35 = 35  60 = 60 5 h = 6 7 k = 2 h ÷55 = 65 k÷ 77 = 27 h = 30 k = 14 check check h ÷5 = 6 k÷ 7 = 2 30 ÷5 = 6 14÷ 7 = 2 6 = 6 2 = 2 Module 4 Lesson 28 Two-Step Problems – All Operations Find the solution of the equation below algebraically. Check your answer. x + 15 − 6 = 18 y + 9 +12 = 40 x + 9 = 18 y + 21 = 40 x + 9 - 9= 18 - 9 y + 21 – 21 = 40 - 21 x = 9 y = 19 check check x + 15 − 6 = 18 y + 9 +12 = 40 9 + 15 − 6 = 18 19 + 9 +12 = 40 18 = 18 40 = 40 x + x =12 n + 2n = 9 2x = 12 3n = 9 2x ÷ 2 = 12÷ 2 3n ÷ 3 = 9 ÷ 3 x = 6 n = 3 check check x + x =12 n + 2n = 9 6 + 6 =12 3 + 2(3) = 9 12 = 12 3 + 6 = 9 9 = 9
17. 17. Barry had 𝟓𝟎 doubles last season which is 𝟏𝟎 more than his best season. Willy had 8 more doubles than Derek last season. Willy had the same number of as Barry’s best season. Let 𝑏 represent the number of doubles Barry had during his best season, 𝑑 represent the number of Derek’s doubles last season, and 𝑤 represent the number of Willy’s doubles last season . How many doubles did Derek have last season? Solution: Barry 50 b 10 Willy b d 8 Derek d Let’s Start with Barry b + 10 = 50 b + 10 – 10 = 50 – 10 b = 40 Now we can solve Willy’s tape diagram b = d + 8 40 = d + 8 40 – 8 = d + 8 – 8 32 = d Derek had 32 doubles
18. 18. Lesson 29 Multi-Step Problems – All Operations Solve the problem using tables and equations, and then check your answer with the word problem. Try to find the answer only using two rows of numbers on your table. 1. The PE teachers are organizing supplies for this year’s field day. In order to have enough materials for all of the students, they need twice as many hula hoops as Frisbees. The number of flags required is ten times more than the number of hula hoops. The number of cones that is needed is half as many flags. If they have a total of 396 supplies, how many cones do they have? ANSWER: Flags Cones Frisbees Hula hoops total 20 10 1 2 33 240 120 12 24 396 They will have a total of 120 cones. Let f represent the number of Frisbees. Therefore, 2f represents the number of hula hoops, and 20frepresents the number of flags and 10f represents the number of cones. f + 2f + 10f + 20 f = 396 33f = 396 33f ÷ 33 = 396 ÷ 33 f = 12 Therefore, the PE teachers have 120 cones because 10(12)=120