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5th Grade PMIAlgebraic Concepts Classwork and HomeworkOrder of OperationsClassworkSimplify by using the Order of Operations. 14 – 7 x 2 8 + 9 – 2 9 – 5 – 8 ÷ 2 4 x 13 + 51 ÷ 3 8 x 2 – 2 – 7 28 – 4 ÷ 2 4 + 11 x 5 - 4 17 + 48 ÷ 3 – 7HomeworkSimplify by using the Order of Operations.20 + 7 x 157 x 5 + 312 – 3 + 10 x 367 – 3 x 19 – 47 - 7 + 9 x 1038 – 6 ÷ 25 x 9 – 10 ÷ 558 – 8 – 10 ÷ 10 – 6Grouping Symbols ClassworkSimplify by using the Order of Operations. (12 – 7) x 2 8 + (9 – 2) (9 – 5) – (8 ÷ 2) 4 x 13 + 51 ÷ 3 (8 x 2 – 2) – 7 [(28 – 4) ÷ 2] [4 x (11 – 5)] + 4 [(48 – 3) + 5] ÷ (17 – 7) 2 x [(14 – 5) + (10 ÷ 2)]{3 + [(15 x 2) – 11]}{[6 x (20 – 5 x 3)] + 9}{[9 x (2 + 9) – 5]} x 4Which expression equals 132? (12 x 2) + 8 or 12 x (2 + 8)HomeworkSimplify by using the Order of Operations.(20 + 7) – 157 x (5 + 3)(12 – 3) + (10 x 3)67 – 3 x 19 – 4(7 x 7 – 9) – 10[(38 – 2) ÷ 6][5 x (9 – 4)] – 5[(58 – 8) – 10] ÷ (10 – 6) 5 x [(10 – 4) + (15 ÷ 3)]{2 + [(20 x 2) – 10]}{[7 x (10 – 5 x 2)] + 14{[10 x ( 7 – 5 + 1)]} – 15Which expression equals 142 (50 – 5) x 3 + 7 or 50 – 5 x (3 + 7)Writing & Interpreting ExpressionsClassworkWrite the algebraic expression for each phrase.16 less than 4the sum of 3 and 15the quotient of 36 and 18ten increased by nineseven times two and a half21 divided by 350 decreased by 2920 divided by 417 less than the product of 3 and 2the quotient of 8 divided by two minus fourWrite a phrase for each algebraic expression.90 – 44279 + 330 ÷ 636 – 42(1/4) HomeworkWrite the algebraic expression for each phrase.4 subtracted from 821 plus 99the quotient of 400 and 20sixteen increased by fivedouble one-half20 divided by 5forty-five decreased by forty55 divided by 11six times the sum of three and twoThe quotient of twenty-one and by seven minus tenWrite a phrase for each algebraic expression.100 – 72457 + 1424 ÷ 898 – 03(5)Writing & Interpreting Expressions Application ProblemsClassworkA company rents bicycles for a fee of $10 plus $4 per hour of use. Write an algebraic expression for the total cost in dollars for renting a bicycle for eight hours.The female lion at a zoo weights 190 pounds more than the female cheetah. Let c represent the weight in pounds of the cheetah. Which expression gives the weight in pounds of the lion? a. c +190c. 190 – c b. c–190d.190cTickets to a play cost $8 each. Which expression gives the ticket cost in dollars for a group of g girls and b boys?a. 8+(g+b)c. 8+(gxb) b. 8x(g+b)d. 8x(gxb)Write a scenario that can be represented by the expression 2 (8 + 4).___________________________________________________________________________________________________________________________________________________________________________HomeworkChoose the correct expression to solve the problem. Mark is 71 inches tall. Suzanne is 7 inches shorter than Mark. Write an expression that represents Suzanne’s height in inches.A subway train has 5 cars. Each car can carry 125 passengers. Which expression gives the number of passengers the train can carry?a. 125 + 5c.125 x 5 b.125 – 5d.125 ÷ 5Nessa and Lisa share lemonade and an order of nachos. Lemonade costs $2 and nachos cost $6. Which expression gives the amount in dollars each girl will pay if they split the cost evenly?a.2 + (6 x 2) b.(2 + 6) x 2 c.2 + (6 ÷ 2) d.(2 + 6) ÷ 2Write a scenario that can be represented by the expression 2 (8 + 4).___________________________________________________________________________________________________________________________________________________________________________Function TablesClassworkComplete each input(x) output(y) table using rule given. Rule: Add 8Input (x)Output (y)081923114Rule: Multiply 4Input (x)Output (y)14166832101248 Rule: Divide by 5Input (x)40302010Output (y)864 Rule: Subtract 9Input (x)1014309Output (y)15 Rule: Multiply 2, then Add 3Input (x)35791113Output (y)91725HomeworkComplete each input (x) output (y) table using rule given. Rule: Subtract 4Input (x)Output (y)20162521303531 Rule: Divide by 10Input (x)Output (y)101202340Rule: Multiply 8Input (x)1357Output (y)245672 Rule: Add 12Input (x)3691215Output (y)15182430 Rule: Divide by 3, then Subtract 2Input (x)306090120150180Output (y)8182848Rule: Multiply 20Input (x)29710Output (y)4010018060140ClassworkStudy the table; choose the correct function.XY113315517719 y = x + 2 y = x + 12 y = 2x XY61122183244 y = x ÷ 6 y = x + 1 y = 6xxY91871461236 y = x – 6 y = 2x y = x ÷ 2 x2024283236y1721252933y = x – 3y = x + 3y = x + 4x410272y14328238 y = 10x – 4 y = 3x + 2 y = 2x + 3Write an equation using the table, and answer the question.Boxes (b)Animals (a)142831241652010?Equation: __________________________________If each gift box contained 4 stuffed animals, what would be the number of animals in ten gift boxes? ___________________________Videos (v)12456Cost (c)5102025?Equation: __________________________________Redbox video rental charges $5 to rent a video. What is the total cost to rent six videos? _________________________The table below shows the number of cards in Flipe’s baseball card collection each week.Given the rule add 2 and starting at zero complete the table below.02The table below shows the number of cards in Ryan’s baseball card collection each week.Given the rule add 4 and starting at zero complete the table below.02Look at both of the tables once they are complete. Explain the relationship between the corresponding terms, and how you can use that to compare Flipe and Ryan’s baseball card collections. _________________________________________________________________________________________________________________________________________________________________________________________________________HomeworkStudy the table; choose the correct function.xY10612814101612 y = x – 4 y = x + 2 y = x – 2XY21426384 y = x + 1 y = x ÷ 2 y = 2xXY144169361248 y = 3x y = 4x y = x + 4 x3691215y1316192225 y = x - 10 y = x + 3 y = x + 10 x41571030y426101656 y = 4x – 2 y = 2x – 4 y = 2x Write an equation using the table, and answer the question.Number of Tricycles (t)Number of Wheels (w)1326394125?618Equation:______________________If one tricycle has 3 wheels, how many wheels are there for five tricycles? Length of call in minutes (L)12345Cost of call (C)?$2.50$3.75$5.00$6.25Equation: __________________________________The table shows the relationship between the length of a phone call in minutes and the cost of the call. What is the cost of one minute? The table below shows the number of minutes until the next #33 city bus arrives.Given the rule add 12 and starting at 0, complete the pattern below.0, ____, ____, ____, …The table below shows the number of minutes until the next #24 city bus arrives.Given the rule add 6 and starting at 0, complete the pattern below.0, ____, ____, ____, …Look at both of the patterns once they are complete. Explain the relationship between the corresponding terms, and how you can use that to compare the frequency of each bus’ arrival. _________________________________________________________________________________________________________________________________________________________________________________________________________Graphing Patterns & Relationships in the Coordinate PlaneClassworkWhich ordered pair is on the graph of the function represented by this table?Week (x)0123$ Saved (y)25303540A (25, 0)B (35, 2)C (2, 35) 457200-457200 228600-114300 397510-252095460115-236846 Which best describes the relationship between the cost of cooling a home and the outside temperature?A. Horizontal lineB. An increasing straight lineC. A decreasing straight lineD. Vertical line2514600185420Graph the following points on line a and b. Label each line. Line a Line b (1,2) (1,3) (2,4) (2,4) (3,6) (3,5) (4,8) (4,6Compare line a and line b from the previous problem. Explain the difference between the rule for line a and the rule for line b.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________HomeworkComplete the following. Which ordered pair is on the graph of the function represented by this table?Gallon of gas (x)0123Distance in miles (y)055075 (3, 50) (1, 25) (75, 3) 457200-228600 576545221980 2514600185420Graph the following points on line a and b. Label each line. Line a Line b (1,2) (1,0.5) (2,4) (2,1) (3,6) (3,1.5) (4,8) (4,2) Compare line a and line b from the previous problem. Explain the relationship between the y-coordinates in line a to the corresponding coordinates in line b.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Algebraic Concepts Unit Review Multiple Choice Questions Evaluate (7 - 3) + 18a. -14b. 22c. -8d. 4Evaluate 25 - (4 ÷ 2) a. 10.5b. 27c. 23d. 19 Evaluate (9 x 8) + (3 x 7) a. 93b. 693c. 83d. 35Evaluate 1 x (5 + 13) x 3a. 54b. 18c. 44d. 28Evaluate 63 ÷ (3 + 4)a. 19b. 25c. 7d. 9 According to order of operations, what would come first? a. multiplicationb. subtractionAccording to order of operations, what would come first?a. multiplicationb. exponentsc. additionWhich expression equals 0?a. 64 ÷ 8 - 2 x 4 b. (64 ÷ 8 - 2) x 4 c. 64 ÷ (8 - 2 x 4) d. 64 ÷ (8 - 2) x 4Which expression equals 16? a. 45 ÷ 9 + (3 x 2)b. 45 ÷ (9 + 3) x 2 c. (45 ÷ 9 + 3) x 2 d. 45 ÷ 9 + 3 x 2 What expression equals 33?a. {[5 x (4 + 3) - 2] ÷ 1} b. (5 x 4) + [3 - 2] ÷ 1) c. {5 x [4 + 3 - (2 ÷ 1)]} d. [5 x 4 + {3 - 2} ÷ 1] Which phrase is the correct algebraic expression: five more than 7a. 7 + 5 b. 5 + 7 c. 7 - 5 d. 5(7) Which phrase is the correct algebraic expression: three times the difference four less than five a. 3(4 - 5)b. 3(5) - 4c. 3(5 - 4)d. 12 - 5 The phrase 13 less than four, is the same as 13 - 4.a. True b. FalseThe phrase 72 ÷ 6 is the same as seventy-two divided by six. a. True b. False For a school project, 3 students each did the same amount of parts for the project. There were 12 parts in all. Which expression represents how many parts each student was responsible for? a. 12 3b. 3 + 12 c. 3 x 12 d. 12 - 3 Which graph shows the correct function?y = x + 3A. B.Which graph shows the correct function?y = 3x + 1A. B. Which of the following points is on the line? a. (4,2) b. (0,1) c. (2,4) d. (3,4) Which of the following points is on the line? a. (-1,-3) b. (-3, -1)c. (1, 3)d. (-1, 3) Which of the following points is on the line? a. (1, 2)b. (2, 1) c. (0, 2)d. (2, -1) Short Constructed Response Questions 7 + 2 x (5 - 6) = ___________________(12 + 3) ÷ 5 x 8 = ___________________4 x (22 -11) + 16 =___________________ ( 6 x 4 - 0) - 6 = _____________________Evaluate the expression. Rewrite each step. 81 - [(6 x 3) + (5 x 2)] 6 x [(9 ÷ 3) + 17] 20 + {12 x [(17 - 2) - (6 + 2)]} Write an expression to represent the following problems:Sophia bought three of each kind of candy in the sweet shop. If there were 21 kinds of candy in the sweet shop, how many pieces of candy did Sophia buy? _____________________________________________In the pizzeria, Lewis sold nine fewer pizzas then Anthony. If Anthony sold 18 pizzas, how many pizzas did Lewis sell? _____________________________________________Lucky collected 18 new stamps for his collection. If he had 72 yesterday, how many stamps are in the collection now?_____________________________________________Kushboo exercised 2 times a day for 1 week. How many times did Kushboo work out?_____________________________________________Write a function or rule for the following tables: xy 172839410xy00598152345xy6512818112414Extended Constructed Response Questions What is the correct order of operations? (Include grouping symbols)Simplify. {3 + [(6 + 4) ÷ 2] - 1} - {60 -[22 +4(3 x 3)]} xy241462081032What are the missing values in the table?What is the rule for this function?Graph the function. What would the value of x be if y was 44? Complete the Function Table by folllowing the rules given for each table. Rule: Multiply by ? Input (x)Output (y)0123 Rule: Multiply by 2Input (x)Output (y)0123Graph and label the coordinate pairs from Table A. Connect the points and label the line a. Graph and label the coordinate pairs from Table B. Connect the points and label the line b.Describe the relationship between the y-coordinates in Table A and Table B that have the same x-coordinate._________________________________________________________________________________________________________________________________________________________________________________Answer Key Algebraic Concepts 0 15 0 69 12 26 55 26 125 38 39 6 90 35 43 43101506971228528223937612 x (2 + 8)1256396301201055321415(50 – 5) x 3 + 74 – 163 + 1536 ÷ 1810 + 97(2 ?) 21 ÷ 350 – 2920 ÷ 4[3(2)] - 17(8 ÷ 2) – 490 decreased by 44279 and 3 moreThe quotient of 30 and 636 decreased by 4Double one-fourth82 – 41 + 99400 ÷ 2016 + 52(1/2)20 ÷ 545 – 4055 ÷ 116 x (3 + 2)(21 ÷ 7) -10100 reduced by 7214 more than 457The quotient of 24 and 898 decreased by 03 times 510(8) + 4 A BAnswers will vary 71 – 7 C DAnswers will vary10 / 124 / 24 / 40221 / 013 / 212630 / 48 / 40 / 921 / 27 / 1838 / 585 / 3 / 200BABABY = 4x 40Y = 5x 30 12341234512344567The values in the 2nd table are 2 more than the corresponding values in the 1st table. This means that, each week, Ryan has 2 more cards in his collection than Flipe. ABBCBY = 3x 15Y = 1.25x $1.25 0, 12, 24, 36, … 0, 6, 12, 18, …The values in the 2nd pattern are 1/2 of the corresponding values in the 1st pattern. This means that, the #24 bus comes twice as often as the #33 bus. CCGraph AGraph ATable AB The difference is the operation. The rule for line a is times 2, while the rule for line b is add 2.BAGraph AThe y-coordinates in line b are ? the value of the corresponding coordinates in line a. Table BAnswer Key – Unit Review bca a dabccaac baabaca b 5246018 53120104 3x2118 – 971 + 182(7) y = x + 6 y = 2x - 1 y = x/2 + 2 or y = 1/2x + 2 p md as, 5 a = 8 b = 26 rule: y = 3x + 2 graph of rule The y-coordinates in Table B are 4 times bigger than those in Table A. ................
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