Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Chapter 4 Practice Test

____ 1. A group of 40 people takes the swan boat ride. Each boat can carry 6 people. If the guide fills as many boats as possible, how many people will ride in the last boat?

A. 34B. 7C. 6D. 4

____ 2. Vanna uses thank-you notes that come in packs of 8. She has to write 29 thank-you notes. How many packs of thank-you notes should she buy?

A. 3B. 3 5

8C. 4D. 5

____ 3. Nolan divides his 88 toy cars into boxes. Each box can hold 9 cars. How many boxes can Nolan fill?

A. 7B. 9C. 10D. 12

____ 4. Selim puts 30 ounces of trail mix equally into 9 bags. How many ounces will be in each bag?

A. 4 ouncesB. 3 1

3ounces

C. 3 ouncesD. 2 1

2ounces

5. The harbor master decides how many trips the ferry needs to make for 37 cars. The ferry can carry 8 cars at a time. The harbor master planned 4 trips. Will every car get a ride on the ferry? Explain your answer.

Name: ________________________ ID: A

2

____ 6. There are 112 seats in a school auditorium. There are 7 seats in each row. There are 70 people seated. They filled all the seats in a row before starting to sit in a new row. How many rows are empty?

A. 6B. 10C. 16D. 28

____ 7. Ursula bought 9 dozen gauze pads for the health office. The gauze pads were divided equally into 4 boxes. How many gauze pads are in each box?

A. 108B. 36C. 27D. 24

____ 8. The school choir has 48 singers with high voices, 53 singers with middle voices, and 39 singers with low voices. The singers stand in 4 equal rows at concerts. How many singers are in each row?

A. 140B. 45C. 35D. 34

____ 9. The are 126 seats in a meeting room. There are 9 seats in each row. There are 90 people seated. They filled all the seats in a row before starting to sit in a new row. How many rows are empty?

A. 36B. 10C. 9D. 4

10. An orchestra has 18 string players, 9 percussion players, 15 brass players, and 12 woodwind players. If all the players sit in rows of 9 chairs each, how many rows of chairs are needed? Explain your answer.

Name: ________________________ ID: A

3

____ 11. There are 9 showings of a film about endangered species at the science museum. A total of 458 people saw the film. About how many people were at each showing?

A. about 40B. about 50C. about 60D. about 90

____ 12. Kelli and her family went to the beach for a vacation. They drove 293 miles in 7 hours to get there. About how many miles did they drive each hour?

A. about 40 milesB. about 30 milesC. about 20 milesD. about 10 miles

____ 13. Between which two numbers is the quotient of 87 ÷ 5?

A. between 5 and 10B. between 10 and 15C. between 15 and 20D. between 20 and 25

____ 14. Between which two numbers is the quotient of 93 ÷ 5?

A. between 20 and 25B. between 15 and 20C. between 10 and 15D. between 5 and 10

15. A worker packed 192 bells into boxes that hold 3 bells each. Explain how to use multiples to estimate the number of boxes the worker will use.

Name: ________________________ ID: A

4

____ 16. Look at the model. What division does it show?

A. 6 ÷ 3B. 6 ÷ 4C. 18 ÷ 3D. 20 ÷ 3

____ 17. Ed used counters to model 4 19 . What quotient and remainder did he

find?

A. quotient: 5 remainder: 1B. quotient: 4 remainder: 3C. quotient: 4 remainder: 2D. quotient: 3 remainder: 7

____ 18. Margie arranged 40 counters into 6 groups of 6. There were 4 counters left over. What quotient and remainder did she model?

A. quotient: 7 remainder: 2B. quotient: 6 remainder: 5C. quotient: 6 remainder: 4D. quotient: 6 remainder: 2

____ 19. Look at the model. What division does it show?

A. 4 ÷ 3B. 12 ÷ 4C. 12 ÷ 3D. 13 ÷ 3

Name: ________________________ ID: A

5

20. Stefan says this quick picture shows 31 ÷ 4. Is he correct? What other division does the picture model? Explain.

____ 21. Taylor took 560 photographs while on summer vacation. She wants to place an equal number of photos in each of 7 albums. How many photos will Taylor place in each album?

A. 7B. 8C. 70D. 80

____ 22. Which number sentence is not true?

A. 200 ÷ 5 = 50B. 400 ÷ 8 = 50C. 2,000 ÷ 4 = 500D. 4,000 ÷ 4 = 1,000

____ 23. A crayon factory packs 5 crayons in a sample pack. The factory gives sample packs to visitors under 12. How many sample packs can be made with 2,500 crayons?

A. 5B. 50C. 500D. 5,000

____ 24. Bayshore Elementary students collected $3,200 for new library books. Each of the 8 classes collected the same amount. How much did each class collect?

A. $4,000B. $400C. $40D. $4

Name: ________________________ ID: A

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25. A factory packs 6 bars of soap into each family pack. Explain how to use basic facts and place value to find how many family packs can be made with 5,400 bars of soap.

____ 26. On Friday, 278 fourth graders went on a field trip to the Arizona State Museum. The staff divided them into 7 tour groups. Which is the best estimate of the number of students in each tour group?

A. 50B. 40C. 20D. 7

____ 27. Amanda and her four sisters divided 1,021 stickers equally. About how many stickers did each girl receive?

A. about 300B. about 250C. about 200D. about 100

____ 28. Use compatible numbers to estimate the quotient 531 ÷ 6. Which is the best estimate?

A. 9B. 90C. 900D. 9,000

____ 29. For Earth Day, 264 students helped out at a tree farm. The staff divided the students into 9 teams. Which is the best estimate of the number of students on each team?

A. 30B. 36C. 40D. 50

30. Mathias and his brother divided 2,029 marbles equally. About how many marbles did each of them receive? Explain how to use compatible numbers to solve.

Name: ________________________ ID: A

7

____ 31. Lakya is using the Distributive Property to divide 128 by 4. Which does not show a way she could break apart the dividend?

A. 128 ÷ 4 = (100 ÷ 4) + (28 ÷ 4)B. 128 ÷ 4 = (120 ÷ 4) + (8 ÷ 4)C. 128 ÷ 4 = (64 ÷ 4) + (64 ÷ 4)D. 128 ÷ 4 = (12 ÷ 4) + (28 ÷ 4)

____ 32. Dawn has 48 finger puppets in 3 baskets. Each basket has the same number of puppets. How many puppets are in each basket?

A. 14B. 15C. 16D. 18

____ 33. The Distributive Property can help you divide. Which is not a way to break apart the dividend to find the quotient of 132 ÷ 6?

A. (120 ÷ 6) + (12 ÷ 6)B. (100 ÷ 6) + (32 ÷ 6)C. (90 ÷ 6) + (42 ÷ 6)D. (72 ÷ 6) + (60 ÷ 6)

____ 34. Gordon took batting practice with a pitching machine. He hit 104 pitches in 8 minutes. If Gordon hit the same number of pitches, how many pitches did he hit each minute?

A. 12B. 13C. 14D. 15

35. Steve has 68 tulips to divide into vases. There will be 4 tulips in each vase. Explain a way to use the Distributive Property to find the number of vases Steve will need.

Name: ________________________ ID: A

8

____ 36. There are 60 people waiting for a river raft ride. Each raft holds 15 people. Which number sentence can be used to find how many rafts will be needed?

A. 60 − 15 − 15 − 15 − 15 = 0B. 60 − 15 = 45C. 60 + 15 = 75D. 60 − 30 − 15 = 15

____ 37. There are 48 people waiting for a fishing tour. Each tour boat holds 12 people. Which number sentence can be used to find how many boats will be needed?

A. 12 + 48 = 60B. 48 − 12 = 36C. 48 − 24 = 24D. 48 − 12 − 12 − 12 − 12 = 0

____ 38. Jessie has 80 rubber bracelets. She arranges the bracelets in piles of 4. Which model shows 80 ÷ 4?

A.

B.

C.

D.

Name: ________________________ ID: A

9

39. Explain how this model shows how to find a quotient and remainder.

____ 40. Keith wants to fill 9 pages of his photo album with the same number of photographs on each page. If Keith has 117 photographs, how many photographs will he put on each page?

A. 8B. 13C. 17D. 23

____ 41. Diego bought 488 frozen yogurt bars in 4 different flavors for a party. If he bought the same number of each flavor, how many of each flavor did Diego buy?

A. 221B. 211C. 122D. 62

____ 42. Three popcorn stores donated a total of 636 bags of popcorn for the school fair. If each store donated the same number of bags, how many bags of popcorn did each store donate?

A. 112B. 202C. 210D. 212

____ 43. Sam filled 6 toy boxes with the same number of toys in each box. If he had 144 toys, how many toys did he put in each toy box?

A. 150B. 24C. 22D. 14

Name: ________________________ ID: A

10

44. Laina and Frank used partial quotients to find the quotient 327 ÷ 3. Laina’s quotient is 19, but Frank’s quotient is 109. Who is correct? Explain.

____ 45. Zack needs to divide these base-ten blocks into 3 equal groups.

Which model shows how many should be in each equal group?

A.

B.

C.

D.

Name: ________________________ ID: A

11

____ 46. Emily earned $72 in 6 days walking dogs. She earned the same amount each day. How much did she earn each day?

A. $22B. $14C. $13D. $12

____ 47. Ethan needs to divide these base-ten blocks into 3 equal groups.

Which model shows how many should be in each equal group?

A.

B.

C.

D.

Name: ________________________ ID: A

12

____ 48. Zora blinked her eyes 96 times in 4 minutes. She blinked the same number of times each minute. How many times did Zora blink in one minute?

A. 22B. 23C. 24D. 25

49. Before finding 80 ÷ 5, Tess said she will need to regroup tens. Do you agree? Explain.

____ 50. Jake writes a division problem to find out how he can distribute 543 marbles among 7 of his friends. In what place is the first digit of the quotient?

A. thousandsB. hundredsC. tensD. ones

____ 51. Sylvia plans to place 617 stamps in an album. Each page of the album holds 5 stamps. She uses division to find out how many full pages she will have. In what place is the first digit of the quotient?

A. hundredsB. onesC. tensD. thousands

____ 52. Jim will use division to find out how he can distribute 750 coupon books among 9 stores. In what place is the first digit of the quotient?

A. onesB. tensC. hundredsD. thousands

Name: ________________________ ID: A

13

____ 53. Hilda wants to save 825 digital photographs in an online album. Each folder of the online album can save 6 photographs. She uses division to find out how many full folders she will have. In what place is the first digit of the quotient?

A. onesB. tensC. hundredsD. thousands

54. Explain in which place you will write the first digit of the quotient 312 ÷ 5.

____ 55. Students made large soap bubbles at a party. They used 224 ounces of dish soap to make the bubble mixture. The dish soap came in 4 containers of the same size. How many ounces of dish soap were in each container?

A. 51 ouncesB. 55 ouncesC. 56 ouncesD. 66 ounces

____ 56. A toy manufacturer has 627 yo-yos to divide equally among 3 stores. How many yo-yos will each store receive?

A. 29B. 209C. 219D. 309

____ 57. Students are making pizza. They put a total of 108 ounces of cheese on 9 pizzas. Each pizza has the same amount of cheese. How many ounces of cheese are on each pizza?

A. 15 ouncesB. 14 ouncesC. 13 ouncesD. 12 ounces

Name: ________________________ ID: A

14

____ 58. A store gave away 1,932 calendars in 7 days. They gave away the same number of calendars each day. How many calendars did the store give away each day?

A. 276B. 281C. 286D. 776

59. An office supply store packed 416 notepads with the same number in each of 4 boxes. Milo said there are exactly 100 notepads in each box. Do you agree? Explain.

ID: A

1

Chapter 4 Practice TestAnswer Section

1. ANS: D PTS: 1 DIF: average REF: Lesson 6: Interpret the Remainder OBJ: Use remainders to solve division problems. NAT: CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. TOP: Use the four operations with whole numbers to solve problems.KEY: remainder | divisor | dividend | quotient NOT: Operations and Algebraic Thinking

2. ANS: C PTS: 1 DIF: average REF: Lesson 6: Interpret the Remainder OBJ: Use remainders to solve division problems. NAT: CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. TOP: Use the four operations with whole numbers to solve problems.KEY: remainder | divisor | dividend | quotient NOT: Operations and Algebraic Thinking

3. ANS: B PTS: 1 DIF: average REF: Lesson 6: Interpret the Remainder OBJ: Use remainders to solve division problems. NAT: CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. TOP: Use the four operations with whole numbers to solve problems.KEY: remainder | divisor | dividend | quotient NOT: Operations and Algebraic Thinking

ID: A

2

4. ANS: B PTS: 1 DIF: average REF: Lesson 6: Interpret the Remainder OBJ: Use remainders to solve division problems. NAT: CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. TOP: Use the four operations with whole numbers to solve problems.KEY: remainder | divisor | dividend | quotient NOT: Operations and Algebraic Thinking

5. ANS: No; Possible explanation: 37 ÷ 8 is 4 r5. The remainder, 5, represents the number of cars that will be left without a ride. The harbor master needs to plan 5 rides for every car to go on the ferry.

PTS: 1 DIF: average REF: Lesson 6: Interpret the Remainder OBJ: Use remainders to solve division problems. NAT: CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. TOP: Use the four operations with whole numbers to solve problems.KEY: remainder | divisor | dividend | quotient NOT: Operations and Algebraic Thinking

6. ANS: A PTS: 1 DIF: average REF: Lesson 7: Problem Solving • Multistep Division ProblemsOBJ: Solve problems by using the strategy draw a diagram. NAT: CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. TOP: Use the four operations with whole numbers to solve problems.NOT: Operations and Algebraic Thinking

ID: A

3

7. ANS: C PTS: 1 DIF: average REF: Lesson 7: Problem Solving • Multistep Division ProblemsOBJ: Solve problems by using the strategy draw a diagram. NAT: CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. TOP: Use the four operations with whole numbers to solve problems.NOT: Operations and Algebraic Thinking

8. ANS: C PTS: 1 DIF: average REF: Lesson 7: Problem Solving • Multistep Division ProblemsOBJ: Solve problems by using the strategy draw a diagram. NAT: CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. TOP: Use the four operations with whole numbers to solve problems.NOT: Operations and Algebraic Thinking

9. ANS: D PTS: 1 DIF: average REF: Lesson 7: Problem Solving • Multistep Division ProblemsOBJ: Solve problems by using the strategy draw a diagram. NAT: CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. TOP: Use the four operations with whole numbers to solve problems.NOT: Operations and Algebraic Thinking

ID: A

4

10. ANS: 6 rows; Possible explanation: I added 18 + 9 + 15 + 12 = 54 to find the total number of people. Then I divided 54 by 9 to find the number of rows of chairs needed, 6.

PTS: 1 DIF: average REF: Lesson 7: Problem Solving • Multistep Division ProblemsOBJ: Solve problems by using the strategy draw a diagram. NAT: CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. TOP: Use the four operations with whole numbers to solve problems.NOT: Operations and Algebraic Thinking

11. ANS: B PTS: 1 DIF: average REF: Lesson 37: Estimate Quotients Using Multiples OBJ: Use multiples to estimate quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: multiple | counting numberNOT: Number and Operations in Base Ten

12. ANS: A PTS: 1 DIF: average REF: Lesson 37: Estimate Quotients Using Multiples OBJ: Use multiples to estimate quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: multiple | counting numberNOT: Number and Operations in Base Ten

ID: A

5

13. ANS: C PTS: 1 DIF: average REF: Lesson 37: Estimate Quotients Using Multiples OBJ: Use multiples to estimate quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: multiple | counting numberNOT: Number and Operations in Base Ten

14. ANS: B PTS: 1 DIF: average REF: Lesson 37: Estimate Quotients Using Multiples OBJ: Use multiples to estimate quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: multiple | counting numberNOT: Number and Operations in Base Ten

15. ANS: Possible explanation: I think of numbers multiplied by 3 that have products close to 192. 60 × 3 = 180, which is less than 192, and 70 × 3 = 210, which is greater than 192. I estimate 60 boxes because 192 is closer to 180 than to 210.

PTS: 1 DIF: average REF: Lesson 37: Estimate Quotients Using Multiples OBJ: Use multiples to estimate quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: multiple | counting numberNOT: Number and Operations in Base Ten

ID: A

6

16. ANS: D PTS: 1 DIF: average REF: Lesson 38: Investigate • Remainders OBJ: Use models to divide whole numbers that do not divide evenly.NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: remainder | divisor | dividend | quotient NOT: Number and Operations in Base Ten

17. ANS: B PTS: 1 DIF: average REF: Lesson 38: Investigate • Remainders OBJ: Use models to divide whole numbers that do not divide evenly.NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: remainder | divisor | dividend | quotient NOT: Number and Operations in Base Ten

18. ANS: C PTS: 1 DIF: average REF: Lesson 38: Investigate • Remainders OBJ: Use models to divide whole numbers that do not divide evenly.NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: remainder | divisor | dividend | quotient NOT: Number and Operations in Base Ten

ID: A

7

19. ANS: D PTS: 1 DIF: average REF: Lesson 38: Investigate • Remainders OBJ: Use models to divide whole numbers that do not divide evenly.NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: remainder | divisor | dividend | quotient NOT: Number and Operations in Base Ten

20. ANS: Yes, 31 ÷ 4 is 7 with a remainder of 3; Possible explanation: Stefan divided 31 circles into 4 equal groups, with 3 left over. The picture also shows 31 circles put into groups of 7. There are 3 left over showing 31 ÷ 7 is 4 with a remainder of 3.

PTS: 1 DIF: average REF: Lesson 38: Investigate • Remainders OBJ: Use models to divide whole numbers that do not divide evenly.NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: remainder | divisor | dividend | quotient NOT: Number and Operations in Base Ten

ID: A

8

21. ANS: D PTS: 1 DIF: average REF: Lesson 39: Divide Tens, Hundreds, and Thousands OBJ: Divide tens, hundreds, and thousands by whole numbers through 10. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

22. ANS: A PTS: 1 DIF: average REF: Lesson 39: Divide Tens, Hundreds, and Thousands OBJ: Divide tens, hundreds, and thousands by whole numbers through 10. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

23. ANS: C PTS: 1 DIF: average REF: Lesson 39: Divide Tens, Hundreds, and Thousands OBJ: Divide tens, hundreds, and thousands by whole numbers through 10. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

ID: A

9

24. ANS: B PTS: 1 DIF: average REF: Lesson 39: Divide Tens, Hundreds, and Thousands OBJ: Divide tens, hundreds, and thousands by whole numbers through 10. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

25. ANS: Possible explanation: I think of 5,400 as 54 hundreds. I know 54 ÷ 6 = 9, so 54 hundreds divided by 6 is 9 hundreds, or 900. So, 900 family packs can be made with 5,400 bars of soap.

PTS: 1 DIF: average REF: Lesson 39: Divide Tens, Hundreds, and Thousands OBJ: Divide tens, hundreds, and thousands by whole numbers through 10. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

26. ANS: B PTS: 1 DIF: average REF: Lesson 40: Estimate Quotients Using Compatible NumbersOBJ: Use compatible numbers to estimate quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: compatible numbersNOT: Number and Operations in Base Ten

ID: A

10

27. ANS: C PTS: 1 DIF: average REF: Lesson 40: Estimate Quotients Using Compatible NumbersOBJ: Use compatible numbers to estimate quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: compatible numbersNOT: Number and Operations in Base Ten

28. ANS: B PTS: 1 DIF: average REF: Lesson 40: Estimate Quotients Using Compatible NumbersOBJ: Use compatible numbers to estimate quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: compatible numbersNOT: Number and Operations in Base Ten

29. ANS: A PTS: 1 DIF: average REF: Lesson 40: Estimate Quotients Using Compatible NumbersOBJ: Use compatible numbers to estimate quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: compatible numbersNOT: Number and Operations in Base Ten

ID: A

11

30. ANS: Possible explanation: Compatible numbers are numbers that are easy to work with mentally. I can think of multiples of 2: 2; 20; 200; 2,000. 2,029 is close to 2,000, so each brother received about 1,000 marbles.

PTS: 1 DIF: average REF: Lesson 40: Estimate Quotients Using Compatible NumbersOBJ: Use compatible numbers to estimate quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: compatible numbersNOT: Number and Operations in Base Ten

31. ANS: D PTS: 1 DIF: average REF: Lesson 41: Investigate • Division and the Distributive PropertyOBJ: Use the Distributive Property to find quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: Distributive PropertyNOT: Number and Operations in Base Ten

32. ANS: C PTS: 1 DIF: average REF: Lesson 41: Investigate • Division and the Distributive PropertyOBJ: Use the Distributive Property to find quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: Distributive PropertyNOT: Number and Operations in Base Ten

ID: A

12

33. ANS: B PTS: 1 DIF: average REF: Lesson 41: Investigate • Division and the Distributive PropertyOBJ: Use the Distributive Property to find quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: Distributive PropertyNOT: Number and Operations in Base Ten

34. ANS: B PTS: 1 DIF: average REF: Lesson 41: Investigate • Division and the Distributive PropertyOBJ: Use the Distributive Property to find quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: Distributive PropertyNOT: Number and Operations in Base Ten

35. ANS: Possible explanation: You need to divide 68 by 4. To divide 68 ÷ 4, you can rename 68 as 36 + 32. Then you can use 68 ÷ 4 = (36 ÷ 4) + (32 ÷ 4), which is 9 + 8. So, 68 ÷ 4 = 17.

PTS: 1 DIF: average REF: Lesson 41: Investigate • Division and the Distributive PropertyOBJ: Use the Distributive Property to find quotients. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: Distributive PropertyNOT: Number and Operations in Base Ten

ID: A

13

36. ANS: A PTS: 1 DIF: average REF: Lesson 42: Investigate • Divide Using Repeated SubtractionOBJ: Use repeated subtraction and multiples to find quotients.NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

37. ANS: D PTS: 1 DIF: average REF: Lesson 42: Investigate • Divide Using Repeated SubtractionOBJ: Use repeated subtraction and multiples to find quotients.NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

38. ANS: C PTS: 1 DIF: average REF: Lesson 42: Investigate • Divide Using Repeated SubtractionOBJ: Use repeated subtraction and multiples to find quotients.NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

ID: A

14

39. ANS: Possible explanation: the model shows 29 ÷ 5 is 5 with a remainder of 4. You begin at 29 and make jumps of 5 backward to subtract until you can no longer subtract 5. The number of jumps is the quotient. The number you land on is the remainder.

PTS: 1 DIF: average REF: Lesson 42: Investigate • Divide Using Repeated SubtractionOBJ: Use repeated subtraction and multiples to find quotients.NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

40. ANS: B PTS: 1 DIF: average REF: Lesson 43: Divide Using Partial Quotients OBJ: Use partial quotients to divide. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: partial quotient NOT: Number and Operations in Base Ten

41. ANS: C PTS: 1 DIF: average REF: Lesson 43: Divide Using Partial Quotients OBJ: Use partial quotients to divide. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: partial quotient NOT: Number and Operations in Base Ten

ID: A

15

42. ANS: D PTS: 1 DIF: average REF: Lesson 43: Divide Using Partial Quotients OBJ: Use partial quotients to divide. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: partial quotient NOT: Number and Operations in Base Ten

43. ANS: B PTS: 1 DIF: average REF: Lesson 43: Divide Using Partial Quotients OBJ: Use partial quotients to divide. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: partial quotient NOT: Number and Operations in Base Ten

44. ANS: Frank; Possible explanation: Frank used 100 as the first partial quotient (100 × 3 = 300) and 9 as the next partial quotient (9 × 3 = 27). When you add the partial quotients, 100 + 9 = 109. Laina’s error may have been that she recorded 10 instead of 100 as the partial quotient.

PTS: 1 DIF: average REF: Lesson 43: Divide Using Partial Quotients OBJ: Use partial quotients to divide. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. KEY: partial quotient NOT: Number and Operations in Base Ten

ID: A

16

45. ANS: A PTS: 1 DIF: average REF: Lesson 44: Investigate • Model Division with RegroupingOBJ: Use base-ten blocks to model division with regrouping. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

46. ANS: D PTS: 1 DIF: average REF: Lesson 44: Investigate • Model Division with RegroupingOBJ: Use base-ten blocks to model division with regrouping. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

47. ANS: B PTS: 1 DIF: average REF: Lesson 44: Investigate • Model Division with RegroupingOBJ: Use base-ten blocks to model division with regrouping. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

ID: A

17

48. ANS: C PTS: 1 DIF: average REF: Lesson 44: Investigate • Model Division with RegroupingOBJ: Use base-ten blocks to model division with regrouping. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

49. ANS: Yes. Possible explanation: using base-ten blocks, divide 8 tens by placing 1 ten in each of 5 groups. You cannot divide the 3 tens left into 5 groups, so you regroup 3 tens as 30 ones. You can put 6 ones in each group. So 80 ÷ 5 = 1 ten 6 ones, or 16.

PTS: 1 DIF: average REF: Lesson 44: Investigate • Model Division with RegroupingOBJ: Use base-ten blocks to model division with regrouping. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

50. ANS: C PTS: 1 DIF: average REF: Lesson 45: Place the First Digit OBJ: Use place value to determine where to place the first digit of a quotient. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

ID: A

18

51. ANS: A PTS: 1 DIF: average REF: Lesson 45: Place the First Digit OBJ: Use place value to determine where to place the first digit of a quotient. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

52. ANS: B PTS: 1 DIF: average REF: Lesson 45: Place the First Digit OBJ: Use place value to determine where to place the first digit of a quotient. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

53. ANS: C PTS: 1 DIF: average REF: Lesson 45: Place the First Digit OBJ: Use place value to determine where to place the first digit of a quotient. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

ID: A

19

54. ANS: Possible explanation: look at the hundreds in 312. There are not enough hundreds to divide by 5, so regroup hundreds as tens. The first digit of the quotient will be in the tens place.

PTS: 1 DIF: average REF: Lesson 45: Place the First DigitOBJ: Use place value to determine where to place the first digit of a quotient. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

55. ANS: C PTS: 1 DIF: average REF: Lesson 46: Divide by 1-Digit Numbers OBJ: Divide multidigit numbers by 1-digit divisors. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

56. ANS: B PTS: 1 DIF: average REF: Lesson 46: Divide by 1-Digit Numbers OBJ: Divide multidigit numbers by 1-digit divisors. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

ID: A

20

57. ANS: D PTS: 1 DIF: average REF: Lesson 46: Divide by 1-Digit Numbers OBJ: Divide multidigit numbers by 1-digit divisors. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

58. ANS: A PTS: 1 DIF: average REF: Lesson 46: Divide by 1-Digit Numbers OBJ: Divide multidigit numbers by 1-digit divisors. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten

59. ANS: I disagree; Possible explanation: I can use multiplication to check division. 4 × 100 = 400. There are still 16 notepads that Milo’s answer does not include. 416 ÷ 4 = 104. Check: 4 × 104 = 416.

PTS: 1 DIF: average REF: Lesson 46: Divide by 1-Digit Numbers OBJ: Divide multidigit numbers by 1-digit divisors. NAT: CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. TOP: Use place value understanding and properties of operations to perform multi-digit arithmetic. NOT: Number and Operations in Base Ten