Name Use Partial 6.5 Quotients to Learning Target: Use an ...

6.56.5Name Use PartialUse Partial

Quotients toQuotients toDivide byDivide byTwo-DigitTwo-DigitNumbersNumbers

Learning Target:Learning Target: Use an area model and partial Use an area model and partial quotients to divide.quotients to divide.Success Criteria:Success Criteria: • I can explain how to use an area model to divide.• I can explain how to use an area model to divide.• I can write partial quotients for a division problem.• I can write partial quotients for a division problem.• I can add the partial quotients to find a quotient.• I can add the partial quotients to find a quotient.

Explore and Grow

261Chapter 6 ⎜ Lesson 5 261

How can you use an area model to find 168 ÷ 14?

Reasoning Explain how your model shows the quotient.

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Think and Grow: Modeling Real LifeThink and Grow: Use Partial Quotients to Divide

262

Show and GrowShow and GrowSSShhhhhhhoowwwwwwww aannnndddddddd GGGGGrrrrrrroowwwwwwwSSSSSSSShhhhhhhhoooooooowwwwwwww aaaaaaaannnnnnnndddddddd GGGGGGGGrrrrrrrroooooooowwwwwwwwShow and GrowShow and Grow

Example Use an area model and partial quotients to find 180 ÷ 12.


Partial Quotients

12 ) ‾ 180 − 120 = 12 × 10 10 60− 60 = 12 × 5 + 5 0

18 ) ‾ 396 − 180 = 18 × 10 10 216− 180 = 18 × 10 10 36− 36 = 18 × 2 + 2 0

Partial Quotients

12 60120

10

Area = 180 square units

5

36180

10

18 180

10


2

So, 180 ÷ 12 = .

So, 396 ÷ 18 = .

Use an area model and partial quotients to divide.

16016 16 13013

2. 2. 182 ÷ 13 =

13) ‾ 182

− = 13 ×

− = 13 × +

1. 1. 176 ÷ 16 =

16) ‾ 176 − 160 = 16 ×

− 16 = 16 × +

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263Chapter 6 ⎜ Lesson 5

Name


Use partial quotients to divide.

7. 7. Writing Explain why there is more than one way to draw an areamodel to find a quotient.

5. 5. 204 ÷ 17

Apply and Grow: Practice

6. 6. 225 ÷ 15

8. 8. A puma jumps 132 inches up onto a rock. How many feet does the puma jump?

9. 9. DIG DEEPER Write two related division equations represented by the model.

10016

70

60 42

3. 3. 154 ÷ 14 =

14) ‾ 154

− = 14 ×

− = 14 × +

4. 4. 224 ÷ 16 =

16) ‾ 224

− = 16 ×

− = 16 × +

14014 16016

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Think and Grow: Modeling Real Life

264

Show and GrowShow and GrowSSShhhhhhhoowwwwwwww aannnndddddddd GGGGrrrrrrroowwwwwwwSSSSSSSShhhhhhhhoooooooowwwwwwww aaaaaaaannnnnnnndddddddd GGGGGGGGrrrrrrrroooooooowwwwwwwwShow and GrowShow and Grow

11. 11. There are 176 fifth graders and 198 sixth graders signed up for soccer. Each soccer team has 11 players. How many more sixth-grade teams are there than fifth-grade teams?

10. 10. A bakery owner tiles the rectangular floor. What is the length of the floor?

12. 12. DIG DEEPER Newton earns $195 for working 15 hours as a radio host. How much money does Newton earn in 3 hours?

Example A zookeeper cleans the rectangular floor of a baboon enclosure. The floor of the enclosure has an area of 156 square feet and a width of 12 feet. What is the length of the enclosure?

Use the area of a rectangle formula. Write the related division equation to find the length of the enclosure.

ℓ ×× w = A Area formula

ℓ ×× 12 = 156

156 ÷ 12 = ℓ

Use an area model and partial quotientsto find 156 ÷ 12.

288 square feet16 ft

12 ) ‾ 156 − 120 = 12 × 10 36 − 36 = 12 × 3 + 0

13 12 36120

10 3

156 ÷ 12 =

So, the length of the enclosure is .

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Name 6.56.5Homework

& PracticeLearning Target:Learning Target: Use an area model and Use an area model and partial quotients to divide.partial quotients to divide.

265Chapter 6 ⎜ Lesson 5

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Use partial products to divide.

3. 3. 156 ÷ 13 4. 4. 121 ÷ 11

So, 187 ÷ 11 = .17

11 ) ‾ 187 − 110 = 11 × 10 10 77 − 77 = 11 × 7 + 7 0 17

11 77110

10


7

11011 55 12012

1. 1. 165 ÷ 11 =

11) ‾ 165 − 110 = 11 ×

− 55 = 11 × +

2. 2. 192 ÷ 12 =

12) ‾ 192

− = 12 ×

− = 12 × +


266

7. 7. Structure Newton finds 506 ÷ 22. Explain how his steps change if he uses 20 as the first partial quotient.

9. 9. Modeling Real Life A vending machine worker has 78 bags of cherry fruit snacks and 91 bags of strawberry fruit snacks. Each row of the vending machine holds 13 items from front to back. How many rows does the worker fill with fruit snacks?

8. 8. Modeling Real Life A rectangular Olympic gymnastics floor has an area of 144 square meters. What is the length of the floor?

Review & RefreshEvaluate the expression.

10. 10. 24 ÷ (6 + 2) + 14 12. 12. (135 + 96 + 165) × 10

5. 5. There are 143 players in a football league. The director divides the players into 13 teams. How many players are on each team?

6. 6. Open-Ended Write a division expression that has a 3-digit dividend, a divisor between 15 and 20, and no remainder. Use base ten blocks to find the quotient.

11. 11. 5 + 10 × 7 – 9

12 m

22 ) ‾ 506 − 220 = 22 × 10 10 286− 220 = 22 × 10 10 66− 66 = 22 × 3 + 3 0 23

So, 506 So, 506 ÷÷ 22 22 == 23. 23.

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Name Use Partial 6.5 Quotients to Learning Target: Use an ...

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