ASSESSMENT RESOURCES Operations with Fractions ... · . . 13: Lesson 10: Checkpoint 2 . ... students have learned about operations with fractions: multiplication and division. Online

$Page 1: ASSESSMENT RESOURCES Operations with Fractions ... · . . 13: Lesson 10: Checkpoint 2 . ... students have learned about operations with fractions: multiplication and division. Online$
ASSESSMENT RESOURCES

Operations with Fractions: Multiplication

and Division

M A T H N A V I G A T O R ®

This work is protected by United States copyright laws and is provided solely for the use of teachers and administrators in teaching courses and assessing student learning in their classes and schools. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted.

Copyright © 2012 Pearson Education, Inc., or its affiliate(s). All Rights Reserved. Printed in the United States of America. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. The publisher hereby grants permission to reproduce these pages, in part or in whole, for classroom use only, the number not to exceed the number of students in each class. Notice of copyright must appear on all copies. For information regarding permissions, write to Pearson Curriculum Group Rights & Permissions, One Lake Street, Upper Saddle River, New Jersey 07458. America’s Choice, the America’s Choice A logo, Math Navigator, the Pearson logo, and the Pearson Always Learning logo are trademarks, in the U.S. and/or other countries, of Pearson Education, Inc. or its affiliate(s).

ISBN: 978-1-40261-348-7 1 2 3 4 5 6 7 8 9 10 16 15 14 13 12

OPERATIONS WITH FRACTIONS: MULTIPLICATION AND DIVISION Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. iii

Contents

Teacher Materials

Pre-Test/Post-Test Administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Checkpoint Test Administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Student Materials

Lesson 5: Checkpoint 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Checkpoint 1A Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Checkpoint 1 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Lesson 10: Checkpoint 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Checkpoint 2A Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Checkpoint 2 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Lesson 15: Checkpoint 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Checkpoint 3A Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Checkpoint 3 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Image Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

OPERATIONS WITH FRACTIONS: MULTIPLICATION AND DIVISION Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved. 1

Pre-Test/Post-Test Administration

test administration

Pre-test: Let students know that this test will help you determine what they already know. Explain that the module will help students learn how to solve problems on the test that seem difficult now.

Post-test: Explain that this test will help you determine what students have learned about operations with fractions: multiplication and division.

Online Testing

Once your testing window has started, you can begin testing.

• Seat students individually in front of a computer.

• Give each student a piece of scratch paper.

• Make sure that students have pencils.

• Have students use their access codes to log in to the pre-test.

• Before each student begins the test, confirm that he or she is taking the correct test.

Tell students that:

• Each question will be displayed on the computer screen. Students should select the answer they think is best by clicking on the option choice and then clicking to confirm the choice.

• After students answer a question, the next question will appear on the computer screen.

• Students may opt to skip a question and flag it to come back to before ending the test.

During the test:

• Observe students as they work to make sure that they are actively engaged in the testing process.

• Support any students who seem to find the material challenging. Encourage them to make a good estimate for any problem they find difficult.

• You may wish to provide manipulatives.

Once students have answered all the questions, they should follow the online prompts to conclude the test.

Pre-test: If any students finish the test early, group them into pairs. Give each of the students a Student Book. Tell them to read the instructions on page 1 and start working with their partners.

➲



Paper-and-Pencil Test

• Print copies of the test and answer sheet from ARO for each student.

• Seat students individually.

• Distribute tests, answer sheets, and scratch paper.

• Make sure that students have #2 pencils.

• Instruct students to fill in the answers on their answer sheets.

During the test:

• Observe students as they work to make sure that they are actively engaged in the testing process.

• Support any students who seem to find the material challenging. Encourage them to make a good estimate for any problem they find difficult.

• You may wish to provide manipulatives.

After students finish, collect their tests, answer sheets, and scratch paper. You will need to upload students’ answers to the ARO system so you can analyze the results.

Pre-test: If any students finish the test early, group them into pairs. Give each of the students a Student Book. Tell them to read the instructions on page 1 and start working with their partners.

analyzing results

Irrespective of the method (online or paper-and-pencil) that you chose to administer the test, your students must be enrolled in the ARO system in order for you to obtain computer-generated reports.

These reports:

• Offer rich, instructionally-relevant information to teachers and administrators at the individual student, class, grade, school, and district levels

• Include total test score performance information and item-level analysis for each student and for all students combined

• Are important references in helping you assess the misconceptions your students are struggling with and decide what concepts to focus on during the module

For results:

• Online Testing: ARO will automatically generate performance reports.

• Paper-and-Pencil Test: Upload students’ data to ARO. Once you have uploaded the data, ARO will generate performance reports.

Additional information about the online test reporting can be found on ARO.

Remember to give a copy of the reports to students’ regular mathematics teachers to help them plan subsequent instruction.

➲



reflection

When students finish working on the test, ask them to open the Student Book and continue with the work time or reflection task that follows.

➲


Checkpoint Test Administration

preparation

• Make a copy of the appropriate checkpoint lesson, answer sheet, and answer key for each student.

• Hand out the checkpoint lesson to each student.

setting the direction

Lessons 5, 10, and 15 of this module are checkpoint lessons. In checkpoint lessons, students practice skills by answering multiple-choice and free-response questions in a test-like atmosphere, and then work in groups to “debug” their procedural knowledge. Each checkpoint lesson is structured as follows:

1. Students work independently on Checkpoint A.

2. Students work in groups to debug their work, concentrating on procedural knowledge.

3. Students work independently on either Checkpoint B or C, based on their success with Checkpoint A. Checkpoint C is easier than Checkpoint B.

4. Students meet in groups to debug their work.

The problems in the checkpoints follow up on the week’s work.

When students have completed Checkpoint A, collect their answer sheets before the debug group. Enter the data from Checkpoints 1A, 2A, and 3A into ARO. The report generated by ARO will help you assess whether students are on track and making sufficient progress.

checkpoint A

A. Work on Checkpoint A

Have students work individually to answer the multiple-choice and free-response problems found in Checkpoint A. Have students show their work in the checkpoint lesson and then transfer their answers to the answer sheet. Give students about 10–15 minutes to complete the checkpoint.

Observe students as they work in order to identify students who are struggling. You will use this information to decide how to organize the debug groups, and to determine which students will work on Checkpoint B versus Checkpoint C later in the lesson.

B. Model Debug Groups in Lesson 5

The debug groups are an important step of the checkpoint lesson because they give students additional opportunities to engage in the mathematical practice of constructing viable arguments and critiquing the reasoning of others (MP3). Many of the problems in the checkpoints ask students to reason abstractly and

➲

➲

➲



quantitatively (MP2) and to attend to precision (MP6). The debug discussions give students a chance to refine their understanding of the content while engaging in these mathematical practices.

In Lesson 5 during Checkpoint 1A, you will deviate slightly from the typical checkpoint lesson structure by first modeling the debug group routine. Spend about 5 minutes modeling this routine in front of the class.

Create a model group to help you. Choose students who have been willing to share their mistakes during the first four lessons. Participate as a member of the group in order to model how students should debug their work.

Model the following debug group routine, which students will use in all checkpoint lessons:

• Hand out the answer key for Checkpoint 1A.

• First, group members check their answers against the answer key. Students can check their own work or they can exchange work with a partner and check each other’s work. You can determine the rules for the process, or you can decide as a group.

• Next, members of the group should each choose a problem that they got wrong, show their work for the problem, and ask the group, “What am I doing wrong?” As resources, group members can use their own work, information they have from earlier lessons, the procedural help in the back of the Student Book, and the Concept Book.

• As a member of the group, model for students. Tell them you answered D for your answer to problem 1. What did you do wrong? Listen to their advice. Ask them where you might get more help. Students might say that you forgot that the question asked for the number of full glasses. The 52 ounces of juice can be divided by 6 to get 8 2

3 servings, which means there are only 8 full

servings of juice. They might tell you to look back to lesson 2 to remind you how to do these, and remember to use estimation to solve these problems.

• Any students who got all of the problems right can share something interesting or helpful about their solutions.

You might not want to take the time to have all the students in the model group present their work. However, emphasize to students that in their own groups, all students should present their work. Be sure to spend the time required for your students to understand the purpose and routines of the debug process.

In subsequent checkpoint lessons, you may skip Part B—Model Debug Groups in Lesson 5.

C. Debug Groups

Divide students into groups of three or four students each and have the groups follow the debug routine. Try to balance the groups with regard to strong and



weak students, based on your earlier observations. In Lesson 5, integrate students from your model group into the other groups.

Make sure all students have a copy of the answer key for the appropriate checkpoint.

Some groups may need more help than others. Spend extra time with groups that need more help, but be sure to take time to monitor all of the groups.

checkpoints B and C

A. Work on Checkpoint B or C

Give the debug groups about 15 minutes to finish. Then assign students to work on either Checkpoint B or Checkpoint C. Checkpoint C is easier than Checkpoint B, so assign Checkpoint C to any students who had difficulty with Checkpoint A. Allow 7–10 minutes for the second checkpoint.

Observe students as they work to assess whether they still need help with the material—either individually or as a class.

B. Debug Groups

Hand out the answer key for the appropriate checkpoint.

If you have time, form debug groups again and have them follow the debug routine. If you run short of time, just have students check their answers using the answer keys.

Spend time with students who are struggling.

reflection

When you have about 2 minutes left, stop the debug groups, even if they are not finished. Have students respond to the reflection prompt in the Student Book.

➲

➲


Checkpoint 1 5➲ setting the direction

For each problem, circle the correct answer or write your solution. Show your work. Copy your answers to the Checkpoint 1A answer sheet. Turn in your answer sheet to your teacher and get an answer key. Check your answers against the answer key. Then have each person in your group share one problem with the group.

• If you got one or more problems wrong, select one and ask the group, “What did I do wrong in this problem?”

• If you answered all the problems correctly, share with the group something that you did to solve a problem that you think was interesting or unusual.

To help you and the members of your group, use the procedural help on pages 95–101 at the end of the Student Book or use the Concept Book pages 152–153.

Then complete either Checkpoint 1B or Checkpoint 1C as instructed by your teacher. When completed, check your answers against the answer key. Have one person in your group share a problem using the routine described above.

➲ checkpoint 1A

1. The hospital provides 6-ounce servings of juice with breakfast. How many full 6-ounce servings can they pour from a pitcher that contains 52 ounces of juice?

A 6 B 52 C 8 D 9

2. Miguel has 48 meters of rope. He plans to use all of the rope to make 5 jump ropes. How much rope will he use in each jump rope if he uses the same amount of rope for each?

A 935

m B 15 m C 5

16 m D 720 m

3. Five boys shared a plate of 24 cookies equally. If all 24 cookies were eaten, how many did each boy eat?

A 5 cookies B 15

cookie C 445

cookies D 48 cookies


5Checkpoint 1

4. Rewrite the fraction 23

as a division problem.

A 23 ÷ 1 B 2 ÷ 3 C )2 3 D )23 1

5. Which of these quotients will be close to 2?

A 5 ÷ 1 B 54 ÷ 100 C 1 ÷ 5 D 100 ÷ 54

6. If the dividend is 32, which divisor will result in a quotient close to 3?

A 32 B 10 C 100 D 3

7. The bicycle club is planning a 70-mile trip over Labor Day weekend. If they want to ride the same distance on each of the 3 days, how far must they go each day?

8. Sandwich buns come in packages of 8 buns. If Mrs. Chi needs 60 sandwich buns for the school picnic, how many packages will she have to buy?

9. Rewrite the division problem 17 ÷ 3 as a fraction.

10. The divisor in a division equation is 12 and the quotient is a little more than 5. What might the dividend be? Explain why you think you are right.

Check your answers using the Checkpoint 1A Answer Key . Then share one problem with the group .


5Checkpoint 1

➲ checkpoint 1B

1. Eight girls drink a 90-ounce pitcher of juice after school. If each of them drinks exactly the same amount of juice, how much does each girl drink?

A 8 oz B 1114

oz C 82 oz D 445

oz

2. Mishaa cut 6 lawns in 10 hours yesterday. If she spent the same amount of time to cut each one, approximately how long did it take to cut one lawn?

A 6 hours B 123

hours C 10 hours D 0.6 hours

3. If the divisor is 45, which dividend will result in a quotient close to 3?

A 45 B 150 C 15 D 3

4. Anna’s biscuit recipe calls for 12 ounces of buttermilk. How many whole recipes of biscuits can she make with 1 gallon (128 ounces) of buttermilk?



Check your answers using the Checkpoint 1B Answer Key . Then share one problem with the group .


5Checkpoint 1

➲ checkpoint 1C

1. During Fitness Week, teams of three students are challenged to bike the distance of a triathlon (40 km) by dividing the distance among them. If each student bikes the same distance, how far must each student ride?

A 14 km B 40 km C 1423

km D 1313

km

2. Find the quotient: 7 ÷ 12

A 84 B 157

C 712

D 5

3. If the dividend is 43, which divisor will result in a quotient close to 2?

A 43 B 20 C 80 D 2



5. Estimate the quotient; do not compute the actual value. Explain why you think the actual value will be close to your estimate.

108 ÷ 24

Check your answers using the Checkpoint 1C Answer Key . Then share one problem with the group .


Checkpoint 1A Answer Sheet

Class Information

School ____________________________________________________________________________

City ______________________________________________________ State __________________

Teacher (mathematics class) _________________________________________________________

Student Information

Grade __________

First name ________________________________________________________________________

Last name ________________________________________________________________________

Date of birth ______ (month) ______ (day) ______(year)

Male o Female o

How many years have you been at this school? _______ years

Do you usually speak English at home? Yes o No o

Does anyone in your home usually speak a language other than English?

Yes o No o


Checkpoint 1A Answer Sheet

Name _______________________________________

A B C D

1. m m m m

2. m m m m

3. m m m m

4. m m m m

5. m m m m

6. m m m m

7.

8.

9.

10.


Checkpoint 1 Answer Key

Checkpoint 1A

1. C 8

2. A 935

m

3. C 445 cookies

4. B 2 ÷ 3

5. D 100 ÷ 54

6. B 10

7. 2313

miles

8. 8 packages

9. 173

or 523

10. Any whole number between 60 and 72



Checkpoint 1B

1. B 1114

oz

2. B 123

hours

3. B 150

4. 10 whole recipes

5. 7 ÷ 9

Checkpoint 1C

1. D 1313

km

2. C 712

3. B 20

4. 4 ÷ 5

5. 4.5






To help you and the members of your group, use the procedural help on pages 95–101 at the end of the Student Book or use the Concept Book pages 149–150 and 152–153.


➲ checkpoint 2A

1. Jong needs 32 hamburger patties for the picnic. If each patty weights 14

of a pound, how much hamburger meat will he use to make the patties?

A 128 lbs B 8 lbs C 32 lbs D 128 ÷ 4 lbs

2. The indoor track at the school is 23

of a mile long. If Melita runs around the track

12 times, how far does she run in all?

A 12 miles B 18 miles C 23

mile D 8 miles

3. Find 13

of 35

.

A 1415

B 4

15 C

15

D 59


10Checkpoint 2

4. Mom put 58

of a bag of apples in a bowl on the counter. The next day, 25

of the

apples in the bowl had been eaten. How much of the bag was eaten?

A 58

B 740

C 14

D 25

5. Find 23

of 45

.

A 68

B 2215

C 56

D 8

15

6. When Tran comes home from school, he finds 78

of a pizza in the refrigerator. If he eats half of the pizza in the refrigerator, how much of a whole pizza will he eat?

A 78

B 716

C 12

D 47

7. Tran needs 214

hours to cut a lawn. If he cuts 12 lawns a week as his

summer job, how much time does he spend working?

8. Find the product: 79

× 214

= y

9. Solve for x: x = 113

• 67

10. Solve for x: x = 27

• 34



10Checkpoint 2

➲ checkpoint 2B

1. Mr. Hakim needs 212 cases of juice for the school picnic. If juice comes in cases of

30 bottles, how many bottles will he buy?

A 30 bottles B 12 bottles C 212 bottles D 75 bottles

2. Solve for n: 37

• 312

= n

A 9314

B 32

C 1014

D 113

3. Solve for n: 38

• 212

= n

A 23

16 B

2416

C 1516

D 4616

4. A gallon of paint covers 130 square feet of surface

area. Anna used 212 gallons painting her bedroom.

What is the surface area of her bedroom??

5. A cake recipe calls for 214

cups of flour. If you want to reduce the recipe to 23

of the

original, how much flour will you need?



➲ checkpoint 2C

1. We sold 36 bags of mixed nuts at the school fair.

Each bag held 34 cups of nuts. How many cups of mixed nuts did we sell in all?

A 34

cup B 27 cups C 36 cups D 38 cups

2. Solve for n: 45

• 58

= n

A 3225

B 9

13 C

12

D 940

3. Find 34

of 58

.

A 56

B 1532

C 1113

D 8

12

4. Two-thirds of the members of the band are girls. If there are 42 students in the band, how many girls are members?

5. Solve for n: n = 23

• 45


Checkpoint 2 10


Answer SheetCheckpoint 2A Answer Sheet

Class Information

School ____________________________________________________________________________

City ______________________________________________________ State __________________


Student Information

Grade __________

First name ________________________________________________________________________

Last name ________________________________________________________________________


Male o Female o




Yes o No o



Name _______________________________________

A B C D

1. m m m m

2. m m m m

3. m m m m

4. m m m m

5. m m m m

6. m m m m

7.

8.

9.

10.


Checkpoint 2A

1. B 8 lbs

2. D 8 miles

3. C 15

4. C 14

5. D 8

15

6. B 716

7. 27 hours

8. 74

or 134

9. x = 87

or 117

10. x = 3

14



Checkpoint 2B

1. D 75 bottles

2. B 32

3. C 1516

4. 325 square feet

5. 32

or 112

cups of flour

Checkpoint 2C

1. B 27 cups

2. C 12

3. B 1532

4. 28 members are girls

5. 8

15







To help you and the members of your group, use the procedural help on pages 95–101 at the end of the Student Book or use the Concept Book pages 149–151.


➲ checkpoint 3A

1. Which expression could be used to get a product of 34

?

A 12

× 22

B 32

× 36

C 14

× 13

D 12

× 23

2. Which representation could be used to understand 16

of 34

?

A

0 1 2 3 4 5

B 34

34

34

34

34

34

C ×

D

0 1

16

34×


Checkpoint 3 15

3. If N is a whole number greater than one, the largest value below is:

A NN

B N • 13

C 3 • N D 32

• N

4. For which positive values of R will this statement be true? R • R > 34

• R

A R = R2 B R = 34

C R > 34

D R < 34

5. Most days, Sue drinks 214

quarts of green tea. On Monday, she

drank 23

of her normal amount. How much did she drink

on Monday?

A More than 214

quarts of green tea B 23

of a quart of green tea

C Less than 12

of a quart of green tea D Between 1 and 2 quarts of green tea

6. Anna needs to make bows for 15 packages. She plans to use 43

of a yard of ribbon for each bow. About how much ribbon will Anna need?

A Between 15 and 25 yards B More than 30 yards

C Less than 8 yards D About 10 yards


Checkpoint 3 15

7. Show me two different positive numbers that could be put in the boxes to make the equation true. You may use any number except 1.

× = 4

15

8. Write a number that has a reciprocal with a value greater than 2.

9. Fill in the box to make the statement true.

× 12 < 4

15

10. Mishaa read 34

of a book over the weekend. Next weekend, she plans to read 23

of what she read this weekend. Will she read more or less than 34

of a book?

Explain how you know.



Checkpoint 3 15

➲ checkpoint 3B

1. Which representation could be used to understand 25

of 34

?

A

0 134

25

B ×

C D

2. If N is a whole number greater than one, the smallest value below is:

A NN

B 15

• N C N • 13

D 5 • N

3. Maria runs around the 34

-mile track in the park twice every day. Melita usually runs 85

of that distance. Melita runs:

A The same distance as Maria B Farther than Maria, but not twice as far

C Twice as far as Maria D Less distance than Maria

4. Fill in the box to make the statement true.

× 34

> 6

5. Mr. Lewis has a rectangle of land that is 34

of a mile long and 23

of a mile wide. He

gives half of his land to his daughter. What are some possible dimensions of the land

that he has left?



Checkpoint 3 15

➲ checkpoint 3C

1. Which expression could be used to get a product of 49

?

A 23

• 32

B 23

• 23

C 14

• 45

D 19

• 14

2. Which value is the greatest?

A 58

• 17 B 17 • 8 C 1717

D 17 • 85

3. Tran sets the copy machine to 45

. If he uses the copy machine to change the height of

a 6” comic that he drew, what will be the new height?

A More than 6” B 45

of a foot C Less than 6” D About a foot

4. Gabby plans to make this fruit punch recipe.

2 quarts of juice

1 lemon

3 quarts of sparkling water

If she makes 34

of a recipe, will she use more or less

than 2 quarts of juice? Explain how you know.

5. Mrs. Chi’s yard is a rectangle that is 13

of a kilometer long and 14

of a kilometer wide.

Is her yard more or less than 12

of a square kilometer? Explain how you know.




Class Information

School ____________________________________________________________________________

City ______________________________________________________ State __________________


Student Information

Grade __________

First name ________________________________________________________________________

Last name ________________________________________________________________________


Male o Female o




Yes o No o



Name _______________________________________

A B C D

1. m m m m

2. m m m m

3. m m m m

4. m m m m

5. m m m m

6. m m m m

7.

8.

9.

10.



Checkpoint 3A

1. B 32

× 36

2. D

0 1

16

34×

3. C 3 • N

4. C R > 34

5. D Between 1–2 quarts

6. A Between 15–25 yards

7. 23

× 25

, 45

× 13

, or 4 × 1

15

8. 0 < x < 12

9. 0 < x < 145

10. She will read less than 34

of a book.



Checkpoint 3B

1. C

2. B 15

• N

3. B Farther than Maria

4. Any number > 8

5. 34

× 13

Checkpoint 3C

1. B 23

• 23

2. B 17 • 8

3. C Less than 6”

4. Less than 2 quarts

5. Less than 12

km2


Image Credits

Grateful acknowledgement is made to the following for copyrighted material:

7 m .r . ©iStockphoto .com/Milan Vasicek 7 m .l . ©iStockphoto .com/Stephen Bonk 8 m . ©iStockphoto .com/Tim Arbaev 9 t . ©iStockphoto .com 10 t . ©iStockphoto .com/Don Bayley 14 t . ©iStockphoto .com/Oliver Wolfson 14 m .l . ©iStockphoto .com/Antonio Muñoz Palomares 14 m .r . ©iStockphoto .com 15 m . ©iStockphoto .com 15 b . ©iStockphoto .com 16 t . ©iStockphoto .com/Jouke van Keulen 16 b . ©iStockphoto .com 20 m . ©iStockphoto .com/Emrah Turudu 20 b . ©iStockphoto .com/Mark Wragg 21 b . ©iStockphoto .com/Lisa Howard 23 m . ©iStockphoto .com Calculator icon throughout ©iStockphoto .com

Note: Every effort has been made to locate the copyright owner of material reproduced in this component. Omissions brought to our attention will be corrected in subsequent editions.

Documents

ASSESSMENT RESOURCES Operations with Fractions ... · . . 13: Lesson 10: Checkpoint 2 . ... students have learned about operations with fractions: multiplication and division. Online