Math Navigator Assessment Resources - Equations and Inequalities

ASSESSMENT RESOURCES

Equations and Inequalities

M A T H N A V I G A T O R ®

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ISBN: 978-1-40261-353-1 1 2 3 4 5 6 7 8 9 10 16 15 14 13 12

EQUATIONS AND INEQUALITIES 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


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

Checkpoint 3A Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29


Image Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

EQUATIONS AND INEQUALITIES 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 equations and inequalities.

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 A for problem 1. What did you do wrong? Students might say that you confused division with multiplication. Listen to their advice. Ask them where you might get more help. Hopefully some students might suggest pages 87–92 of the procedural help, which shows you how to write and solve equations.

• 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 77–82 at the end of the Student Book or use the Concept Book pages 355–384.

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. Write as an equation: “The product of 5 and k is 20.”

A k5

= 20 B k = 20 • 5 C 5k = 20 D 5 + k = 20

2. Write as an equation: “x divided by 7 is 7.”

A x = 7 ÷ 7 B 7x = 7 C 7x

= 7 D x7

= 7

3. Solve: –15 = n + 27

A n = 42 B x = –42 C n = 12 D n = –42

4. Solve: 2x = 15

2A x = 15 B x = 3

3

4 C x = 60 D x =

7

2


5Checkpoint 1

5. Which equation is equivalent to 12 = 9x?

A x3

= 4 B 3x = 3 C x = 9

12 D 4 = 3x

6. Solve: r – 5 = 13

7. Solve: x8

= 5

8. Solve: (–8) + x = 17

9. Solve: (–10) – 2x = 120

10. Solve: 1 + 2

3

x = 14

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


5Checkpoint 1

➲ checkpoint 1B

1. Solve: 9x

= 4

A x = 9 B x = 213

C x = 59 D x = 2

14

2. Solve: x – 23

= 72

A x = 95

B x = 53 C x = 4

16

D x = 156

3. Solve: 2 – x5

= 23

A x = –623

B x = 1023

C x = 320

D x = 623

4. Solve: 3(16.4 + x) = 75.6

5. Solve: –2x

= 32

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


5Checkpoint 1

➲ checkpoint 1C

1. Solve: 4s = 20

A s = 4 B s = 15

C s = 5 D s = 20

2. Solve: –17 = n + 31

A n = 48 B n = –14 C n = –48 D n = –51

3. Solve: n – 18 = 17

A n = 35 B n = –1 C n = 1 D n = –35

4. Solve: x3

– 1 = 0

5. Solve: y – 7 = –12

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.

7.

8.

9.

10.


Checkpoint 1 Answer Key

Checkpoint 1A

1. C 5k = 20

2. D x7

= 7

3. D n = –42

4. B x = 33

4

5. D 4 = 3x

6. r = 18

7. x = 40

8. x = 25

9. x = –65

10. x = 19.5



Checkpoint 1B

1. D x = 214

2. C x = 416

3. D x = 623

4. x = 8.8

5. x = –4

3

Checkpoint 1C

1. C s = 5

2. C n = –48

3. A n = 35

4. x = 3

5. y = –5






To help you and the members of your group, use the procedural help on pages 77–82 at the end of the Student Book or use the Concept Book pages 355–384.


➲ checkpoint 2A

1. Write as an equation: “The product of 4 and x is 1 plus x.”

A 4x = 1 B 4x = 1 + x C 4 + x = x D 4 = x + 1

2. Write as an equation: “x divided by 3 is 2 plus x.”

A x3

= 2 + x B x3

= 2x C 3

x = x + 2 D

3

x = 2x

3. Find an equation equivalent to 2(x + 4) = 16.

A x = 8 B 2x + 8 = 8 C 2x = 8 D 2x + 4 = 16


10Checkpoint 2

4. Solve: 2x + 3 = x + 4

A x = 1 B x = 7 C x = 213

D x = 13

5. Which equation is equivalent to 2x

= 1?

A 2x = 1 B 2x = 2 C x = 4 D 2x = 4

6. Solve: 2(x + 3) = 5x

7. Solve: 3x – 2 = 10 + x

8. Solve: x5

– 6 = x

9. Solve: x – 3 = 2(x – 1)

10. Is this equation always true, never true, sometimes true, or you cannot tell?

2(x + 4) = 2x + 8



10Checkpoint 2

➲ checkpoint 2B

1. Solve: x – 2 = 2(4x + 1)

A x = 4

7 B x =

7

4 C x = –

4

7 D x = –

7

4

2. Solve: –x3

= –3

A x = 9 B x = 3 C x = –3 D x = –9

3. Solve: x x+

= +2

31

2

A x = 2 B x = –2 C x = 3 D No solution

4. Solve: x

x2

3

2= –

5. Is this equation always true, never true, sometimes true, or you cannot tell?

x + 5 = x + 1



10Checkpoint 2

➲ checkpoint 2C

1. Solve: x – 1 = 1 – x

A x = 1 B x = –1 C x = ±1 D No solution

2. Solve: 2(x + 1) = 10

A x = –4 B x = –1 C x = 4 D x = 1

3. Solve: 6(x + 4) = 9(x + 3)

A x = 1 B x = –1 C x = 3 D x = – 3

4. Solve: 2x + 7 = x + 8

5. Solve: 3x – 1 = 2 + x



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.

7.

8.

9.

10.


Checkpoint 2A

1. B 4x = 1 + x

2. A x3

= 2 + x

3. C 2x = 8

4. A x = 1

5. D 2x = 4

6. x = 2

7. x = 6

8. x = –712

9. x = –1

10. Always true



Checkpoint 2B

1. C x = –4

7

2. A x = 9

3. B x = –2

4. x = 3

5. Never true

Checkpoint 2C

1. A x = 1

2. C x = 4

3. B x = –1

4. x = 1

5. x = 32







To help you and the members of your group, use the procedural help on pages 79–85 at the end of the Student Book.


➲ checkpoint 3A

1. Solve for x: 16 (2x + 12) = 1

3(3x – 2)

A 21 B 4 C 2 D 1

2. Solve for x: 5(3x + 52 ) = 4x + 7

A – 132

B – 92

C – 12 D –1


Checkpoint 3 15

3. Matt and Terry have a landscaping business. They pay themselves $20 each per hour that they work. They add in the cost of any materials they use. Which equation could they use to calculate what they should charge for a job?

t is the total cost of the job

n is the number of hours the job will take

m is the cost of their materials?

A 2(20 • m) + n = t B 40n – m = t

C 40n • m = t D 40n + m = t

4. Sarah babysits for $10/hour. She also gets $15/week for an allowance. If she works 5 hours this week and next week she works 11 hours, how much will she make including her allowance?

A 5(10) + 11(10) + 2(15) B 16(10) + 4(15)

C 16(10) + 15 D 15 + 15 + 5(10)

5. Troy and Laura are the same age. When you add their ages together and subtract 11, you get Shari’s age. Shari is 25.

How old are Troy and Laura?

A 14 B 12 12

C 18 D 16


Checkpoint 3 15

6. Oranges are on sale for $0.60 for a pound. Steve and Jorge plan to make orange juice to sell at the school fund raiser. If it takes 1 1

2 lbs of oranges to make a glass of orange juice, write an equation that tells how much they will make if they sell the orange juice for $3 a glass.

Use x = number of glasses of orange juice they sell

T = total amount they will make if they sell x glasses of orange juice

7. The sum of 2 even numbers is 234. Write an equation and solve for the numbers.

8. Rosa is buying school supplies. If she needs x number of notebooks and each notebook cost a dollars, and she needs y number of pens that cost b dollars each, write an equation for T, the amount of dollars she will spend.


Checkpoint 3 15

9. If the number of hours a repair job will take is n, the charge per hour is c, the charge for going to the house is h, and the materials for the job cost x, write an equation for the total cost of the job.

10. Use your equation from problem 9 to calculate the cost of a job to replace a dishwasher if the dishwasher costs $563, it will take 2 hours to replace the old dishwasher, and the cost for an hour of work is $35. The charge for going to the house (including delivery of the dishwasher) is $80.



Checkpoint 3 15

➲ checkpoint 3B

1. Solve: 4 45

2452

xx

+ 1 =+( )

A x = 237

B x = 3 C x = 2 D x = 43

2. Jenny is 5 years older than her sister, Teresa. Twice Teresa’s age minus 3 is 13. How old is Jenny?

A 10 B 13

C 14 D 8

3. Three consecutive odd integers add to 63. What are the integers?

4. Jessica is baking a cake for the school bake sale. She uses a cake mix that cost m, and the eggs and milk that she needs to add to the mix cost x. She thinks she will be able to cut the cake into 8 pieces and sell each piece for $2.00. Write an equation that will tell the amount of money she will raise for the school.

5. Peter walks along the lake shore for an hour. Then June jumps in her kayak to go find him. June kayaks at a speed of 3 miles/hour along the shoreline. It takes her 30 minutes to catch up to Peter. Write an equation and solve it to find what Peter’s average speed is.



Checkpoint 3 15

➲ checkpoint 3C

1. Solve: 3(2x + 1) = 2( 12 x + 4)

A x = 35

B x = 1 C x = 12 D x = 2

2. Mark is 5 years younger than 2 times Steve’s age. If Steve is 12, how old is Mark?

A 29 B 17 C 24 D 19

3. Three consecutive whole numbers add to 57. What are the numbers?

4. Scott and Jessica paint houses. They charge $500 as a flat rate and add the price of the paint and a cost per hour for their labor. If the price of paint is $20 for a gallon and they charge $30 per hour for their labor, write an equation they could use to calculate the price of any job.

Let n = number of hours it takes to paint a house

And x = number of gallons of paint needed

5. A box of 42 oranges costs $27.89. The cardboard box alone costs $3.56. After taking out the cost of the box, how much does one orange cost?




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.

7.

8.

9.

10.



Checkpoint 3A

1. B 4

2. C – 12

3. D 40n + m = t

4. A 5(10) + 11(10) + 2(15)

5. C 18

6. 3x – 0.9x = T or 2.1x = T

7. x + x + 2 = 234 2x = 232 x = 116The 2 numbers are 116 and 118.

8. ax + by = T

9. nc + h + x = total cost of the job

10. nc + h + x = 2 • $35 + $80 + $563 = $713



Checkpoint 3B

1. C x = 2

2. B 13

3. x + (x + 2) + (x + 4) = 63 3x + 6 = 63 x = 19 The 3 integers are: 19, 21, 23

4. 8($2.00) – (m + x) = the amount of money she will raise for the school

5. At the time June catches up to Peter, they both will have gone the same distance.Since Rate • Time = distance,

Peter’s rate (or speed) • Peter’s time = June’s rate • June’s time

Let P = Peter’s speed

Then P • 1 12 hour = (3 miles/hour)( 1

2 hour)

P = 1 mile/hour

Checkpoint 3C

1. B x = 1

2. D 19

3. x + x + 1 + x + 2 = 57 3x = 54 x = 18 The 3 numbers are 18, 19, 20.

4. $500 + ($30/hour)(n hours) + ($20/gallon)(x gallons) = total price

5. $27.89 – $3.56= $0.5842


Image Credits

Grateful acknowledgement is made to the following for copyrighted material:

24 t . ©iStockphoto .com/Brent Melton 24 m . ©iStockphoto .com 24 b . ©iStockphoto .com/Chris Schmidt 25 t . ©iStockphoto .com/Daniel Loiselle 25 b .l . ©iStockphoto .com 25 b .r . ©iStockphoto .com/Tom England 26 t . ©iStockphoto .com 26 b . ©iStockphoto .com/George Peters 27 t . ©iStockphoto .com/Jani Bryson 27 b . ©iStockphoto .com/Brenda McEwan 28 t .l . ©iStockphoto .com/Lisa F . Young 28 t .r . ©iStockphoto .com/George Peters 28 m . ©iStockphoto .com 28 b . ©iStockphoto .com/Adam Korzekwa Calculator icon throughout ©iStockphoto .com

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Math Navigator Assessment Resources - Equations and Inequalities