ASSESSMENT RESOURCES Using Expressions and Equations to ... · pages 64–65 of the procedural help, which explain how to solve equations using division and multiplication. • Any

ASSESSMENT RESOURCES

Using Expressions and Equations to Solve Problems

M A T H N A V I G A T O R ®

ASSESSMENT RESOURCES

Using Expressions and Equations to Solve Problems

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: 978-1-40261-357-9 1 2 3 4 5 6 7 8 9 10 16 15 14 13 12

UsING expRessIONs ANd eqUATIONs TO sOlVe pRObleMs 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

UsING expRessIONs ANd eqUATIONs TO sOlVe pRObleMs 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 using expressions and equations to solve problems.

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. The checkpoints in this unit review the proficiency necessary to solve the problem in the lessons. They don’t necessary set up a complex problem solving situations like in the lessons but the questions check the students’ ability to manipulate and solve equations and inequalities. 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 model debug group, model for students how you would present an incorrect answer. Tell them you got s = 1

5 for the answer for problem 4. What did you do wrong? Listen to

students’ advice. Ask them where you might get more help. Hopefully, some students will suggest pages 64–65 of the procedural help, which explain how to solve equations using division and multiplication.

• 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 CA. 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 62–66 and 71–73 at the end of the Student Book or use the Concept Book pages 23–44.

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

Carlos is downloading Apps onto his smart phone. The cost of each App is shown below. Use the table to answer questions 1–3.

1. Carlos downloads 5 Bronze, 3 Silver, 1 Platinum, and 10 White Apps. What is the total cost?

A $19.91 b $20.00 C $20.91 d $20.99

Cost of Apps

Type Cost ($)

White Free

Bronze 0.99

Silver 1.99

Gold 4.99

Platinum 9.99


5Checkpoint 1

2. Carlos’s friend Abby has a $50 gift card. How many Silver Apps can she get if she has already downloaded 5 White, 2 Bronze, and 3 Gold Apps.

A 14 b 15

C 16 d 17

3. Write the proportion that represents the relationship between the number of Gold Apps downloaded, g, and the total cost, t.

4. Solve for s: 4s = 20

A s = 5 b s = 15 C s = 15 d s = –5

5. Solve for z: 15z = 24 + 3z

A z = 0.5 b z = 2 C z = 1.33 d z = –2

6. Solve for r if q = 13 : q = 0.5 r

A r = 13 b r = 16 C r = 1.5 d r = 23

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


5Checkpoint 1

➲ checkpoint 1b

1. Marissa’s summer job paid her $7.80 an hour and 50% more for overtime hours. Her pay for just overtime hours last month was $286.65. Write a formula that could be used to calculate the number of overtime hours, h, that Marissa worked.

2. Solve the equation 2 ( x + 3 ) = 5x + 16.

3. Dina went to a basketball summer camp. She and her friend Alli combined to contribute 19 points to their basketball team’s victory. Dina made 3 fewer points in the game than Alli. How many points did Alli make?

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


5Checkpoint 1

➲ checkpoint 1C

1. Solve for d if w = 6 : d = 8w + 3

A d = 5 b d = 51 C d = 2.67 d d = 11

2. Solve for n if k = 25 : k = –15n + 5

A n = – 43 b n = 4

3 C n = – 34

d n = 34

3. When Carla sells a CD in the music store where she works, she earns one-quarter of the price of the CD plus 25 cents. If she sells a CD for $12.40, how much does she earn?

A $3.00 b $3.25

C $3.30 d $3.35

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.

4. m m m m

5. m m m m

6. m m m m


Checkpoint 1 Answer Key

Checkpoint 1A

1. C $20.91

2. C 16

3. tg

= 4.99 or t = 4.99g

4. A s = 5

5. b z = 2

6. d r = 23



Checkpoint 1B

1. 7.80h + (7.80) (0.5) h = $286.657.80 (1 + 0.5) h = $286.657.80 (1.5) h = $286.6511.70 h = $286.65

2. 2x + 6 = 5x + 162x – 5x = 16 – 6–3x = 10

x = – 103

3. x is the number of points Alli madex – 3 is the number of points Dina made x + (x – 3) = 19x + x = 19 + 32x = 22x = 11Alli made 11 points and Dina made 8 points.

Checkpoint 1C

1. b d = 51

2. A k = – 43

3. d $3.35


Checkpoint 2 10➲ setting the direction




To help you and the members of your group, use the procedural help on pages 69–73 at the end of the Student Book or use the Concept Book pages 23–44.


➲ checkpoint 2A

1. Solve for h if w = 3 : h = 6w + 5

2. Solve for x: 4 ( x – 1 ) = 32

3. Solve for r: r – 3 = –14.9


10Checkpoint 2

4. Select the number line that represents the solution set to the inequality below:

z > –3

A

b

C

d

5. Solve for x: 7x + 18 = 5x + 9

6. Solve for x: 3 ( x + 8 ) = 2x + 16

7. Select the solution set to the following inequality: 3 ( 9 + t ) < 42

A t < 5 b t > 5 C t < –5 d t > –5

8. Rich fills a tank with a 250-liter per minute hose. What is the total time needed to fill an 8,200-liter tank?


0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7


10Checkpoint 2

➲ checkpoint 2b

1. Solve for s if r = 3 : 21r = 18 + 5s

2. Select the inequality that matches the solution set indicated on the number line.

A 31 > 4 + q b 31 < 4 + q C 31 > 4 + (–q) d 31 > –4 + q

3. Select the solution set to the following inequality: 3 ( 8 + t ) < 51

A t < 7 b t < 8 C t < 9 d t < 10

4. The Lincoln Middle School band wants to make a profitthat is greater than $2,000 selling garden plants in the spring. It makes $2.50 profit on each plant sold. How many plants, n, does the band need to sell? Select an inequality that models this situation.

A 2.50 n < 2,000 b 2.50 n > 2,000

C n > 2,000 – 2.50 d n > 2,000 + 2.50


302520151050 35 40 45 50


10Checkpoint 2

➲ checkpoint 2C

1. Select the number line that represents the solution set to the inequality below:

k < –5

A

b

C

d

2. Select the inequality that matches the solution set indicated on the number line.

A 20 > 5 + (–z) b 20 > –4 + z C 20 > 5 + z d 20 < 5 + z

3. This table represents a proportional relationship. Fill in the missing values.

4. Solve for y if x = 2 12 : y = 3x

A y = 5 12 b y = 56 C y = 6 1

2 d y = 152


0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

302520151050 35 40 45 50

b t1 82 16345


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.

2.

3.

4. m m m m

5.

6.

7. m m m m

8.


Checkpoint 2A

1. h = 23

2. x = 9

3. r = –14.9 + 3r = –11.9

4. b

5. x = –4.5 or x = – 92

6. 3x + 24 = 2x + 163x – 2x = 16 – 24x = –8

7. A t < 5

8. 8,200 ÷ 250 = 32.8It will take Rich 32.8 minutes to fill the tank.

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7



Checkpoint 2B

1. s = 9

2. A 31 > 4 + q

3. C t < 9

4. b 2.50 n > 2,000

Checkpoint 2C

1. A

2. C 20 > 5 + z

3.

4. d y = 152

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

0–1–2–3–4–5–6 1 2 3 54 6 7 98 10–10 –8–9 –7

b t1 82 163 244 325 40



15Checkpoint 3

➲ setting the direction




To help you and the members of your group, use the procedural help on pages 63–68 at the end of the Student Book or use the Concept Book pages 23–44.


➲ checkpoint 3A

1. The formula that represents the relationship between profit, p, income, i, and expenses, e, is: p = i – e The Spanish Club is selling pizza kits as a fund-raiser. They want to make a profit of $200. If they have expenses of $175, how much income do they need to receive?


Checkpoint 3 15

2. Lexi knows that the cost per pizza kit is $3.50 and the Spanish Club will sell the pizza kits for $8.00. We can write a formula to calculate the profit, p, in terms of number of pizza kits sold, k : p = $ 8.00 k – $ 3.50 k Write the formula in the form of a proportion between p and k.

3. Using the proportion from problem 2, complete this table.

Pizzas Kits Sold

Profit

0

1

2

3

4

5


Checkpoint 3 15

4. Tom made this graph of profit, p, and number of pizza kits sold, k. Read the graph and determine the profit for 15 pizza kits sold.

5. Suppose that the Spanish club determines that it needs to make more than $200 profit. Write an inequality that this situation represents in terms of the total number of pizza kits sold, k. Graph the solution set on the number line below.

6. Given the following relationship: $3.50 d + 2 ( $1.90 ) + 12 ( $5.00 ) = $400Solve for d, rounding your answer to the nearest penny.


0k0

25

50

75

100

125

150

175

200

225

p

25 50 75 100

Pizzas Sold

Pro�

t

6050403020100 70 80 90 100


Checkpoint 3 15

➲ checkpoint 3b

1. Jerome’s soccer team is selling T-shirts to raise $210 for a weekend competition. Tommy’s parents make a $50 donation to the team. Assume that the total T-shirt expenses are $100. The formula to determine profit, p, in terms of T-shirts sold, s, is: p = $4.00 s – $ 100.00 + $ 50.00 How many T-shirts would need to be sold to make $210?

2. Suppose that instead of donating $50, Tommy’s parents decide to donate $1 for every T-shirt sold, s. Rewrite the formula in problem 1 to show this change.

3. Use this new formula from problem 2 to calculate how many T-shirts would need to be sold to make a profit of $210.



Checkpoint 3 15

➲ checkpoint 3C

1. Suppose p = i – e. If p = 250 and e = 75, what is i?

2. Suppose p = $12.00 k – $7.00 k. Write the formula in the form of a proportional relationship.

3. Using the proportion: b = 2.00 t, complete the table below:


t b0510152025



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.

2.

3.

4.

5.

6.



Checkpoint 3A

1. 200 = i – 175200 + 175 = i375 = ii = 375The band needs to receive $375 in income.

2. p = (8.00 – 3.50) kp = 4.5 k or k = 1

4 5. p

3.

4. Approximately $67.50Note: Any answer that is close to $67.50 is reasonable.

5. 4.5 k > 200 k > 200 ÷ 4.5k > 44.4

6. 3.50 d + 3.80 + 60 = 4003.50 d + 63.80 = 4003.50 d = 400 – 63.803.50 d = 336.20d = $96.06

Pizzas Kits Sold

Profit

0 0

1 $4.50

2 $9.00

3 $13.50

4 $18.00

5 $22.40

6050403020100 70 80 90 100



Checkpoint 3B

1. p = $210$210 = $4.00 s – $100.00 + $50$210 = $4.00 s – $50.00$210 + 50 = $4.00 s$260 = $4.00 s$260 ÷ $4 = 65 65 T-shirts need to be sold.

2. p = $4.00 s + $1.00 s – $100.00 or p = ($4.00 + $1.00) s – $100.00

3. $210.00 = $4.00 s + $1.00 s – $100.00$210.00 + $100.00 = $4.00 s + $1.00 s$310.00 = $5.00 s62 = s62 T-shirts need to be sold.

Checkpoint 3C

1. 250 = i – 75250 + 75 = i325 = i

2. p = ($12.00 – $7.00) k

p = 5k or k = 15 p

3. b t0 05 1010 2015 3020 4025 50


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ASSESSMENT RESOURCES Using Expressions and Equations to ... · pages 64–65 of the procedural help, which explain how to solve equations using division and multiplication. • Any