COHORT 3

DEPARTMENT OF MATHEMATICS/COMPUTER SCIENCE/INFORMATION TECHNOLOGYCourse Outline for

Course Information/ Semester Title Quantitative Reasoning 1 Credit Hours 4.5 Credit hours (non-credit) Number MAT 012 Section _____________________ Semester/Term _____________________ Meeting time _____________________ Location _____________________

Instructor /Contact Information Name ____________________________________________________________ Office location ____________________________________________________________ Office hours ____________________________________________________________ Office telephone and fax numbers __________________________________________________ Email address ____________________________________________________________ Blackboard link ____________________________________________________________ Website ____________________________________________________________ Other __________________________________________________________________

Course DescriptionA non-credit course that prepares students to take a college-level general liberal arts course in mathematics. This course integrates quantitative literacy with mathematical concepts such as fluency with numbers, proportional reasoning, data interpretation, algebraic reasoning, graphing lines, and modeling. A significant portion of class time is devoted to collaborative group work with instructor facilitation and guidance. Students should be prepared to actively participate in class discussions during every class meeting. Class discussions will be used to investigate mathematical concepts based on real-life examples. Some examples include: social justice; home repair; population growth and density; and congressional structure. Students who intend to major in science, technology, engineering or mathematics should take MAT 002 or MAT 003 instead of this course. Graded on an S-U basis. Satisfactory completion of Math 001 or by college placement test; RDG 001, may be taken concurrently.

This course will not satisfy the prerequisite for MAT 109 - Algebra and Trigonometry. If

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MAT 012 Quantitative Reasoning 1

you will need MAT 109 as a degree requirement, please see an adviser to discuss proper course sequence.

Detailed Topic Outline

Module 1 Working with and Understanding Large NumbersPlace value and naming large numbers Scientific notation Calculations with large numbers Relative magnitude and comparison of numbers

Estimation and CalculationRounding Fractions and Decimals Relationship of multiplication and division Order of operations Properties that allow flexibility in calculations: distributive property, commutative property Perform multistep calculations

Percentages and RatiosEstimations with fraction and percent benchmarks Calculate percentages Write and understand ratios Calculate percentages from a two-way table Use percentages as probabilities and ratios

Module 2

Using RatiosUnderstand meaning of equivalent ratios in context Use units with ratios Calculate a unit rate Use ratios and proportionality to calculate new values Interpret and use index numbers to calculate new values

Applications of PercentagesCalculate and interpret absolute change between two quantities Calculate and interpret relative change between two quantities Calculate and interpret absolute change between two percentages Calculate and interpret relative change between two percentages Make and interpret comparisons of absolute measurements versus relative measurements

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Graphical DisplaysRead and interpret pie graphs, bar graphs, and line graphs Recognize distortion of graphs due to different scales Calculate absolute and relative change from a graph Measures of Central TendencyCalculate mean, median, and mode of a data set Interpret the meaning of and differences between the mean, median, and mode

Module 3

Making ConversionsUnderstand use of units in making conversions Use dimensional analysis to make a conversion involving multiple conversion factors Geometric ReasoningUnderstand concepts of and units for linear measurement, area, and volume Identify and use the appropriate geometric formula in a given situation

Using Formulas and Algebraic ExpressionsUnderstand the use of variables in formulas and algebraic expressions, including the appropriate way to define a variable

Understand the role of a constant in a formula Use a formula to solve for a value

Using Graphical DisplaysRead and interpret a pictograph Understand the limitations of and potential for distortion in pictographs

Creating and Solving EquationsSolve a linear equation in one variable Interpret the solution to an equation Solve an equation or formula for a variable Write and solve proportions Solve complex equations with multiple variable terms and variables in the denominator Solve or estimate the solution to equations with a variable raised to the power of two

Module 4

Linear ModelsCreate, interpret, and use the four representations of a linear model Translate between the four representations of a linear model Identify and interpret vertical intercept, horizontal intercept, and slope from a graph Identify the slope and vertical intercept from an equation Understand that a linear model is defined by a constant rate of change Identify a model as linear based on any of the four representations Understand the role of units in a linear equation Calculate and interpret slope

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Create a linear equation to model data Understand the limitations of models based on data Use equations, tables, and graphs to solve or estimate solutions to problems Write and use linear equations based on a percentage increase or decrease

Exponential Models – TIME PERMITTINGCreate, interpret, and use the four representations of an exponential model Write and use an exponential model Understand that an exponential model is defined by a percentage change Identify an exponential model as growth or decay

Learning Outcomes/ObjectivesGeneral Objectives:To provide students with the ability to: Develop a critical problem solving mindset Develop a habit of critically examining quantitative information and learn to test it for

reasonableness, and to explain their reasoning. Read extensively and learn to extract quantitative information from text. Communicate quantitative information through writing and orally presenting their work.

Specific Course Goals:

1. Quantitative reasoning with Multiple Literacies:Students will develop their quantitative reasoning abilities through learning and practicing other essential literacies and reasoning skills.

1.1 Read and interpret quantitative information from a variety of real-world sources.

1.2 Communicate quantitative results by writing and use quantitative information to support an argument.

2. Numeracy Skills:Students will develop and apply the concepts of numeracy to investigate and describe quantitative relationships and solve problems in a variety of contexts.

2.1 Demonstrate an understanding of and competency in using magnitude in the context of place values, fractions, and/or numbers written in scientific notation.

2.2 Demonstrate measurement sense including units, precision, accuracy, and error.

3. Proportional Reasoning:Students will represent proportional relationships and solve problems that require an understanding of ratios, rates, proportions, and scaling.

3.1 Recognize proportional relationships from verbal and numeric representations.

3.2 Apply quantitative reasoning strategies to solve real-world problems with proportional

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relationships based on an understanding that derived quantities can be described with whole numbers, fractions, or decimals, and that to fully explain these relationships, units must be used.

4. Algebraic Reasoning:Students will reason using the language and structure of algebra to investigate, represent, and solve problems.

4.1 Construct and use equations to represent relationships involving one or more unknown or variable quantities to solve problems.

5. Mathematical Modeling:Students will reason using the language and structure of mathematics to investigate, represent, and solve problems.

5.1 Create models of authentic contextual situations and demonstrate an understanding of linear or exponential models.

6. Statistical Thinking:Students will reason using the language and structure of statistics to investigate, represent, and solve problems.

6.1 Critically evaluate and demonstrate an understanding of statistics being presented in a media report, statement, and/or graph.

Instructional MethodThis course should be taught in a small group setting with a student-centered approach to problem solving and little emphasis should be placed on note-taking. Students should read through the attached “What to expect in a collaborative classroom” sheet.

Textbooks and MaterialsRequired textbook: MAT 012 Quantway Core (ver 2.7)Required online access: Quantway Core (ver 2.7) digital access code for Mobius

Electronic references: https://portal.carnegiemathpathways.org Other: instructors may optionally recommend supplementary materials such as Khan

Academy videos etc. All students must bring a calculator to class each day. It will be used during class and for all exams. No graphing calculators or algebraic manipulators (such as the TI83/TI 89/TI 92) are allowed (Strongly recommended – TI-30XIIS or the TI-30XS Multiview).

Student Responsibilities/Course PoliciesInstructors need to complete the following for their specific policies.

Participation ____________________________________________________________5

Homework Homework in this course has two aspects. Students are expected to complete the “Preparing for the Next Lesson”(PNL) before the start of each class. The PNL is designed to prepare students for the content of the lesson. After the lesson has been completed in class, students are expected to complete the “Out of Class Exercises” (OCE) for each lesson. OCE’s are designed to reinforce the content of the previous lesson and may also give new context and deepen students’ understanding.

The Math Department will provide students with the Quantway Core textbook at no cost. Students will be required to purchase access to an online course management system. Access can be purchased directly online through Carnegie or at the NCC Bookstore. Registration information for this system will be provided by the instructor. Students are required to complete surveys and homework assignments in this online system. Students are encouraged to complete the work on paper as well as online. ONLY the online work will be graded.

Online discussions Faculty and students are encouraged to use an online discussion forum to assist understanding of the content and completion of assignments. There is a forum option in each course’s Blackboard class.

Projects ____________________________________________________________ Group work (include information on effective group procedures) Students should read

through the attached “What to expect in a collaborative classroom” sheet.Students will work in groups of 3 or 4 every day, and are expected to interact with their peers. Classwork is dependent upon completion of homework and every member of the group should be prepared with their book and pencil.

Exams/quizzes 2 in-class module exams, midterm exam, 3 in-class quizzes, cumulative final exam

Attendance/lateness policy No more than 6 absences in a fall or spring semester section that meets 3 times/week. No more than 4 absences in a fall or spring semester section that meets 2 times/week.

Missed exams/ quizzes policy____________________________________________________________

Extra credit ____________________________________________________________ Faculty teaching developmental math classes will be required to use the Early Warning

System. Academic Dishonesty & Plagiarism:

Academic dishonesty, which includes plagiarism and cheating, will result in some form of disciplinary action that may lead to suspension or expulsion under the rules of the Student Code of Conduct. Cheating can take many forms including but not limited to copying from another student on an examination, using improper forms of assistance, or receiving unauthorized aid when preparing an independent item of work to be submitted for a grade, be it in written, verbal or electronic form. Anyone who assists or conspires to assist another in an act of plagiarism or any other form of academic dishonesty may also be subject to disciplinary action.Plagiarism is a particular type of academic dishonesty that involves taking the words, phrases or ideas of another person and presenting them as one's own. This can include using whole papers and paragraphs or even sentences or phrases. Plagiarized work may also involve statistics, lab assignments, art work, graphics, photographs, computer programs and other materials. The sources of plagiarized materials include but are not limited to books,

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magazines, encyclopedias or journals; electronic retrieval sources such as materials on the Internet; other individuals; or paper writing services.A student may be judged guilty of plagiarism if the student:(a) Submits as one's own an assignment produced by another, in whole or in part.(b) Submits the exact words of another, paraphrases the words of another or presents statistics, lab assignments, art work, graphics, photographs, computer programs and other materials without attributing the work to the source, suggesting that this work is the student's own.Allegations of student plagiarism and academic dishonesty will be dealt with by the appropriate academic department personnel. It is the policy of Nassau Community College that, at the discretion of the faculty member, serious acts will be reported in writing to the Office of the Dean of Students, where such records will be kept for a period of five years beyond the student's last semester of attendance at the College. These records will remain internal to the College and will not be used in any evaluation made for an outside individual or agency unless there is a disciplinary action determined by a formal ruling under the Student Code of Conduct, in which case only those records pertaining to the disciplinary action may apply. A student whose alleged action is reported to the Office of the Dean of Students will be notified by that office and will have the right to submit a letter of denial or explanation. The Dean will use his/her discretion in determining whether the alleged violation(s) could warrant disciplinary action under the Student Code of Conduct. In that case the procedures governing the Code of Conduct will be initiated.

Copyright statement: The Higher Education Opportunity Act of 2008 (HEOA) requires the College to address unauthorized distribution of copyrighted materials, including unauthorized peer-to-peer file sharing. Thus, the College strictly prohibits the users of its networks from engaging in unauthorized distribution of copyrighted materials, including unauthorized peer-to-peer file sharing. Anyone who engages in such illegal file sharing is violating the United States Copyright law, and may be subject to criminal and civil penalties. Under federal law, a person found to have infringed upon a copyrighted work may be liable for actual damages and lost profits attributable to the infringement, and statutory damages of up to $150,000. The copyright owner also has the right to permanently enjoin an infringer from further infringing activities, and the infringing copies and equipment used in the infringement can be impounded and destroyed. If a copyright owner elected to bring a civil lawsuit against the copyright infringer and ultimately prevailed in the claim, the infringer may also become liable to the copyright owner for their attorney's fees and court costs. Finally, criminal penalties may be assessed against the infringer and could include jail time, depending upon the severity of the violation. Students should be aware that unauthorized or illegal use of College computers (such as engaging in illegal file sharing and distribution of copyrighted materials), is an infraction of the Student Code of Conduct and may subject them to disciplinary measures. To explore legal alternatives to unauthorized downloading, please consult the following website: http://www.educause.edu/legalcontent.

Course Resources Web sites

o https://portal.carnegiemathpathways.org homework and course content o https://www.khanacademy.org/ supplemental videos

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Library services ____________________________________________________________ Labs and learning centers:

MATH CENTER REQUIREMENTAs part of this course, students should avail themselves of further study and/or educational assistance available in the Non-Stem Math Lab (B 125), Math Learning Center (B130), the Math Success Center (B116), and the Math Anxiety Center (B126). Use of the resources in these areas is deemed an integral part of the course, and will help the student master the necessary knowledge and skills for the course.

Study groups ____________________________________________________________ Extra help options ____________________________________________________________

Assessments and Grading Methods for Cohort 3 Overall Average: Students who maintain an overall academic average of at least 70%

when using the following grading scheme will receive an S in the course:Computerized Midterm 35%Computerized Final (first attempt) 35%In-class Exams, HW & Quizzes 30%

Final Exam: Students who pass the computerized final exam will receive an S in the course.

Final Exam Eligibility: All students that adhere to the instructor’s attendance policy are eligible to take the first attempt at the computerized final exam. If the student does not have an overall academic average of at least 70%, and the student did not pass the first attempt at the final exam, then the student will be eligible to take the second attempt at the computerized final exam in MAT 012 if, and only if, the student maintained an overall academic average of at least 60% (including first attempt at final exam) and has taken advantage of 2 or more of the 4 incentives listed below:

Incentives:1. Student submits test and quiz corrections throughout

the semester.2. Student attends the Math Success Center on a regular

basis throughout the semester.3. Student completes homework quizzes used as

incentives.4. Student submits classwork or groupwork to be

evaluated as incentives.NOTE: Incentives will NOT be used when calculating the student’s overall academic average.

Grading Methods: Students who pass either computerized final exam or have maintained an overall academic average of at least 70%, will receive a grade of S in the course. Students who do not pass the computerized final exam and have not maintained an overall academic average of at least 70%, will receive a grade of U in the course.

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Students that receive a grade of U, UU or W for this course, must repeat MAT 012 next semester. Students are given three attempts to successfully complete MAT 012.

Grades: o Students must meet one of the above conditions in order to receive a grade of S

[Satisfactory] for the course. After successfully completing MAT 012, the student may enroll in a credit math course [MAT 100, MAT 101, MAT 102, MAT 114, MAT 118] for next semester.

o If the student doesn’t meet any of the conditions above, a grade of U [Unsatisfactory] will be given and MAT 012 must be taken again next semester.

o There are two other possible final grades for developmental courses: W [official withdrawal] and UU [unofficial withdrawal]. If a student stops attending a developmental course before the 10th week of the semester, the student shall be treated as an unofficial withdrawal and the instructor must assign the grade of UU, which carries the same penalty as a U (new policy as of Fall 2012).

o A student cannot receive a grade “I” [incomplete] in this class. o No credit will be given for this class. o Any combination of 3 W’s, UU’s or U’s (in any combination) will result in

dismissal from the college. All faculty should administer a minimum of three in-class module exams (including the

midterm) and three in-class quizzes each semester. Additional exams and quizzes may be given at the instructor’s discretion. These dated grades must be recorded by the instructor on the hard copy class roster. All students should receive frequent feedback as to their performance during the semester.

Attendance policy: (http://collegecatalog.ncc.edu/current/policiesandprocedures/records_registration/attendance.html) Students are expected to attend all classes. Absences due to illness or for other serious reasons may be excused at the discretion of the instructor. Students are advised that absences in excess of 10% of the total class meetings may result being dropped from the course. Some departments may have additional attendance guidelines and related grading policies. The instructor shall detail the specific attendance policy for his/her class. Students are responsible for all course work missed. Students receiving Veterans Administration educational benefits are reminded of their legal obligation to withdraw officially and to notify the VA Certifying Officials in the Office of the Registrar if there are any changes in enrollment.

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Provide a clear explanation of evaluation, including a clear statement on the assessment process and measurements. Be explicit! Include format, number, weight for quizzes and exam, descriptions of papers and projects as well as how they will be assessed and the overall grading scale and standards. Frequent evaluation of student work is required and students should receive feedback in a timely manner.

Americans with Disabilities Statement & Non-Discrimination StatementIf you have a physical, psychological, medical, or learning disability that may have an impact on your ability to carry out the assigned coursework, I urge you to contact the staff at the Center for Students with Disabilities (CSD), Building U, (516)572-7241, TTY (516)572-7617. The counselors at CSD will review your concerns and determine to what reasonable accommodations you are entitled as covered by the Americans with Disabilities Act and section 504 of the Rehabilitation Act of 1973. All information and documentation pertaining to personal disabilities will be kept confidential.

Course Schedule

Week Section Topic Assignment1 1.0-1.1 Introduction to the course – Mobius, Group roles and responsibilities,

language script (Starting Strong Package)Have students complete survey in Mobius1.1: Introduction to Quantitative Reasoning (Situation 1)Why Study Mathematics?, Engaging in Production Struggle, Quantitative Reasoning (Situation 2)

Homework

2 1.2-1.3 Growth Mindset Activity1.2: Seven Billion and Counting1.3: Percentages in Many Forms

Homework

3 1.4-1.6 1.4: The Flexible Quantitative Thinker1.5: The Credit Crunch1.6: Whose Footprint is Bigger?

Homework

4 1.7-1.9,Quiz #1

1.7: A Taxing Set of Problems (1-4), further application if time permits1.8: Interpreting Statements About Percentages1.9: Percentages and Probabilities (Time Permitting)mid-module Quiz #1Have students complete survey in Mobius

HomeworkQuiz #1

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5 Exam #12.1-2.2

Module 1 Exam2.1: How Crowded Are We?2.2: Counting Our Votes (omit question 8)

Homework Exam #1

6 2.3-2.5 2.3: Measuring Population Change2.4: Picturing Data with Graphics2.5: Risk Reduction

Homework

7 2.6-2.7Quiz #2

2.6: What is Average?2.7: Making Good Decisions with Good StatisticsMid-Module Quiz #2

HomeworkQuiz #2

8 2.8Midterm Exam

2.8: Has the Minimum Wage Kept Up? (Time Permitting)Midterm Exam (Module 1 and 2.1-2.5)

HomeworkMidterm exam

9 3.1-3.2 3.1: Salary per Minute3.2: The Cost of Driving part 1 and part 2, 1-3a,b only

Homework

10 3.3-3.4 3.3: The Fixer Upper3.4: Breaking Down the Variable

Homework

11 3.6-3.7 Quiz #3

3.6: Balancing Blood Alcohol3.7: A Return to Proportional ReasoningMid-Module Quiz #3

Homework Quiz #3

12 3.8, 4.1 -4.2 3.8: Solving More Equations4.1: Lining Up4.2: Comparing Change

Homework

13 4.34.4 and beyond if time permits

Have students complete survey in Mobius4.3: That is Close Enough

Homework

14 Exam #3, Review

Exam #3 (2.6-3.8)Review for Computerized Blackboard Final Exam

Exam #3Blackboard Final Exam

15 Review Review for Computerized Blackboard Final Exam Blackboard Final Exam

Revised 1/20Approved for: Spring 2020, Summer 2020

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What to expect in a collaborative classroom

This class will be different in many ways from other math classes you may have taken in the past. You are going to interact with each other quite a bit and talk to each other about mathematics. I will put you into groups, and I will expect that you will contribute to the discussion of the problems that your group is working on. I know that some of you do not like to talk in class and that others of you like to talk a lot. So, we will be following a couple of easy rules. We give everyone a chance to talk. We respond to whatever anyone says with respect. We are concerned here about concepts that will help you learn mathematics, and I expect that students in this class will support each other in working together. Please take a few moments to answer the following questions:

1) What makes a good group member?

2) Have you ever been involved in a situation (including group work) where you could clearly identify a person who is not contributing in a positive way? If so, what (appropriate) words could you use to describe that person?

Read over the information on the back of this page; Ten Qualities of an Effective Group Member , by Marty Brounstein Characteristics of Effective and Ineffective Groups (Source: http://www.fisherhouse.com)

3) Do you agree or disagree with these lists? What do you agree or disagree with?

4) What qualities or characteristics of an effective group member do you believe are most important?

5) What characteristics do you have that make an effective group leader?

6) We all can make self-improvements… What improvements do you want to make? Think about your goals in terms of a timeframe as well. Are the improvements you want to make for this semester, this year, etc.? Are they for this class, other classes, or in your personal life?

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Ten Qualities of an Effective Group Member, by Marty Brounstein

1. Demonstrates reliability2. Communicates constructively3. Listens actively4. Functions as an active participant5. Shares openly and willingly6. Cooperates and pitches in to help7. Exhibits flexibility8. Shows commitment to the team9. Works as a problem-solver10. Treats others in a respectful and supportive manner

Characteristics of Effective and Ineffective Groups (http://www.fisherhouse.com) Effective Groups

o All members actively participate.o Participation is encouraged.o When someone speaks, others pay attention.o When someone speaks, others actively try to understand the full meaning of the speaker's

message.

Ineffective Groupso Some members dominate while others are relatively inactive.o People work only to ensure that their own ideas are stated.o When someone speaks, others formulate their own ideas or interrupt the speaker.o When someone speaks, others may believe they understand but often do not.

In order to be a successful group member in MAT 012, it is essential that you understand what an effective group member is and what your group roles will be. All group members are expected to be active in group discussions:

1) Ask and answer questions.2) Suggest ideas and/or explain concepts.3) Come to class prepared for the lesson of the day (book, pencil, PNL completed).

At times, group roles will be assigned. Roles and responsibilities:

Group Manager 1. Keep group on task.2. Eliminate distractions (ex: cell phones put away).3. Make sure everyone in the group has a chance to contribute.

Recorder 1. Write down your group’s responses for questions asked.2. Make sure that every group member is writing a response to each question.

Presenter 1. Present your group’s responses.2. Discuss group work with others.

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3. Speaker of the group if questions/problems arise. Name____________________________________________ Date ______________________

MAT _____________________ Syllabus Quiz

Directions: Take a few moments to quietly review the syllabus. Then answer the questions below. Be prepared to share with your group and the class.

1. How many exams and quizzes will there be this semester?

2. Is there a final exam for this course?

3. How is your grade calculated in this class? What is a passing grade for this class?

4. How many absences are you allowed?

5. What books or other material do you need or have to purchase?

6. What does “PNL” and “OCE” stand for?

7. How big will the in-class groups be?

8. Where can you go to get extra help if you need it?

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MAT 012 – Quantitative Reasoning I Textbook and Digital Access Options

Students will have the following options when purchasing the textbook and digital access for the course:

Option 1 – Purchase Digital Access Online and Obtain the Textbook from the Math Department at No Additional Cost:Students may purchase digital access to Quantway Core (Mobius platform) online directly through Carnegie Math Pathways for $35 (instructions on how to purchase digital access online are on the next page). Students can obtain the custom MAT 012 Quantway Core textbook from the Non-Stem Math Lab in room B 125 at no additional cost. In order to obtain a copy of the textbook, the student must show their NCC ID.

OR

Option 2 - Purchase Digital Access at the NCC Bookstore and Obtain the Textbook from the Math Department at No Additional Cost:Students may purchase digital access to Quantway Core (Mobius platform) at the NCC Bookstore (instructions on how to redeem a digital access code online are on the next page). Students can obtain the custom MAT 012 Quantway Core textbook from the Non-Stem Math Lab in room B 125 at no additional cost. In order to obtain a copy of the textbook, the student must show their NCC ID.

***Students have the option of deferring payment and registering for a 28-day courtesy access. Courtesy Access for all students will end on February 17, 2020 and all students must purchase full access to Mobius in order to submit homework from this date on.

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