MM150_2102C 2

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Purdue Global University *

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150

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Mathematics

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Feb 20, 2024

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MM150 Survey of Mathematics Module Preview This guide contains a preview of the materials for all course modules in this series: Module 1 MM150M1 Examining Data Module 2 MM150M2 Graphical Methods Module 3 MM150M3 Variable Relationships Module 4 MM150M4 Applying Probability Module 5 MM150M5 Confidence Intervals Be sure to follow the detailed directions found within the actual course modules after you receive access. The content in this guide is only a preview and course content may have changed.

MM150 Module Preview Statistics Page 2 of 15 Course Materials Title: Math in Our World. Edition: 4th (2019) with ALEKS Author: David Sobecki Publisher: McGraw Hill Ebook ISBN: 9781259969690 Course Code MM150M1 Competency Title Estimation and Critical Thinking Outcome(s) MM150-1: Use estimation to predict results. Learn: Reading and Research Read the assigned chapters from the following textbook: Sobecki, D. (2019) Math in Our World (4 th ed.). New York: McGraw Hill In Module 1 of Survey of Mathematics, you will see a variety of math applications that you can use in your personal and professional lives. Specifically, this course will focus on the enjoyable, real-life nature of mathematics. Some people make a living predicting the future: the future of a certain stock, the future earnings of a business, the future inventory needs in a hospital ward, and even the future winners of a football game. During Module 1, you will be exposed to reasoning techniques that will allow you to make predictions of what will come next and identify patterns. With the time constraints that life puts on everyone, pulling out a calculator or opening a spreadsheet for every math problem that you come across can be very impractical. How much will the items in your shopping cart be at the checkout? What will your monthly expenses total? How many miles will you put on your car on your next family vacation? Learning estimation techniques for real-life problems in Module 1 can be a true time saver. Another topic covered in this module is solving problems. No matter what career sector you are looking to go into, employers are looking for problem solvers. Perhaps you have to figure out why your company is spending so much on transportation costs and develop a plan to reduce those costs. Problem-solving is also commonplace in your personal life. Perhaps you have one test left in your college course and you want to be sure that you get at least a B in the course to keep up your GPA. You can calculate the minimum score needed on that test to get at least a B and then make a plan for studying. As you work your way through Module 1, you will get an opportunity to see how problem-solving occurs. You will view a general problem-solving procedure that can help you find solutions to problems you may encounter in the workplace or your everyday life. And you will encounter a few riddles that may be fun to think through. There are two places you can access the course textbook. First, on the Content menu in your classroom, you can click “Digital Book.” Another place that you may access the textbook in digital form is through the ALEKS program.

MM150 Module Preview Statistics Page 3 of 15 Reading the digital book and reviewing the examples for each of the unit’s reading assignments are excellent methods for starting each module. Chapter 1: Problem Solving  Section 1.1: The Nature of Mathematical Reasoning  Section 1.2: Estimation and Interpreting Graphs  Section 1.3: Problem-Solving Strategies Competency Assessment This Competency Assessment assesses the following outcome(s): MM150-1: Use estimation to predict results. It is time to demonstrate what you have learned in this module. You have used inductive reasoning, deductive reasoning, and estimation along with a defined process for solving problems that you may encounter outside of math class. The Competency Assessment Labs give you the opportunity to prove that you have mastered these topics. There are four Competency Assessment Labs to be completed in the ALEKS Lab tool. 1. CA Lab 1 - Solve problems using inductive and deductive reasoning. 2. CA Lab 2 - Round numbers to a specific place value. 3. CA Lab 3 - Solve problems using estimation. 4. CA Lab 4 - Solve real world problems. Please note the following when completing the Competency Assessment Labs:  You will have 45 minutes to complete each Competency Assessment Lab.  The Competency Assessment must be completed in one sitting. You do not have the option to save and come back to finish the assessment.  You are allowed unlimited attempts to successfully complete the ALEKS Competency Assessment Labs.  The ALEKS Competency Assessment Labs will be manually scored by your instructor.  Within the ALEKS Competency Assessment Labs, you will NOT find support resources (i.e., eBook, guided solutions, examples, etc.) that were available in the ALEKS Lab Practice. After you receive access to each module, you will be able to see the submission requirements and a Checklist Rubric for the Competency Assessment.

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MM150 Module Preview Statistics Page 4 of 15 Course Code MM150M2 Competency Title Equations in Real Life Outcome(s) MM150M2: Solve real-life problems using equations. GEL-1.02: Demonstrate college-level communication through the composition of original materials in Standard English. Learn: Reading and Research Read the assigned chapters from the following textbook: Sobecki, D. (2019) Math in Our World (4 th ed.). New York: McGraw Hill “When will I ever use this in real life?” Math teachers hear this question all the time, and it’s a valid concern. The truth is, math problems are all around us, but we often don’t recognize them because they aren’t written out as equations when we first encounter them. Instead, they are ordinary scenarios that can be modeled using equations if we understand how to translate verbal expressions into mathematical symbols. Imagine you have just received a package with an order that you placed online for school uniforms for your child. You want to double check that you have received everything you ordered but can’t remember how many uniforms you were supposed to receive. You know that the uniforms were $15 each, and you ordered one hat for $8. The invoice shows your total to be $53. This situation can be modeled with a linear equation: 53 = 15x + 8. You can solve this for x in order to figure out how many uniforms you ordered. Have you ever noticed how making one change can result in another related change? For example, increasing the amount of savings you have tucked away may also increase your peace of mind; decreasing the amount of sugar in your diet may result in a decrease in your weight; and increasing the time you spend studying for a quiz may result in increasing the score you get on that exam. On the other hand, spending more time scrolling through social media feeds may result in decreased contentment; sleeping fewer hours at night may increase your fatigue the next day; and spending more time at the office may result in a weaker sense of connection to your family and friends. In the first examples, both variables increased or decreased together. This is called direct variation. In the second examples, one variable increased while the other decreased. This is called inverse variation. In Module 2, you’ll see how to write these kinds of relationships as equations that you can solve. There are two places you can access the course textbook. First, on the Content menu in your classroom, you can click “Digital Book.” Another place that you may access the textbook in digital form is through the ALEKS program. Reading the digital book and reviewing the examples for each of the unit’s reading assignments are excellent methods for starting each module.

MM150 Module Preview Statistics Page 5 of 15 Chapter 5: The Real Number System  Section 5.2: The Integers Chapter 6: Topics in Algebra  Section 6.1: Applications of Linear Equations  Section 6.2: Ratio, Proportion, and Variation Chapter 7: Consumer Math  Section 7.1: Percents Competency Assessment This Competency Assessment assesses the following outcome(s): MM150M2: Solve real-life problems using equations. GEL-1.02: Demonstrate college-level communication through the composition of original materials in Standard English. It is time to demonstrate what you have learned in this module. You have simplified expressions using the Order of Operations, solved equations and proportions, and worked problems involving percents. All of these are problems that you may encounter outside of math class. The Competency Assessment Labs give you the opportunity to prove that you have mastered these topics. There are four Competency Assessment Labs and a Written Assignment to be completed in the ALEKS Lab tool. 1. CA Lab 1 - Use the order of operations to simplify expressions. 2. CA Lab 2 - Solve equations. 3. CA Lab 3 - Solve proportions. 4. CA Lab 4 - Solve problems involving percents. 5. Written Assignment – Percentages and Budgets (see below) Please note the following when completing the Competency Assessment Labs: ● You will have 45 minutes to complete each Competency Assessment Lab. ● The Competency Assessment must be completed in one sitting. You do not have the option to save and come back to finish the assessment. ● You are allowed unlimited attempts to successfully complete the ALEKS Competency Assessment Labs. ● The ALEKS Competency Assessment Labs will be manually scored by your instructor. ● Within the ALEKS Competency Assessment Labs, you will NOT find support resources (i.e., eBook, guided solutions, examples, etc.) that were available in the ALEKS Lab Practice. Written Assignment: Percentages and Budgets

MM150 Module Preview Statistics Page 6 of 15 Being involved in your local community is important for a variety of reasons. It affords you the opportunity to connect with, help, and strengthen the lives of others. It can give you a sense of satisfaction and accomplishment as you form bonds with your neighbors. If you find a need in your community, it is a good idea to collect data regarding that need. The data may reinforce your idea that there is a need, or it may even point you in a different direction of need. Using a data-driven approach to solve a community problem will help you be successful. Write an essay about civic participation. Propose a community program that you would like to kick start. Choose something you are passionate about: health care, sports, politics, education, community outreach, crime prevention, beautification, animals, etc. It can be something you do once or something you do on an ongoing basis. Your 250-word minimum essay should include: ● A brief overview of the community program you would like to kick start. ● Proposed budget percentages for your program to help prepare for fundraising (administrative costs, supplies, rent, advertising, etc.). ● Proposed number of volunteers needed for your program. Also calculate the percentage of volunteers based on total number of people in the community (number of volunteers ÷ population of community). ● Estimated percentage of people (or animals) in the community that would benefit from the program. Every piece of writing should have an introduction, body, and conclusion. A good way to plan this particular reflective essay is to write an introduction to the essay. Next, write at least three body paragraphs. Finish with your conclusion paragraph. Your essay and outside sources for this essay need to be cited in proper APA format. You can find numerous APA resources in the Academic Success Center Reference Library on the Research, Citation, and Plagiarism page . Your essay should include a highly developed purpose and viewpoint; it should also be written in Standard English and demonstrate exceptional content, organization, style, grammar, and mechanics. There should be no evidence of plagiarism. If you are unsure about what constitutes plagiarism, please review the plagiarism policy. After you receive access to each module, you will be able to see the submission requirements and a Checklist Rubric for the Competency Assessment.

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MM150 Module Preview Statistics Page 7 of 15 Course Code MM150M3 Competency Title Professional and Personal Math Outcome(s) MM150-3: Use mathematics in personal and professional contexts. GEL-2.03: Solve real-world problems using mathematical skills. Learn: Reading and Research Read the assigned chapters from the following textbook: Sobecki, D. (2019) Math in Our World (4 th ed.). New York: McGraw Hill Most people at some point in life have had to take out a loan for something that is difficult to pay for at the time of purchase. This could be a car, boat, house, or even your college education. An important factor to consider when choosing a loan is the amount of interest you will have to pay the bank or lender. The interest rate and amount of time you take the loan out for - or the terms of the loan - can have a huge effect on the total payback amount for the loan. Borrowers do not always consider the total amount of interest that they will be paying to a bank or other lender for the right to take out a loan. Instead of presenting the amount of interest, the lender often provides the monthly payment. For example, an advertisement that states, “Purchase car - $199 a month for 72 months,” sounds much more manageable financially than purchasing a $10,000 car and paying $4,328 in interest. In this module, we will also look at student loans and mortgages in greater detail. In both cases, you may have many options to choose from: different interest rates, different timeframes for repayment, etc. With student loans, you’ll also need to consider the benefits and risks associated with subsidized, unsubsidized, and private loans. Scientia potentia est is a Latin saying that translates as, “Knowledge is power.” Generally attributed to Sir Francis Bacon in 1597, perhaps in no other arena of life is the phrase more applicable than to major financial decisions. In this module, you will discover the necessary knowledge to make smart decisions with powerful implications. There are two places you can access the course textbook. First, on the Content menu in your classroom, you can click “Digital Book.” Another place that you may access the textbook in digital form is through the ALEKS program. Reading the digital book and reviewing the examples for each of the unit’s reading assignments are excellent methods for starting each module. Chapter 7: Consumer Math  7.3: Simple Interest

MM150 Module Preview Statistics Page 8 of 15  7.4: Compound Interest  7.6: Student Loans and Home Buying Competency Assessment This Competency Assessment assesses the following outcome(s): It is time to demonstrate what you have learned in this module. You have solved problems involving simple interest, compound interest, student loans, and mortgages. The Competency Assessment Labs give you the opportunity to prove that you have mastered these topics. There are four Competency Assessment Labs and a Written Assignment to be completed in the ALEKS Lab tool. ● CA Lab 1 - Solve problems involving simple interest. ● CA Lab 2 - Solve problems involving compound interest. ● CA Lab 3 - Solve problems involving student loans. ● CA Lab 4 - Solve problems involving mortgages. ● Written Assignment – Comparing Mortgage Options (see below) Please note the following when completing the Competency Assessment Labs: ● You will have 45 minutes to complete each Competency Assessment Lab. ● The Competency Assessment must be completed in one sitting. You do not have the option to save and come back to finish the assessment. ● You are allowed unlimited attempts to successfully complete the ALEKS Competency Assessment Labs. ● The ALEKS Competency Assessment Labs will be manually scored by your instructor. ● Within the ALEKS Competency Assessment Labs, you will NOT find support resources (i.e., eBook, guided solutions, examples, etc.) that were available in the ALEKS Lab Practice. Written Assignment: Comparing Mortgage Options Purchasing a home is a major life decision. Searching for just the right place can be both fun and stressful. For most people, a large part of the home-buying process involves finding a home loan that is a good financial fit. There are many different options to consider. Today, you’re going house-hunting (virtually, of course). Go online to your favorite real estate listing site and find a home in your area that you would love to buy. Why would this be a great home for you? Be sure to include the URL for the listing. Search online for current interest rates for 30-year mortgages. Include the URL for this information as well. Given the information you have found, calculate the following: ● What is the amount needed for a 20% down payment? ● What is the mortgage amount? ● What is the monthly payment (principal + interest) for a 30-year mortgage? ● At the end of the 30 years, how much interest will have been paid? ● What is the monthly payment (principal + interest) for a 15-year mortgage?

MM150 Module Preview Statistics Page 9 of 15 ● At the end of the 15 years, how much interest will have been paid? ● How much interest can be saved by choosing a 15-year mortgage? Submitting Your Written Assignment Submit the Written Assignment portion of the Competency Assessment by clicking on “Assignments” along the top menu bar of the course, then Competency Assessment Dropbox. After you receive access to each module, you will be able to see the submission requirements and a Checklist Rubric for the Competency Assessment.

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MM150 Module Preview Statistics Page 10 of 15 Course Code MM150M4 Competency Title Measurement Systems Outcome(s) MM150M4: Convert between and within measurements systems. PC-1.2: Contribute to team goals and objectives through active participation and collaboration. Learn: Reading and Research Read the assigned chapters from the following textbook: Sobecki, D. (2019) Math in Our World (4 th ed.). New York: McGraw Hill Our world is more connected than ever before, and it’s important to be able to collaborate with people from around the globe. Bilingual and multilingual employees are often highly sought after because they enable us to communicate verbally with others. Being able to communicate in a variety of numerical ways is also a needed skill. The United States is one of only a small handful of countries that do not use the metric system. While those who have grown up in the US may be very familiar with feet, pounds, and gallons, others around the world measure in meters, grams, and liters. Whether you are in the medical field, manufacturing, or business, it’s important to know how to translate in order to communicate. In Module 4, you will explore conversions within the English system, but you will also explore to convert between measurements in the metric system. Perhaps most importantly, you will explore to convert between the English and metric systems. Another interesting topic in this module that can take you in many practical directions is Geometry. Perhaps the company you work for needs to fill containers with the materials that you are manufacturing. In order to do that, they need to figure out how much volume is ideal for each of the containers. Geometry can help! At home, you may find yourself needing to replace your patio. In order to do that, you need to mark off a right angle from the outside wall of your house so that the patio is nice and square. Geometry can help! In this module, you will work with angles, polygons, circles, and much more. You will explore many practical applications of geometry. Next time you tackle a home improvement project, you might just need some of these geometry applications. There are two places you can access the course textbook. First, on the Content menu in your classroom, you can click “Digital Book.” Another place that you may access the textbook in digital form is through the ALEKS program. Reading the digital book and reviewing the examples for each of the unit’s reading assignments are excellent methods for starting each module.

MM150 Module Preview Statistics Page 11 of 15 Chapter 8: Measurement  Section 8.1: Measures of Length: Converting Units and the Metric System  Section 8.2: Measures of Area, Volume, and Capacity  Section 8.3: Measures of Weight and Temperature Chapter 9: Geometry  Section 9.1: Points, Lines, Planes, and Angles  Section 9.2: Triangles  Section 9.3: Polygons and Perimeter  Section 9.4: Areas of Polygons and Circles Competency Assessment This Competency Assessment assesses the following outcome(s): MM150M4: Convert between and within measurements systems. PC-1.2: Contribute to team goals and objectives through active participation and collaboration. It is time to demonstrate what you have learned in this module. You have used inductive reasoning, deductive reasoning, and estimation along with a defined process for solving problems that you may encounter outside of math class. The Competency Assessment Labs give you the opportunity to prove that you have mastered these topics. There are four Competency Assessment Labs and a Written Assignment to be completed in the ALEKS Lab tool. 1. CA Lab 1 - Convert units within measurements systems. 2. CA Lab 2 - Convert units across measurements systems. 3. CA Lab 3 - Solve problems involving geometric figures. 4. CA Lab 4 - Find the perimeter and area of geometric figures. 5. Written Assignment – Peer Review (see below) Please note the following when completing the Competency Assessment Labs: ● You will have 45 minutes to complete each Competency Assessment Lab. ● The Competency Assessment must be completed in one sitting. You do not have the option to save and come back to finish the assessment. ● You are allowed unlimited attempts to successfully complete the ALEKS Competency Assessment Labs. ● The ALEKS Competency Assessment Labs will be manually scored by your instructor. ● Within the ALEKS Competency Assessment Labs, you will NOT find support resources (i.e., eBook, guided solutions, examples, etc.) that were available in the ALEKS Lab Practice.

MM150 Module Preview Statistics Page 12 of 15 Written Assignment: Peer Review You are an employee of My Awesome Company, a start-up company in the New England area. You are a quality control project manager and you are a part of a special team consisting of yourself and Lisa (a media specialist). Teamwork is an important aspect of your position within the company. Your team’s goal is to collaborate on the creation of a How To video on calculating mileage reimbursement for both travel within the US and travel within Canada. Lisa’s contribution to the team is to create a draft of the video; your contribution is to review the video for quality and accuracy. Unfortunately, Lisa made a poor choice in units when communicating a calculation in the video. Your contribution as a teammate is to compose an email that effectively and tactfully communicates with Lisa where the error is (include a timestamp), what the error is, and how the error can be remedied. The link to the video is below. Review the video. Your email to Lisa needs to be at least 150 words and should include the following: ● Address Lisa by name. ● Include at least one sentence of praise mentioning something that was done well in the video. ● Mention specifically where the poor choice in units was made (include a timestamp). ● Describe in detail why it was a poor choice in units and what the best choice would be. Include a reworking of the math using the new, recommended choice of units. ● Wrap up your email with encouraging words, thanking Lisa for her contribution to the team by composing this video draft. Submitting Your Written Assignment Submit the Written Assignment portion of the Competency Assessment by clicking on “Assignments” along the top menu bar of the course, then Competency Assessment Dropbox. After you receive access to each module, you will be able to see the submission requirements and a Checklist Rubric for the Competency Assessment.

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MM150 Module Preview Statistics Page 13 of 15 Course Code MM150M5 Competency Title Basic Statistical Techniques Outcome(s) MMM5:150 Analyze data using basic statistical techniques in real-life situations. Learn: Reading and Research Read the assigned chapters from the following textbook: Sobecki, D. (2019) Math in Our World (4 th ed.). New York: McGraw Hill Why do you think your new video-gaming system comes with a one-year warranty, but your clothes dryer comes with a three-year warranty, and your car comes with a ten-year or 100,000-mile warranty? It is because these different companies have calculated the probability of a major repair or replacement of these items within the warranty period and feel they can accept the small risk. Probability has many useful applications. Insurance companies use probabilities to determine the probability that an eighteen-year-old might get into an accident and make a claim. They use these probabilities to calculate insurance premiums. Meteorologists use probabilities to make predictions about the weather. You may use probabilities to determine how much traffic you will encounter on your morning commute. You will also spend time in this module using counting techniques that help you calculate probabilities as well as find out how many permutations of passwords there can be when you log into your online bank account. Another topic you will see in this module is Statistics. Statistical claims can be seen almost everywhere. Companies in the weight-loss business might try to convince you that you will lose 50 pounds on their program. A politician might try to convince you to vote for them because the average crime rate under their administration is low. A company might try to convince you that they are a good company to work for because their average salary is higher than their competitors. How can you know if these claims are valid? There are many ways to evaluate a claim, but one good starting point is to ask how the data was collected. What was the sample size? What type of sampling was done? Could that sampling method have impacted the results? Statistics is collecting, organizing, analyzing, interpreting, and presenting data. In this module, you will be exposed to some of the most common sampling methods. You will also see a variety of techniques to calculate an “average” and further analyze your results. In your future coursework as well as your future personal life, you will encounter statistical information. With what you explore in this module, you will have a better understanding of the

MM150 Module Preview Statistics Page 14 of 15 terms being used. You may also be able to interpret statistical claims and recognize biases more easily. There are two places you can access the course textbook. First, on the Content menu in your classroom, you can click “Digital Book.” Another place that you may access the textbook in digital form is through the ALEKS program. Reading the digital book and reviewing the examples for each of the unit’s reading assignments are excellent methods for starting each module. Chapter 10: Probability and Counting Techniques  Section 10.1: Basic Concepts of Probability  Section 10.2: The Fundamental Counting Principle and Permutations  Section 10.3: Combinations Chapter 11: Statistics  Section 11.1: Gathering and Organizing Data  Section 11.3: Measures of Average Competency Assessment This Competency Assessment assesses the following outcome(s): MM150M5: Analyze data using basic statistical techniques in real-life situations. It is time to demonstrate what you have learned in this module. You have calculated probabilities and used the formulas for permutations and combinations. You have also found different measures of central tendency. The Competency Assessment Labs give you the opportunity to prove that you have mastered these topics. There are four Competency Assessment Labs to be completed in the ALEKS Lab tool. 1. CA Lab 1 - Calculate probabilities. 2. CA Lab 2 - Calculate permutations. 3. CA Lab 3 - Calculate combinations. 4. CA Lab 4 - Solve problems involving measures of central tendency. Please note the following when completing the Competency Assessment Labs: ● You will have 45 minutes to complete each Competency Assessment Lab. ● The Competency Assessment must be completed in one sitting. You do not have the option to save and come back to finish the assessment. ● You are allowed unlimited attempts to successfully complete the ALEKS Competency Assessment Labs. ● The ALEKS Competency Assessment Labs will be manually scored by your instructor.

MM150 Module Preview Statistics Page 15 of 15 ● Within the ALEKS Competency Assessment Labs, you will NOT find support resources (i.e., eBook, guided solutions, examples, etc.) that were available in the ALEKS Lab Practice. After you receive access to each module, you will be able to see the submission requirements and a Checklist Rubric for the Competency Assessment.

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