Textbook Features

How To Approach The Mathematical Problem (The PUPP Model)

Our students struggle with completing math exercises from beginning to end. They are unfamiliar with mathematical thought process and the techniques involved. A systematic approach is needed to help students learn how to think. This textbook’s core design centers around a structured thinking process termed The PUPP Model (Plan, Understand, Perform, and Present). This process is found throughout the textbook in every guided example to help students develop a step-by-step problem-solving approach.

1. Plan. One of the most common difficulties is when students rush into calculations and have no clue what they are solving for! This step focuses and reminds students about what it is they are doing. The goal is to encourage students to recognize what question has been asked and what variable(s) need to be calculated.
2. Understand. It is critical to know what you are doing and how you are going to get there. Before performing calculations, this step urges students to think through the entire process required in order to logically arrive at the solution. There are two critical elements:
   1. What You Already Know. Students must read through the question and assign the correct values to appropriate variables. If necessary, diagrams such as timelines are drawn to help visualize the information being provided and what to do with that information.
   2. How You Will Get There. Everybody needs a roadmap. This step focuses students on describing the steps, procedures, and formulas required to arrive at the solution.
3. Perform. This stage is all about the mathematics. Students execute their roadmap and perform the needed calculations and procedures to arrive at the root(s) of the problem.
4. Present. The final part of the model encourages students to express their solution(s) in the context of the question. It’s not good enough just to calculate a number. They have to understand what it means and how it fits into the situation. This also makes it easier to see if the solution makes sense. If not, there is a higher chance of spotting an error. Additionally, visual charts and graphs assist students in understanding how the various numbers fit into the cohesive puzzle.

What Are The Steps Needed To Arrive At The Final Answer? (How It Works)

Have you sometimes known what the destination is but you just couldn’t figure out how to get there? Students commonly experience this problem in financial mathematics, particularly when questions become grander in scope. Integrated into the PUPP Model is another core feature of this textbook called "How It Works". In this section, students can find:

1. Detailed, step-by-step sequential procedures to address common business mathematical problems.
2. Handy reference flowchart guides that summarize the key steps required to arrive at the solutions.
3. Where possible, quick and simple examples to further illustrate the procedure. In every section of the textbook, the “How It Works” is introduced. These steps are then utilized in all guided examples to assist students in taking a problem from beginning to end.

The Repetitiveness Of Annuities

I have heard from instructors, professors, textbook reviewers, and students alike the same concerns about the repetitiveness in teaching the four types of annuities. It is no secret that there are only minor differences between the annuity types. Many have expressed that their courses are highly time-constrained. Other textbooks address most or all annuity types separately. Each annuity type is then solved for the five common unknown variables. This can result in up to twenty different lectures.

An overwhelming number of educators have indicated that they find it better to teach the four annuity types up front. Once students understand how to recognize the annuity type and the key differences, students can solve any annuity for any variable!

In this textbook, the four annuity types are thoroughly introduced and discussed, followed by sections discussing the solving for each formula variable. Key knowledge is offered in a single chapter. This textbook also utilizes only four annuity formulas - two for ordinary annuities and another two for annuities due. Incorporated into the design of these formulas are the mathematics needed to address both simple and general formats. To reduce the chance of error, students are not required to use combinations of annuity formulas nor substitute solutions of one formula into another.

When solving for other annuity variables, students use their algebra skills to substitute and rearrange the four formulas. There are no long lists of formulas that are nothing more than algebraic rearrangements of existing formulas. There are two formulas for ordinary annuities and two formulas for annuities due. Clean and simple.

Relevant Algebraic Symbols

There are two key student concerns here: irrelevant algebraic symbols and algebraic symbols with multiple usages. Both of these concerns are addressed through symbol choices and formulas utilized in this textbook.

Nothing is more frustrating for students than algebraic symbols that have nothing to do with the variable. For example, it is common to let "j" represent the nominal interest rate. To students this is like apples and oranges. What makes more sense is to use relevant algebraic symbols that help students to understand the formulas being presented. Doesn't IY for interest rate per year make much more sense than “j”? This text utilizes representative singular (such as P for profit) or plural (such as PMT for annuity payments) symbols to further student understanding.

Additionally, having identical algebraic symbols with different interpretations is very confusing for students. For example, the symbol for future value (FV) is used to represent the future value of a single payment, an ordinary annuity, or an annuity due. However, many questions require students to execute combinations of single payments and annuities. This requires multiple appearances of the same FV symbol each requiring different computational formulas. Except where industry standards exist, this textbook differentiates algebraic symbols so that each symbol has only one meaning. Thus FV is for the future value of a single payment, FVORD is the future value of an ordinary annuity payment stream, and FVDUE is the future value of an annuity due payment stream. This means less confusion for our students.

How And Why A Formula Works

We all agree that understanding a formula and not just memorizing it goes a long way in business mathematics. In this respect, this textbook offers annotated and detailed formulas allowing students to simultaneously visualize the formula as a whole and by its various components. Instead of cross-referencing variable definitions and concept explanations, each part of the formula is visually addressed and the elements explained as a cohesive whole. Handbook Design It is difficult to get students to look at and use their textbook. An easy reference handbook design forms a cornerstone to aiding our students in two ways.

1. The book offers a friendly, strong visual appeal. It is not just page after page of endless and uninviting formulas. Instead, students find modern graphics, pictures, and an appearance designed to encourage their interaction.

2. Unlike other textbooks, every section and chapter follows an identical structure. The goal is to make material easy to find. Throughout the book there are constant guides and locators.

• In addition to the table of contents, every chapter introduction and summary provides key topic summaries.
• If a student needs to know the steps in solving a problem, students always find the details in the "How It Works" section. If they just need a summary or reminder, they can always find a nutshell summary at the end of each chapter.
• If students need calculator function instructions, they always find it in the Technology section of each chapter summary. Call the book a reference manual if you will. It is about students finding what they need when they need it made easy. Relevance As educators, we constantly hear, “…and when will I ever use that in my life?” This textbook demonstrates to students both personal and professional applications in discussions, guided examples, case studies, and even their homework questions. 1. On a personal level, students are shown realistic scenarios, companies, and products that they commonly are exposed to. It is always easier to learn something when students can relate to it.

On a professional level, this textbook demonstrates business situations in different business fields so that students can see applicability regardless of their chosen career path. Whether students are planning on becoming accountants or marketers, there are applications to be found in this textbook. This book offers to your student:  Math organized by business function using products and companies that are familiar to students.  Both business and personal application sections ranging from HELOCs and Promissory Notes to RRSP planning and purchasing vehicles. Integration Of Technology & Resources Texas Instruments BAII+ Calculator One of the most widely used calculators in Canada, the Texas Instruments BAII+, is illustrated and fully integrated into this textbook. For those instructors and professors utilizing this calculator, step-by-step calculator button solutions are provided at the bottom of relevant PUPP model examples. Improving this integration is the usage of similar formula and calculator symbols that allows students to make the easy transfer between algebraic variables and calculator buttons. If calculators are not used in your course or you use an alternate calculator, the layout and design of the textbook strategically places these calculator solutions in an inconspicuous manner in the guided solutions. Thus, they do not interfere with your students' coverage of the material and are easily skipped. Structured Exercises Every section, as well as chapter end, has approximately 18 practice questions for the students. Students comment that having more than that appears daunting and discourages doing their homework. Imagine reading a section and finding eighty homework questions at the end! Solutions to all exercises are found at the back of the book. The exercises are broken into three sections:

1. Mechanics. This section focuses on fundamental mathematical skills and practicing of the formulas. These questions are straightforward and may appear in a table format that encourages students to become more familiar with the formulas and how to solve them. After completing this section, your students should have the basic mathematical skills however will not be able to demonstrate adequate competency in the subject matter without continuing to the next section.
2. Applications. Once students has mastered the mathematics, it is time to put their skills to work and solve various business and personal applications. The questions in this section are in word format and require the students to execute their problem-solving skills. After completing this section, students will be able to demonstrate adequate competency in the subject matter.
3. Challenge, Critical Thinking, and Other Applications. This section raises the difficulty bar and asks challenging questions. Solutions may require multi-stage approaches or integration of different concepts. Strong problem-solving skills are needed. Questions may also take students in new directions by having them interrelate different concepts. Students completing this section demonstrate a high level of competency in the subject matter.

Identification Of Common Errors & Finding Shortcuts

Built-in to the design of this book are the standard elements that make students aware of the common errors (Things To Watch Out For) as well as some tips and tricks (Paths To Success) along the way. What makes these different in this book is that they are an integrated component of the textbook and not separated into text boxes that are generally ignored by our students.

How Do All The Pieces Fit Together?

Helping your students integrate their concepts is accomplished in two main ways: 1. End Of Chapter Exercises. These questions allow students to explore the various concepts outside of their chapter section. Where possible, various concepts are combined in questions that allow students to integrate their acquired knowledge. 2. Short Case Studies. A fictional company called Lightning Wholesale is used throughout this textbook. Almost every chapter features a short case study showing how a single business applies all the various mathematical concepts into its daily operations. Students can learn how various chapter elements combine together into business scenarios. Basic Version Business Math: A Step-by-Step Handbook 2018 Revision A Creative Commons License (CC BY-NC-SA) J. OLIVIER vii

Am I Understanding The Material? (Give It Some Thought)

The students have read the material, but did they take the time to understand the material? Throughout the textbook, after concepts have been introduced, is a question and answer section called "Give It Some Thought". This is not a mathematical computation section. It features conceptually based questions whereby no calculations are required. Instead, this section offers students periodic checkpoints to determine if they are understanding the relationships of various variables and the concepts being presented.