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**Financial Algebra © 2011 Gerver/Sgroi Pub date: 1/27/10**

Welcome to your brainshark on Financial Algebra hosted by Robin LeFevre and Eve Lewis. FA publishes on January 27, 2010.

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**National Sales Consultant**

Financial Algebra Debbie Henson National Sales Consultant

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**www.cengage.com/focus/IL Mary Sommers Mary.sommers@cengage.com**

Counties I Cover Toya Moore Kimberly Lourinia , x2606 Larry Schneider , x1571 Margie Schneider , x1553 Heather Cramer , x2605

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**Business and Finance Applications**

Financial Algebra Math Content Business and Finance Applications Financial Algebra Everything you need to know, but no one teaches you! FA provides math content plus business and finance applications. FA teaches you everything you NEED to know, but no one teaches you. It shows students that there a purpose to mathematics.

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**Financial Algebra Math course with a Finance setting**

3rd or 4th year math credit Prerequisite: Algebra I College Prep course Freshman Sophomore Junior Senior Algebra 1 Geometry Algebra 2 Financial Algebra *FA can be taken concurrently with Alg 2 or Geometry Financial Algebra is a true Math textbook designed for a math course with a Personal Finance Setting. It is designed to serve as a student’s 3rd or 4th year math credit. For example, students may take Algebra I, then Geometry, then Algebra II, and then Financial Algebra. FA can be taken before or concurrently Algebra 2 and Geometry. This course CANNOT REPLACE Algebra I – Algebra I is a must have pre-requisite for this course. Several teachers I have spoken with would like to use this book for their College Prep Math Course. College Prep math is usually a senior level course that reviews Algebra I, Algebra II, and touches on Precalculus topics. Algebra, Geom, FA Alg, FA, Geom, Alg 2 Alg, Geom, FA, Alg 2 Alg, Geom, Alg 2, FA They can concurrently take Alg 2 with FA They can concurrently take Geom with FA They must have Alg 1 as a prerequisite.

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**Who will take this course?**

Juniors and Seniors Senior who hasn’t taken math since the 10th grade, but needs to fulfill a 3rd Math credit to graduate. Non-College bound students going straight into the workforce College bound students who are not going to major in Science or Mathematics This course will be taken by mostly Juniors and Seniors. This is a perfect solution for a Senior who hasn’t taken math since the 10th grade, but needs to fulfill a 3rd Math credit to graduate. Many schools and even states are beginning to require students to take 4 years of Mathematics. This is the perfect course for students who are not college bound and are going to go directly into the workforce, as well as, for students who ARE college bound, but are not going to major in Mathematics or Science and do not choose to take the traditional Precalculus or Calculus course. Many of the teachers I have spoken with would like this to be a required course for ALL of their students because these are concepts that every single person whether you are college bound or not is going to have to face throughout your life.

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**Financial Algebra 10 chapters under six financial umbrellas: Investing**

Banking Credit Income Taxes Insurance Household Budgeting The book features 10 chapters under six financial umbrellas.

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**Algebra Mechanics and Problem Solving Advanced Mathematics Topics**

Coverage Algebra Mechanics and Problem Solving Advanced Mathematics Topics Basic algebra formulas with variables Equations Functions Systems of equations Graphs Statistics And more! Piecewise functions Regression Limits Exponential functions Linear and Quadratic systems And more! It reviews and strengthens algebra mechanics and problem-solving skills while at the same time addresses selected advanced mathematics topics such as piecewise functions, limits, quadratics systems, and natural log.

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**Financial Algebra Table of Contents**

1 The Stock Market 2 Modeling a Business 3 Banking Services 4 Consumer Credit 5 Automobile Ownership 6 Employment Basics 7 Income Taxes 8 Independent Living 9 Planning for Retirement 10 Prepare a Budget It is important to understand that this is a true Math textbook, not a Personal Finance text. If you look at the brief TOC, it appears to be a personal finance book. This is because the math concepts are presented in real-world context, so the book is organized by real world topic.

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**Detailed TOC Math topics covered in the chapter!**

We decided to create a detailed Table of Contents that highlights the math concepts taught in each chapter to show that this is not a PF text. The blue bullet points describe the Math Concepts taught in that chapter. This is very important to point out to your instructors.

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In section 5.5 the students will be learning how to write, interpret, and graph a straight line. These concepts will be taught in the context of automobile depreciation.

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How can you model automobile expense (loan payments) and depreciation over a fixed period of time? What is the value of your car? Read problem… This particular problem is an offshoot of straight line depreciation and expense equations which was covered in previous chapter.

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**Equation of a line y = mx + b Remember this?**

In this example, the students are learning about linear equations and the slope of a line.

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**EXPENSE and DEPRECIATION FUNCTIONS**

(35.24, ) As you can see from the graph Expenses increase and value depreciates. At this point the class will discuss - What is so important about the intersection point? (35.24, 23,7333)? What happens before and after that point? What decisions can be made? Explaining to the students that you are still paying money, but the value of your car is decreasing. The day you pay off your car and make the 25,000 dollar payment, your car may only be worth 14,000. So, you are going to be putting more money into car than what the car is worth. Students are dumb founded by this. This is a great class discussion. At this point, students can’t believe that they are not “hating” math class – they are supposed to hate math. They are actually getting to talk about things that are important to them.

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**The next example is from section 3. 4 on Compound interest**

The next example is from section 3.4 on Compound interest. Instead of giving students the compound interest formula and telling them “believe me, it works” and then asking them to plug and chug… Gerver and Sgroi break it down day by day so that students can understand the concept of gaining interest on your interest.

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**How does your money grow? What is compound interest? SAVINGS ACCOUNTS**

Read problem… Gerver and Sgroi don’t jump into the formula. One of the things that the formula won’t handle is if you make deposits and withdrawals throughout the year. The formula only works if you deposit money and then don’t touch it. So what the book does is show students on a day by day basis how compounding interest works.

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**Principal Used to Compute Interest**

Date 11-Jul 12-Jul Opening Balance $1,234.98 Deposit (+) $34.00 $345.77 Withdrawal (-) $200.00 Principal Used to Compute Interest Day’s Interest rounded to the nearest cent Ending Balance (this is also tomorrow’s opening balance) So here, we are showing the opening balance, the deposit and withdrawal on July 11th.

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**Principal Used to Compute Interest $1,068.98**

Date 11-Jul 12-Jul Opening Balance $1,234.98 Deposit (+) $34.00 $345.77 Withdrawal (-) $200.00 Principal Used to Compute Interest $1,068.98 Day’s Interest rounded to the nearest cent $0.09 Ending Balance-(this is also tomorrow’s opening balance) $1,069.07 The principal used to compute the interest is after the deposit and withdrawal. That day’s interest is calculated by multiplying by the rate and dividing by There is no formula for that. Then add the 9 cents to the principal. Penny double everyday – in the book somewhere. After 30 days you are making over a million dollars. Let it unfold over 5 minutes rather than a teacher saying take my word for it.

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**Principal Used to Compute Interest $1,068.98 $1,414.84**

Date 11-Jul 12-Jul Opening Balance $1,234.98 $1,069.07 Deposit (+) $34.00 $345.77 Withdrawal (-) $200.00 --- Principal Used to Compute Interest $1,068.98 $1,414.84 Day’s Interest rounded to the nearest cent $0.09 $0.12 Ending Balance-(this is also tomorrow’s opening balance) $1,414.96 The ending balance is the beginning balance for the next day, so they see that they are gaining interest on their interest. Kids don’t get this if you jump right into the formula. You don’t get this kind of aha moment until you look at it day by day. Sometimes you really need to visualize this. Penny double everyday – in the book somewhere. After 30 days you are making over a million dollars. Let it unfold over 5 minutes rather than a teacher saying take my word for it.

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**Here is what these images look like in the book.**

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**In the next section the students will make computations using the compound interest formula.**

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In section 7.1 students are going to learn about piecewise functions within the context of tax tables, worksheets, and tax schedules.

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**How can you model and graph the tax schedules? FEDERAL TAXES**

Here is the tax schedule for taxpayers filing jointly. So, for example if you make over 61,300 but not over 123,700 dollars then you will pay a fixed 8,440 plus 25% of the amount over 61,300 that you make.

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**We can model the schedule using piecewise functions.**

There are 6 taxable income intervals in the chart. If x represents any taxable income, then those intervals can be expressed in tax schedule notation, interval notation, and compound inequality notation as follows:

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**Tax Liability Equation**

For each interval in the tax schedule beyond the first, the tax is calculated by adding a fixed tax to a percentage of the difference between the taxable income and some number that is stated in the schedule. Let y represent the tax liability and x represent the taxable income. The tax liabilities can be expressed algebraically as shown here: Tax Schedule Notation Tax Liability Equation Over $0 but not over $15100 Y = 0.10x Over $15100 but not over $61300 Y = (x ) Over $61300 but not over $123700 Y= (x – 61300) Over $ but not over $188450 Y= (x – ) Over $ but not over $336550 Y= (x – ) Over $336550 Y = (x – ) So now, we are going to take that information and write in tax schedule notation and the tax liability equations.

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**Compound Inequality Notation Over $0 but not over $15100 **

Tax Schedule Notation Interval Notation Compound Inequality Notation Over $0 but not over $15100 0 < x £ 15100 (x > 0 and x £ 15100) Over $15100 but not over $61300 15100 < x £ 61300 (x > and x £ 61300) Over $61300 but not over $123700 61300 < x £ (x > and x £ ) Over $ but not over $188450 < x £ (x > and x £ ) Over $ but not over $336550 < x £ (x > and x £ ) Over $336550 x > (x > ) Now we are going to write the income in three different notations… tax schedule notation, interval notation, and compound inequality notation. All 3 notations mean the same thing… your income is greater than 61,300 and equal to or less than 123,7000.

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Piecewise Function If f(x) represents the entire tax liability function for married taxpayers filing jointly, then this function can be written in piecewise function notation as Now, we can write the entire schedule as a piecewise function. You might remember seeing something like this in your high school math class. I sure do, but I never really understood what piecewise functions were because I didn’t know what their purpose was? Now, I understand the need and it makes sense why the equations are different for different values of the domain.

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**HOW DOES THE TAX COMPUTATION WORKSHEET RELATE TO THE PIECEWISE FUNCTION?**

100,000 25,000 18,115 The IRS includes the tax schedule for information purposes only. For taxable incomes over $100,000, taxpayers must use the tax worksheet. In colomn you would enter in your taxable income, then mutliply that by .25 and then subtract 6,885. At this point, you may be asking yourself… where did the 25% and 6,885 come from?

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**For taxable incomes over $61300 but not over $123700, the equation is stated as**

y = (x – 61300) where y represents the tax liability and x represents the taxable income. Use the distributive property and combine like terms as follows: y = (x – 61300) y = x (61300) y = x – 15325 y = 0.25x – 15325 y = 0.25x – 6885 Well, remember the equation for the income range is… If we simplify this equation we get y = .25 x – 6,885

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y = 0.25x – 6885 100,000 25,000 18,115 Which is exactly what the worksheet guided us to do.

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Instructional Model A relevant quote and chapter introduction set the stage for the topics covered in the chapter.

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Instructional Model Really? Really! grasps students’ attention by discussing a fascinating real-life topic related to the chapter content. Really The Really? Really! chapter opener lures the students into the chapter by discussing a fascinating real-life topic related to the content.

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Instructional Model An intriguing quote at the beginning of each lesson motivates the learning of lesson content Each lesson begins with a discussion of terms and concepts related to the lesson topic. The first couple paragraphs of each lesson is where students and instructors will be learning the real world topics and vocabulary needed to complete the chapter exercises. In many cases, the instructor, especially if they are a young new teacher right out of college, may be learning about these topics right along with the students. That is okay… the book is very scripted so the teacher does not have to be an expert on these topics.

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Instructional Model Skills and Strategies, teaches the math concepts through worked-out examples. Several examples teach each math concept step-by-step. All math concepts are taught within real-life context. When am I every going to use this in real-life? is answered here! Skills and Strategies, the heart of the lesson, teaches the math concepts through worked-out examples. Several examples teach each math concept step-by-step. This is basically providing teachers with a script for the lesson. These are the examples the teacher will use to teach the math concepts. script

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Instructional Model Check Your Understanding allows students to immediately practice the concept on their own. Extend Your Understanding provides an opportunity to solve a more challenging problem. Check Your Understanding allows students to immediately practice the concepts on their own. The questions are similar (parallel) to the example and will help students gauge their understanding of the skills being taught. Extend Your Understanding provides an opportunity to solve a more challenging problem. This helpful for classes with a wide range of ability levels.

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Instructional Model Carefully developed, proven applications at the end of each lesson require students to apply concepts to a specific question or scenario. As you can see, there are no naked number throughout this entire text. Every example and exercise is presented within real world context.

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Instructional Model Chapter Assessment provides an opportunity for students to check their knowledge of chapter content. Real Numbers: You Write the Story asks students to examine a graph and write a story focused around the graph’s information. Real Numbers: You Write the Story, begins the chapter assessment asks students to examine a graph and write a story focused around the graph’s information, giving the students the opportunity to be creative while at the same time sharpening their graph interpretation skills.

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Instructional Model Reality Check assists in extending the learning experience beyond the classroom with specific suggestions for research opportunities, projects, and guest speakers. Reality Check extends the students’ learning experience well beyond the classroom with suggestions for field work, activities, projects, and guest speakers.

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Instructional Model Dollars and Sense guides students to the companion website where they will find up-to-date information and activities related to the chapter content.

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Instructional Model Meaningful applications at the end of each chapter require students to apply concepts that were taught throughout the chapter.

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**Supplements Annotated Instructor’s Edition Instructor’s Resource CD**

Lesson plans, PowerPoints, and Workbook Answers ExamView Test Generator Student Workbook eHomework Interactive online homework Adobe eBook Companion Website

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**eHomework – Interactive Online Student Workbook**

Saves time and ensures immediate student understanding! Automatically graded assignments for the instructor Immediate feedback on every question for the student eHomework is an interactive online version of the student workbook. It provides automatically graded assignments for the instructor and immediate feedback for the student. eHomework is available for BOTH Financial Algebra and Business Math.

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**Hear from the authors! www.cengage.com/school/teamup Dr. Robert Gerver**

If you would like to learn more information about Financial Algebra, please visit TeamUp to access the recorded author webinars. Dr. Richard Sgroi

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**Financial Algebra © 2011 Gerver/Sgroi Pub date: 1/27/10**

Thank you for your attention! Happy Holidays!

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**Prepare Florida Students for Tomorrow’s World**

Business Math Mary Hansen 17th Edition Course Title: Consumer Math Introduction I am a mathematics and special education teacher who has taught consumer math, math of money, tech prep, alg, geom, alg 2 through college algebra. I co-authored an algebra, geometry, algebra 2 series that was adopted in Florida in a previous adoption. I am here today to talk to you about my latest project, which covers the course standards and access points for Florida Consumer Math. © 2010

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**Prepare Florida Students for Tomorrow’s World**

Correlated for Florida Consumer Math success Complete Student and Instructor support package Excellent organization for effective instruction and student learning Mathematics is taught, reinforced, and assessed with real-world applications In the next few minutes, we will look at how the text and resources will prepare students and teachers for Florida consumer math success, the many resources that will support teaching and learning, how the text is organized with both teacher instruction and student learning, so that students can be successful with real world consumer math issues.

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**Correlated to Florida Standards and Access Points**

MA.6.A.1.3 Solve real-world problems involving multiplication and division of fractions and decimals. xxv-xxvi, xxviii, 63, 80-86, 99, , 137, 143, 147, 170, 173, 188, 192, 243, 249, 278, 289, 299, 347, 351, 353, 357, 365, 367, 370, 429, 432, 438, 455, 487, 498, 537, 552, 563, 569 I MA.6.A.3.1 Write and evaluate mathematical expressions that correspond to given situations. xxii, xxxv, 5, 6, 15, 21, 81-84, 112, , 274, 296, 304, 310, 338, 392, 427, 439, , MA.6.A.3.4 Solve problems given a formula. 5, 6, 15, 21, 22, 81, 84, 112, , 274, 296, 392, 439, , MA.6.A.5.1 Use equivalent forms of fractions, decimals, and percents to solve problems. xxxi-xxxii, 4, 8, 14-19, 40, 43-45, 56, 61, 62, 63, , 128, 134, 138, 148, , 258, 290, 293, , , 359, MA.6.S.6.1 Determine the measures of central tendency (mean, median, mode) and variability (range) for a given set of data. xxvii, 27-31, 33, , , 518, see also (**Click on the 2009 Adoptions tab on the left) MA.7.A.1.2 Solve percent problems, including problems involving discounts, simple interest, taxes, tips, and percents of increase or decrease. xxxi-xxxii, 14-19, 43-45, 57, 65, 81, 108, , , , , , , , , 367, , , You will find complete and thorough coverage of the course standards and the access points in the text itself, as well as online where there are additional workshops created specifically for Florida teachers. Additional online workshops created for Florida teachers

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**Aligns with the Jump$tart Coalition’s National Standards for Personal Financial Literacy**

The text aligns with the JumpStart Standards for personal Financial Literacy so you can be confident that students are not only learning course standards, but you are equipping them to make wise financial decisions now and in the future.

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**Major Tools: Students www.cengage.com/school/business/math**

Student Edition (hardcover text) Companion Web Site The student text and companion website are the major tools for students. The website supports the content learning, and also helps students complete net bookmark internet activities that appear in the text.

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**Ancillary Materials: Students**

Student Workbook (softcover) Extra practice for every lesson Online E-book: Student Edition View with free Adobe® Acrobat® Reader™ Ancillary materials for students include a workbook, with extra practice for every lesson of the text, and an online e-book so students can access the text anywhere they have Internet access.

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Major Tools: Teacher Instructor’s Wraparound Edition Companion Web Site: The major teacher tools includes the teacher’s wraparound edition with reduced student pages and teaching resources in the margins and a companion teacher website with a wealth of additional resource material to support your instruction.

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**Ancillary Materials: Teacher**

Instructor’s Resource CD Lesson Plans, Algebra and Geometry Activities, Technology Activities, Chapter Test Masters and Answers; Competitive Event Guide; Instructor’s Edition of Workbook ExamView Assessment Suite More than 40 questions per chapter Multiple choice, numeric response, completion, short answer Data Activities CD The teacher’s ancillary materials include three CD’s. The instructors resource CD is packed full of resources such as lesson plans, additional activities, test masters and wealth of other materials that are also available online. ExamView Assessment Suite provides more than 40 questions per chapter in a variety of question formats and the ability to add your own questions to create paper or online tests. The Data Activities CD has the spreadsheets for the technology activities.

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**Effective Instruction Design**

Open Goals, key terms, real-world lesson starter Start Up revisited in the Wrap Up. The text uses an effective instruction design. The start up sets the context by giving a real-world scenario that can be solved using the skills of the lesson. The Start Up question will be revisited at the close of the lesson in the wrap up. Access Point MA.912.F.4.Su.a Distinguish between income and expenses.

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**Lessons-Focused on Math**

Teach Math Skill Builder reinforces basic skills Correlated to the Skills Workshops. The Math Skill Builder reviews basic math skills that are used in the lesson. In the teacher’s edition, each question is correlated to a skills workshop at the beginning of the text. So, if students are struggling with the problems in the skill builder, extra practice is available right in the textbook. MA.6.A.5.1 Use equivalent forms of fractions, decimals, and percents to solve problems.

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**Lessons-Focused on Math**

Teach Math content taught step-by-step in context. The content is taught through step-by step examples in context. Students will never ask you the dreaded “When am I ever going to use this question!” MA.7.A.1.2 Solve percent problems, including problems involving discounts, simple interest, taxes, tips, and percents of increase or decrease.

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**Reinforcement Activities**

LA The student will use new vocabulary that is introduced and taught directly. Access Point MA.912.F.1.Su.c Identify interest rates used in real-world situations. Throughout each chapter there are reinforcement activities that ask students to apply the knowledge to consumer and financial issues, and group or communication activities.

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**Tips Provide Extra Help**

Switch out with high res DONE Only include tips on this slide DONE Possible a new heading for this title? DONE

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**Integrated Technology**

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**Data, Technology & Careers**

The text offers a host of other ways to get students using and thinking about mathematics in a variety of contexts. Statistical insights provides real-world data to analyze, while the technology workshop and the net bookmark give students an opportunity to use technology to further their understanding. A career connection in each chapter helps students to see that mathematics is important in many different careers.

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**Ongoing Assessment and Review**

Practice Basic Math Practice Consumer Math Practice Best Buy Financial Decision Making Integrating Your Knowledge Critical Thinking Mixed Review Each lesson closes with a wealth of practice exercises. Each lesson set begins with basic math review that is tied to the math skill builder from the beginning of the lesson and ends with mixed review. In between are lots of consumer math practice exercises including exercises that ask students to find the best buy, make financial decisions, integrate their knowledge, or to think critically. Access Point MA.912.F.4.In.b Use real-world strategies needed to manage personal income.

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**Ongoing Assessment and Review**

The text provides many opportunities for ongoing assessment and review. In addition to a chapter review and assessment in each chapter, there is a cumulative review every other chapter that includes multiple choice, open ended and constructed response questions.

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**Prepare Florida Students for Tomorrow’s World**

Next Generation Sunshine State Standards (NGSSS) Real-world consumer applications Wealth of activities and exercises Resources include Instructor’s Wraparound Edition Instructor’s Resource CD Data Activities CD ExamView Assessment Software Student resources include Student Edition Workbook Website Ebook Cengage’s Business Mathematics will put powerful tools in teacher’s hands to help students meet and exceed the expectations in the Next Generation Sunshine State Standards.

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**Prepare Florida Students for Tomorrow’s World**

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