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From Middle School Portal

Money, Money, Money: The Mathematics of Finance

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Finance depends on a multitude of math skills: arithmetic operations, reading and interpreting graphs, algebraic thinking, probability, and basic statistics. At the fundamental level, these skills are covered thoroughly in the middle school curriculum---although often not in the context of everyday living. When problems on sales, profit, and interest are presented solely within textbook pages, the material can come across as dry and disconnected from a teenager’s reality, despite students’ inherent interest in the topic of money.

Hence the challenge: to immerse students in financial scenarios that connect to their real worlds. Money itself, its invention and history, seemed a compelling and necessary starting point. From there, this resource guide presents a section of problems, followed by a section of full-blown lesson ideas.

These digital resources were selected in line with middle-grades standards set out by the National Council of Teachers of Mathematics, which encourages effective use of mathematics in quantitative scenarios outside the classroom.

A special section on background for teachers offers links to a deeper history of money as well as resources that can be used in creating lesson plans. We hope you will find these resources useful in connecting your students to the practical world of finance!

Contents


Background Information for Teachers

These resources offer material that can answer your own questions on the origins of finance, as well as give you material for class discussions and activities. I especially recommend the images of early coins and paper money.

History of Money from Ancient Times to the Present Day Brief essays and excellent reference material! I suggest the link to Comparative Chronology of Money, a timeline conveniently broken into periods from 9000 B.C. to the present century. Here we learn that “cattle are probably the oldest of all forms of money.” You will also find interesting links to Money in North American History and to The Word “Dollar” and the Dollar Sign---and much more.

The History of Banking This Wikipedia article presents a concise history of the first banks (“probably the religious temples of the ancient world”) to modern-day global banking.

U.S. Census Bureau: Income How much do people make? An in-depth resource for reports on national income and measures of poverty and income, these statistics can serve you in creating classroom challenges or directing investigations

If You Made a Million On one level, this is just a picture book, but on another it is an introduction to fundamentals of personal finance. For the middle school student, it discusses such topics as savings, compound interest, and borrowing, and for years it has inspired lesson plans. The site does not contain the book but does offer ideas from teachers on how to use it in a math class.

From Barter to Coins to Credit Cards

Three pages begin here, each a display of items used as money. Images range from items used in barter, such as stone axes and beaver pelts, to intricately designed coins to paper money. Students may use this as a resource for projects or as an introduction to the topic of finance.

Historic Highlights From the U.S. Mint, a brief history of minting U.S. currency. A timeline extends from 1790 through 2010 with comments, tailored for students, on the most important points in design and distribution.

I Owe You: Understanding Credit Cards and Credit Card Debt In this lesson, students examine and learn the basics about credit cards and credit card debt, then create an informational brochure for graduating high school seniors or other students.

The MegaPenny Project This site illustrates the magnitude of large numbers by showing and describing arrangements of large quantities of U.S. pennies. It begins with16 pennies that measure one inch when stacked and one foot when placed in a row. The next visual shows a thousand pennies, and in progressive steps the site builds to a quintillion pennies. All pages have tables at the bottom listing the value of the pennies on the page, size of the pile, weight, and area (if laid flat).

Money Problems

The study of finance can begin with simple money problems, the kind we all have, even our students. Especially selected for middle school students, this set of problems can introduce a topic, open a class conversation, or simply give students practice. A wide range of problem scenarios here!

Movie Money: Do Movies Make Money? Does showing movies make money for theater owners? With information about box office receipts, the percentage that theater owners must pay to movie distributors, and operating expenses, students answer the question by making profit-and-loss calculations.

Working Hours: How Much Time Do Teens Spend on the Job? This activity challenges students to interpret a bar graph to determine the average number of hours teenagers work per week. A hint suggests that students assume that 100 students participated in the survey. Interesting statistics about the hourly wages and annual salaries of various occupations are given.

Soda: Does It Make a Difference Where You Shop? In this online activity, your students compare soda prices from two stores using data displayed on a scatter plot graph. Students are shown how the line y = x can be used to analyze the data and draw a conclusion. Further problems involving scatter plots compare car mileage and the performance of NBA players.

Salaries: Will Women Ever Earn as Much Money as Men? In this activity, students are given a data set that compares the salaries of men and women over a period of years and asked to determine if women's salaries will ever be equal to those of men. The page gives a hint, the solution, related math questions, and resources for learning more about income and data.

What's Round, Hard, and Sold for 3 Million Dollars? This activity challenges students to determine which is worth more today, Babe Ruth's 1927 home-run record-breaking ball or Mark McGwire's 70th home-run record-breaking ball that sold in 1999 for 3 million dollars. To solve this challenge, students build a table and observe the growth pattern as the value of Ruth's ball doubles every seven years.

So How Much Does It Cost? A rack of clothing, originally on sale for 30 percent off the original price, has been discounted by an additional 50 percent. Is the new price actually 80 percent of the original price? Multiple approaches to the problem are given in the solution section.

Problems from 19th Century American Textbooks The problems here, except for the first, all deal with money situations from long ago. What’s interesting is the context of the times; for example, in one problem the teacher earns only $3.25 per week and “keeps” the school 11 ½ weeks. But what if the town paid her only $2.875 per week? For how many weeks could it afford to keep the school open?

A Problem from Alcuin of York Alcuin of York, educator and advisor to Charlemagne, devised this intriguing inheritance problem. The page includes solutions given by 8th-grade students and others.

Plan and Analyze Expenses with Given Parameters In this question from the National Assessment of Educational Progress (NAEP), students must show their work and reasoning. Presented with various expenses associated with attending a basketball camp, students must find all combinations of activities whose total cost would be less than $1,000. Representative student responses are given as well as a scoring guide.

Find the Total Cost of Three Items, Including Tax For this multiple-choice NAEP question, students find the total cost of three items, given the cost of each and the rate of sales tax. Included with this sample test item are access to performance data, a scoring key, and discussion of the item’s content.

Solve Problem Involving Money This NAEP problem, intended for the grade 8 test, requires multiple steps. Besides the solution, student responses and performance data are offered.

Lesson Ideas

These lesson plans and activities aim to immerse students in financial situations that require their math skills to navigate.

Savings and Credit These pages deal with the principles and vocabulary of simple and compound interest, and what they have to do with credit cards and savings accounts. An interactive activity sets students to work out which is better: to lease or to buy a car. All in all, a good introduction to the financial world.

Million Dollar Giveaway My prize for winning a contest is cash up to $1,000,000—in one-dollar bills. The catch is that I am only allowed one suitcase in which to carry away as much money as it will hold. I show the students my suitcase; they devise plans to estimate the amount of money that would fill it.

Torn Shirts Inc. A challenging but well-guided activity, Torn Shirts has students analyze data to reach a decision on a business question. They first determine the probability that a customer calling to order a shirt gets a busy signal, then estimate the amount of money the company might lose when customers get a busy signal. Work with graphs and averages, especially the median, helps students reach a conclusion.

Hot Dog Sales The main activity here is creating an equation that connects profit and revenue for a small business. Given the start-up cost for a hot dog stand and a selling price for each hot dog, students determine how many hot dogs would have to be sold before any profit would be realized—first, by creating a simple table; next, by developing a graph; and finally, by writing an equation.

Fun and Sun Rent-a-Car The Green family is planning a one-week vacation in Florida and needs to rent a car while there. They estimate they will drive between 500 and 1,000 miles. They must choose one of four rental plans available. Students are guided to construct graphs to see which plan is better for different amounts of mileage.

Hollywood Box Office Older middle school students can investigate the average earnings of a movie in a given week using actual data collected from web or print sources. Various statistical measures come into play in this activity: measures of center, outliers, box plots, histograms, and stem-and-leaf plots. These abstract terms take on meaning when applied to a real situation.

Maximizing Profits on Donut Sales For those students taking algebra, this rich problem presents an appropriate challenge. The central question: "Will raising the price lead to more income?" highlights the use of graphs (price vs. income) and culminates in an algebraic formula that describes the profit-and-loss situation.

Math Behind the Market The site offers sample lesson plans at both the intermediate and the advanced levels on What Is a Stock? and Dividends and Earnings. The well-set-out lessons involve solid practice in arithmetic, graphing, and algebra, all in the context of the stock market. Teachers can receive the complete set of these lesson plans free when their student teams participate (for a moderate fee) in The Stock Market Game.

The Cost of a Great Looking Floor Students create and estimate the cost of a tile floor design using geometric shapes, ratios, proportions, and percents. All cost estimates are based on the purchase of full boxes of tiles so students have to weigh cost against design considerations. Cost estimates also include labor and taxes for a more realistic estimate of total cost. An activity sheet, instructions, and suggestions for assessment are included.

Football Finances In this lesson, students analyze pictures of football stands to make estimates related to the attendance at the Super Bowl. An activity sheet plus class discussion guides their estimates not only of attendance but also of gallons of soda, pounds of hot dogs, value of all tickets sold, number of parties held, and so forth. A valuable lesson in estimation!

Taking Its Toll In this two-period lesson, students compare the price of a toll to the distance traveled. They investigate data numerically and graphically to determine the per-mile charge, and also predict the cost if a new tollbooth were added along the route. Teacher-friendly instructions explain how to link to toll road sites in your state.

SMARTR: Virtual Learning Experiences for Students

Visit our student site SMARTR to find math-related virtual learning experiences for your students! The SMARTR learning experiences were designed both for and by middle school aged students. Students from around the country participated in every stage of SMARTR’s development and each of the learning experiences includes multimedia content including videos, simulations, games and virtual activities. '

Careers

The FunWorks Visit the FunWorks STEM career website to learn more about a variety of math-related careers (click on the Math link at the bottom of the home page).

NCTM Standards

The materials here, both problems and lessons, align with the Process Standards set out by the National Council of Teachers of Mathematics in Principles and Standards for School Mathematics. In particular, applying their math skills within financial scenarios connects students to the world they live in, a world of interest rates, census statistics, costs and sales, profit and loss. The Connections Standard points out that interdisciplinary experiences “help students see the usefulness of mathematics both in school and at home,” in such a way that “mathematics and other disciplines [are] seen as permeating life and not as just existing in isolation” (NCTM 2000, 279).

Problem Solving is another process standard addressed through these resources. Selected for the opportunities they offer middle-grades students to build on their understanding and to extend their reasoning powers, these resources aim to involve students in compelling investigations, whether at the individual-problem or the full-lesson level.

These materials also align with the Content Standard of Number and Operations, presenting financial situations that require practice in computing with decimals and percents even as students develop their understanding of how mathematics is utilized in everyday transactions.

In this publication, we hope you will find problems that demonstrate the connection between school mathematics and finance, problems that immerse your students in interesting, challenging investigation even as they hone students' mathematics skills.

Reference

National Council of Teachers of Mathematics (NCTM). 2000. Principles and standards for school mathematics. Reston, VA: Author.

Author and Copyright

Terese Herrera taught math several years at middle and high school levels, then earned a Ph.D. in mathematics education. She is a resource specialist for the Middle School Portal 2: Math & Science Pathways project.

Please email any comments to msp@msteacher.org.

Connect with colleagues at our social network for middle school math and science teachers at http://msteacher2.org.

Copyright August 2009 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0840824. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.