The consumer education movement aims to teach people how to seek out, **use and evaluate consumer information so that they can improve their ability to purchase or consume the products and services they deem most likely to enhance their well-being**. It seeks to teach consumers how to interact in the marketplace in a way that **allows them to make the best consumption choices for themselves**, given their values and lifestyles. (p. 33) Bloom & Silver, Harvard Business Review, 1976

In 2006, the Financial Literacy and Education Commission (FLEC) published: “Taking Ownership of the Future: National Strategy for Financial Literacy,” which defined the purpose of financial literacy as to: “empower consumers to be better shoppers” (p. v), to help deal with a “

market place that is constantly changing” and to “understand and select the products and services that best suit their needs” (p. vii).

Learning to Read the fine Print: We have to find ways to help students learn to care about the details – learn to ask questions, learn to think it’s worth investigating financial agreements

Show Students the Fine Print (see examples below):

- Let them read it
- Let them make what sense they can of it
- Let them ask questions about it and explore outcomes

Credit Card Examples:

APR or “annual percentage rate” is an annualized interest rate. Different APRs may apply to different balances on your account, such as your purchase balance or your cash advance balance. We use the APR that applies to each balance to calculate the interest that you owe us on the account.

The bill we send you will state your due date and the minimum amount that you must pay us by that date. This amount is your minimum payment. If you do not pay the minimum payment by the due date, we may charge you a late payment fee. You will also be in breach of the contract.

You may pay all or part of your account balance at any time. However, for each bill, you must pay at least the minimum payment by the due date stated on that bill.

Sample problem from the Math Forum’s Financial Education focus:

Choosing CharityIn the wake of the recent tsunami, a company decided to donate to a disaster relief fund. The company started by pledging a certain amount of money. To encourage their 60 employees to make individual contributions, the company pledged to also donate an additional fixed amount for each employee who made a personal donation to the fund.

The company treasurer determined that if one-third of the employees chose to make a donation, the company’s part of the total donation would be $7000. If 50% of the employees donated, the company’s part of the total donation would be $7750.

Find an equation that expresses the company’s part of the total donation in terms of the number of employees who donate.

If every employee chose to donate, what would the company’s part of the total donation be?

If the company’s part was $8875, what percent of the employees chose to make personal donations?

Tools to Start Conversations & Develop the Practices of Financial Decision Making:

Story from the Baltimore Sun about McDonalds and living wages.

Video about McDonalds and hidden debit card fees.

Video about McDonalds and budgeting.

Council for Economic Education’s National Standards for Financial Literacy

CFPB’s Credit Card Contract Definitions

How long will it take to pay off my credit cards

What is my employee total compensation package worth?

National Endowment for Financial Education — resources for educators, check out the High School materials

]]>The consumer education movement aims to teach people how to seek out, **use and evaluate consumer information so that they can improve their ability to purchase or consume the products and services they deem most likely to enhance their well-being**. It seeks to teach consumers how to interact in the marketplace in a way that **allows them to make the best consumption choices for themselves**, given their values and lifestyles. (p. 33) Bloom & Silver, Harvard Business Review, 1976

In 2006, the Financial Literacy and Education Commission (FLEC) published: “Taking Ownership of the Future: National Strategy for Financial Literacy,” which defined the purpose of financial literacy as to: “empower consumers to be better shoppers” (p. v), to help deal with a “

market place that is constantly changing” and to “understand and select the products and services that best suit their needs” (p. vii).

Learning to Read the fine Print: We have to find ways to help students learn to care about the details – learn to ask questions, learn to think it’s worth investigating financial agreements

Show Students the Fine Print (see examples below):

- Let them read it
- Let them make what sense they can of it
- Let them ask questions about it and explore outcomes

Credit Card Examples:

APR or “annual percentage rate” is an annualized interest rate. Different APRs may apply to different balances on your account, such as your purchase balance or your cash advance balance. We use the APR that applies to each balance to calculate the interest that you owe us on the account.

The bill we send you will state your due date and the minimum amount that you must pay us by that date. This amount is your minimum payment. If you do not pay the minimum payment by the due date, we may charge you a late payment fee. You will also be in breach of the contract.

You may pay all or part of your account balance at any time. However, for each bill, you must pay at least the minimum payment by the due date stated on that bill.

Sample problem from the Math Forum’s Financial Education focus:

Choosing CharityIn the wake of the recent tsunami, a company decided to donate to a disaster relief fund. The company started by pledging a certain amount of money. To encourage their 60 employees to make individual contributions, the company pledged to also donate an additional fixed amount for each employee who made a personal donation to the fund.

The company treasurer determined that if one-third of the employees chose to make a donation, the company’s part of the total donation would be $7000. If 50% of the employees donated, the company’s part of the total donation would be $7750.

Find an equation that expresses the company’s part of the total donation in terms of the number of employees who donate.

If every employee chose to donate, what would the company’s part of the total donation be?

If the company’s part was $8875, what percent of the employees chose to make personal donations?

Tools to Start Conversations & Develop the Practices of Financial Decision Making:

Council for Economic Education’s National Standards for Financial Literacy

CFPB’s Credit Card Contract Definitions

How long will it take to pay off my credit cards

What is my employee total compensation package worth?

National Endowment for Financial Education — resources for educators, check out the High School materials

]]>The Math Forum’s Financial Education Page

Video from the Cosby show of Cliff talking to Theo about the cost of living, and another Cosby video about buying used cars.

A couple sample problems:

Taxi Rates:

Cell Phone Plans — great for noticing & wondering:

And a Problem of the Week on Texting:

What’s involved in understanding problems with a financial context?

*Examining the given information and asking:*What do you notice? What do you wonder?*Digging a littler deeper and asking:*What information that’s given is useful? What given information or other information might help you make a decision? What else might we want to know?

Other resources, easily accessible and make for great conversations and problem solving opportunities/projects:

Cable Pricing Schemes

Cell Phone Pricing Schemes

Credit Card Offers

Apps and Applets that graph repayment plans

Interpreting Health Care Plans — look at HR websites to find information

Interpreting Retirement account options

Reading personal finance blogs (i.e., http://www.getrichslowly.org/blog/, http://www.bargaineering.com/, http://www.thesimpledollar.com/, and more) — blogs like this often talk about how to make personal finance decisions and weighing what’s important to you and/or your family and the trade-offs sometimes inherent in such decisions.

mathalicious.com has a great library of problems that tackle many of the concepts above, are connected to the common core and come with lesson plans. Here’s a blog post about their work that I wrote a while back.

]]>I have asked teachers I know who are teaching financial concepts in their classrooms, many of whom have participated in a Math Forum professional development course, to contribute their stories to this blog, this is the third, courtesy of Patty, about an activity that she did with high school students.

Fitting financial topics into my regular curriculum has proven quite challenging!

Recently, we worked on the topic of exponential functions and some of their applications. We did many activities and explorations including the ever famous m & m lab! However, the following is my favorite performance assessment of the unit for two reasons:

- it required an understanding of the mathematical concepts, the scenario and reflection of solutions.
- it let me work in financial topics and discussions that often get overlooked in the typical curriculum.

A Hypothetical Scenario:

An eccentric billionaire has recently decided to give you all $10,000 to invest in one of the options below. You cannot take the money out until 10 years from now. Compare for each option the amount of money that would be available at the end of 2 years, 5 years, 7 years and 10 years. Explain which of the following investments you would place your money in and why. You must include graphs and computations to validate your conclusions. Click here for a copy of the worksheet used to help students organize their thinking.

**Option 1: Place your money in an account earning 4% annual simple interest.****Option 2: Place your money in an account earning 3 6/8 % annual interest, compounded quarterly.****Option3: Place your money in an account earning 3 ½ % annual interest, compounded continuously.**

After students completed the above, they had to pick 5 more data points to include in each option (they were encouraged to use a wide variety ranging from 6 months to 75 years).

Students then answered the following questions:

- At any time do the options yield the same amount of money or return? How do you know? Explain your answer with a graph(s).
- Is there any time simple interest would be the best choice? Any time compounding continuously is best? Explain your answers in a sentence or two.

The tasks created thoughtful discourse for days! Students developed a real understanding of compound interest and have since demonstrated the ability to transfer that knowledge to the behavior of other exponential functions.

]]>I’ve asked Patricia to share some of her students’ work and hope to be posting that here soon!

I have asked teachers I know who are teaching financial concepts in their classrooms, many of whom have participated in a Math Forum workshops of professional development courses, to contribute their stories to this blog, this is the second of what I hope will be many to come, courtesy of Stacey, about an activity that was used with 8th graders.

Middle school students seem so ready to grow up. One of their biggest anticipations is the moment when they will be handed their license and given the opportunity to drive. What they don’t realize is that with a driver’s license comes the cost of driving a car. That’s why I created an activity to show my students just how much gasoline prices have changed, and what that could mean for their wallets in the future.

Click on the image below to download a PDF version of the entire activity

Students were asked to create box-and-whisker plots on a TI-83 graphing calculator. Once they had the graphical display of the data, they were asked to analyze the results. They were asked to find in which decade the gasoline prices were highest and lowest, as well as most stable. They were also asked to find the decade that had the highest average price per gallon of gasoline. As an extension, students researched that decade to find what was happening to cause such high prices. They were really surprised by what they found!

Students gained a new appreciation for all of the talk in the news lately about gas prices and when they are expected to rise, and when they are expected to fall. They also began to realize that, once they drive, they are going to have to plan appropriately for the cost of that privilege.

]]>One example great example is Big Foot Conspiracy, in which students examine the pricing structure of shoes by looking at the cost of children’s vs. adult’s shoes and if it makes sense that a size 6 shoe should really cost the same as a size 11 shoe. Through this exploration students plot data, look at linear and non-linear relationship and compare unit pricing by weight. This lesson helps potential entrepreneurs think about setting prices based on the cost of materials and whether or not potential customers might respond well to various pricing schemes.

A couple others I like are: Go Big Papa in which you explore how good pizza deals really are and iCost which explores whether or not the pricing scheme of apple products is linear. Also keep an eye out for **Tip Jar** which will be back up shortly, but is being updated as we speak. In Tip Jar, students explore the mathematical concepts of proportional relationships using tables, graphs and equations, solve ratio and percent problems **and** they also explore not just how to calculate a tip, but also how tipping works in different countries in terms of the percentage of the wait-staff’s salary that is based on tips. Too often I have found that many real world based lessons stop at the tip calculation, the lessons on this site dig deeper and offer opportunities to make real connections between mathematics, financial options and financial decision making.

I have asked teachers I know who are teaching financial concepts in their classrooms to contribute their stories to this blog, this is the first of what I hope will be many to come, courtesy of Maria, a 3rd grade teacher.

My students are third graders and we had a great time using a tool from The Math Forum. It illustrated the difference between gross and net pay by showing the students how to calculate deductions for federal income tax, social security and medicare. The outcome that I was aiming for was twofold:

1. I wanted my students to understand that you don’t get to take home all of the money that you make and

2. The money that is taken out of our pay goes toward running the city and to take care of us when we are older.

It was very exciting for them because they didn’t have any prior knowledge about payroll deductions. They were actually a bit upset and angered because they didn’t want to part with any of their money. This led to another interesting conversation about how the city has bills to pay. First we talked about how their parents have to pay bills and then it segued into the city. We started talking about how tax dollars go towards repairing roads and streets and bridges and tunnels and city workers. The connection to their parents and bills really helped them to understand that the city has bills to pay. This also led to a question: How does the city make its money? From here, we talked about how collecting taxes from people is not the only way the city makes money. I asked if they had any ideas how the city could make money besides charging taxes. One student said, “The city could charge a fee for using the stores.” Then I asked them if they ever crossed a bridge or went through a tunnel and what they had to do either at the beginning or the end of it. Here, they had an “a ha” moment and said in unison, “Paid a toll”. We could have gone on all day with this one activity as it opened up so many sub-topics and conversations. I hadn’t expected it to go this far but was pleasantly surprised by it.

Even though my students are very young, I feel that it is so important to introduce them things that they will have to do as adults.

]]>For example, in the case of the first questions in this survey, what if instead of posing that questions as it is, you gave your students the following information:

Suppose you have $100 in a savings account earning 2 percent interest a year. What do you think would happen after 5 years?

There are lots of opportunities to take financial education content and work it into math classrooms in ways like this – getting kids talking about money (investments or debt) and the ways it might grow – linearly and exponentially – and what happens over time and how long those times frames might be. This can help to create awareness of the different types of financial products available and what those difference might really be about.

]]>I found the quiz in this article to be particularly interesting not only because it make a strong connection between common middle school mathematical concepts (percents, fractions, etc) and financial decisions, but it also raised for me a less discussed notion that people need not just understand these ideas, but they must be able to make sense of them quickly and in potentially stressful situations. At times of large purchases, like homes or car purchases, or for that matter, college, people often may not have a concrete idea what they are getting into as compared to what they can really handle (as evidenced by the recent US housing crisis). People tend to think of purchases like this at fixed monthly expenses, but in truth the decisions are even more complicated. One is not just buying a house and incurring a mortgage payment, he or she needs to know what they would do if the roof leaked, if the washing machine broke, etc. These decisions are complex beyond being able to calculate a sale price based on a percentage discount or the likelihood of winning the lottery (although those kind of calculations and understandings are important to financial decisions).

This raises questions for me about two things, first – how can we help students build fluency (that is their ability to do mathematical calculations quickly and accurately in their heads) with the concepts presented in this quiz in meaningful ways beyond (or in addition to) repetitive practice with contexts they think they will never use (or without context at all); and second – are there ways we can use the math classroom to help students make more sense of these kinds of decisions and how to model the true costs of home ownership, car ownership, the penalties (costs) of not making timely payments and other realistic scenarios.

]]>**Building Functions**

Sasha and Tony look at the deals on CDs at a music store Website

*Sasha: Look, at the bottom of the page are all these CDs for 28% off.*

*Tony: Yes, but by the time you add in sales tax and shipping, you’d be better off going to the mall to get them.*

*Sasha: Are you sure? We’d better try pricing some. I’ll choose a bunch, but I won’t order them until we see how much they really cost.*

They pick out six CDs and add them to the shopping cart. Then they click the checkout button.

Sasha and Tony’s checkout page looks like this:

1. Copy and complete this table

Sasha and Tony look at the checkout page, and the totals agree with their calculations.

*Sasha: It’s pretty mechanical. Look, for the next one, I write this.*

*So the total cost is $13.33 and that’s what’s in the table!*

*Tony: Look, the calculations are even more mechanical if you keep track of the steps. They go this way. Suppose the cost is some number C.*

Now Tony writes on a piece of paper.

*Sasha: Good job! The last line is like a machine that does it all.*

(C – 0.28C) + (C – 0.28C) x 0.05 + 2

*The rule calculates the total cost of any CD during the sale.*

2. Use Sasha and Tony’s machine to calculate the total cost of each CD in their list. Check your results against the total costs that you found on the checkout page.

I like this example because it’s realistic context in terms of the kinds of decisions we regularly make as shoppers. Obviously, there are other factors that may come into play for such decisions — how far is the mall, how long does it take to get there, how much does it cost to get there (bus fare, gas cost, etc.), how much time do we have, but overall this problem represents a nice first step to thinking about this kind of decision and connects it to math we’d see in the classroom. More importantly, there’s nothing to prevent these other factors from entering a conversation in a math class about a problem like this.

]]>