Text, Email and Phone Phishing
If I was playing some sort of financial scam bingo, I would surely be a winner. In the past three days, I've received phishing scam attempts through three different communication channels: text message, email and phone call. Two days ago I got a text message from the "Bank of Nova Scotia" alerting me to the fact that they had noticed unusual activity on my account. They suggested that I should go to a website to "verify my identity". In other words, they wanted me to give them my personal information (I don't have an account at Scotiabank). I recently learned that these types of text message scams are called "smishing" (short for "SMS phishing").
Yesterday I received an email from "RBC Royal Bank" letting me know that, "You have been locked out of your account!" Again, to unlock my account, I would have to visit a website and enter some personal information (I don't have an account at this bank either). Usually, these emails are blocked by my email providers spam blocker, but for some reason, this one sneaked through. This morning at 6:30 am, as I was getting my toddler dressed and ready for breakfast, I go a phone call. The caller, from an international phone number, greeted me by name and said his name was "Francis" and that he worked for the Visa Security Department. He wanted to alert me that someone had purchased a Western Union money transfer with my credit card and asked me to confirm the purchase. I told "Francis" that I would call Visa directly and hung up the phone. This early morning phone call credit card phishing scam has been around for a while, but this is the first time I got a call like this.
Financial Literacy Education
This recent surge in phishing scam attempts has highlighted the importance to me of teaching financial literacy to our students. High school students are at an age where they will soon be experiencing financial independence and need to make important decisions about budgeting, making purchases, investing and assuming debt such as student loans and credit cards. They will also have to learn how to protect themselves from fraud. The Nova Scotia high school mathematics curriculum contains a number of financial mathematics outcomes. These outcomes vary depending upon which mathematics courses a student takes. These outcomes deal with personal budgets, understanding pay and income, borrowing money, investing money and making purchases.
Avoiding fraud and scams is not explicitly covered in any of these outcomes but could easily be included when teaching these topics. For example, when learning about banking services and credit cards, students could be taught how to recognize scams and what to do if they realize that they've been the victim of identity theft. They could also be taught how to keep their financial information secure and how they should and should not communicate with their bank and other financial institutions.
The Canadian Anti-Fraud Centre maintains a list of fraud types and how to identify and report fraud. It is a very worthwhile website to check out: http://www.antifraudcentre-centreantifraude.ca/
Nova Scotia High School Mathematics Curriculum Outcomes relating to Finance
Mathematics 10 - FM01, FM02, FM03, FM04
Math at Work 10 - N01, N02
Math Essentials 10 - Earning and Purchasing, Banking
Math at Work 11 - N02, N03, N04, N05, A01
Math Essentials 11 - Housing, Banking
Mathematics 12 - FM01, FM02, FM03
Math at Work 12 - N02, N03
The Sno Cap Drive In in Sisters, Oregon is a diner that serves homemade ice cream and old fashioned burgers. The food here is great and the homemade ice cream is delicious. I stopped in this summer for a scoop of Cookie Monster ice cream. While waiting in line, I had some time to notice and wonder about the prices listed on the menu. What is going on here?
I noticed the differences in price between having your burger with potato chips or with french fries. Depending on the burger you're having, it costs anywhere from 45¢ to 95¢ more to have fries instead of chips.
I also noticed the difference between the burgers with cheese and those without cheese. To add cheese to your deluxe burger is an additional 80¢ but to add cheese to your bacon burger is only an additional 30¢.
Is there a pattern or rule to the price differences between having a burger with chips or fries? The list of differences between chips and fries is: 70¢, 70¢, 65¢, 60¢, 45¢, 80¢, 75¢, 75¢, 95¢, 70¢, 65¢, 70¢, 70¢, 65¢, 80¢, 60¢. The values range from a minimum of 45¢ to a maximum of 95¢. The mean difference is 70¢ and the standard deviation (a measure of variation) is 11¢.
I tried sorting the burgers in a variety of ways but there appears to be no pattern to the difference in price between chips and fries. This restaurant is in Oregon, which has no sales tax (one of only five such states), so the prices are not set so that when tax is applied, the total is a round number. I'm assuming that every burger gets the same amount of fries, but perhaps this isn't the case. I wonder if they get many questions about this?
If you wanted to give the prices on this menu an overhaul, how would you price these burgers, chips and fries? Could you come up with a more logical system of pricing? What factors would go into making these price decisions? Which burger do you think is currently the most profitable based on the current prices?
Nova Scotia Mathematics Curriculum Outcomes
Grade 7 SP01 - Students will be expected to demonstrate an understanding of central tendency and range by: determining the measures of central tendency (mean, median, mode) and range; determining the most appropriate measures of central tendency to report findings.
Grade 7 N02 - Students will be expected to demonstrate an understanding of the addition, subtraction, multiplication and division of decimals to solve problems (for more than one-digit divisors or more than two-digit multipliers, the use of technology is expected).
Mathematics 11 S01 - Demonstrate an understanding of normal distribution, including: standard deviation and z-scores.
Students and Staff at J.L. Ilsley High School recently returned from a March break trip to Italy. Their stories about Rome and pizza and gelato inspired this "Would You Rather?" math question. Most students are pretty familiar with pizza and have strong opinions to share on their favourite type and restaurant for pizza.
Would you rather have a slice of pizza from New York or from Rome? The New York pizza costs $2.75 US per slice. The Rome pizza costs 1,50€ per 100 grams.
In Rome, pizza by the slice or "pizza al taglio" is typically sold in rectangular pieces by weight. Prices are often listed per 100 grams. Prices can vary greatly depending upon the type and location of restaurant. Restaurants close to major tourist attractions in Rome are often much more expensive. The price I quote above is from Pizza Florida in Rome. Estimating the weight of a typical slice of pizza might be difficult for students. How much does a typical piece of pizza weigh? According to Pizza Pizza, a 1/10 slice of a 14 inch diameter pizza is approximately 110 grams. There is also the issue of currency conversion. You could ask for 3 Euros worth of pizza, but how much will that cost you in Canadian dollars? An online currency conversion website or app can help with currency exchange.
The Nova Scotia Mathematics 10 curriculum has outcomes on both currency exchange and SI to imperial unit measurement conversions so I thought this would be a nice warm up question to be used in that course.
In case you were wondering where you should go to eat pizza, here are the 14 top cities for pizza, as identified on the Conde Nast Traveler Best Pizza in the World list. Note that a Canadian city, Edmonton, made the list.
Nova Scotia Mathematics Curriculum Outcomes
Mathematics 10 - M02 Students will be expected to apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.
Mathematics 10 - FM01 Students will be expected to solve problems that involve unit pricing and currency exchange, using proportional reasoning.
One of my favourite activities recently has been Fawn Nguyen's Snap Hotel. This activity can also be found on the NCTM Illuminations website. You might see this activity online under a few different names... my favourite is Hotel^3. It is an engaging problem solving task. Students are given 50 multi-link cubes and instructed to build a model hotel. Each cube represents one hotel room. Some rooms are more desirable than others and can be rented for higher prices. The number of windows and whether or not the room has a roof determine the rental price. Students also have to consider costs associated with property and height. The hotels that students create in this activity remind me of Montreal's Habitat 67. Students might talk about the costs and benefits of this type of architecture. This activity can be used to assess a number of Nova Scotia mathematics curriculum outcomes.
The Rules - As a team, build a hotel that yields the highest profit.
Below are some hotel's created by teachers during a session at the NS MTA conference in Oct. 2015.
Suggestions for Improvement
Below are my Powerpoint introduction and a student handout. Also included is an analysis of several different hotels to see how their profits compare.
Why I Like This Task
Nova Scotia Curriculum Outcomes
I was inspired recently by Jocelyn Procopio's new site Storied Math. She posts a video or a picture and asks students to submit a question and solution that goes with the image. I really like the invitation to students to get in on the action of creating real world problems and contexts that are interesting to them. Thinking about a question that I could suggest made me think of a question about tree planting from the Grade 10 Math Finance textbook. When I did this question in class, my students questioned the numbers given in the problem. We decided to research at bit more using the internet to find a tree planting company and find out how they pay their tree planters. The process reminded me of Dan Meyer's Makeover Monday blog posts from a couple of summers ago where he invited teachers to reconstruct a problem from a textbook. Below is a problem ripe for a makeover.
How could we make this question better... lets start by removing all of the information and instead give the students a video of a young person planting trees and ask students what they notice and wonder.
Some questions that I had while watching this video were... How many trees can he plant in a hour/day? How much does that bag weigh when it is full of tree saplings? How much money does he get paid for each tree he plants? How many hours a day does he work? How many of those tree saplings survive and grow? Lots of interesting questions could be asked here. Like "How much of my daily income will be spent on massage therapy for my aching back?" This is a physically demanding job!
Selecting a Question to Explore
The next step is settling on an interesting question to explore and pose a solution. Once students have formulated a question, we can start to figure out what information we will need in order to answer the question. Not only does the textbook problem tell you what question to answer, it gives you exactly the information you need to solve that particular problem. There is no place for the students to think or be curious. They just take the numbers from the text and do some mathematical operations on them and hope they get the correct answer.
Let's decide to answer the same question that the textbook asked... "What would the tree planter's gross pay be for 6 weeks of work?" Now we have to figure out what information we need in order to answer this question.
Digging up the Facts
Solving the Problem
So what will the tree planter make in six weeks of work? The answer to the textbook question would be 3500 trees/wk * 6 wks * $0.17/tree = $3570 gross pay. This is not a whole lot better than working at a fast food restaurant earning minimum wage. 40 hrs/wk * 6 wks * $10.60 hr = $2544 (minimum wage in Nova Scotia as of April 1, 2015 is $10.60 per hour). Consider the cost of travel required to get to BC as well as the special equipment you might have to invest in (shovel, boots, tree bag, camping gear) and the tree planting job listed in the textbook doesn't sound so great. Not to mention days of backbreaking labour in hot and difficult conditions.
Lets say that our planter can plant 2000 trees per day for 5 days per week and earn $0.14 per tree. This would give us a gross pay of $8400 for 6 weeks. This seems a bit more enticing for a student to go out west to plant trees instead of working for minimum wage.
Instead of gross pay, you could have students figure out net pay. What will his deduction be for CPP, income tax, EI, etc? How much will have actually have in his bank account at the end of the six weeks? What are some high-paying summer jobs that are available to young people in Nova Scotia?
There is an article in the October 2015 NCTM publication Mathematics Teaching in Middle School titled Social Justice and Proportional Reasoning. The author, Ksenija Simi-Muller, has a great table at the end of the article listing strategies and advice for modifying textbook tasks to become real-world problems. One of her strategies is, "Require students to create a written argument based on the information given in the textbook problem. This is one of the most effective ways to engage students with real-world problems." I really like this suggestion to get student to critically think about the questions being posed and not just plugging numbers into equations.