Warm-up

Scams and money.

As I mentioned before, I received two different texts on my phone offering me jobs which according to everything I read, are scams.  They are variations of the fake check scam where you are sent a check, you deposit it, withdraw a certain amount and wire it off to a third party, leaving you with a few hundred for doing very little.  By the time you find out the check is fake, the scammers have moved on.

I wondered how effective these scams are because I had a family member come to me about the text offering her $550 per week for driving her wrapped car around town.  I told her it was a scam so she wouldn't get ripped off. They appeal to those who want to make money quick.

I found a site from Australia called Scam Watch which provides data in chart form  showing the types of scams most common for 2018 up to the end of June.  They analyze the data or the year showing number of reports versus amount lost, the top 10 scams by amount lost or number of reports, amount lost versus method they were contacted, the age group of the victims, amount or number of reports by gender, and amount lost versus number of reports broken down by states.

You can find the information broken down by the year back to 2015,  by the month for each year,  by the type of scam or all scams or by both year, month, and scam.  Great data for students to take and enter into a spreadsheet to further analyze the data by comparing months, or years.  They could interpret the data to draw conclusions.

The above information but what about Americans?  According to Market Watch  the number of scams rose almost 60% over a one year period from 2015 to 2016.  In the same time period, it is said that one in ten have lost on average $430 to a scam to total $9.5 Billion.  In 2015, the average amount lost was $274 per person who participated in a scam.

According to another article from Market Watch, the amount of money lost to a scam increased 7 percent from 2016 to 2017.  In addition 40 percent who made fraud complaints lost money in the 20 to 29 age group as compared to only 18% in the 70 and older group.  Although fewer seniors lost money, they lost more at $621 versus the $400 for the younger group.  Over all, the number of complaints dropped from 2.98 million to 2.68 million, totaling $905 million, an increase of 7%. 

One last article is from the Federal Trade Commission's Consumer which lists information on the top frauds of 2017.  The number one scam was the imposter scam in which 350,000 people lost $328 million. This is where someone contacts you pretending to be a loved one, a government official, or someone else they are not. This is a great article to have students practice extracting specific pieces of information to interpret.

This is a cool, real life use of mathematics.  Let me know what you think, I'd love to hear.

Benford's Law and Securities Fraud.

  If you are a Numbers (The TV show) fan, you might remember this from Season 2.  Charlie used it to help track down a stolen DNA synthesizer in 'The Running Man'.

Your average person has no idea what the law states and what it is used to find but it is also known as the 'first digit law'.

Although this was first discovered in 1881 by an astronomer but it was rediscovered in 1938 by physicist Dr. Frank Benford.  Over a period of eight years, he analyzed a variety of data and discovered an interesting fact.

He discovered that the chance of a certain digit appearing in the first position depends on the number.  For instance, there is a 30% chance of being the first digit while there is a 17.5% chance that 2 appears first and so on.  The higher the number, the lower the probability it will appear first.


It's these probabilities that help investigators determine if a public company is more likely to end up in trouble with the Securities and Exchange Commission (SEC).  If a companies financials have different percentages than those from Benford's law, they are more likely to be caught for accounting irregularities.  It does not matter what the company produces, this seems to hold true.

This was supported when someone went through the companies who had been busted by the SEC.  The statistical deviation between the numbers submitted by those companies and Benford's law was 20 times the average for all firms.  That is significant.

When the companies who were caught restated their earnings, the numbers fell within the boundries for Benford's law.  It has been admitted they cannot catch every company due to the limited budget and employees by the SEC but it appears they catch the ones who are falling apart.

In addition to catching companies who are not using good financial methods, this law has been used to find voter irregularities, Greece's effort to hide debt, alteration of digital photographs and other forensic applications.

If you'd like to give your students a chance to use Bednord's Law, you could check out these three activities.  The first is from Cornell University.  It offers three different activities which utilize this law so they can see how it works in different situations.  The second is from Texas Instruments.  It has students calculate the percentages based on the rates provided. 

This topic came about as I looked for information on how much money is scammed from things like the car wrap and the mystery shopper scams both of which I received via a text.  In the process, I came across this and thought I would share it.

Let me know what you think, I'd love to hear.

Mars Math By NASA

  NASA has created a whole series of Space Math books filled with a variety of problems for grades 3 to 12.  Today, I am looking at one of those books whose math deals specifically with the planet Mars.

Mars is one of those planets which has caught everybody's attention from the past to the present.  Even the cartoons had Marvin the Martian who gained quite a bit of popularity.

Although the ebook is not very thick, only about 78 pages, all activities are only one page long and include the answers.  The book includes a 'Math Topic Matrix'

If you look the lesson on 'Modeling the daily temperature of Mars', you'll see it covers averages, a graph or table analysis, coordinate plane/points, modeling, and trig.  Multiple skills to challenge the students and put a more realistic feel to activities.  It is not like the problems to practice the one skill found in a text book.

Another page contains the standards being met.  Although the phrasing is a bit older, it is easy to find the current Common Core or NCTM ones and use those. 

Each lesson includes the information a student needs to use to solve the problems given.  This lesson includes a line graph using the time in sols vs temperature.  The last questions asks students to predict the temperature at a time in the future based on the pattern.  There is a third page with the information on Viking 1 and Viking 2 so you could have students graph the information from Viking 2 before answering the same questions for this new graph.

One of the questions asks students to create a sine function to provide best fit for the information. As I said the answers are provided complete with the math calculations if you are not that strong in figuring out the equations. 

The activities are divided into three grade groups,  3-5, 6-8, and 9-12 but those are guide lines.  I've looked at some of the exercises in the first group and several of my students would struggle to complete them because they have issues applying fractions in this type of setting where they are given information as clues.  The clues are set up to tell you that something is a fractional size of another planet which is a fraction of a planet whose size you have.

I have to travel in August to a conference at the beginning  of school and I think I might just go ahead and use a few of these for math while I'm gone.  The sub can use the answers to help students complete the assignment if needed. 

Check it out and let me now what you think.  I'll be checking out other books in the near future and reporting back.  I'd love to hear back from you.

Geometry and Mars

I recently started receiving updates from Space.com.  The other day, there was an article on how they used geometry to figure out something about the water on mars.

If you look at closeups of Mars, you'll see something that looks like scars created by running water. Scientists have argued about where the water came from and where it went.

A group of scientists decided to use a statistical approach to determining where the water came from. 

They looked at the angle that those scars crossed each other.  The angles indicate if the area is dry and where the water might have come from.

They discovered the angles are fairly low, indicating the channels were not formed by ground water. In addition, the narrow angles of the valleys indicate a desert climate such as one found in Arizona.  Wider angles of the valley would indicate groundwater coming up from the ground.

The best theory is the channels were formed by sporadic heavy rainfalls over a long period of time.  The rain falls and runs off quickly creating a network of these valleys. 

At this point in time, there does not appear to be any water on the surface but scientists believe the northern hemisphere contained an ocean about 4 billion years ago. It is thought Mars had an atmosphere which allowed the planet to have a water cycle. 

As water evaporated, it condensed around the volcanoes in the southern hemisphere before raining down and carving channels in the planet.  Unfortunately, it appears the atmosphere only lasted a few hundred of millions years before the atmosphere is lost and water disappears.

This is not the first time scientists have used geometry to determine things in relation to Mars. Back in 2013, NASA's Mars Reconnaissance Orbiter discovered the sand dunes in a crater are in a polygon shape.  In addition, these types of sand dunes are fairly common but only in the bottom of craters and other low lying terrain.

The micro climates along with heating and cooling causes wind to blow in certain directions to form these polygon shaped sand dunes.  Furthermore, the dark sand appears to be from an iron rich basalt such as that found in Hawaiian volcanoes.  We do not have anything like this on Earth.

If you do a search on this topic, you'll find several different papers on using geometry to help explore certain facets of Mars.  I find it quite fascinating.  I actually attended a talk a couple years ago in which a scientist compared geologic formations on Mars with the same type of thing on Earth. 

Let me know what you think, I'd love to hear.

Kitchen Nightmares

Over the past week, I have been doing a marathon viewing of "Kitchen Nightmares" with Gordon Ramsey.   The basic idea is he comes in to help a failing restaurant turn around.

Usually, the food sucks even though the owners state it is great.  There are always some type of personality conflicts between the owners, the owners and the staff, and sometimes between the owners and the customers.

Often the people who bought the restaurant have wanted to run one but do not have the experience or its been in the family forever and no one is willing to make changes, fire the chef, or step back.  The process is for Gordon Ramsey to come in and try out the food which is bad.  As he's commenting on the food, he gets more info on what's wrong with the place from the servers because the owners know its not them.

Then he watches the dinner service, checks out the refrigerators and freezers often discovering the food in them is in bad shape, or they've mixed the raw and cooked foods together, or it was all made days ago, or they use purchased food.  Of course the owners are shocked into changing by their workers comments and Ramsey gives the restaurant a makeover before they redo the menu and have the grand reopening.

Somewhere in the middle of the fourth season (there were 7), I wondered how many of these restaurants were unable to survive and had to close.  According to a Business Insider article from 2014, more than 60 percent of the restaurants closed while 30 percent of those closed within one year.  I wondered how accurate those figures were.

I found a site by the Kitchen Nightmare people which listed updates for every restaurant helped during the seven seasons of the show.  According to them, 57 out of 77 places closed, 18 are still open, two moved and two were sold.  There is information on each restaurant whether open or closed.  If it closed, the author provides a bit more detailed information such as one place closed because the state seized it for nonpayment of taxes.

Another site also has information on which restaurants are open or closed.  It contains a bit more information than the other site but the other one has it all in one place. 

The nice thing about both sites is that it provides enough information for students to analyze.  They can look at the 57 closed businesses and break that information down further into how long after appearing on the show they closed.  Students could also look to see how many of those closed down after they were sold, or did they close for some other reason than just went out of business due to being too far in debt.  As stated earlier one business was closed by the state while another closed due to serving liquor due to an expired license. 

The majority of episodes include information for the amount in debt each restaurant is.  Students could calculate an average amount for the restaurants although one business went into debt due to the wife remodeling the place.  Instead of the 350,000, she ended up spending 950,000 because she didn't bother asking the cost for each thing she wanted and her husband not saying no.

They could even look at each season and see which seasons had more businesses going out of business or staying in business.  It will change from season to season but does averaging the seasons together match the same for the seven seasons?  Pose that question to the students and see what they come up with.

Let students write up a short article outlining their finding from this exercise so they can learn to write reports to communicate with others.

Warm-up