Category Archives: Searching For Math Problems

Find My location in Western Nebraska – Orienteering

In this video I traveled out to western Nebraska to lose myself.  Use the sectional map, Geogebra, and a little trigonometry to find my location in the video below.  Click on the map and you can download and print a larger image.

The three landmarks I have chosen for this orienteering video are Scottsbluff, Chimney Rock, and Jailhouse Rock monuments.

And to the right is the map image that you could copy and inset into a Geogebra file.


GeoGebra Needs an App for the iPad

Math educators that use java based programs on the internet in their daily teaching are unfortunately being held hostage by Apple.  I teach in a school district that is in the middle of its 8th year of a Apple one-to-one initiative.  Because of this initiative we no longer had funds to purchase graphing calculators, so we have been using Geogebra in the classroom as a tool to show about everything mathematical.  Lets face it, although Graph it on Apple is OK, this program can’t even come close to Geogebra’s capabilities.

This year when our school talked about iPads instead of computers . . . .  my blood froze.  I new that the iPad does not support Java, and all of the online apps I have built on Geogebra and placed on my moodle course would not work with the iPad.  Granted there are many free apps out there that graph on the iPad, but none of them can hold a candle to Geogebra.

Geogebra is asking for your assistance to develop the iPad app.  Here is their kickstarter link. HELP GEOGEBRA!!!!

and video.

How many Ball Bearings?

Recently my father’s combine auger fell off while he was unloading wheat.  What had happened was the ball bearing were rusty, bound up and fell out of the auger.  Without these ball bearings the entire auger fell off of the machine.  It was impossible to count them because we couldn’t find them all anymore, and so the question became . . . How many ball bearings do I need to order from the parts store in order to have the correct amount.  The parts store is a one day drive away, and so we had to have an accurate count before we drove to go get them or we would have lost an entire day, and still could not fix the machine. So here is your problem.  All you have is a dollar bill to measure with.  You could only find four ball bearings.  How many bearing do you need to order to completely cover the outside of the ring so that we can fix the auger?

Chocolate Chip Statistics and the Normal Curve

Several years ago, I went to NCTM in Salt Lake City.  A great experience!  I saw a presenter use fathom to analyze our chips ahoy chocolate chip counting.  It is hard to decide what a chip is in this case, because chips ahoy chocolate chips are just slivers of chocolate.  This adds some nice variability to the number of chips, but it just seemed messy both numerically and on my desk.

This year my wife and I baked 4 dozen chocolate chip cookies.  I gave each student two cookies and had them count the chips as they ate them.  I then had them add this class data in a spreadsheet and find the mean, variance, and standard deviation.  I noticed that one student was taking out the chips and giving them to another student to eat. Most noticed the mode and range right away.  One cookie had 5 chips and one cookie had 20 chips.  The student giving away chips said she wishes she had a cookie with less than 5 chips in it and the other student eating all of the chips wished he had a cookie with more than 20 chips in it.

With that in mind I placed these two questions on the board. If all cookies were placed in a bag, what is the probability of pulling out a cookie with less than 5 chips in it (assuming that the data is normally distributed)?  What is the probability of pulling out a cookie with more than 20 chips in it?

Toilet Paper Roll Comparison

Ok, so we have all opened that big puffy bag of potato chips and were disappointed by the small number of chips in the bag, but this recent scandal hits below the belt.  I noticed after purchasing an economy package of toilet paper there was something strange when comparing the old roll to the new roll.  Notice the credit card in the middle with the old roll on the left and the new roll on the right.  My questions was, in a pack of 24 rolls how much toilet paper did they short us by using a larger tube?  I also place two other photos here so we can somewhat ignore the geometry of the camera angles and get perpendicular views of each tube opening.  What I would do with a class of students is give them a credit card, ruler, and these three photos so that they can go to work, and become mathematically literate shoppers.

Financial Analysis Risk VS Return

I just recently took a course at the University of Nebraska Lincoln called Math in the City.  It is a problem based course where our group looked at stock analysis and Modern Portfolio Theory.  It started out slow, but at the end of the course everything fell together.  What I gleaned from the course that can very useful for high school students in the teaching of spread and central tendency was a fabulous, easily approachable way to intelligently compare stocks using Google docs spreadsheets.

There is a set of code in Google docs that can be used to retrieve daily data from the New York Stock Exchange.  Type this set of code into the first cell of your Google spreadsheet. =googlefinance(“Stock Symbol”, “type of Data”, “Beginning Date”, “Ending Date”) For example, in the photo below, I set up the formula to read Disney’s closing price from 5/10/2007 to 5/9/2012.  The spreadsheet then displays all closing bell prices for Disney between and including those dates.  With this data it is then possible to generate the daily rate of growth for that stock.  Using the same rate of change formula I teach to eighth graders which is Rate of growth =(new – original)/original.  In the photo above I used = if(b5<>””,(b5-b4)/b4,””) Thanks Jerel.  Then you find the mean of this daily return rate along with the variance (which represents the risk of the stock) and plot these two numbers on an x-y scatter where return rate is the y – axis and variance is the x-axis.   The graph with stock data is plotted below and right.  For example it would be easy to see in this graphic that IBM has a high positive return with low risk, while XIDE has a negative return with a high risk based on five years of data.  (This is for educational purposes only, and is not intended as investment advice.) Here is the actual spreadsheet Just change the symbols in each sheet and the dates.

In the course we went into more detail about the efficient frontier, and comparing stock portfolios where we calculated the rate of investment for each stock to maximize return and minimize risk, but this just seamed like an easily accessible application for almost every student I teach in 10th – 12th grade.  You can only look at the document right now.  As soon as I figure out how to protect all the math stuff I will allow anyone to enter the stocks they want to analyze.


Land Conservation and The Mathematics of Area

The problem – We have a field that currently uses gravity fed irrigation (the lighter colored field in the center of the picture).  This mode of irrigation is very wasteful, and so a more efficient center pivot irrigation system needs to be put in place.  Design a center pivot irrigation system for the field below.  Your design must utilize exactly the amount of irrigated acres available.  Additional irrigated acres are not allowed and utilizing less than is currently there will loose you money!!

Once the designs are completed we will do a cost analysis of their designs.  Prices to consider.  Each Center pivot costs approximately $50,000.  Running electricity and water pipe from the well to the center point $7.00 per linear foot.

Transferring dry land to irrigated acres costs $50 per acre.   Transferring pasture to irrigated costs $500 per acre.

Consultant fee for asking the teacher a math related question- $1,000 per question answered. (an idea to make it more lifelike).

When we are done with this project I will post some of their plans after Christmas.

Estimating Slope Take One

In this silent video I show how a group of Ag and math students estimate slope in order to calculate how erodible the newly planted field will be.   I just wanted the video up fast.  I will spend some more time later refining it and adding some other explanations.

A major question I had as a math teacher, after hearing this is how the Ag class estimates slope at a range management competition.

How is it possible to use the hypotenuse to calculate a fairly accurate estimate?