Data & Probability

Learn the ADFGX cipher from world war I. In this first step we learn how to crack a simplified version using the frequency of letters. Click here for a downloadable file to help students crack a simplified ADFGX cipher.

 

Learn how to encipher and decipher an ADFGX cipher.  Click here for a downloadable pdf.

Maps are a wealth of data. The best maps are easy to read and give lots of information. Instead of starting with an English map – start with a map in a different language. See how much your students can understand about this Russian map of an Island.

After you explore this map in Russian I will give you the English translations. Just see what your students can figure out.

These maps are from the inspired cartographer Eric Gaba (Wikimedia Commons user: Sting)

Do you think the blue or black print would refer to the name of the island. Do you see anything that would give a clue about whether this is an island in a lake or an island in the middle of the ocean.

These maps are from the inspired cartographer Eric Gaba (Wikimedia Commons user: Sting)

Next, it is time for us to see the whole Island.

 

Let’s see how well the map maker Eric Gaba succeeded in imparting data to you and your students. Let’s look at the same maps, but this time in English.

 

I’ll go through each of the close-up slides. Back and forth between English and Russian.

 

Did your students guess that the white patch was an airport? The little icon of a plane might have helped. Did they guess the height of the tallest point on the island?  Did they figure out where a battle was fought in 1814?

 

Even in Russian, Eric Gaba’s clean presentation of data allows you to figure out a LOT.

 

The blue text names the body of water. The black text names the Island. The legend shows that the altitude of the surface of the lake is about 170 meters above sea level. This is definitely a lake. Not the ocean.

 

 

Again, your students probably figured out some of this even in Russian.

 

Did your students figure out about how big the island is? Did they figure out the symbol for a lighthouse? For a road?

 

They may even have figured out the urban areas.

 

What did your students think the dotted lined areas might be? Are they natural or man-made?

 

Good luck with maps in your classroom. (In another map slide show I’ll be exploring maps as a way of introducing ordering. Which mountain is the tallest?)

Minard’s graph showing the destruction of Napoleon’s Grande Armée in 1812-1813. You can find an English translation of this graph here. How many types of data are presented on the graph? It is a map, so there are coordinates (not labelled!). There is the width of the line which indicates the size of the army. There is the temperature plotted for the retreat.

Minard’s graph is recognized as one of the greatest. All classrooms discussions of statistics need to showcase such complex, multivariate examples of how to tell a story with data.

 

Dr. John Snow collected data on the cholera outbreak in London in 1854. Each line behind a door indicates a death. The prevailing theory was that the sickness was due to bad air. This map pointed to the Broad Street pump as being the culprit, but was this due to a bad smell emanating from the pump – or from something in the water that people were drinking?

The statistically riveting story about this map and the data anomalies (like the brewery workers who stayed healthy) make for a fantastic story for all students of statistics.

In the video I describe how to play Bracket with sticks, but you can also just download this pdf board. Each player would play with two markers.

You will need to come up with your own questions. They should be hard enough that an average person will have some idea about the answer, but could be out by a factor of 10. Email me your list of questions and I’ll give you credit.

PS. Bracket is one of my best game designs for the math classroom.  I have been looking for a publisher for over two decades, but perhaps it is just a little bit too logarithmic for the average household 😉

My off-the cuff thoughts about how to introduce statistics long before children see any formula.

Life and death statistics from around the world. I’m not totally happy with this activity, but because of the pathos of the subject matter, it is sure to have reasonably high engagement.

 

Sports tournaments should be celebrated in the math classroom.

PS. Despite assurances in this video that I will post the follow-up results… I’m not going to do it.  My predictions sadly went down in flames…

 

Here is some beautiful data and graphs from the web.

Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 For a free poster of MathPickle's ideas on elementary math education go here.

Gordon Hamilton

(MMath, PhD)