At an assembly in the fall at Washington International School had a guest speaker from the organization Free Syria speak to our students about the current crisis. She gave the students more of a background the crisis and referenced data on the amount of refugees. This inspired me to do some research and to encourage a student to do a mathematical paper on the topic.

I looked for the data on the amount of Syrian refugees leaving as well as the amount of refugees that other countries have historically accepted and registered. I found raw data from the World Bank on countries from 1990 to 2014. (If you have not looked at the World Bank’s data, I highly recommend seeing what they have based on topics). In my spare time, I have been sorting the data and looking for trends, as any math teacher would do. Recently I sorted the countries by income level based on the World Bank’s definition and already stated in the data sheet. The graphs of the totals since 1990 of the countries based on income is displayed in the following graph using Excel.

I find it rather surprising that the High Income countries admit fewer refugees than most other countries. When looking at the data of the High Income countries closer, Quartile 1 and median are relatively close.

I made another graph of individual High Income countries: USA, France, Germany, Canada, Sweden, and UK.

With the exception of Germany, most of the graphs gradually increase or decrease. When looking at the graphs of the 5 statistical measures, we can see that Germany’s data influences the standard deviation. For the graph of the USA there is an interesting spike in 2006. What explains that spike in USA’s policy?

I am going to continue to run different statistics in preparation for my grade 9 statistics unit. I am curious what is happening with the Low & Middle Income countries that allows them to admit more refugees.

Recently when looking up a grocery store on my phone on google maps I noticed the following graph on popular times.

Google provides data/predictions for customers about when people typically visit the specific store. I am not sure how the data is collected, so if any one knows please share.

I used these graphs in a statistics lesson after I had introduced normal distributions. We talked about who this information is important to and estimated the standard deviation on a curve that looked normal. We discussed the missing information on the y-axis as well as how a store opened 24 hours would have a different standard deviation and possible shape to the graph. Then we looked at the rest of the week.

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The students were able to recognize patterns in the specific store and relate it to human behaviors in the work week, we estimated the mean for each graph. We also discussed other locations through Washington, DC and if they would have the same types of distributions. Would stores downtown have a different distribution from stores in the suburbs? Will all types of stores have a similar distribution based on location or is it more based on the type of store (for example, grocery, hardware, clothing).

It would be interesting to see how Thanksgiving preparation will affect the graphs.

My students amazed me with their attention to detail with the Linear Programming art assignment. The objective of the assignment was to use linear programming to make an art piece, but I also wanted students to have the option to challenge themselves and be exposed to other types of functions. I introduced the students to sliders so that the students would have the structure and confidence to work with unfamiliar functions. Here are a couple of examples of their work.

Alexandra pays great attention to details and was motivated to make an eye. Her process was so methodic and her conversations with her peers and me about the functions she needed to use focused on the attributes of the graphs you only wish your students would eventually notice. She played around with ellipses but noticed that she could not get the crease of the eyes. She was explaining her problem and I suggested using parabolas and was able to discuss cusps that occur in graphs. In her write up for the assignment she was able to reflect on the different aspects of the functions she used. In her reflection she wrote:

“I was finished with the eye very soon after I started working on it, and I decided that I wanted to challenge myself even more. I attempted to draw eyeliner on the eye and draw an eyebrow as well. I experimented with parabolas and modified some equations and added sliders to figure out the correct equations and finally they turned out the way I wanted them to.“

Lily wanted to work do a character with more than just linear lines and choose Carl Fredricksen from the movie Up. The emotion and facial expression she captured only using functions is true to the character. In Lilly’s reflection she discussed her use of different types of equations and use of sliders.

“I had reached a point where I knew I had to start putting in my circles, parabolas and ellipses. …. I realized that my hesitation to begin using the equations for circles, parabolas and ellipses was because I felt that the equations were a bit intimidating. …. more values are involved; the more numbers there are, the more intimidating the equation becomes. ….. The use of sliders made creating equations and graphing lines go much more smoothly and much quicker, making work more efficient and less time consuming, allowing me to complete it on time.”

The assignment and the graphing tool desmos provided a situation for the students to take risks, explore different types of functions and be motivated to find equations that would best work in their art piece.

For my grade 12 class we reviewed the five statistical measures with the following activity. I found a website that releases the data for the top selling songs on iTunes for the past 24 hours, called Digital Sales Data. We did the activity on September 3rd which was after Justin Bieber’s new single What do you mean? was released.

Outline of activity:

The students were in groups of 3-4 students and each group was given data of the top 25 selling song from a different country: USA, Finland, Australia, Malaysia, and Nigeria.

Each group had to find the 5 statistical measures and we compared as a group.

What was interesting was that Finland and Nigeria had similar types of numbers, The students were a little confused about if the units were in the thousands or just units as some of the data was so small. One student pointed out that Finland owns Spotify so we talked about the economies of the countries. We also talked about why the values were so different discussing the population of the countries and buying power. It would have been helpful if I had the countries’ population and GDP to compare.

Overall it was a good activity that brought in a global perspective and interesting to see what types of music are listened to elsewhere and helped the students stay focused and interested. We found that Justin Bieber was the top selling in all the countries. We also were able to talk about grouped data and deciding on appropriate class grouping ranges depending on the data given and discussed the standard deviation of each set.

Here is and example of the data from the USA and Finland.