Its FIFA fever everywhere!! As the teams are closing on the Round of 32 and heading to the Round of 16, I recently found an interesting infographic from usatoday that analyses teams’ travel routes when they advance to the Round of 16. It shows the distance of travel between venues from the Round of 32 to the Round of 16.
This infographic brings in lots of mathematical concepts to be explored in a real-life scenario. Here are few questions which we could use for contextual learning. The questions are framed with varying levels of difficulty/grade levels.
Relocation from Kansas City to Vancouver– 1572 miles
It is rounded to 1600 miles
Data set:
85, 254, 406, 594, 704, 736, 1215, 1224, 1349, 1372, 1385, 1423, 1572
Mean of travel distances = 12,319/13 = 947.61 miles
Median = 1215 miles (With 13 values, Median is the middle value, the 7th)
The distance from Boston to NY/NJ: 254 miles
So, the scale factor = Actual distance / Ruler measurement
= 254 miles/2.5 cm
How can we reason this division problem?
250/2.5 = 2500/25 = 100 (using equivalent strategy)
4/2.5 = 40/25 =1.6
Totaling, we get 100 + 1.6 = 101.6 miles/cm
Looking at the map, the travel distance between San Francisco and Seattle is 704 miles
Total fuel consumed = 704 miles x 0.9 gallons/mie
= (704 x 1) – (704 x 0.1) = 704 – 70.4 = 633.6 gallons
Total number of routes = 13
No. of routes < 1000 miles = 6
Probability that the selected route is lesser than 1000 miles = 6/13
Routes with distances over 1000 miles: 7
Routes that end in NY/NJ or Philadelphia: 2
Probability = 2/7
Including the data of non-travelling teams, the new data set would be:
0, 0, 0, 85, 254, 406, 594, 704, 736, 1215, 1224, 1349, 1372, 1385, 1423, 1572
The total number of data points is now 16
Hence, Mean = 12,319/16 = 769.93 miles
With an even number of data points, Median is calculated as the exact midpoint between the 8th and 9thvalues.
Adding zeros as data points increases the number of data points without increasing the total miles, so the mean decreases.
Median = (704 + 736) / 2 = 1440/2 = 720
As we can see, adding three zeros at the start shifts the center of tendency downward towards a smaller value.
We can also extend the discussion further to analyze how the distance of 85 miles from NY/NJ to Philadelphia affect the mean /median? Is it an Outlier?
Here is a printable activity where you can complete the tournament results and see which team becomes the champion.
Connect 2 Context 