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## Your Homework: Play Temple Run

Summer is here. Yippee for me!  This means that I can get back to blogging some of ideas.  So, here is my next idea, The Math of Temple Run.

Have your ever played Temple Run?  Probably, yes, given the game’s popularity.  If not, here is information about the game. http://www.imangistudios.com  The game is free to play. Did you catch that – FREE! But what is better than being free is that Temple Run has a lot math problems waiting to be explored.  Here are some that I will be trying out.

• How fast is the person running?  The game keeps track of how far you run in meters.  This means that you can time how long the person runs and then calculate the speed.
• Is the person’s speed possible?  I won’t spoil it for you but you need to see how fast the person runs.
• The person runs faster as the game progresses.  Students can make a chart of distance and time because the game flashes up the distances as you travel.  Does the increase of speed follow a quadratic pattern or is it more like a piece-wise linear?
• Next have students play the game and record 15 rounds of data.  Here is a link to the table of data that I made. https://www.desmos.com/calculator/barud9egsn

Blue Dots: Coins vs Distance – Red Dots: Distance vs Score

The data looks to have a strong linear correlation, which allows us to explore rates of change.  What does the rate of change mean for the blue dots and what does the rate of change mean for the red dots?  Are certain games better than others?  Is a better game based on the distance? Is a better game based on the amount of coins? Is a better game related to the number of coins compared to the score?

• In Desmos we can use a slider to create a line of best fit.  The  ones I made were y=(coins/dist)x and y=(score/dist)x  I will probably discuss with students why we can make the initial value of zero.  (Actually, one of the goals in the game is to go 1,000 meters and get zero coins.)  Next, with the slider values we can either make the numerator or denominator equal to 1 and adjust the other slider accordingly. Once they have the line of best fit, we can talk about what it means for the data points to be above/below the line of best fit.
• Remember that each student will be playing the game, hopefully.  So, this means we will have many different graphs.  This will allows us to talk about how you can look at a graph and say, “That is good player. This is a so-so player. Etc.” or to be able to look at graph and point out who has had more experience playing the game.
• How is the score calculated?  After students record the amount of coins, distance, and score they will have some data to try and figure out how the score is calculated.  The game does not tell how the score is calculated.  All you see is a running total in the upper right corner.  Wikipedia does give a formula for the score.  http://en.wikipedia.org/wiki/Temple_Run However, that formula was not working for me.  I might doing some type of error.  But this is good because it gives students the opportunity to figure it out.  Plus, the formula opens up the door to the floor function and ordinal numbers.
• I might throw in Game Theory at the end.  Not quite sure.

Plenty of stuff to work on there.  I have not made the worksheets yet but I will update the post soon.  If you could, please play the game 15 times and record your data into this Desmos graph https://www.desmos.com/calculator/b2bycwrenn.  Save your work and then post it here in the comments or on twitter @LukeSelfwalker.  I will gather up the data and post it later.  Thanks for your help.