Posted May 22, 2017 by sgibbs

Reflect on the Trailblazers activity.  Were you able to accurately follow the path using the signposts you left?  Did you make any mistakes (such as forgetting to color certain squares or using the wrong color squares)?  Next, consider whether you think there is more than one right solution, and if so, how you would decide which solution is best?


Submitted by sircollins88 on Sun, 06/11/2017 - 05:58 · Permalink

While I did not play the game, it is easy to understand some of the pitfalls that students would encounter.  Such as forgetting to color the correct square.  A possible extension would be to complete the maps on a transparency.  Then by stacking the maps you could see all of the iterations made by the group.  The traveling salesman problem has been plaguing mathematicians for years.  While the shortest path may be my 'right' solution, the best solution depends on how you define success.  

Submitted by Bright_Eyed_Science on Sun, 06/11/2017 - 19:28 · Permalink

My husband and I challenged each other with this game. We were both able to create paths with accurate signposts. The debate over defining the "optimal" solution lasted longer than playing the game. I completely agree with @sircollins88. Possible criteria: shortest path, best fuel efficiency (least left turns, lowest proximity to other agent), and fastest time (e.g. tornado slingshot could give you a turn and a step in a single round as opposed to a turn counting as a round). 

Submitted by eso on Tue, 06/13/2017 - 21:25 · Permalink

I definitely agree with sircollins88 in that this reminded me of the traveling salesman problem. I also didn't play the game, but anticipate it being a great activity for my scholars to practice writing clear directions and giving peer feedback. 

When reading the rules, the first thing I though was, "Woah! I have to make sure to reference the color key a lot!". I think this is a great lesson to teach my scholars, both in following rules and using a key. 

The "right" solution depends on what you're trying to optimize for, like Bright_Eyed_Science said. Those potential optimizations could be distance, proximity to various agents, or number of turns.

Submitted by kcwgtt on Tue, 06/20/2017 - 22:38 · Permalink

I was able to accurately follow the path using the signposts. I did make mistakes navigating all of the obstacles by using the wrong color for some of the signposts. Unlike the travelling salesman problem mentioned in other posts, the trailblazer activity did not require the path to take the shortest amount of time or some other criteria. This distinction makes choosing a path easy because the only constraint was to touch all of the pots of gold. There are many paths that would be able to accomplish this goal. For me, the best path had the least amount of turns.

Submitted by person11d on Sat, 08/05/2017 - 02:13 · Permalink

I was able to follow the path of the signposts without mistakes. There are many different ways to complete the objective in this game. I chose the path that would require the least amount of signposts or turns in the path, but there were various paths you could take to complete the objective successfully.