Friday, August 29, 2014

Problem Solving with NPR

A friend of mine introduced me to the free app "Stitcher" this summer (thanks, Solana!), which essentially is a way to organize podcasts that you enjoy listening to.  I wasn't much of a "podcaster", but with the help of the app, I've learned a TON about a lot of really cool stuff!  One of my favorite podcasts is the NPR Series: Sunday Puzzle.  Considering I'm a math teacher, that should be no surprise to you!

The way the Sunday Puzzle works is they start the podcast with a recap of last week's puzzle and they reveal the answer.  Then, they contact a random winner (someone who answered the puzzle correctly online) and have them on the show (via phone) to go through a series of smaller puzzles/riddles.  These puzzles are not necessarily related to the Sunday puzzle.  Finally, they introduce the new Sunday puzzle and give you until the following Thursday to submit your answer.

On August 17, the title of the show was, "Is There An Echo In Here?" and the Sunday Puzzle was one from Sam Lloyd.  Here it is...

"You have a target with six rings bearing the numbers 16, 17, 23, 24, 39, and 40.  How can you score exactly 100 points by shooting at the target?"

I thought this would be a great puzzle for my students to try.  After introducing it, they had some clarifying questions, which I thought were great!

"How many times do you shoot at the target?"  I told them that it did not specify, so they could decide.

"Can you hit a number more than once?"  I told them, again, that it did not specify, so they could decided.

I gave them about 3 minutes to work independently, trying it on their own, and it was completely silent.  Every student was engaged.

After this independent work time, I wanted to tap into the minds of my students, so I just asked for their initial strategies.

Lots of students said that they were just randomly adding numbers to see what happened.  Others said that they added all 6 numbers to get 159 and then tried to see if they could combine any of the numbers to get 59 that could be taken away.  Students found that they could get close to 100, either just over or just under.  Students also explored finding a factor of 100 and then repeating that process.  Lots of good stuff here!

Students who arrived at a solution found that they could get to 50 by adding 16 + 17 + 17 and then they doubled it.  Another approach that was shared was very sophisticated and inspiring.  A student said that she added 16 six times and found that she got 96, which was 4 short of 100.  She knew that 4 was not an option for a ring, but thought there might be a way to gain 4 by adding in a 17.  She tested it by adding 16 five times and then 17 once to get 97.  Her strategy was working...she was getting closer to 100.  Ultimately, she found that four 17s and two 16s was the combination she needed.  I loved it!

As I described earlier, the 5 minute podcast starts with the answer from the previous week's puzzle, so I shared the solution with my students (Ben Parks, August 24, "A Puzzle Hokey Pokey, That's What It's All About").  They were delighted to know that they had arrived at the (only) correct solution.

I decided to play the rest of the podcast for them, which they loved!  The riddles involved 2-word phrases (first word has 5 letters, the second word 4 letters) that were generated by dropping the last letter of the first word, then reading the remaining 4 letters backwards to get the second word of the phrase.  (Try this one...Where Peruvian pack animals shop: Llama Mall) :)

Finally, the moment came to hear the new puzzle for the week.  Students were excited to get in on the action.  Here's the latest Sunday Puzzle from Jason Zuffranieri:

"Name a world leader of the 1960's, 2 words, change the last letter of the 2nd word, then switch the order of the words, that is putting the 2nd word in front, and the result will name a hit song of the 1990's.  Who's the leader and what's the song?"

I didn't know what to expect, but I sent my students home with the challenge of figuring this out.  I offered extra credit for getting a correct solution, but they had to somehow defend their process, so I would know that Google didn't deserve the points. :)

I returned to class today (Friday) after introducing this on Wednesday and I was pleasantly surprised that two of my students in my 3rd period class had figured it out!  One young man said that he had his cell phone open to Google looking up world leaders, while his mom's phone was open to iTunes looking up hit songs of the 90's.  He started piecing things together and arrived at his answer.

The other student said that she started with song titles from the 90's, looking for ones that included names (Mr. Jones, Mrs. Robinson, Jane, etc.).  Then she looked at a list of leaders and found a last name that could easily be changed to a common word and pieced it together.

Here's what they came up with...

SO proud!  I can't wait to incorporate this into my classroom on a more regular basis and even encourage my students to submit their answers online!  It was obvious that these two students were not motivated by the extra credit, they were just enthusiastic puzzle solvers.  What more could I ask for from a math student?

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