Monday, March 12, 2018

Adventures in Problem Solving - Make 37

I recently had dental surgery and woke up in the middle of the night in a bit of pain.  So, I did what every other crazy rational teacher does in the wee hours of the night, and jumped on Twitter for a little PLC time.

I bumped into this Tweet from  @inspiringmaths which featured this math problem:

I shared the problem with a team member and he was so excited to share it with his class, that he gave it to them the first thing in the morning even though that is usually our reading block.  

He came into my classroom with a white board with one of his student's solutions.  I glanced at it quickly and noticed that the student used 10 numbers and that the sum was 37.  

I totally glazed over the fact that they had a 4 in it. (Also, just a note on my teammate's shorthand to write the solution - those dashes apparently represent multiplication - don't ask... LOL!). 

 I was impressed and asked how long it took the student to solve.  He said they had been working at it for a full 25 minutes.  "They were so into it!" He said.

The gauntlet was down, I challenged my class to see if they could solve the problem as well!  

Just like my teammate had experienced, my class was super engaged with the challenge as well.

About 15 minutes in, one of my students came up with a similar solution to the student above, (but again, I did not spot her use of the 4) and I sent her over to the other classroom to show my teammate. He somehow spotted her use of the 4 and called Foul.  My students continued to mull over the problem all day.

When I got home, I continued mulling over the problem as well.  I even put together an Excel spreadsheet to keep track of my attempts. The pains joys of being a "life-long learner", and a testament to the power of an engaging question.

I struggled, and struggled, and couldn't find an answer.  So, I Googled it.  I found the original problem from NRICH maths (an amazing resource filled with so many rich math problems to solve)!

(*Spoiler Alert*)

It said the problem couldn't be solved.  It is impossible to make 37 with the numbers if you add them ten times.  The reason for this is that when you add odd numbers an even amount of times, your resulting sum will be an even number.

I texted my co-worker and asked him what his student's answer was.  He texted me the picture back and that is when I finally saw the 4 the student had used.

I shared the link to the solution with him and mentioned that we should try another activity with the students next week.  We would ask them - "Can you add an even number of odd digits and have an even sum?" Sometimes, Always, or Never?

I will share those results in another post!

If you try this math problem with your students, I would love to hear how it goes! 

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