A Clothesline Math Mistake

It’s the beginning of a new school year and something magnificent happened during one of my beginning of the year activities.

I usually play “Guess My Number” with my class, but decided to do a number talk with the class.    I have done this number talk plenty of times during presentations!  Or at least you would have think I’ve done this tons of times.  I usually don’t think about it anymore during presentations because I do it by rote memory. 

My number talk consists of me giving the numbers 40, then 10, then 70,  and then 120 or 140.  I purposely use that order because I want to see what kids say about how these numbers are related in regards to spacing.  As students talk, I’m picking up their number sense and how in tune they are with it. This simple routine also shows them how the Clothesline works as a numbers line and that we can keep adjusting the numbers as needed.   

And in the midst of setting up, corralling the kids, and getting things started —–a mistake happened.  Not one that the kids picked up…but I immediate realized.  But I decided to go with the flow and see where the mistake took us.  

Instead of pulling the numbers in a random order (40, 10, 70, and 120)…..I pulled out 10 first.   The students debated as to how close to the left hand side of the clothesline it should be placed because they wondered if any numbers less than 10 would be pulled.  (Fair enough).

Then I pulled the 40.  They knew that the 40 should go to the right of 10.  The students made sure to leave enough space in between.  Next I pulled the 70.  Some of the students told me that the “gaps” should be the same between 10 and 40 and between 40 and 70.    Next I pulled 120.  I had hoped that they would double the space of 70 and move it to the left a bit…instead they managed to make sure the space between 70 and 120 was just a little bigger then the “gaps” between 10 and 40 and 40 and 70.  

My last card is usually the question mark card.  Instead of putting it into the middle of all the numbers (giving them the parameters that the mystery card is between 10-120, I decided to put it on the far right side with the intention of it being 210.  I made sure that the spacing was correct and let it lie there.

And this is where I got some answers that made me want to write this blog post.  One kid said that the answer must be 240 because I doubled the space of 120.  Another student claimed it to also be 240 because if you add up 10, 40 , 70 , and 120 ….you get 240.  (?!?!?!?!? You can only imagine my reaction when I heard that answer.)  Another student came up with 220 just because she it looked like it could be around that number.  

I think I got more information out of my students with my little mistake.  With my students, I tell them to expect mistakes because that’s where we are learning.  As teachers, when a lesson doesn’t go the way you had planned, we learn to pivot and forge on.  After all…we all are human.  But this ended up being a happy mistake…one that I was eager to share.

Until next time,

Kristen