A Tale of Two Puzzles

This summer at TMC, Chase Orton (@mathgeek76) suggested that I should write a series of blog posts reflecting on returning to the classroom after a 5-year hiatus and how what I learned during that time has changed and improved my teaching.  It´s a lovely idea.  But for the moment, challenge not-accepted.

INSTEAD, I have  stories to tell from the first few weeks of school.  I have about 70 students this year which is a relatively low amount for my district.  I am teaching 80%: 3 sections of 7th grade math and 1 section of 7th and 8th grade math intervention.  I have tons of stories to tell from my year so far: highs, lows, reflections, etc; but for the moment, I want to talk about a student who is doing everything he can do opt-out of learning.  He taps on his desk, quietly at first, and increasingly louder if I try to ignore him.  He takes supplies from the student supply area and spends time hooking paper clips together or stacking Solo colored plastic cups left over from Martin Joyce´s Cup Challenge which will eventually be used for Avery Pickford´s  group-work signals of how well a group is functioning.  He argues when I ask him to sit in his assigned seat, eats in class when he knows he shouldn´t, and opt-outs of learning in nearly every way he can invent.  His behavior has clear, consistent consequences and he hears from me every day how much I believe in him and care for him.  We have had lunch together, he´s earning snacks for after class, and we are building a positive relationship together.

Students opting out of learning is something which never leaves my mind.  It happens in nearly every classroom, in subtle and not-at-all subtle ways.

screenshot-www.google.com-2018.09.16-15-18-37My story, however doesn´t start or end there.  This child LOVES puzzles. I learned this during the first week of school when I had a play table with an assortment of Christopher  Danielson´s tiling turtles and pentagons.  He couldn´t put them down and made beautiful tessellations every (and yes, I do mean every) opportunity he had.


During the first week of school I hand each student a ziplock bag filled with a metal screenshot-www.google.com-2018.09.16-15-22-57puzzle of 2 parts hooked together and they have to figure out how to get the 2 parts apart, and then back together.  The types where getting the 2 pieces apart is seemingly impossible.  I have them in 3 levels of difficulty and after solving one, I ask the student if they´d prefer their next one to be the same level or a harder one.  I am only easily able to solve the level 1 ones, so when they get stuck and ask me for hints on the harder one, I love being able to say that I have no idea how to solve them, but I believe that they will if they stick with it.  And yes, most of the diabolic ones eventually get solved.  I find it´s a wonderful way to talk about what math is to me: you don´t always know if you´ll use a day´s lesson later in life, but really good math should always feel like those puzzles…worth solving because they make you curious and fascinated.  I talk about how nearly every student I have ever had ALWAYS chooses a more challenging puzzle  after solving a previous one and how knowing that their teacher can´t solve it makes them even more determined.

We did these puzzles for a day during the first week of school and I left a few out in baskets in the back of the room as something for students to play with when they had down time.  I loved this idea, but as the days wore on, I realized how LOUD those metal puzzles can be if someone is doing one when they should be in their seat with the rest of the class.  The student who I mention above, absolutely loved these.  I offered to let him take one home each day, but what he really wanted was to do them instead of everything else we were doing that week.  And between him being off task and it being so loud, I decided I needed some quieter puzzles for him to use as brain breaks.

He is now in love with Manifold puzzles.  I bought a pack just for him (and a few others to use for other students when the need arises) The idea is to fold the paper to get a 4×4 square of black tiles on one side and 4×4 square of white tiles on the other side. They are leveled, #1-100.  The initial ones look something like this and he had really quick success:


And eventually, they become really, really tricky, like this one


And although I have not yet had a huge amount of success getting him to attempt the grade level material, he is no longer searching for a reason to opt-out of everything and is no longer disrupting us all in his search.  I have walked over numerous times, pulled a puzzle out of my pocket and said, ¨Don´t get up and don´t say a word to me until this is solved.¨ And it works.  He becomes determined to solve the puzzle and comes over gleefully once he does.  This is chapter 1 of what I am sure is a long journey we will take together this year.   And I am sure, at some point soon, I will be celebrating with him his successes on the grade level math content of my course.  He knows that´s part of this story.  I do too.

I would LOVE more ideas of low floor individual puzzle ideas which ramp up into harder challenges  https://krazydad.com/ was shared this week through the Desmos Fellowship and it´s exactly the type of ideas I need.  But ones that involve manipulating things, like these Manifold Puzzles are even better.  I will buy whatever you recommend, so send me your best ideas! I have a list of tons and tons of ideas from Sarah Carter (https://mathequalslove.blogspot.com/), but don´t entirely have time to curate the lists and choose a few to use for now.  What I would love from you is just 1-2 of your favorite ones which can be used with minimal prep and/or minimal instructions (like the Manifolds).  THANK YOU.


7 thoughts on “A Tale of Two Puzzles

  1. Allison – I love this post. This child is so lucky to have you as a teacher. Does he like to play with numbers? KenKen are abundant and free, and start with 3×3 and get much harder. I also like these: https://findthefactors.com/ for logical thinking about numbers. They come in several levels for every day; although I haven’t found a way to incorporate them in my classroom, I’ve envisioned having them in a basket (or baskets, for different levels of difficulty) for students to pull out as needed/wanted.

    • Thanks, Wendy. I love KenKens, but don´t know findthefactors so I am really excited to explore something new. Doing puzzles with numbers is probably phase 2. But he and I can explore them together at first over lunch.

    • Yes! I do know those and love those. I did the whole book last summer with my son and was so bummed when we finished. I was actually thinking about ordering a book of them just for this student. I have xeroxed the first few puzzles into a packet, but there´s something more special about having your own book. Thanks for this great idea.

  2. Thank you for sharing how you are building trust with your student. It makes me smile thinking of about all the work teachers like yourself are out there doing in the classroom to build connections and not just trying to get all students in lock-step with the status quo.
    For your puzzle request, I’ve been working through Puzzle Ninja (https://www.amazon.com/Puzzle-Ninja-Against-Japanese-Masters/dp/145217105X/), which is a collection of puzzles from Japan. (No sudoku, this book digs much deeper into the puzzle culture of the country). Each puzzle has an intro with the rules and a sample play and then 5-10 puzzles of that type to solve starting with easier ones and then getting much more challenging. The book has been a delight to me so far and some of the puzzles seem so very simple but put your brain into some deep thinking.

  3. Pingback: Puzzling Things – mathy moments

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