Math = Love: 1-4-5 Square Puzzle Challenge

Friday, May 8, 2015

1-4-5 Square Puzzle Challenge

This year, Thursdays in my classroom were actually Brain Teaser Thursdays.

This has been a lot harder than I anticipated.  Now, I love brain teasers.  But, there's a definite difference in the brain teasers I find engaging and my students are interested in.  I've found quite a few though that kept them busy and intrigued.  I've decided I need to blog about them before I forget which ones worked and which didn't.

On my school computer, I only have four bookmarks: Remind, a site with trig lesson plans, a site that makes printable flashcards, and a site with puzzles/brain teasers to solve.

This square puzzle that I'm about to blog about came from the puzzle site.  I'll show you how the site presented the puzzle.  Then, I'll show you how I did it in class with my students.

I knew that if I projected this picture on the board, my kids would be less than interested.  I needed to print off the pieces for them so they could actually manipulate the pieces with their hands.  I don't know about you, but I would have no clue how to go about solving this without printing off the pieces...

For my first period class, I put this image into a file 4-to-a-page and printed it on orange card stock.  I fed that card stock through my mini laminator to make the pieces durable enough to last a day with six classes of high school students.  My first hour was tasked with cutting apart the puzzle and solving it.  This means my first hour saw the square made with 1 piece and the square made with 4 pieces.  They had to combine these to make one square with 5 pieces.

The students claimed the puzzle was impossible.  I promised them it wasn't.  Eventually one student was able to figure it out.  I had my students put their pieces in a ziploc bag for the later classes.  One of my students wrote Algebra 1 on the bags.  But, I used this activity with my Algebra 2 and trig classes, too.

As my later classes trickled in, I instructed them to pick up a bag from the front desk and wait for further instructions.  Many of my students assumed that the shapes in this bag were tangrams.  On the first day of school, I had students try to make a square using all 7 tangrams.

Now that the pieces were already jumbled in a bag, I could change up my instructions.  Instead of asking students to take the single square and the square made out of four pieces and construct a square out of all five pieces, I broke the puzzle down into three mini-challenges.  This worked MUCH, MUCH, MUCH better.  The students who didn't successfully complete the third challenge still had the satisfaction of completing the first two challenges.  

Challenge 1:  Using one piece, make a square.  

Every student could be successful at this challenge!  

Challenge 2:  Using exactly four pieces, make a square.  

Some of my students saw how to do this right away.  Others took a little more time.  That was perfectly okay.  

Challenge 3:  Using all five pieces, make a square.  

This truly was a challenge for most of my students.  The idea that a small square could be added and the pieces would still make a square was kinda mind-blowing.  Honestly, it blows my mind, too.  

Some kids tried to make the square with four pieces and lay the single square on top and claim that they had made a square with all five pieces.  Later in the day, my instructions became more precise to avoid this attempt at overlapping pieces.  

This made a great five-minute class opener.  It got my students a bit agitated and frustrated.  But, I view these as good things to happen in math class.  I will take students that are agitated and frustrated over students who are lethargic and couldn't care less any day of the week.  

Want to download the files to print these yourself for your students to use?  Click here.  

I'm hesitant to post the solution picture, but I'm going to.  But, don't be surprised if I change my mind in a few hours and take the solution off.


  1. thanks a lot for your excellent idea.

  2. I have just printed the squares.... I will use it to motivate ladies to work in teams to find solutions when there seems to be no way. :). Thanks for the idea!!! Lots of applications can be done!