A couple of weeks ago, my students took a test on GCF and equivalent expressions.  As I planned for the review, I wanted to incorporate some type of hands-on activity, so I decided to search online for puzzles.  Originally, I wanted to find a puzzle that I could just print, cut, and have them piece together.  I didn’t have much luck with GCF, but I did come across an interesting puzzle for equivalent expressions using 16 triangles.   Unfortunately, everything was either too small/blurry for me to use, or it cost money to download, which I’m not willing to do.  I prefer to pay $free dollars.

I knew this was something I was going to have to create myself, so I began by printing out a blank template.  I was planning to make several of these and cut them out for my students to piece back together (matching pairs of numbers to its GCF), but then it occurred to me that I should just have them create it!  All I had to do was go through the process myself, so I could teach them how to do it.


The first thing I did was think of a pair of numbers whose GCF was any number besides one; I happened to choose 4 & 24 and started filling from the bottom up.  It really doesn’t matter where you start.  As I filled in the puzzle, I thought about directionality and how I was going to explain this to my students.  GCFTrianglePuzzle2I thought, a pair of numbers should always be adjacent to its answer (the GCF).  The edges that don’t have adjacent triangles are extra numbers (tricks for the puzzle).  I wrote my numbers on the edges/lines of the triangles, and continued until every edge had a pair of numbers or a GCF .  I told my students that their numbers should always be written on a line.  Meaning, the bottom of each number should touch a line (as if they were writing on lined paper).  This helped them understand how to turn their triangles as they created their own GCF puzzles.


Once I was done, I decided to color my puzzle because I wanted the end product to look nice.  I gave my students two choices:  they could either color their entire puzzle one color (this would make it more challenging for people to piece it back together once we cut it up since all of the triangles are the same color), or they could use two colors and create a pattern as seen in the final pictures (this would be less challenging for people to piece back together since it is understood that the same color would not be adacjent to each other).


It ended up working out nicely.  I’m glad I wasn’t able to find something online because it gave my students the chance to create their own puzzles and problems, which was an even better review for them!  There were a handful of students that struggled with creating their own problems; I had them use their math books to find GCF problems, but they still had to think of the solution.  Here are a few finished student samples!

GCFPuzzle4 GCFPuzzle3  GCFPuzzle1

Since this was such a fun review for them, I had them create equivalent expressions puzzles too.  Here’s a student sample!


I ended up laminating some of these to keep and use as stations or independent practice for students who finish classwork early.  I cut them up and put each set of 16 triangles (each puzzle) into a Ziploc bag.  Students who made the cut (got their puzzles laminated) were very excited to see other students working on the puzzle they had created.


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  • I'm puzzled

    I can’t wait to try this with my kids.

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