Exploring Patterns With Project-Based Learning: Rotations, Reflections & Translations

"Ms. Willis, this is hard!"

I was looking for a way to cement my students' learning in geometry, one that would include exploring spatial relationships, patterning, and translations, rotations, and reflections (slides, flips and turns). I also wanted to explore this using visible thinking routines because I find that every time I use these routines, my students take ownership of their learning.  This was a 4-day process.  I hesitated because of the amount of time I knew it would take up, but I'm so glad I pushed forward with my idea.  The rewards were well worth the time.

 Day 1

I began by showing examples of tessellations.  I used a mini-definition poster that I created to explain what a tessellation is and then gave each student a tessellation photo card.  These tag cards are photos from nature and man-made structures, as well as computer-generated patterns, and they all are examples of tessellations, except for one card.  I used that card to challenge students to use the mini-definition poster to determine whether or not it was a tessellating pattern.  They determined that it isn't, and they would be right!   Each student received a numbered card.  We spent some time looking at each other's cards. 

Then I put my tessellation card on the document camera to project it on the Smart Board.  Using a response sheet, I modeled my thinking about my tessellation.  The response sheet used questions combining "See, Think, & Wonder" and "3-2-1"  thinking routines.  For example, we wrote three math words that described our tessellating pattern.  We also wrote two questions we had about what we were seeing.  We described what we were seeing on our cards, as well as what we were thinking about what we were observing.  Doing this gave students an opportunity to practice using their math vocabulary, and it gave me an opportunity for a formative assessment as I wandered the room conducting my own observations.  We also wrote a simile for each of our patterns.

After using the response sheet, students sat in groups of three to share their thoughts, questions, and observations. 

Day 2

Day 2 was eagerly anticipated by my students.  I issued "the challenge" to them: Create your own tessellating pattern using pattern blocks; your tessellation MUST include rotation, reflection, and translation.  I gave each student a paper on which to create so they had boundaries for their tessellations. 

I allowed students time to explore with the pattern blocks while I watched.  One of the things I noticed that the majority of them were struggling with is that they began to make pictures instead of patterns. I approached many students, asking them the question, "What comes next?"  When they couldn't answer the question, it was a tip off for them that they were not creating a pattern. 

I called students together and modeled the difference between making a cool picture and making a pattern.  As I made my pattern, I repeated it out loud for students to hear, "Hexagon, parallelogram, parallelogram, trapezoid...hexagon, parallelogram, parallelogram, trapezoid..."  This seemed to turn the collective light bulb on for them. They went back to their own workspaces to complete their patterns. 

At the end of this session, all students had a pattern block tessellation.  I took pictures of these on my phone and uploaded them to my classroom computer so I could print copies for them to refer to the next day. 

Day 3

By the time day 3 rolled around, student excitement was pretty high.  We revisited the photos of our tessellations from the day before.  Then, I gave students the direction guide for making their paper tessellations, as well as the rubric I developed.  I wanted them to know the learning targets for this assessment BEFORE they began their final project.  After we read through both of these documents together, students began coloring and cutting their paper pattern blocks. The paper pattern blocks are another resource I created.  They arranged these on an 8x8 inch square of black construction paper, gluing only after they had practiced their patterns again.  

                           

This took all of our math session for day 3.  As I walked around monitoring, I reminded students to keep their rubric in sight so they would remember the learning targets. 

Day 4

Day 4 was spent writing about our tessellations.  I provided a writing page on which students recorded their thinking and descriptions of their tessellating patterns.  They were required to use math vocabulary from a word bank in their explanations.  This gave students another opportunity to practice using math vocabulary in their writing.  It also allowed me to check, once again, for their understanding. 

Finally, I asked students to take out their rubric sheets and self-assess their tessellation projects and writing. 

I am very please with how this project went.  One of my students who has high math ability gave me the ultimate compliment.  He said, "Ms. Willis, this is hard!"  What is always interesting to me is WHO finds this project difficult.  Many of my students who are average or lower skilled math students loved this project and found it to be "just right" for them.  Some of my very high math students were challenged by it!  I love this.  That same student told me that "open-ended assignments are harder" for him.  I love that he knows this about himself.  Projects like this leave room for everyone to succeed, don't they?  I saw very complicated patterns over the four days of this project, but I also saw very simple patterns.  Project-based learning allows for flexibility with differentiation and gives us, as educators, a window into students' thinking that we might not see otherwise. 

Another student asked at the end of the fourth session, "When can we do another math project, Ms. Willis?" I can hardly wait.  I've got coordinate geometry and Van Gogh on my brain.

                                                                                

If you liked reading about this interdisciplinary project, then you should check out the links below! Simply click on the pictures. They're great sanity savers for your end-of-year lessons. 

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