Geometry Cafe!

Throughout this past school year, I have been so fortunate to be part of an ongoing partnership with several wonderful professors and research mathematicians out of New Mexico State University.  This partnership has opened the doors to many learning opportunities for both my students and myself, including several classroom visits from a real-life mathematician!

  

I can't speak highly enough about "Mr. Ted", as my students call him, because he brings his expertise and passion for mathematics to my students in a way that keeps them on the edge of their seats while deeply engaging in math concepts.  According to them, he walks on water...and invented math.  But that's a whole different post altogether!

Recently, Mr. Ted paid a visit to our classroom with one of my all time favorite math lessons, "Geometry Cafe".  Common Core tells us that geometry is HUGE in 3rd grade, representing an entire Critical Area (that's 25% of ALL 3rd grade Critical Areas!!!).  But as teachers, we know that in order for students to reach the depth of understanding mapped out in CCSS, the foundation is laid in the primary grades, and continues to build and extend all the way through high school.  With that in mind, "Geometry Cafe" provides students with an opportunity to reason about shapes and their attributes through cooperative learning while using the Standards for Math Practice to demonstrate their understanding.

The premise behind "Geometry Cafe" is that students are given a scaffolded geometric "order" in which they must fulfill for the "judges".  Students use the Standards for Mathematical Practice to create the order and present their argument to the judge.  The judges are responsible for critiquing the reasoning of their peers, asking clarifying questions, and finally, accepting or rejecting the 'order'.  Since the order cards are scaffolded, students can choose to either continue to work on the same level of cards, or move on to more challenging, and sometimes even impossible, order cards.   

At the start, students were told that while during this lesson, we would be focusing specifically on Math Practice 3 (Constructing viable arguments and critiquing the reasoning of others) and Math Practice 6 (Attending to Precision), they would most likely need to use those MP's to explore polygons. Four students were selected to be the "judges"- three were chosen based on their strength in communicating ideas and critiquing the reasoning of others, and the final student was randomly selected.  The judges were told that they were not allowed to "show" the groups how to solve their problem, but instead, must question, critique, and discuss what the group had done.

Students quickly began working in groups of three and four to draw and satisfy their orders on dot and grid paper.  For the 'green' (easiest) orders, many groups were quickly ready to share with a judge.  The 'yellow' cards took a bit longer, as they were more challenging, and many groups continued to work on yellow cards for the entire math time.  Some groups chose to move on to the most challenging, 'red' cards, and this is where I some of the greatest examples of the Standards for Mathematical Practice in action.  One group made sense of a single problem and persevered in proving it impossible for about 45 minutes!  Another group sought out pattern blocks to (choosing appropriate tools strategically) to prove to their judge that their order was in fact, correct!  Students were precise in their geometric vocabulary, especially when conversing with their judge and when sharing out their solutions with the whole group.

As a teacher who is still learning about the Common Core State Standards, I work tirelessly to create math experiences for my students that weave content and Mathematical Practice Standards, because the learning that results is priceless.  Lessons like "Geometry Cafe" are gems, and Mr. Ted knocked it out of the park with this one.

Since you've made it this far, and with his permission, I would like to share* this lesson with you- Geometry Cafe.  Included are detailed directions and a plan, as well as scaffolded orders for 3rd, 4th, and 5th grade.  This is what I would consider math Christmas!!  I hope your kiddos enjoy it as much as mine did.

**This lesson was graciously shared by Ted Stanford.  It is his intellectual property, and we all know that stealing others ideas and property gives you 7 years of bad juju :-)