Category Archives: Common Core

Another Tool for Implementing the Common Core


It’s hard to have a conversation with anyone in education these days without the two C’s coming up: Common Core.  Now I know there are lots of opinions on whether we should abandon them, whether they create an increased focus on testing, and whether they are suitable for all students.  I’m not going to weigh in on any of those debates.  At least not right now.

What I am going to do is to talk about is a resource that might help you if you are trying to implement common core standards in your classroom.   In an earlier post, I talked about one resource I find particularly helpful:  I received a lot of positive feedback about the tool from both teachers and parents.

So when I stumbled across another resource that I think is useful, I thought I would share it.  The website Illustrative Mathematics  provides tasks, videos, lesson plans, and curriculum modules that illustrate the Common Core Standards.  What I like about the site is that the tasks are submitted by a variety of individuals:  teachers, researchers and mathematicians.  Before being posted, each task is reviewed by both a classroom and mathematics expert.  I think this collaboration across different groups allows for a rich set of tasks.

It’s still a work in progress so not all standards have accompanying tasks or lessons plans.  However, I’ve found the K-8 tasks that are posted to be very helpful.  What I really like is that you can easily download and print a task for a particular standard you are teaching.  Included with the task and solution is a commentary on the purpose of the task and some suggestions on modifying or extending the task.

How you use these tasks with your students is up to you.  Some are better suited to be used as assessment items, while others are well suited for whole class lessons.   Your professional judgment, as well as your understanding of your students, will help you to decide how to best use the tasks.

I’d love to hear if you find the site useful.

Learning Trajectories: A research-based tool you can use right now


In an earlier post, I talked about the gap between the work being done by researchers and the work being done by teachers in classrooms.  Today, I’d like to talk about a resource that I think is a good example of a tool that connects research and practice.

The Common Core Standards have received a lot of attention lately.   I often struggle when trying to unpack the Standards in order to develop a lesson.  A research team from NC State has created an interactive tool, available at, which I have found very useful in designing lessons.  The researchers developed 18 learning trajectories for the K-8 Common Core Standards for Mathematics.   These learning trajectories describe how students develop an understanding of a particular concept, or set of concepts, over time.

The hexagon map allows you to click on one of the trajectories or on an individual standard and get detailed information about how students might move from prior knowledge and informal ideas to sophisticated understandings of various concepts.  Also included throughout are common student misconceptions and a variety of models and representations that have been shown to foster particular understandings.   What I love about the trajectories is that they include the research that was used to build them.

So how do I use them?  Recently, I needed to prepare a lesson for fourth graders on angles so I went to the site and clicked on the Shapes and Angles Trajectory.  I was able to view suggested activities, such as the angle game where students stand and follow directions to rotate a half turn or quarter turn.  I also read about common student misconceptions, such as the fact that students sometimes think that an angle with longer rays is larger than an angle with shorter rays, and viewed questions that assess this misconception.   The references were also included in case I wanted to go back to some of the original papers and explore any of the ideas further.

Of course, it wasn’t the only resource I used when I was preparing the lesson.  I used my prior experience of teaching angles and other resources I have collected over the years.  But it was nice to have place to go that summarized the major research in a way that allowed me to think about how the students might develop a concept and the challenges they might face along the way.

I’d love to know of any resources you use that connect research and teaching.