I begin this third day of Building a Dog Kennel by using the student data I have gathered over the last two days of observations. In our first day, I realized many students lacked a way to organize their thinking about design of a dog kennel. Although the lesson's objective is centered on changing perimeter with constant area in a large space, an organized approach is an important habit of mind that I want to develop in my students.
To model approaching a problem by first organizing our thinking, I begin by asking my students how they might go about organizing their desks if we were to clean them. I ask one student to model their actions.
Here is what she did:
After discussing that it is a good idea to group like things together, we talk about how math can be approached in the same way. I ask, "What in our dog kennel project can be grouped together to make our task easier?"
Here are two students explaining how "grouping" makes things easier to see and understand.
Obviously, grouping the kennels for each size dog may be helpful. We then discuss color coding the kennels by size.
I show the students my kennel design, which is color coded by array shape. I ask them to turn and talk with their partners about what made it easy to understand my math. Here I am looking for students to notice the array differences between each type of kennel area, realizing how many of each type are grouped in one space. If the students can recognize this method of organization as well as its purpose, then I know that the next day of instruction I can discuss taking a sub-area of a large space and work to create even smaller, equal sized areas.
After this discussion, I explain that they will now work on a second plan in their architect packets and that they must color code and organize their sections based on dog type. I also explain that in order to service the community fairly, they should work to build 10 kennel spaces for each size dog. This means that their work should include 10 (20 square foot kennels), 10 (15 square foot kennels), and 10 (10 square foot kennels).
As the students work on today's designs, I walk around and confer about how they have "organized" their work. Make sure to stress with students that they need to be precise in selecting and representing the different perimeters and maintain the necessary areas in order to create a successful kennel (MP6).
I find it best to work with each group based on what they are already doing, helping to adjust something manageable, rather than work to recreate a design to push a larger conceptual leap. This is abstract work for third grade students, and I know from experience that if I am to teach for understanding I must work where they are, moving in small steps.
This partnership was very close to realizing that figuring out how to create 10 large dog kennels meant they needed 200 square feet in all, plus "walkway" space.
These girls have an organized space and are working with various perimeters.
As a close today, I decide to have students share with the entire class about what was tricky for them. I think it is important for students to understand that math is not always neat and tidy and that others' may have different strategies, approaches, and ideas and still be correct.
After our share, I explain the home practice piece, which is to find the area of a large rectangle in their reflection journal. They are told to write their understandings, show a model, and be ready to share at the open of the next math session. This is an easy assignment, but good practice with a critical concept of area.