As I teach, I’m wondering about the role that overarching concept plays in the teaching/learning choreography.
For example, once I understood what made up a system, I could apply that concept to learning about all systems with central questions:
- What is the main function of the system?
- What are the parts?
- Where are the parts located?
- How do those parts function together?
- What are the critical factors of this system?
Now that students are beginning their unit on place value, I’m thinking more about proportional reasoning.
I’ll start the unit with the illustration below and ask, What do you see?
I imagine students will say some or all of the following:
- I see rectangles.
- I see small, medium, and big rectangles.
- I see __ # of rectangles.
- I see a design.
Then I’ll remind them of the recent lesson where we tried to describe locations on an aerial map of the playground. The descriptions were vague using words like behind, past, next to instead of precise locations. Then when we placed the coordinate grid on top, it was much easier to be precise.
What can we do to be more precise about describing this picture? Then I imagine students will say, “put the shapes in groups,” “order from smallest to largest,” and “measure.”
Then I’ll say, “Yes, similar to the use of a coordinate grid, mathematicians have come up with systems of measurement--ways that tell us how big or how little an object is. These systems help us to compare and combine values with precision.” When is it helpful to have exact measurements and/or values? Again students will offer all kinds of examples which we’ll list.
Then I’ll show them the models below. I’ll explain that I made these models with estimation, not precise measurement. I’ll ask again what they notice about the models? What is the same, and what is different? What relationships do they see?
We’ll spend some time talking about the concept of “big and little,” and the many ways to communicate that using precise numbers and measurements. After that, we’ll make some models that are precise and hang them around the school to remind everyone about the accurate proportional measurements related to time, money, measurement, and place value. I can imagine that this will build a strong foundation for our upcoming study of place value. Do you agree?
Models:
