The first issue that concerns me is that neither definition makes any connection to measurement. The second being that students are explaining how to solve for perimeter which is not the question I asked.
Perimeter is the distance around a plane figure and area is the amount of two-dimensional surface that is contained within that shape (6th grade teachers would love us if we defined area this way). Area is really difficult for students to conceptually digest…and I get that! As mentioned in my last post, students can easily solve for area by using the formula (length x width) but they have no conceptual understanding of square units (inch, foot, etc).
The Measurement Progressions document start in 3rd grade with the definition of Perimeter and I don't know if I personally agree with this. Many teachers and textbook companies (I think I just threw up) will take this for meaning that perimeter and its formal definition should be taught before area!!! This can be extremely misleading and detrimental to a fundamental understanding.
What I'm suggesting is this…don't mention the term perimeter until after students have had ample time exploring area and "covering" a surface!!! If you already do this then you have reaped the benefits!
This year we started with the 3-Act task Piles of Tiles. We worked for 2 full weeks on area and culminated this idea with the Flooring Your House task. By delaying the introduction of the term perimeter it was much easier for students to conceptually see the length (in units) around different figures because of their understanding with area.
The last reason to delay: area and arrays go hand in hand which could lead to students deriving the formula for area themselves…Not the teacher telling students.
So from my experience I know that the egg, the chicken and area all came first!
Thank you for sharing your thoughts on this. We have had similar conversations in our district and have tried out using problem stems so that students draw or create representations of the context first before they ever know the question being asked. When we did one using sod and fencing, the students were able to represent what both parts of the context referred to before they were asked to solve any calculations. Their teacher shared that throughout the rest of the unit, the students would refer to perimeter questions as "the fence" and any area questions as "sod". I do, personally, feel that area needs to be investigated and understood first so that students then make stronger connections to what the perimeter truly represents.
I'm totally "diggin" your idea of introducing area and perimeter within the context of fencing and sod. Definitely a nugget I am going to stash away until next year.
I love the fact that throughout the unit, students were able to make connections back to the original context in which their primary understanding was developed. Your comment reemphasizes the importance of teaching math in a context and not in isolation.
Such a thoughtful comment. Thanks bunches for sharing!