This post provides a conceptual approach to understanding perimeter and area.
Students are prompted to build an rectangular animal pen for some farm animals. The number of fences represents the perimeter. The number of squared segments of grass inside the pen represents the area.
The photos below are used to introduce length and area as part of a CRA approach. First a student is asked to build a Lego garage. He first builds the bottom row of a wall and the teacher asks for length in terms of how many Legos are lined up. After building a wall the teacher asks for area in terms of how many Legos are used in the wall. Then the student is given a handout with the following photos. Following this handout the student finds length and area of tiled floor and walls made up of cinder blocks, if available. Eventually a ruler is introduced and multiplying to find area is presented at the end.
For the photo above the student is asked to count Legos to compute length. In the photo below the student is asked which is longer and to explain.
In the photo above the student is first asked to determine the area of the red wall in terms of number of Lego squares. Then the student is asked which wall has more area. This is followed by the photo below. This allows a different perspective of area.
Students have trouble with irregular shapes largely because they cannot visualize or determine the measures the dimensions of the individual parts. The photos below show a hands on activity to help students with these challenges. The students are cut out the individual shapes and write in the dimensions. This method allows them to see the individual parts and the respective dimensions. (The second has calculation errors.) This activity is followed by a handout in which students can shade in the different parts which is a step towards more abstraction – CRA.