Students in Mrs. Martz’ third grade math class recently used their skills to discover an important relationship between perimeter and area. The young mathematicians were challenged to use fencing to create a rectangular pen for a pet rabbit with a specific perimeter. The goal was to build a pen that would provide the rabbit with the most area to roam and nibble on grass. Students modeled all of the possible rectangles with perimeters of 20, 36, and 40 feet. Students strategically ordered the dimensions of the rectangles and recognized a pattern with which to reason about the relationship of the perimeter to the area. The closer the shape of the perimeter came to being “square-like” the greater the area! The students were then able to use this relationship to quickly and accurately determine all of the possible dimensions using 100 feet of fencing. A 25 ft. by 25 ft. square did indeed yield the greatest area of 625 square feet!
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