Learning Goals of the Unit
The focus of this unit is to deepen students’ understanding of perimeter and area while reasoning about the relationships and differences between the two concepts. For that purpose, students will explore area and perimeter through manipulation and concrete representation to develop the conceptual understanding of the concepts before the use of formulas.
During the exploration, students will study figures made by combining unit squares and will learn that changing the arrangements of the unit squares in these figures, while not changing the area, may result in changing perimeters. Through a sequence of activities, students will experimentally discover area as the square units on (or inside) a rectangular figure as opposed to the length units around (perimeter). Finally, an extension activity will challenge students to create more than one arrangement for a given area to find the longest possible perimeter. During the unit, students will be able to explore what happens to the perimeter and area of a rectangular figure when the figure is changed in some way by removing unit squares. In particular, they will find that, although removing squares reduces area, the perimeter may stay the same, or even go up! Students will be able to draw rectangles and other rectilinear shapes and determine their area and perimeter. Students will be able to communicate effectively through drawings and numbers, work cooperatively in small groups, and successfully apply their comprehension about area and perimeter in a real-life situation.
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