This document discusses extending understanding of perimeter, area, and volume of polygons and prisms. It includes relating these concepts, comparing perimeter and area, comparing area and volume, generalizing strategies and formulas, analyzing effect of orientation, and solving situational questions. It provides examples of exploring how area changes with perimeter for different rectangles and whether a field with longer fencing necessarily has greater area.
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Area and Perimetre
1. SS6.2 Extend and apply understanding of perimeter of polygons, area of
rectangles, and volume of right rectangular prisms (concretely, pictorially,
and symbolically) including:
relating area to volume
comparing perimeter and area
comparing area and volume
generalizing strategies and formulae
analyzing the effect of orientation
solving situational questions.
Things to explore:
1. How many rectangles can you make with a perimeter of 16 units? What is
the area of each?
2. What happens to the area of a rectangle as you increase the perimeter?
Problem: Tinas puppy has a pen that measures 2 m by 3 m. Because her
puppy has grown so much, her dad plans to double the length and width of
the pen. What will happen to the area of the pen after her dad makes these
changes?
Another problem: A and B are two flat rectangular fields. The fence around
field A is longer than the fence around field B. Does that mean that field A
has a greater area than field B? Explain and use a model or sketch to
support your solution.