They use square tiles to create designs and to cover pictures of designs to find areas and perimeters, and they transform designs to fit a prescribed perimeter or area. Measuring Odd Shapes Students consider the measuring of things with curved or irregular edges that can't be laid along a ruler. This calls for using other tools, such as string, to help find an approximation. They trace their feet on grid paper, estimate the perimeters and areas of the tracings, and discuss how these measurements might be helpful to shoe manufacturers. Students construct tables to help highlight and reveal patterns in data.
Students confront the misconception that area determines perimeter and vice versa.
Measuring Parallelograms Students cut and rearrange parallelograms to make rectangles and develop strategies for using what they know about finding the area of a rectangle to find the area of a parallelogram. Most students will develop good formulas for finding the area of a rectangle and parallelogram. For students who need them, the use of grids and other more informal reasoning methods are encouraged. Measuring Triangles Students are introduced to finding areas and perimeters of triangles by using grids, arranging triangles to form parallelograms, and measuring with rulers. These discoveries lead students to the idea of the value of pi.