Students will apply their knowledge of area and perimeter of a variety of shapes to determine area and perimeter of complex shapes and to solve real problems. Students will examine an Olympic symbol and determine the area of the shapes on it. They will suggest a layout that would yield the pieces for a flag of the symbol with a minimum of waste.

• Students will understand and apply concepts and procedures from measurement.

• Students will apply the formulas for areas of rectangles, circles, trapezoids, and triangles to compute the area of complex shapes.

• Students will use a variety of tools and technologies to perform geometric constructions.

• Students will apply appropriate methods, operations, and processes to construct a solution.

• Students must know how to find the area of a circle, rectangle, and triangle.

• Students must know how to find the perimeter of a rectangle and the circumference of a circle.

Students should research and find a copy of the USA Olympic flag or another reasonably simple flag of their choice. The symbols on the flag should include some complex shapes. Students should copy or build a reasonable representation of the flag (such as the one shown below), and apply the drawing to a coordinate grid.

Using estimation skills and appropriate formulas, they should calculate the area of the darkened region.

Next students should consider the unconnected pieces of the design. If a flag were to be sewn, with dark regions affixed to a light background, how much dark cloth would be needed? Students will need to research the dimensions of a standard-sized Olympic flag. They must determine the scale conversions necessary for their drawing to make the sizes of the pieces appropriate for the size of the flag, and then apply those sizes to a grid which represents the fabric. They must take into consideration the width of the fabric used. Students should move and rotate unconnected pieces upon the grid field until they have a "cutting layout" which minimizes waste. An extension of this might be to create a layout which would make three or five flags. Students can consider how increasing the number of flags gives them an opportunity to improve their layout, and potentially minimize waste even further.

Another measurement problem involves laying out a track for a running event. Students should research to find the size of a standard Olympic track. They should then measure their own school track to see how it compares. (Have students break the track into a rectangle and two semicircles. They can measure diameter and length of the straightaway.) Older schools may have a track which is measured in feet, rather than meters. Students will need to convert to one system of measurement in this case. Student should construct a scale drawing of the school track on a grid. If the distance of the inside track is, for instance, 400 meters, each lane moving out from the inside lane is progressively longer. Students need to determine how much longer the running distance of each lane is, using an increasing diameter, and determine a start line for each lane for a particular race. (Different groups of students could figure different races, if that is desired.) Students should mark a line on their drawings for a uniform finish line and start lines for each lane for a race.

Students should work in pairs.

• Computer(s)
• Printer
• Internet Connection
• Word Processing Software
• Image Processing Software

Gifted Students:

Have students modify a quarter mile track to meet metric specifications. Have them include start lines for a variety of track events, such as 50 meters, 100 meters, 200 meters, 400 meters, 800 meters, 1600 meters, and relay races. Students must research the differences in how the different races are run. They must also try to minimize the number of different finish lines on the track.

Assessment Tools:

Assess students' collaboration, accuracy of research, stated assumptions and drawings, completeness of calculations, insight, and problem-solving skills on self-assessment.