Standard Four – Top Level Problems
Prompt: A tangram is an ancient Chinese puzzle in which a square is cut into seven
pieces: five triangles, one square, and one parallelogram. If the area of the entire
tangram is 1, what is the area of each piece?
Answer: a = ¼, b = ¼, c = 1/6, d = 1/8, e = 1/6, f = 1/8, g = 1/8
Mathematics Teacher December 1995 V88 N9
Prompt: A cone has a lateral edge of 9 inches and holds 2 quarts of ice cream. If only
1 quart of ice cream is put in the cone, how far will it reach on the lateral edge?
Answer: ~7.143 inches
Mathematics Teacher December 1995 V88 N9
Prompt: In the figure, the two circles are tangent to the right angle and to one another.
If the larger circle has radius 1, what is the radius of the smaller circle?
Answer: 3-2sqrt(2)
Mathematics Teacher April 2003 V96 N4
Prompt: Explain this paradox: the area of the rectangle is 104 square units, but the
area of the parts is 20 + 52 + 24 + 7.5 = 103.5 square units.
Answer: it is not a rectangle. The slope from AB is 3/5 where the slope of BC is 5/8.
Michael A. Stueben, “Mind Benders,” Discover 4 (June 1983).
Prompt: Inscribe a rectangle in a square so that each of the four triangles formed is
isosceles. Determine the length of the diagonal of the rectangle if the sum of the areas
of these four triangles is 200 square inches.
Grassl and Mingus. "Problem Solving: Exploring paths less Travled." 2005: 77-99