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Geometry Project of the Month         What Figure?

Project of the Month: Sept. 1995 - May 1996

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  1. September 1995 - How many squares?
    If you connect (0,0) to (5,3) with a line segment, it goes through seven unit squares. If you connect (0,0) to (p,q) where p and q are positive whole numbers, how many squares do you go through? Experiment, look for patterns, and summarize your findings.

  2. October 1995 - Quadrilateral relationships.
    Take seven specific quadrilaterals and draw a diagram that shows the relationships between them. The quadrilaterals are: kite, parallelogram, rhombus, trapezoid, scalene quadrilateral, rectangle, and square.

  3. November 1995 - How many cubes will be painted?
    A cube with sides n units long is painted on all faces. It is then cut into cubes with sides 1 unit long. Explain how many of these smaller cubes will have paint on:
    a) 3 surfaces b) 2 surfaces c) 1 surface d) no surfaces

  4. December 1995 - What figure is formed?
    What figure is formed when the consecutive midpoints of the sides of a quadrilateral are joined? What if the original quadrilateral were a rectangle? A kite? An isosceles trapezoid? A square? A rhombus? Other shapes?

  5. January 1996 - Angles formed by the hands of a clock.
    a) At how many different times will the hands of a clock make a right angle? At what times will this occur? Determine your answers to the nearest second. b) Find a time at which the hands of a clock make a 45-degree angle. Generalize your method to find a time at which the hands of a clock form any given angle. c) What angle will the hands of a clock form at 3:20? Do not use a protractor. Generalize your method to give the angle formed by the hands of a clock at any given time.

  6. February 1996 - Sides of a triangle
    Tell me about the altitudes, medians, angle bisectors, and perpendicular bisectors of the sides of a triangle. Be sure to mention anything interesting that happens when the triangle is "special" - equilateral, isosceles, right, etc.

  7. March 1996 - Rep-tiles
    A rep-tile is a tile that can be used to tile a larger scale copy of itself. Can you find a way to divide any triangle into 4 congruent similar triangles? How would you divide squares, rectangles, and parallelograms? Can you find other quadrilaterals that are rep-tiles? How about other polygons? Are there things that make a polygon a good candidate for being a rep-tile?

  8. April 1996 - Tangrams
    For which N's is it possible to make a perfect square using all the pieces from N sets of Tangrams? Example: We know you can make a square with one set of tangrams. If you take all the pieces from two sets, can you make a square? How about with three sets? Four? More? Explain why some of the numbers work and some don't.

  9. May 1996 - A Single Formula for Area
    Write a single formula for area that will work for a rectangle, a parallelogram, a trapezoid, a triangle, and a square. Explain how it works.

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