GEOMETRY PROJECTS CORRELATED TO CHAPTERS IN TEXTBOOK

by

Adella S. Croft, Skyline High School and Marilyn L. Keir, University of Utah Salt Lake City, UT

  1. The Language of Geometry   "Getting into Shape"

    This assignment will help you to become aware of geometric shapes and their frequent occurrence in daily life. You will find pictures in magazines with examples of each of the following:

    point line plane
    circle right triangle isosceles triangle
    square non-square rectangle equilateral triangle
    trapezoid pentagon hexagon
    octagon non-square rhombus kite


    These pictures must be mounted without tape on several sheets of construction paper or posterboard. Please trace outline the shape within the picture with a black felt tip pen.


  2. Reasoning and Introduction to Proof   "The Logic of Advertising"

    This assignment will give you practice using some of the principles of logic that are necessary in geometry. You will select an advertisement from a magazine as the focus of this project. Please choose an ad for something that is considered legal, moral, and appropriate for high school students. You will mount your advertisement on a piece of construction paper without tape. Mount a separate sheet of notebook or typing paper on the reverse side of the construction paper. Write and label the following sentences:

    1. A conditional statement of your choosing as suggested by your ad.
       Write the statement in if-then form.
       For example: If I pop Pringles, then the fun won't stop.
    2. The converse of your conditional statement.
    3. The inverse of your conditional statement.
    4. The contrapositive of your conditional statement.


  3. Parallels   "An Unparalleled World"

    You will illustrate how different the world would be if the there were no parallel line by drawing a picture or series of pictures or by writing a poem or story.


  4. Congruent Triangles   "Knowing All the Angles"

    You will be given several sheets of dot paper. Illustrate one vocabulary item below on each square of the dot paper. Write the title below each picture and spell it correctly! Use color and pictures to give your illustrations personality!! Outline or darken the subject of each picture so that it is easy to see.

    1. Labeled Angle-Draw and
    label all the parts of the angle:
    vertex, sides, interior, exterio    		 5. Vertical Angles



    		 9. Opposite Rays
    2. Acute Angle



    		 6. Complementary Angles
    (Non-Adjacent)

    		 10. Adjacent Angles
    (Non-right)
    3. Right Angle



    		 7. Supplementary Angles
    (Non-right, Non-adjacent)

    		 Angle bisector
    (Non-right)
    4. Obtuse Angle



    		 8. Linear Pair



    		 12. Perpendicular Bisector
    (Non-right)
  5. Applications of Triangles   "Building Toothpick Bridges"

    See "Building Toothpick Bridges" by Jeanne Pollard, published by Dale Seymour. The following form is for grading the students at the end of the unit.

    Bridge Building Group Evaluation


    COMPANY NAME:_____________________________________________________

    Your group should fill out this form together under the Project Supervisor's direction. Note: The & column should sum to 100%.

    Name Participation Quality of Work (grade)
    12345 12345 12345
    12345 12345 12345
    12345 12345 12345
    12345 12345 12345
    12345 12345 12345
    Total Expenditure for Bridge $________ Bearing Weight for Bridge________
    Expenditure/Weight Ratio________ Overall Grade ________


  6. Quadrilaterals   "Let's Tessellate!"

    Create a picture using a parallelogram that you have modified. Be sure to use color, illustrations and your imagination! Give your creation a title. (See "Discovering Geometry" by Michael Serra, published by Key Curriculum Press.)


  7. Similarity   "Creating Your Own Fractal" You will complete a fractal on an 8.52 x 112 of paper. All triangles must be separate and complete, none may overlap. Each triangle must be isosceles with the altitude drawn and labeled as above. The ratio of growth/reduction must be stated and be constant for both the base and the altitude. Must give the depth of your fractal (number of iterations).

    Isosceles Fractal Worksheet


  8. Right Triangles   "Here's a Little Song I Wrote about Pythagoras"

    You will do research and write a song about the mathematician, Pythagoras. In addition to dates and places of birth and death, find out 10 unique facts about Pythagoras. Your song must have three verses which contain some true information about Pythagoras and a chorus which contains the Pythagorean Theorem in words (not a2 + b2). You may set your words to a favorite tune.

    Puny Facts about Pythagoras Worksheet

    Puny Tune for Pythagoras Worksheet


  9. Circles   "Crazy Daisy"

    This assignment will help you to practice what you've learned about constructions. Follow the directions to construct a "daisy" using only a compass and straightedge. Use your imagination to turn it into a work of art! Be colorful!


  10. Polygons   "Flatland Newspaper"

    You will prepare a written project on the inhabitants of Flatland based on the book of the same name by Edwin Abbott. You will do this in the form of a storybook or newspaper. If you choose to do the newspaper make sure it contains at least four (4) different sections, i.e.: front page, sports, classifieds, births/deaths. This assignment will be graded on originality, neatness, understanding of Flatland and the geometric concepts presented in the book. Use illustrations! Be creative!! You may even catch yourself enjoying this project!!!


  11. Solids, Area and Volume   "What's My Volume?"

    You may choose to work with one other person on this project. Please do not share your answers with others.

    1. You will create a set of solids using the attached templates. You will make the five Platonic solids, a triangular prism, and a square pyramid. You will also make a cylinder, which will exactly hold a tennis ball and a cone, which will exactly fit into the cylinder.
    2. Find the surface area and volume of each of the solid figures you created. (Measure in centimeters and round to the nearest tenth.) If finding the volume is not a matter of a simple formula, find a way that you might estimate it and do that. Be sure to explain in detail how you calculated each area and volume.
    3. For each of the 10 solids (including the tennis ball you should list the name of solid, dimensions, shape of faces, surface area and volume.

    Volume Project Worksheet

    Surface Area/Volume Competition Worksheet


  12. Coordinate Geometry   "AlgeBrush"

    Sketch a picture on graph paper using only circles and lines. On a separate piece of paper, write the equations necessary to re-create your drawing. To make the picture precise, you must give the exact domains you wish to have used. You must give instructions for the picture as well as a drawing of how it looks when your directions are followed precisely. You should have more than 25 equations used in your picture, but no more than 100! Color it. Use AlgeBrush to verify your picture. You may want to add further detail.

    Hand in:
       a) The equations as you wrote them,
       b) The picture as you drew it,
       c) The drawing form the computer,
       d) The list of equations from the computer.

    Graph Paper Worksheet


    (If you are interested in purchasing a copy of AlgeBrush for a minimal charge, contact the creator, Marilyn Keir. mkeir@earthlink.net)


  13. Transformations   "Seeing Symmetry"

    This project will help you to become aware of the symmetry in the world around you. You will create a small poster. The minimum size you may use is one-fourth of a poster board. You will cut out pictures from magazines to illustrate different types of symmetry. You will neatly paste you pictures to the poster board, outline the symmetry, and label each example. Be sure to use a variety of examples and make it attractive.

    Your poster will contain five (5) examples in each of the following categories:
       a) Vertical symmetry only
       b) Horizontal symmetry only
       c) Point or turn symmetry only
       d) Two or more types of symmetry


  14. End-of-Year Review and Summary   "ABC's of Geometry"

    You will create a book using vocabulary words that you have learned this year. To do so you will choose a geometry term for each letter of the alphabet. For example, angle for A or endpoint for E. For each page in your book you will:

       1) State the letter of the alphabet,
       2) Give the geometry term and a brief definition,
       3) Provide an illustration of something man-made which contains/describes the term, and
       4) Provide a picture of something from nature which contains/describes the term.
       (Your pictures may be drawn by hand or clipped from a magazine.)


  15. Math Books Worth Having