STOMACHION PUZZLE – Colour, Shape, Contrast

Students follow instructions to draw the 14 pieces of a stomachion puzzle, cut out the shapes in different colours of construction paper, then rearrange the pieces to make fun images. 

Required Time

120 Minutes

Grade Level

Grade 3 to Grade 8

Subject

Mathematics
Visual Arts

Vocabulary

contrast shape space stomachion

Materials

Crayola Construction Paper - 30 cm x 45 cm (12" x 18") - 12 Colours Crayola Glue Sticks Crayola Scissors Rulers - 1 per student Pencils

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Steps

STOMACHION PUZZLE – Colour, Shape, Contrast - Step One

Step One

  1. Follow the instructions on the How to Make a Stomachion worksheet to draw the 14 pieces of the stomachion puzzle. (Downloads - Stomachion.pdf)
  2. Cut the pieces out.
STOMACHION PUZZLE – Colour, Shape, Contrast - Step Two

Step Two

  1. Trace the puzzle pieces onto different colours of construction paper.
  2. Carefully cut out each piece.
STOMACHION PUZZLE – Colour, Shape, Contrast - Step Three

Step Three

  1. Rearrange the pieces to make a fun image.
  2. Choose a piece of construction paper for your background that contrasts with the colours of your image.
  3. Carefully glue the pieces onto the construction paper.

Learning Goals

Students will be able to:

  • follow instructions to draw the 14 pieces of a stomachion puzzle;
  • use all of the stomachion pieces to create a collage of a fun image;
  • use contrasting colours to make their image stand out;
  • demonstrate technical accomplishment and creativity.

Extensions

Have students:

  • create a 3-D version of a stomachion puzzle using cardboard or foam board;
  • challenge peers to put the pieces of the puzzle together in a 12 x 12 grid;
  • draw a small diagram of each new 12 x 12 stomachion arrangement completed;
  • tally the number of variations discovered over a set period of time;
  • figure out what percentage of the possible 536 arrangements the participants have found.

Prepare

  1. Download and display the Space and Contrast posters available on this website.
  2. Provide some time for students to work with different kinds of puzzles.
  3. Download and copy the How to Make a Stomachion worksheet, enough for groups of students to share. (Downloads - Stomachion.pdf)
  4. For younger students download and copy the Stomachion Puzzle Pieces template and have them trace the shapes. (Downloads - StomachionPuzzlePieces.pdf)
  5. Teach or review dissection puzzles.
    - dissection puzzles involve taking a figure such as a square and cutting it into a variety of shapes that can be reassembled into one or many different shapes
    - one of the oldest types of puzzles
    - earliest facts about dissection puzzles comes from ancient Greek and Chinese civilizations
    - in the late 1800s newspapers began to publish dissection puzzles making them popular
    - they are fun to do alone
    - fun to do in social gaming groups for competitions in speed solving
    - they develop logical thinking and shape recognition
  6. Provide time for students to work with tangrams.
    - an ancient Chinese dissection puzzle consisting of 7 pieces made using 3 basic geometric shapes
    - 2 small, 1 medium and 2 large triangles, 1 parallelogram and 1 square
  7. Precut construction paper in a variety of colours - 15.2 cm x 22.9 cm (6" x 9").

Introduction

  1. Ask students to share their favourite tangram solution.
  2. Discuss dissection puzzles and what makes them interesting.
  3. Explain that a stomachion is like a tangram only more complicated because it has 14 pieces.
  4. Provide some background information about the stomachion, for example,
    - considered the world's oldest puzzle
    - a geometric game
    - shapes can be rearranged into interesting new shapes such as animals, buildings and so on
    - there are 536 different ways to rearrange the shapes into a square 
    - also known as Ostomachion
    - may have been played by several people with pieces made of bone
    - Archimedes, the most famous mathematician and inventor in ancient Greece, investigated the geometry involved in the puzzle and wrote about it  
    - it is sometimes called Archimedes' Box
  5. Introduce the challenge.

Activities

The Challenge

  1. Follow instructions to draw the 14 pieces of a stomachion puzzle.
  2. Use all of the stomachion pieces to create a collage of a fun image.
  3. Use contrasting colours to make your image stand out.
  4. Demonstrate technical accomplishment and creativity.

The Process

  1. Ensure that everyone understands the challenge.
  2. Establish success criteria with your students, for example,
    I know I am successful when I have:
    measured accurately
    - cut out shapes carefully
    - rearranged the shapes so they touch but do not overlap
    - glued the pieces flat and smooth
    - created a fun image using all 14 shapes
    - kept the paper in good condition
  3. Guide students through the steps outlined in this lesson plan.
  4. Observe students as they work.
  5. Provide individual assistance and encouragement.

Sharing

  1. Once all the images are complete ask students to share them in partners or small groups. 
    Ask them to:
    Look closely at the images and how they are made.
    - Share thoughts about the work.
    - Talk about how the shapes have been used differently to create something unique.

    - Talk about what was difficult about making the puzzle image and explain why.
    - Tell what was satisfying about making the puzzle and explain why.
  2. Ask some students to share their ideas with the whole class.
  3. Display all the images in the classroom so students can view them over the next few weeks.

Assessment

  1. Observe students as they work – thoughtful focus, discriminating, seeking more information, elaborating, experimenting.
  2. Observe students as they discuss their work – active listening, insightful contributions, supporting ideas with evidence found in the artwork and from personal experience.
  3. Use a checklist to track progress. (Downloads – Stomachion_tracking.pdf)
  4. Have students use the self-assessment form to evaluate their work. (Downloads – Stomachion_self-assessment.pdf)