TITLE:    Constructing a Tetrahedron
 

CONTENT  AREAS (What areas of mathematics does this lesson cover?):   Geometry
 

GRADE  LEVEL:    Middle
 

MATERIALS   NEEDED:    Compasses, Tape, Measuring Tape or Rulers, Calculators, Craft Paper, Markers, Scissors, Glue sticks
 

KEY   CONCEPTS:    Vocabulary, Angle measure and 3-D space awareness pertaining to the equilateral triangle and the tetrahedron, Prep for Planar Geometry Constructions, Measurement, Algebraic reasoning: applying relationships derived from measurement to algebraic functions
 

EALR'S and GLE'S (Make the connections clear and specific) : Requirement 1,    “The student understands and applies the concepts and procedures of mathematics” subheading
 1.3.  Understand and apply concepts and procedures from geometric sense.

GLE 1.3.1, 1.3.2 and 1.3.4 for the 9 th and 10 th Grade level require similar understandings as are practiced in this lesson.

Learning Goals: Students will be able to write about or explain the geometric concepts that a circle can be used to construct an equilateral triangle and that an equilateral triangle is composed of four smaller equilateral triangle which provides the number of faces needed for a tetrahedron.(What do you expect students to learn and be able to do from this lesson.)
 

PROCEDURES:  (Label each step in the process:  Activating Prior Knowledge, Disequilibration, Elaboration, Crystallization)

• Introduction/Preassessment: Inquire how students may attempt to produce a 3-dimensional shape with four faces, seek to find out if students have had exposure to such a shape, if the term tetrahedron is familiar, if any prior knowledge of tetrahedral coordination in the natural world exists and if the requirement of equilateral triangles is known. Activities for this may include show and/or tell about objects or materials or trial constructions with supplies or in plan (possibly the work of small groups.
    

• Activity : Students present any ideas they have from the introduction and can discuss what they already know of and how they would produce an object with four equal sides. I would present the procedure for producing a tetrahedral from a circle: Make a circle cut out of paper with a marked center point and a marked point on the edge, fold the circle so that the points are brought together and then cut along the line made by the fold, draw and cut two other lines from the first to produce an equilateral triangle, mark a straight line from each angle, through the center, to the other side of the triangle and then fold and unfold each angle across to these points of intersection ( this should produce four smaller equilateral triangles), tape the sides together in a 3-dimensional shape. As construction proceeds, make a list of observations, vocabulary and geometric rules emphasizing the equality of the various aspects. If time permits, students may combine there tetrahedral with glue sticks to see the way volume and shape changes when many are grouped face to face.

• Closure : Impotant! Be sure to discuss why the construction worked as it did and what other approaches would be possible. Assist students in recording measurements and expressing relationships between the amounts if interest is there.In any case, strive to have each student express aspects of the activity and the new learning gained in writing.   
   

Accomodation Plan:

1.race/ethnicity : students background exposure will hopefully be divulged in the introduction. Examples that may exist in the real world will be valuable to the whole class.

2.language: The use of manipulative and visual props is intended to make the project possible for student who are English Language Learners. Each student would have time to express their ability to do the project and even with a language difference, teacher and student could communicate through observation of the construction process and object produced.

3.gender: Students will have the opportunity to do the work of the lesson and express their learning in a variety of modalities and styles. The teacher will be attentive to status issues among the group(s), and support the student’s individualized ways of learning. Students will be given equal access to all the tools of the project.

4.class: In the event of student’s inability to do the activity, various examples of the process along the development of the construction will be available, and students will be able to return to the activity when they like.

POST-ASSESSMENT : Students will need to provide a representation of the ideas covered in the lesson (written, drawn, displayed visually, explained verbally, or as mathematic expression).