Pieces of Proof

From NCTM "Illuminations".  This lesson is an intermediate step in the teaching of proofs.  It is a group activity in which the statements of a proof are cut into pieces and the group must properly arrange the pieces.  It does require teacher prep time, and students should know the triangle congruency theorems.  Includes detailed lesson plans, student handouts, assessment options and lesson extensions. Hands-on activity that allows for peer help and encouragement. It gives the students what they need, but makes them think their way though the logical steps. Can be modified to require students to do more of the work and thought process.

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Pieces of Proof

Standards & Objectives

Learning objectives: 

By the end of this lesson students will:

  • Identify the properties that exist in a given figure
  • Apply postulates and theorems to a figure to build a formal proof
Essential and guiding questions: 

Explain how working backwards from what you are trying to prove can be helpful in developing a proof.
Explain why it is necessary to label corresponding parts of congruent figures in the same order.
How does having each statement and each reason written on separate strips of paper help you build the proof?
If you had to choose between being given just the statements or just the reasons, which would you prefer? Why?

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 
  • Provide proof kits that contain only statements. Students have to determine the reasons as well as write out the proof.
  • Provide students with proof kits that contain extraneous statements or reasons. Students have to identify which statements or reasons are not needed for the proof as well as write out the proof.
  • Provide students with proof kits that have some statements or reasons missing. Students have to supply the missing pieces as well as write out the proof.

Helpful Hints

Materials:

  • Proof kits consisting of envelopes with the statement and reason strips and diagrams inside. If you use all the proofs, you'll want to print copies of each proof on different colored paper to help keep them separate.
  • Scissors
  • Poster paper and markers (optional)

References

Contributors: 
Lisa Leach
Originator: 
Ayers Institute for Learning & Innovation