Using Sequencing with Parallelogram Proof
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The activity of "sequencing" has many useful applications to mathematics.  Sequencing is the breaking down of a process into a series of steps which can be arranged in some chronological order.  Since mathematics is such an "organized" language, it is possible to apply this strategy to many units.

This activity is simple.  Prepare ahead of time a process which has a sequence of events (such as an Euclidean proof).  Write the process on a sheet of paper leaving enough room between the steps so that the steps may be easily cut apart.  Cut the steps apart, shuffle the strips of paper, and place them in an envelope.  Students may work alone or in pairs.  The task is to reassemble the sequence in a mathematically correct order (which may at times be different than the teacher's original answer.)

Here is an example of a sequence ready to be cut apart:

Put the problem and the diagram on the board for everyone to see (or put it on the front of the envelope).

Given: 
     
 
ABCD is a parallelogram
            
Prove: 
 
 
   DEFC is a rectangle

STATEMENTS                             REASONS

ABCD is a parallelogram Given

A parallelogram had 2 sets of parallel sides.

Given

Two lines perpendicular to the same line are parallel.

DEFC is a parallelogram If both pairs of opposite sides of a quadrilateral are parallel, the quadrilateral is a parallelogram.

<DEB is a right angle Perpendicular lines meet to form right angles.

DEFC is a rectangle If one angle of a parallelogram is a right angle, the parallelogram is a rectangle.


 

Ask students to place the strips back in the envelopes when the
activity is over.  You are all set to repeat the activity with another class.

If you want to create a more challenging activity,
cut the pieces apart both horizontally and vertically.