Included are patterns for twenty-six polygons, as found in the Shapes activity sheet.
These polygons are numbered so that teachers can pull out
certain ones for use in an activity and so that students can identify a
particular polygon more easily. Teachers can make durable figures by
copying the polygons onto card stock and then laminating them.
Each group of students needs one set of polygons, and the
teacher should have a special set of the polygons made from
transparencies. Each individual set can easily be stored in a
reclosable plastic bag.
Below are overhead masters and images of the Venn diagrams
that teachers need to copy and laminate for the students and also make
into transparencies for themselves.
The terms and phrases in the Sorting Cards
activity sheet should also be made into transparencies and cut into
cards for use by the instructor. Alternatively, the instructor may use
an overhead marker to write the following terms on the transparencies.
OPPOSITE SIDES PARALLEL
AT LEAST ONE OBTUSE ANGLE
AT LEAST ONE RIGHT
ALL SIDES CONGRUENT
ALL ANGLES CONGRUENT
TWO CONSECUTIVE SIDES CONGRUENT
OPPOSITE ANGLES CONGRUENT
|Terms and phrases for describing
One simple activity is to place the Venn Diagram with One Circle
overhead on the overhead projector and put a phrase, such as "all sides
congruent," on the circle. Ask students to separate all the polygons,
placing them either inside or outside their circle. When the groups
have finished, the teacher can ask different groups to state the number
of a polygon that they have placed in their circle, and the class can
agree of disagree and present reasons to support their comments.
Using the Venn diagrams with more circles increases the level of difficulty. One choice for the Venn Diagram with Two Intersecting Circles
overhead might be "quadrilateral" for one circle and "opposite sides
parallel for the second. Besides highlighting the idea that all
parallelograms are quadrilaterals, this choice lends itself to using
the terms set and subset. Instructors can show a proper
subset using the Venn Diagram with One Circle Inside Another Circle overhead. This activity allows teachers to use quite a bit of set notation and terminology.
The terms and phrases chosen by the teacher from the Sorting Cards
activity sheet make the activity more or less difficult. If the
identifying phrase is "opposite angles congruent," student can discuss
how one determines opposite angles or opposite sides, or whether that
term has meaning for polygons other than quadrilaterals. Polygon 16 can
be used to address difficulties that students have with qualifiers,
such as at least and all,
as in the phrases "at least one obtuse angle" and "all angles
congruent." The phrase "two consecutive sides congruent" will elicit
discussion about whether this term means any two consecutive sides congruent or every pair of
consecutive sides congruent. The class can proceed to discuss whether the phrase itself should be modified.
Teachers can create another activity by showing students a Venn
diagram with the polygons already sorted according to categories known
only to the teacher. The students must determine the correct phrases
that apply to each circle. Alternatively, a group of students can
devise and display a secret sort criterion that the other groups must
try to discover.
You may wish to introduce the Shape Sorter tool for students to practice sorting using an online tool.