Group Size: Individual


Summary: Students will create, classify and sort quadrilaterals.
Materials:
Additional Resources
 Navigating Through Geometry in Grades 35, edited by M. Katherine
Gavin and Gilbert J. Cuevas (NCTM Publication);
ISBN 087353512X
Attachments
Background For Teachers:
A common activity involving geometry is for students to recognize
and name various polygons. Their experiences with foursided polygons
may lack depth or may have some misconceptions. For example,
students are often taught to categorize rectangles and squares separately.
Typically, a polygon with four equal sides and four equal angles is
referred to as a square; whereas, a polygon with four equal angles but one
pair of long sides and one pair of short sides is referred to as a rectangle. We hear students refer to rectangles as being “long” or “tall.” Their
system for differentiating between squares and rectangles is based on
narrow experiences with a few specific examples.
These constructions may cause confusion later as students learn that
squares also fit the description of rectangles. This new information does
not fit logically to what they have already learned, and it does not allow
for growth in understanding that a square is a more specific classification
of a rectangle; just as a rectangle is a more specific classification of a
parallelogram; and that a parallelogram is a specific classification of a
quadrilateral. These shapes all fit in the quadrilateral “family.”
To aid understanding, teach quadrilaterals as a whole. Define
quadrilaterals as a foursided figure and give students the opportunity to
create a variety of quadrilaterals. They look for similarities and
differences and sort them into several different categories according to
their attributes. The sorting activity offers insight into the mathematical
hierarchy used in classifying quadrilaterals. It will become clear that
every quadrilateral falls into three categories:
 those with two pairs of parallel sides,
 those with only one pair of parallel sides, and
 those with no parallel sides.
This activity will set the stage for students to understand that many
types of quadrilaterals exist and that these shapes have some elements in
common.
Intended Learning Outcomes: 1. Demonstrate a positive learning attitude toward mathematics.
3. Reason mathematically.
4. Communicate mathematically.
5. Make mathematical connections. Instructional Procedures:
Invitation to Learn
Provide each student with a geoboard and geoband. Ask them to
create several foursided polygons, then choose their most unique
quadrilateral to share with their group.
Instructional Procedures
 Ask the students to compare their quadrilateral with those made
by other members in their group. Are all quadrilaterals different?
If not, agree on how to make them look different. Record
quadrilateral on Geodot Paper and cut shape out for
display.
 Invite each group to post their quadrilaterals in one of three
columns:
 those with one pair of parallel sides,
 those with two pairs of parallel sides, and
 those with no parallel sides.
Give students time to determine if all the quadrilaterals are in
their appropriate columns. Discuss congruent and similar shapes
and remove any duplicates.
 Identify the columns with the appropriate headings: trapezoids (one pair of parallel sides), parallelograms (two pair of parallel
sides), and trapeziums (no parallel sides).
 Use the Quadrilateral Family Tree handout to discuss
the properties, attributes, and characteristics, as well as the
interconnective and hierarchical commonalities and differences,
between and among quadrilateral shapes.
 Have the students look at the relationship between squares and
rectangles. What are the characteristics of each? Is a square a
rectangle? (Yes, it has four equal angles.) Are all rectangles
squares? (No, many rectangles do not have four equal angles
and four equal sides.)
 Have the students look at the relationship between squares and
rhombuses. What are the characteristics of each? Is a square
a rhombus? (Yes, it has four equal sides.) Are all rhombuses
squares? (No, many rhombuses do not have four equal sides and four equal angles.)
 A Venn Diagram is a good visual aid to illustrate that a square
is both a rectangle and a rhombus.
 Further explore the relationships between quadrilaterals by having
the students work with roping quadrilaterals. Provide each pair of
students a set Quadrilateral Pieces and two or three
pieces of string to make a Quadrilateral Venn Diagram. Ask them to place the appropriate quadrilateral pieces in each ring
according to the following labels:
Ring 1 (Left side): At least one pair of parallel sides
Ring 2 (Right side) No sides parallel
Ask students to justify their placement of different pieces. What
do all the shapes in one ring have in common? How might the
shapes in one ring be different? (Some shapes in Ring 1 are
trapezoids, and some are parallelograms.) What different label
would eliminate one or more of the shapes from a ring? (Only one
pair of parallel sides.) If we drew a giant circle around everything,
including any shapes that are outside the rings, what might the
label for this new ring be? (Quadrilaterals) Try further
explorations using the following labels:
Ring 1 (Inner ring): All sides of equal length
Ring 2 (Outer ring): At least one pair of parallel sides
Ring 1 (Left side): At least one right angle
Ring 2 (Right side): No right angles
Ring 1 (Left side): All sides the same length
Ring 2 (Right side): At least one acute angle
Ring 1 (Left side): At least one set of parallel sides
Ring 2 (Right side): At least one obtuse angle
Attachments
Extensions:
 Have students make their own labels and then challenge a partner
to use them to create quadrilateral rings.
 Have students make “mystery rings” for their partner to solve.
Simply sort quadrilaterals into the Venn Diagram rings according
to some characteristic and have a partner try to decide how the
quadrilateral pieces have been sorted.
Family Connections
Have students take home the quadrilateral pieces to share with
their family. Show them how to sort the pieces in each ring
according to the labels given. They may need to overlap some
rings to form intersections. Make “mystery rings” for family
members to solve.
Assessment Plan:
 Have students justify the placement of quadrilaterals in the Venn
Diagram. Journal reflections explaining the placement of
quadrilaterals are useful for checking students’ understanding.
 Have students explain the relationship among the rectangle,
rhombus, and square.
Author: Utah LessonPlans
Created Date : Oct 26 2004 10:05 AM
