Lesson Title: Qualities of Quadrilaterals or Quadrangle Tango
Creator: Lori Symes
Grade Level: 4th
Big Idea: Geometry
Essential Question: What relationships exist among the various kinds of
quadrilaterals (quadrangles)?
CSO: M.O. 4.3.1 Identify, classify, compare, and contrast 2 dimensional
shapes and 3 dimensional geometric figures according to attributes.
Learning Skill: 21C.O.3-4.1.LS.3 Student, cognizant of audience and purpose,
articulates thoughts and ideas accurately and effectively through oral, written, or
multimedia communications.
Technology Skill: 21C.S.3-4.1 The student will access, analyze, manage,
integrate, evaluate and create information in a variety of forms using appropriate
technology skills and communicate that information in an appropriate oral,
written, or multimedia format.
Launching/Introduction
Activating Prior Knowledge:
 Hand out gel boards.
 Tell students they have 2 minutes to draw their favorite animal & a clone
of their favorite animal. Ask what math term this shows? (Congruency)
 Right Angle: Students show something at their desks with a right angle
and point to the right angle on the object. Then have student brainstorm
objects with right angles on them. Ask, “How can right angles be useful
in designing furniture?”
 Parallel: Students hold up 2 crayons/pencils/ markers to show an
example of 2 parallel line segments. Have students draw parallel lines on
board/overhead to show that they can be diagonal, vertical, horizontal, etc.
Ask, “How would parallel lines be important when designing?”
such as airplane runways, highways, train tracks...
 Triangle: Have students draw different triangles on board. Have
students explain the ways they are the same 3 lines/ 3 angles Break
down the word: tri (3), + angle=3 angles.
Specialized Vocabulary Development
 Quadrangle (The kinds will be introduced, etc. during the explore part of
the lesson): Students brainstorm as a class as many words as they can

think that start with qua. Look at these words and discuss what it has in
common: (Quarter, quart)
Tell them to think what a quadrangle is. Have each person draw a
quadrangle and on his/her individual board. Then break down
quadrilateral (4 sides) & discuss its meaning the same shape as
quadrangle. (Take up boards and styluses.)
Investigate/Explore:
Hand out a bag of materials (a quart bag containing 12 each of 3 sizes of
straws, 36 pieces of inch long pipe cleaners, a glue stick) to each group of
approximately 2 students and a worksheet with the following 3 headings:
quadrangle, definition, and drawings. (For modifications you can use definitions
with the reviewed math terms defined again in parenthesis.) Also pass out the
snack bags with definitions.
Then have students construct as many of each of the following
quadrangles as possible, debriefing about every 5 minutes after each new
definition.
1. Ask students to take out the definition strip numbered 1 from their snack bags:
2 pairs of parallel sides.
 Ask groups to make as many different kinds of quadrangles from their
bag of materials that would meet this definition.
 After 5 minutes have students bring up parallelograms to the Elmo.
Have the class vote (show thumbs up/thumbs down) on each to
decide if the form reflects the definition and why or why not. (Keep
probing until these quadrangles are drawn: typical parallelogram,
square, rectangle, rhombus).
 As each parallelogram object is approved by the class and teacher,
have students draw it in the 1st box beside #1. “What do you notice
about these drawings?” Then have them write the name you now tell
them “parallelogram.” (The definition then can be glued on the paper
from strips you give them.)
 Also on large poster board, have each group glue their accepted
quadrangle in the space labeled “Parallelogram.”
2. Follow the same procedure with the definition strip numbered 2 in the snack
bags: Only one pair of parallel sides.
 After 5 minutes have students bring up trapezoids to the Elmo voting
on each as a class to decide if it is a true reflection of definition & why
or why not.
 After each trapezoid object is accepted by class & teacher, have
students draw it in the 2nd box beside #2. Then have them write the
name you now tell them “trapezoid.” (The students then glue on the
definition from strips you have given them.) Keep probing until
students determine that trapezoid can be drawn with or without a right
angle by asking, “How can trapezoids be drawn differently?”


Also on the same large poster board as #1, have each group glue their
accepted quadrangle in the space labeled “trapezoid.”
Referring to poster board, have students compare and contrast
parallelograms and trapezoids.
3. After following the same procedure with definition 3: 4 congruent sides for
rhombuses, have students compare and contrast rhombuses with trapezoids
and parallelograms. Ask, “How are rhombuses and trapezoids the same?
How are rhombuses and parallelograms the same? How are rhombuses
and trapezoids different? How are rhombuses and parallelograms different?
Keep probing until squares and a rhombus without right angles are drawn.
4. Again, follow the same procedure with definition 4: 2 pairs of parallel sides,
4 right angles for rectangles, have students compare and contrast
rectangles with rhombuses, trapezoids, and parallelograms. Keep probing
until squares and a typical rectangle are drawn. Ask, “How are rectangles
and rhombuses the same? How are rectangles and rhombuses different?
How are rectangles and trapezoids the same? How are rectangles and
trapezoids different?”
5. After following the same procedure with definition 5: 4 congruent sides, 4
right angles for squares, have students compare and contrast squares with
rectangles, rhombuses, parallelograms, and trapezoids. Ask, “How are
squares and rectangles the same? How are squares and rectangles
different? How are squares and rhombuses the same? How are squares and
rhombuses different? How are squares and parallelograms the same? How
are squares and parallelograms different? How are squares and trapezoids
the same? How are squares and trapezoids different?
Summarize/Debrief Lesson
Groups can discuss the most important thing they learned about
quadrangles, and put it into a catchy line for a pantuom, a type of poem. See
Teacher Notes for more about pantuoms. (If there are more than 8 groups,
combine some of the groups to work together until there are 8.) Here is an
example the fourth grade students from Glade Creek wrote and revised:
Quadrangle Tango
(1) Quadrangles are a fun math activity, a fun math activity.
(2) Quadrangles have 4 sides. Qua, qua, qua…Whoo hoo!
(3) Quadrangles sometimes have equal sides such as squares and rhombuses,
Yee, ha!
(4) Quadrangles can even be found in the sky, a kite shaped cloud soaring high
in the sky.
(2) Quadrangles have 4 sides. Qua, qua, qua…Whoo hoo!.
(5) Many have parallel sides: trapezoids, rhombuses, rectangles, squares,
parallelograms.
(4) Quadrangles can even be found in the sky, a kite shaped cloud soaring high
in the sky.
(6) A square has awesome congruent sides, Oh, yeah!
(5) Many have parallel sides: trapezoids, rhombuses, rectangles, squares,
parallelograms.
(7) Parallelograms can have 4 equal straight sides like squares and rhombuses,
yeah!
(6) A square has awesome congruent sides, Oh, yeah!
(8) Quadrangles are shapes like squares, rectangles, trapezoids, and more. Yes,
they are!
(7) Parallelograms can have 4 equal straight sides like squares and rhombuses,
yeah!
(3) Quadrangles sometimes have equal sides such as squares and rhombuses,
Yee ha!
(8) Quadrangles are shapes like squares, rectangles, trapezoids, and more. Yes,
they are!
(1) Quadrangles are a fun math activity, a fun math activity.


As groups make up a line, the shortest person in the group can bring it up on
an index card while the teacher prints it on the laptop prepared ahead of time
with pre-numbered lines in the following order: 1,2,3, 4,
2,5,4,6,5,7,6,8,7,3,8,1. (Group 1’s line will be on the 1st and 16th line, Group
2’s on the 2nd and 5th line, Group 3’s on the 3rd and14th line, etc.) If time
allows, teacher may allow students to copy and paste lines.) After students
have returned to their seats, they may design a robot using quadrangles while
waiting on the other groups. These could be displayed in the room or hallway
when finished.
When all groups have turned in lines and lines are on overhead, discuss lines
together, having groups vote on if they agree or disagree with other groups’
lines, explaining why they disagree. As groups present lines with
characteristics of pantuoms, ask the class what quadrangles possess those
characteristics. A Venn diagram could be put on another document page on
the computer to show which quadrangles do and do not possess each
characteristic. (Revise lines as class desires and as appropriate. Practice
reading it together, alternating boys and girls. Then tell class they will
perform this poem the next day in physical education.
Materials
Per group: in a quart size zip lock bag
A ziplock snack bat with twelve 2 inch straws,
A ziplock snack bat with twelve 3 inch straws
A ziplock snack bat with twelve 4 inch straws
36 pieces of inch long pipe cleaners
glue stick
index card
A snack bag with 3 each of the following definitions (Each group of
the same definition can be paper clipped together.) These definitions are
available in two forms, with one written to provide more support for
struggling students.
1. Only one pair of parallel sides,
2. 2 pairs of parallel sides,
3. 4 congruent sides,
4. 2 pairs of parallel sides, 4 right angles
5. Congruent sides, 4 right angles
Materials per student:
Gel board with stylus, available from gelboard.com (Individual
whiteboards or slates would work just as well.)
Chart with 3 columns labeled “quadrangle, definition, drawings”
Unlined white paper for robot drawing
Materials for class:
One poster board sheet divided into 6 sections. At the top it should
be labeled “Quadrangles/Quadrilaterals.”
Elmo
Laptop
Teacher Notes
Most years, students seem to struggle with understanding that one
type of quadrangle can actually be another kind such as a square is also
a rectangle. Besides giving students the opportunity to use higher level
reasoning skills to break down the parts of the different quadrangles, I am
hoping this lesson will clearly help students completely understand the
definition of each type of quadrangle. This should be taught only after
students have a clear understanding of right angles, parallel lines, and
congruency. (One quadrangle not included was kite due to time
limitations and the desire to keep students from getting bored by staying
on a similar task too long.)
In the language arts, it would be helpful if pantuoms had been
taught.
A Language Arts Extension
The class can revise the pantuom written using techniques you are
currently teaching or would like to introduce. (A pantuom is a poem that
repeats the lines in the way explained on the next dot.)
The Physical Education Follow Up
Students line up on opposite sides of the room. (Students in same
group should be on opposite sides. A third person in a group may get on
either side.) As the class reads their lines students who authored that
line, gallop up to each other giving their partner a high five and then return
to group. (Thus the Quadrangle Tango.) When performance of “Tango”
is finished, children on one side of room get in one circle with other side in
another circle, placing hands on top of each others in middle (like a sports
cheer) and yelling “Quadrangle Tango!” Then students return to their
seats.