Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 70616
Trapezoids
Students are asked to consider how the hierarchy of quadrilaterals would change based on the two different definitions of trapezoids.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_Trapezoids_Worksheet.docx
MFAS_Parallelograms_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task should be implemented individually.
1. The teacher shows the student the two trapezoids on the attached Trapezoids worksheet and reads the following aloud to the student:
These two shapes are both trapezoids. Some mathematicians classify trapezoids as quadrilaterals with exactly one pair of parallel sides. Other mathematicians classify
trapezoids as quadrilaterals with at least one pair of parallel sides.
2. Next, the teacher should provide the student with the Parallelograms worksheet and say, "We classify parallelograms as quadrilaterals with two pairs of parallel sides. All the
shapes on this page are parallelograms. Would parallelograms be classified differently as a result of which definition of trapezoids we adopt? Why or why not?"
3. If needed the teacher may prompt with, "If we classify trapezoids as quadrilaterals with exactly one pair of parallel sides, would parallelograms also be classified as
trapezoids?" The teacher then follows with, "If we classify trapezoids as quadrilaterals with at least one pair of parallel sides, would parallelograms also be classified as
trapezoids?"
Note: In the mathematics community, there are two prevailing definitions of a trapezoid. The more commonly used exclusive definition states that trapezoids are classified as
quadrilaterals with exactly one pair of parallel sides. Alternately, the inclusive definition states that trapezoids are classified as quadrilaterals with at least one pair of parallel
sides. The exclusive definition “excludes” all parallelograms (including rhombuses, rectangles, and squares) as trapezoids and the inclusive definition “includes” all parallelograms
(including rhombuses, rectangles, and squares) as trapezoids. This task is intended for the student to consider how the hierarchy of quadrilaterals would change based on
which definition is used.
TASK RUBRIC
page 1 of 3 Getting Started
Misconception/Error
The student does not understand the hierarchy of quadrilaterals.
Examples of Student Work at this Level
The student is unaware of the existing hierarchy of quadrilaterals and is unclear how either definition affects the structure of this hierarchy. For example, the student simply
compares trapezoids to the other shapes on the Parallelograms worksheet and does not reference either definition of trapezoids in the explanation.
Questions Eliciting Thinking
Can you explain the diagram on the Parallelograms worksheet? How are the shapes alike? How are they different?
If we say that trapezoids are classified as quadrilaterals with exactly one pair of parallel sides, would parallelograms also be classified as trapezoids? What would that mean
about rectangles? Squares? Rhombuses?
If we say that trapezoids are classified as quadrilaterals with at least one pair of parallel sides, would parallelograms also be classified as trapezoids? What would that mean
about rectangles? Squares? Rhombuses?
Instructional Implications
Consider using the MFAS task Classifying Quadrilaterals (5.G.2.4) to assess the student’s understanding of the relationships among quadrilaterals.
Review the terms quadrilateral, polygon, parallelogram, rhombus, square, and rectangle and their definitions. Provide the student with extensive exposure to a variety of
different quadrilaterals. Guide the student to focus on the defining attributes of each shape (e.g., rectangles are quadrilaterals with four right angles, and a rhombus is a
quadrilateral with four congruent sides). Model the precise and accurate use of mathematical terminology to describe specific attributes of shapes. Help the student develop
an understanding of the concept of types of quadrilaterals by showing a variety of examples and non-examples. Assist the student in using mathematical terminology to
describe quadrilaterals (e.g., quadrilaterals are polygons with four sides; quadrilaterals also have four angles and four vertices; the lengths of the sides of quadrilaterals are not
always the same).
Have the student practice analyzing, comparing, and classifying shapes based on properties by providing the student with a set of shape cards or power polygons. Have the
student sort the shapes into categories that are provided or allow the student to create categories. Ask the student to justify classifications by referring to defining
attributes.
Making Progress
Misconception/Error
The student does not understand all of the implications that the two definitions hold.
Examples of Student Work at this Level
The student understands that each definition will provide a different structure. For example,the student understands that the inclusive definition will include all
parallelograms as trapezoids in the hierarchy, but is unclear about what the exclusive definition will do to the structure of the hierarchy of quadrilaterals.
Questions Eliciting Thinking
How would changing the definition of trapezoids impact the definition of parallelograms?
What is the definition of a parallelogram? How are parallelograms related to rectangles, rhombuses, and squares?
If we include parallelograms as special trapezoids using the inclusive definition, how does that affect the definitions of rectangles, rhombuses, and squares?
If we exclude parallelograms as special trapezoids using the exclusive definition, how does that affect the definitions of rectangles, rhombuses, and squares?
Instructional Implications
page 2 of 3 Provide the student with an image showing the hierarchy of quadrilaterals using the exclusive definition (as shown below). Ask the student to identify changes to the
hierarchy if the inclusive definition is adopted. Provide feedback.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student explains that if the exclusive definition is used, parallelograms, rectangles, rhombuses, and squares are not considered to be trapezoids and if the inclusive
definition is used, then all parallelograms, including rectangles, rhombuses and squares can be classified as trapezoids.
Questions Eliciting Thinking
Can you create a model to show how each of these definitions affects the hierarchy of quadrilaterals?
Which definition of trapezoids do you think mathematicians should adopt? Why?
Instructional Implications
Define a kite as a quadrilateral with two pairs of adjacent congruent sides. Have the student consider how a kite fits into the hierarchy of quadrilaterals. Note: The definition
does not exclude the possibility that all four sides are congruent.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Trapezoids worksheet
Parallelograms worksheet
Scratch paper for drawing shapes (if necessary)
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.5.G.2.4:
Description
Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures.
page 3 of 3