Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 64905
Area of Quadrilaterals
Students are asked to find the area of a trapezoid and a parallelogram by composing or decomposing into triangles and rectangles.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, area, trapezoid, parallelogram, quadrilateral, rectangle, triangle, decompose, compose, polygon,
real-world problem
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_AreaOfQuadrilaterals_Worksheet.docx
MFAS_AreaOfQuadrilaterals_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Area of Quadrilaterals worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not have a correct strategy to determine the area of the quadrilaterals.
Examples of Student Work at this Level
The student:
Calculates the perimeter of the figure (correctly or incorrectly).
Multiplies all the values given in the diagram.
page 1 of 5 Does not have a consistent strategy to find area.
Does not provide enough work (or clarity in their work) to determine their solution strategy.
Questions Eliciting Thinking
What does the problem ask for? What do compose and decompose mean in this context?
How will finding the perimeter help you?
What were you trying to find by multiplying those numbers?
Can you explain the steps you have taken in your calculations? What are you trying to find?
Instructional Implications
Ensure that the student is familiar with triangles and rectangles and the terms used to describe their dimensions such as base and height. Provide the student the
opportunity to identify and label the base and height of a variety of triangles including obtuse triangles. Emphasize that the height must be perpendicular to the base.
If needed, review area and perimeter. Reinforce that perimeter is a linear measurement determined by adding the lengths of all the sides while area is measured in square
units and is a measure of the surface contained in the interior of a polygon. Have the student experimentally verify the relationship between the area formulas for rectangles
and triangles, demonstrating how the area of a triangle is one-half the area of a rectangle with the same dimensions.
Model for the student how to decompose parallelograms and trapezoids into triangles and rectangles. Explain (or use a demonstration) to show that the sum of the areas of
the parts is equal to the area of the whole. Guide the student to compose or decompose the parallelogram and trapezoid into familiar shapes. Ask the student to label
relevant dimensions and calculate the areas. Encourage the student to show all work neatly and completely and to label the answer with the appropriate unit.
Provide manipulatives such as pattern blocks for the student to explore in order to gain hands-on experience with composition and decomposition of two-dimensional
shapes. Partner the student with a classmate to practice composing and decomposing shapes into familiar figures such as rectangles and triangles and to develop strategies
to calculate area. Provide additional opportunities for the student to compose and decompose polygons into rectangles and triangles in order to find area.
Moving Forward
Misconception/Error
The student makes conceptual errors in finding the area of the quadrilateral.
Examples of Student Work at this Level
The student demonstrates an understanding of composing or decomposing the figure into rectangle(s) and triangle(s) to find the area, but is not able to correctly solve the
problem. The student:
Incorrectly calculates the dimensions of the shapes.
Incorrectly identifies the base and height of shapes.
page 2 of 5 Finds the areas of two (or more) composing shapes but does not find their sum.
Uses the wrong formula.
Uses the wrong values in the formula [e.g., does not identify the base(s) and height of the figure correctly].
Performs the operations in the wrong order when evaluating the formula.
Writes the formula correctly, but omits a step when evaluating (does not divide by two or multiply by
as needed).
Questions Eliciting Thinking
How did you decide which values to use when calculating the area of each shape? Can you outline each shape individually and show me its base and height?
When you decomposed the shape into a rectangle(s) and triangle(s), what were the dimensions of each new shape?
What type of angle must the base and the height of a triangle make?
What is the question asking you to determine? What do you need to do to find the total area of the figure?
Why did you choose that formula? What does each variable represent? Can you show me where those values are in the figure?
What is the correct procedure for evaluating this formula?
Instructional Implications
Model for the student how to decompose parallelograms and trapezoids into triangles and rectangles. Explain (or use a demonstration) to show that the sum of the areas of
the parts is equal to the area of the whole. Guide the student to compose or decompose the parallelogram and trapezoid into familiar shapes. Ask the student to label
relevant dimensions and calculate the areas. Encourage the student to show all work neatly and completely and to label the answer with the appropriate unit.
Provide additional opportunities for the student to compose and decompose polygons into rectangles and triangles in order to find area. This worksheet can be edited to
change the lengths of each dimension for further practice.
Almost There
Misconception/Error
The student makes minor mathematical errors when calculating the area.
Examples of Student Work at this Level
The student makes a minor error in computation or when labeling units. The student:
Calculates incorrectly in one step of the problem but all other work is correct.
Transposes a number from one step to the next.
Uses the wrong units or no units at all.
page 3 of 5 Writes
rather than 105
.
Writes a mathematically incorrect statement in some step of the work [e.g., writes multiple steps together into one long (incorrect) equation:
x 7 x 6 = 21 + 12 x 7
= 84 + 21 = 105].
Writes the equation incorrectly, but evaluates it correctly.
Questions Eliciting Thinking
Can you check over your work for errors?
What units should be used in this problem? Why?
How is
Does
different from105
? What does each mean?
x 7 x 6 = 105? Can you show your work in individual steps?
Instructional Implications
Review multi-digit multiplication and division and order of operations as needed.
Provide specific feedback concerning the error(s) made and ask the student to revise his or her work. Provide additional opportunities for the student to compose and
decompose shapes and to use formulas to find the areas of polygons.
Consider implementing the MFAS tasks Area of Triangles (6.G.1.1) or Area of Kite (6.G.1.1).
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 finds an area of 105
for the trapezoid and 168
for the parallelogram showing work clearly to support those answers. The student may:
Decompose the shape into rectangle(s) and triangle(s) and find the sum of their areas.
Use a formula for the area of the given quadrilateral.
page 4 of 5 Questions Eliciting Thinking
Can you think of a different way you could have found the area?
When using the formula, what does each part mean? How could you show the formula is equivalent to the sum of the areas of the decomposed shapes?
How could you find the perimeter of the figure? Are there any missing dimensions you would need to find first? If so, how could you find those?
Instructional Implications
Ask the student to find areas of polygons whose dimensions include rational numbers.
If not already known, challenge the student to find formulas for the areas of parallelograms and trapezoids.
Consider implementing other MFAS tasks from the standard (6.G.1.1).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Area of Quadrilaterals worksheet
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.6.G.1.1:
Description
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and
mathematical problems.
page 5 of 5