Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 65115
Octagon Area
Students are asked to find the area of a composite figure.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, area, decomposition, polygon, composite figure
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_OctagonArea_Worksheet.docx
MFAS_OctagonArea_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 problem on the Octagon Area worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to decompose the octagon in order to find its area.
Examples of Student Work at this Level
The student:
Does not decompose the shape but attempts to apply a single formula to determine the area of the octagon or multiplies two given measurements.
page 1 of 4 Decomposes the octagon into “unfamiliar” shapes whose areas he or she cannot calculate.
Questions Eliciting Thinking
What is area? What do you have to do to find it?
Is there a single formula for area that will work for this figure?
Can you decompose the figure into familiar shapes?
How many sides are in a trapezoid? How many sides are in the shape you made?
Instructional Implications
Review the concept that the area of a composite figure can be found by decomposing the figure into familiar shapes and finding the areas of the parts. Provide
opportunities for the student to decompose both two-dimensional and three-dimensional figures into familiar two-dimensional and three-dimensional shapes. Ask the student
to clearly identify the decomposed parts and any relevant dimensions. Guide the student in systematically decomposing the octagon into familiar shapes. Ask the student to
label relevant dimensions and calculate the areas.
Provide manipulatives such as pattern blocks for the student to explore in order to gain hands-on experience with decompositions of composite figures. Partner the student
with a classmate to practice decomposing shapes into familiar figures and creating strategies to calculate area. Provide additional opportunities for the student to decompose
shapes and use formulas to calculate area. Include scenarios involving whole numbers, fractions, decimals, ratios, and conversions of various units of measure within the same
system.
Consider implementing the MFAS task Composite Polygon Area (7.G.2.6).
Moving Forward
Misconception/Error
The student makes significant errors when calculating areas.
Examples of Student Work at this Level
The student demonstrates an understanding of the need to decompose the solid figure but:
Uses an incorrect formula or procedure to determine area.
Uses an incorrect length when substituting into a formula.
Questions Eliciting Thinking
What shape is this? How do you calculate the area of this shape?
What measurements do you need to calculate the area of this shape? Can you determine the dimensions if they are not given?
Do you know a formula to find the area of this shape?
Instructional Implications
Ask the student to clearly identify the decomposed parts and any relevant dimensions. Guide the student in systematically decomposing the octagon into familiar shapes.
Ask the student to label relevant dimensions and calculate the areas.
Provide additional opportunities for the student to decompose shapes and use formulas to calculate area. Include scenarios involving whole numbers, fractions, decimals,
ratios, and conversions of various units of measure within the same system.
Consider implementing the MFAS task Composite Polygon Area (7.G.2.6).
page 2 of 4 Almost There
Misconception/Error
The student makes a minor mathematical error.
Examples of Student Work at this Level
The student successfully decomposes the octagon into familiar shapes and selects appropriate formulas for calculating area. However, the student:
Makes a calculation error when summing the areas of the component figures.
Neglects to sum the areas of the component figures.
Makes a multiplication error when calculating component areas.
Labels units incorrectly or not at all.
Questions Eliciting Thinking
How should the units be labeled?
I think you may have made a calculation error. Can you check your work?
What one value represents the area of the octagon?
Instructional Implications
Provide specific feedback and allow the student to revise his or her work.
Provide additional practice opportunities. Include shapes whose dimensions are given by fractions and decimals.
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:
Decomposes the octagon into eight triangles and calculates an area of 2784 square meters.
Decomposes the octagon into rectangles and trapezoids and calculates an area of 2786 square meters.
Note: Because the given apothem is an approximate value, the two decompositions will yield slightly different areas.
Questions Eliciting Thinking
How did you determine the area of the octagon? What measurements did you need? How did you find the measurements you needed?
Instructional Implications
Represent the dimensions of the figure with variables and challenge the student to write a single expression for finding the area of the composite figure.
Provide practice problems involving composite figures with fractional edge lengths and problems in which area is given and the student must identify a missing measurement.
Provide opportunities for the student to explore how changing a dimension of a figure affects the area.
Consider implementing other MFAS tasks for standard 7.G.2.6.
ACCOMMODATIONS & RECOMMENDATIONS
page 3 of 4 Special Materials Needed:
Octagon Area worksheet
Calculator
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
Description
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional
objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
MAFS.7.G.2.6:
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
Work toward meeting this standard draws together grades 3–6 work with geometric measurement.
page 4 of 4