Authentic
Assessment
Workbook
Geometry
SOL G.10
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Authentic Assessment Workbook
Geometry G.10
Overview
This authentic assessment workbook provides performance tasks for student completion. All
items focus on authentic, real-world situations that begin to prepare students for college and
career readiness. Teachers are encouraged to engage with each student response to determine
the ‘how’ and ‘why’ of the student’s thinking when responding to the task. In that regard, since
multiple responses may be correct, no answer key is provided. A rubric for student and teacher
use is provided with each task.
Additionally, the mastery of these tasks can provide documentation toward the completion of the
essential knowledge, skills and processes, as outlined in Flexible Creativity’s Mathematics
Observation Form for the given grade level. Further, when appropriate, material from previous
grades is incorporated to build on the natural spiral of mathematics content.
This document represents the essential knowledge, skills and processes related to
Geometry G.10 – The student will solve real-world problems involving angles of polygons.
These tasks can be found on the following pages within this document:
Task 1: Fountain Seating (EKS G.10a, G.10d) ............................................................................... 2
Task 2: Picnic Patio (EKS G.10a, G.10d) .......................................................................................... 4
Task 3: Final Project (EKS G.10a, G.10d) ........................................................................................ 6
Task 4: Bathroom Tile Types (EKS G.10a, G.10b) ...................................................................... 8
Task 5: Museum Exhibit Room (EKS G.10a, G.10d) ................................................................ 10
Task 6: Gazebo Plans (EKS G.10a, G.10d) ................................................................................... 12
Task 7: Cattle Gate (EKS G.10a, G.10d) ........................................................................................ 14
Task 8: Sun Room (EKS G.10a, G.10d) .......................................................................................... 16
Flexible Creativity, Inc.
©2015 All rights reserved
Page 1
Authentic Assessment Workbook
Geometry G.10
Task 1: Fountain Seating
In the center of a town is a fountain pool surrounded by rectangular walls. The city planners want
to create seating in the open spaces between the rectangular walls so that the community can
enjoy the fountain when the weather is nice.
Part A: The city planners have hired your architectural company to create the plans.
A1.
Determine the measure of the angle 𝑃 for the benches to fit between the rectangular walls.
Document your work for the city planners.
A2.
Write a summary explaining to your manager how you found the measure of the angles for
the benches.
Flexible Creativity, Inc.
©2015 All rights reserved
Page 2
Authentic Assessment Workbook
Geometry G.10
Task 1: Fountain Seating
Scoring Rubric
Score
Description
4
Exceeds Expected Proficiency
I have answered completely and correctly all aspects of the question. My responses effectively
communicate my mathematical understanding. My strategies and ability to carry out my
strategies meet the content demands of all parts of the task.
Proficient
I have answered some aspects of the question completely and correctly. My responses
demonstrate adequate evidence and understanding necessary to complete the task with minor
errors in execution. I demonstrate some mathematical understanding and will be able to revise
my work with discussion and/or feedback from my peers or teacher. My errors may include:
 Minor error in finding the angle of the benches
 Minor error in justification
Not Yet Proficient
Many of my answers do not provide complete and correct responses. I demonstrated effort to
complete the task; however, there are many conceptual errors throughout the task. My work will
require significant revisions. My errors may include:
 Errors in finding the angle of the benches
 Misconceptions about interior or exterior angles of polygons
 Unable to provide thorough explanation of work
Limited Proficiency
I attempted to complete the task, but do not understand the concepts or the directions of the task.
I demonstrated some effort, and made some connections to the content. After discussing the task
with my peers or the teacher, I will need to re-attempt the task.
No Proficiency
I did not attempt the task. I do not understand the concepts or the directions of the task.
3
2
1
0
Comments:
(Student Notes)
Flexible Creativity, Inc.
(Teacher Notes)
©2015 All rights reserved
Page 3
Authentic Assessment Workbook
Geometry G.10
Task 2: Picnic Patio
The senior class of Washington Memorial High School is donating money to have the outside lunch
picnic patio paved. The class voted and chose a regular hexagonal pattern below and want to use
the school colors.
Part A: The principal has approved the pattern, but has asked you, the class president to complete
the pattern with the missing angle measures and segment measures to save money on having a
professional designer complete them.
A1.
Complete the plans by adding all the angle measures on the plans. Provide an explanation
for your angle measurements for the principal.
A2.
You have determined that the side of each regular hexagon is 16 inches. Find all of the
other missing side measures. Show all your work and provide support for your answers.
Flexible Creativity, Inc.
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Page 4
Authentic Assessment Workbook
Geometry G.10
Task 2: Picnic Patio
Scoring Rubric
Score
Description
4
Exceeds Expected Proficiency
I have answered completely and correctly all aspects of the question. My responses effectively
communicate my mathematical understanding. My strategies and ability to carry out my
strategies meet the content demands of all parts of the task.
Proficient
I have answered some aspects of the question completely and correctly. My responses
demonstrate adequate evidence and understanding necessary to complete the task with minor
errors in execution. I demonstrate some mathematical understanding and will be able to revise
my work with discussion and/or feedback from my peers or teacher. My errors may include:
 Minor error in finding the angles and applying knowledge about interior and/or exterior
angle of polygons
 Minor error in calculating the segment measures
 Minor error in justification of work
Not Yet Proficient
Many of my answers do not provide complete and correct responses. I demonstrated effort to
complete the task; however, there are many conceptual errors throughout the task. My work will
require significant revisions. My errors may include:
 Multiple errors in finding the angle measures; misconceptions about interior or exterior
angles of polygons
 Errors in finding segment measures
 Incomplete justification of work
Limited Proficiency
I attempted to complete the task, but do not understand the concepts or the directions of the task.
I demonstrated some effort, and made some connections to the content. After discussing the task
with my peers or the teacher, I will need to re-attempt the task.
No Proficiency
I did not attempt the task. I do not understand the concepts or the directions of the task.
3
2
1
0
Comments:
(Student Notes)
Flexible Creativity, Inc.
(Teacher Notes)
©2015 All rights reserved
Page 5
Authentic Assessment Workbook
Geometry G.10
Task 3: Final Project
3-D Design is when the depth of an object, as well as its height
and width, is considered when an object is designed. This
allows people to see an accurate representation of a design.
You are enrolled in an introductory 3-D Design course at the
local community college. Your course instructor has assigned
you the project of creating a wall clock out of 4 inch multicolor
strips of hard plastic.
Part A: Before you can begin building the clock, you have to
submit a detailed plan to your course instructor.
A1.
Create a plan for a dodecagon that can be used to build your clock. Include the interior
angle measures in your plan. Show all your work.
A2.
Your instructor wants you to explain how you determined the interior angles for your
plans. Write a summary using mathematical proof and reasoning to support your position.
Flexible Creativity, Inc.
©2015 All rights reserved
Page 6
Authentic Assessment Workbook
Geometry G.10
Task 3: Final Project
Scoring Rubric
Score
Description
4
Exceeds Expected Proficiency
I have answered completely and correctly all aspects of the question. My responses effectively
communicate my mathematical understanding. My strategies and ability to carry out my
strategies meet the content demands of all parts of the task.
Proficient
I have answered some aspects of the question completely and correctly. My responses
demonstrate adequate evidence and understanding necessary to complete the task with minor
errors in execution. I demonstrate some mathematical understanding and will be able to revise
my work with discussion and/or feedback from my peers or teacher. My errors may include:
 Minor error in finding the angles and applying knowledge about interior and/or exterior
angles of polygons
 Minor error in justification of work
Not Yet Proficient
Many of my answers do not provide complete and correct responses. I demonstrated effort to
complete the task; however, there are many conceptual errors throughout the task. My work will
require significant revisions. My errors may include:
 Errors in finding the angle measures
 Misconceptions about interior or exterior angles of polygons
 Incomplete justification of work
Limited Proficiency
I attempted to complete the task, but do not understand the concepts or the directions of the task.
I demonstrated some effort, and made some connections to the content. After discussing the task
with my peers or the teacher, I will need to re-attempt the task.
No Proficiency
I did not attempt the task. I do not understand the concepts or the directions of the task.
3
2
1
0
Comments:
(Student Notes)
Flexible Creativity, Inc.
(Teacher Notes)
©2015 All rights reserved
Page 7
Authentic Assessment Workbook
Geometry G.10
Task 4: Bathroom Tile Types
You are a new employee at Tiles Plus, a company that sells various types of ceramic and porcelain
tiles. Tiles are often used on bathroom walls or in kitchen or bathroom floors. A customer has
decided to re-tile the bathroom floors in her home and is deciding on new tile patterns. You show
the customer four different tile shapes: square, regular pentagon, regular hexagon, and regular
octagon.
Part A: The customer wants your help in deciding which tile to use. She only wants to buy one
shape type. For each of the shapes indicated below, explain whether or not the customer will be
able to use only that shape type to tile the floor.
A1.
Square tile:
A2.
Regular pentagon tile:
A3.
Regular hexagon tile:
A4.
Regular octagon tile:
Flexible Creativity, Inc.
©2015 All rights reserved
Page 8
Authentic Assessment Workbook
Geometry G.10
Task 4: Bathroom Tile Types
Scoring Rubric
Score
Description
4
Exceeds Expected Proficiency
I have answered completely and correctly all aspects of the question. My responses effectively
communicate my mathematical understanding. My strategies and ability to carry out my
strategies meet the content demands of all parts of the task.
Proficient
I have answered some aspects of the question completely and correctly. My responses
demonstrate adequate evidence and understanding necessary to complete the task with minor
errors in execution. I demonstrate some mathematical understanding and will be able to revise
my work with discussion and/or feedback from my peers or teacher. My errors may include:
 Minor error in determining which shapes tessellate
Not Yet Proficient
Many of my answers do not provide complete and correct responses. I demonstrated effort to
complete the task; however, there are many conceptual errors throughout the task. My work will
require significant revisions. My errors may include:
 Errors in knowing which shapes tessellate
 Incomplete explanation of tessellations
Limited Proficiency
I attempted to complete the task, but do not understand the concepts or the directions of the task.
I demonstrated some effort, and made some connections to the content. After discussing the task
with my peers or the teacher, I will need to re-attempt the task.
No Proficiency
I did not attempt the task. I do not understand the concepts or the directions of the task.
3
2
1
0
Comments:
(Student Notes)
Flexible Creativity, Inc.
(Teacher Notes)
©2015 All rights reserved
Page 9
Authentic Assessment Workbook
Geometry G.10
Task 5: Museum Exhibit Room
A new exhibit room at the Museum of Art has been built as a regular hexagon. Each of the walls is
50 feet long. The intention for the room is for the art to be around the perimeter of the room with
a large installation in the center.
Part A: You are working for the summer as an intern with the museum and are working with the
lead curator to place the first exhibit in the room.
A1.
One artist has a sculpture that needs to be viewable from an angle wider than 90 degrees.
The lead curator asks you to determine the interior angles at the intersection of the walls of
the new exhibit room and determine if the sculpture will be appropriate at one of the
intersections. Write a response to the curator.
A2.
The curator has asked for an explanation of your work. Write a clear explanation of how
you explain to the curator how you determined the interior angles of the room.
Flexible Creativity, Inc.
©2015 All rights reserved
Page 10
Authentic Assessment Workbook
Geometry G.10
Task 5: Museum Exhibit Room
Scoring Rubric
Score
Description
4
Exceeds Expected Proficiency
I have answered completely and correctly all aspects of the question. My responses effectively
communicate my mathematical understanding. My strategies and ability to carry out my
strategies meet the content demands of all parts of the task.
Proficient
I have answered some aspects of the question completely and correctly. My responses
demonstrate adequate evidence and understanding necessary to complete the task with minor
errors in execution. I demonstrate some mathematical understanding and will be able to revise
my work with discussion and/or feedback from my peers or teacher. My errors may include:
 Minor error in determining the interior angles of a regular polygon
Not Yet Proficient
Many of my answers do not provide complete and correct responses. I demonstrated effort to
complete the task; however, there are many conceptual errors throughout the task. My work will
require significant revisions. My errors may include:
 Errors in determining the interior angles of a regular polygon
 Incomplete written justifications
Limited Proficiency
I attempted to complete the task, but do not understand the concepts or the directions of the task.
I demonstrated some effort, and made some connections to the content. After discussing the task
with my peers or the teacher, I will need to re-attempt the task.
No Proficiency
I did not attempt the task. I do not understand the concepts or the directions of the task.
3
2
1
0
Comments:
(Student Notes)
Flexible Creativity, Inc.
(Teacher Notes)
©2015 All rights reserved
Page 11
Authentic Assessment Workbook
Geometry G.10
Task 6: Gazebo Plans
For the summer, you are interning at an architectural firm. The plans below are for a gazebo that
will be added to a deck. The gazebo is a regular hexagon and square 𝐵𝐶𝐷𝐸 is a walkway from the
deck. The deck connects at segment DC.
Part A: The lead architect wants you to provide further information on the gazebo plans.
A1.
Complete the current hexagonal plans by adding the interior angles of the gazebo and the
exterior angles at the intersection of the walkway and the gazebo. Include a written
explanation of how you determined the angle measurements for the lead architect to
review.
Part B: The lead architect wants to extend the gazebo plan options the company offers to
customers and wants to add gazebos in octagonal shapes.
B1.
Create a set of gazebo plans with an octagonal shape. Include in the plans the interior
angles of the gazebo and the exterior angles at the intersection of the walkway and the
gazebo. Provide a written explanation for how you determined the angle measurements.
Flexible Creativity, Inc.
©2015 All rights reserved
Page 12
Authentic Assessment Workbook
Geometry G.10
Task 6: Gazebo Plans
Scoring Rubric
Score
Description
4
Exceeds Expected Proficiency
I have answered completely and correctly all aspects of the question. My responses effectively
communicate my mathematical understanding. My strategies and ability to carry out my
strategies meet the content demands of all parts of the task.
Proficient
I have answered some aspects of the question completely and correctly. My responses
demonstrate adequate evidence and understanding necessary to complete the task with minor
errors in execution. I demonstrate some mathematical understanding and will be able to revise
my work with discussion and/or feedback from my peers or teacher. My errors may include:
 Minor error in determining the interior angles of a regular polygon
 Minor error in finding the measure of the exterior angle
Not Yet Proficient
Many of my answers do not provide complete and correct responses. I demonstrated effort to
complete the task; however, there are many conceptual errors throughout the task. My work will
require significant revisions. My errors may include:
 Multiple errors in determining the interior angles of a regular polygon
 Errors in finding the measure of the exterior angle
 Incomplete written justifications
Limited Proficiency
I attempted to complete the task, but do not understand the concepts or the directions of the task.
I demonstrated some effort, and made some connections to the content. After discussing the task
with my peers or the teacher, I will need to re-attempt the task.
No Proficiency
I did not attempt the task. I do not understand the concepts or the directions of the task.
3
2
1
0
Comments:
(Student Notes)
Flexible Creativity, Inc.
(Teacher Notes)
©2015 All rights reserved
Page 13
Authentic Assessment Workbook
Geometry G.10
Task 7: Cattle Gate
You are enrolled in an animal science class and
assigned you to work on the plans for a cattle
enclosure and gate. A plan for a cattle enclosure is
shown below. The enclosure is a regular hexagon
and has a gate that opens at vertex 𝐴.
Part A: Your instructor explains the importance of having gates open only a limited amount to
control the movement of cattle. It is recommended that gates open less than 75°.
A1.
Determine if the plan above would meet the requirement to open less than 75°. If the gate
can open to form a straight angle with ̅̅̅̅
𝐵𝐴, what is the angle of the opening, indicated by
angle 𝑥? Show all your work.
A2.
The instructor asks you to explain your work and provide mathematical proof of your
findings.
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©2015 All rights reserved
Page 14
Authentic Assessment Workbook
Geometry G.10
Task 7: Cattle Gate
Scoring Rubric
Score
Description
4
Exceeds Expected Proficiency
I have answered completely and correctly all aspects of the question. My responses effectively
communicate my mathematical understanding. My strategies and ability to carry out my
strategies meet the content demands of all parts of the task.
Proficient
I have answered some aspects of the question completely and correctly. My responses
demonstrate adequate evidence and understanding necessary to complete the task with minor
errors in execution. I demonstrate some mathematical understanding and will be able to revise
my work with discussion and/or feedback from my peers or teacher. My errors may include:
 Minor error in determining the exterior angle of a regular polygon
Not Yet Proficient
Many of my answers do not provide complete and correct responses. I demonstrated effort to
complete the task; however, there are many conceptual errors throughout the task. My work will
require significant revisions. My errors may include:
 Multiple errors in determining the exterior angle of a regular polygon
 Incomplete written justification
Limited Proficiency
I attempted to complete the task, but do not understand the concepts or the directions of the task.
I demonstrated some effort, and made some connections to the content. After discussing the task
with my peers or the teacher, I will need to re-attempt the task.
No Proficiency
I did not attempt the task. I do not understand the concepts or the directions of the task.
3
2
1
0
Comments:
(Student Notes)
Flexible Creativity, Inc.
(Teacher Notes)
©2015 All rights reserved
Page 15
Authentic Assessment Workbook
Geometry G.10
Task 8: Sun Room
You are interning with GT Construction. Construction builders rely on blueprints and plans for
completing their responsibilities. GT Construction specializes in adding rooms to existing homes.
The current project is adding a sun room on the back of a house based on the sketch below.
Part A: The sun room connects to the house at segment 𝑊𝑋.
A1.
The site supervisor has asked you to find the angle of intersection between the house and
the sun room. Show all your work.
A2.
The site supervisor needs you to explain your calculations and provide an explanation for
your work to ensure the builders plan appropriately.
Flexible Creativity, Inc.
©2015 All rights reserved
Page 16
Authentic Assessment Workbook
Geometry G.10
Task 8: Sun Room
Scoring Rubric
Score
Description
4
Exceeds Expected Proficiency
I have answered completely and correctly all aspects of the question. My responses effectively
communicate my mathematical understanding. My strategies and ability to carry out my
strategies meet the content demands of all parts of the task.
Proficient
I have answered some aspects of the question completely and correctly. My responses
demonstrate adequate evidence and understanding necessary to complete the task with minor
errors in execution. I demonstrate some mathematical understanding and will be able to revise
my work with discussion and/or feedback from my peers or teacher. My errors may include:
 Minor error in determining the exterior angle of a regular polygon
Not Yet Proficient
Many of my answers do not provide complete and correct responses. I demonstrated effort to
complete the task; however, there are many conceptual errors throughout the task. My work will
require significant revisions. My errors may include:
 Multiple errors in determining the exterior angle of a regular polygon
 Incomplete written justification
Limited Proficiency
I attempted to complete the task, but do not understand the concepts or the directions of the task.
I demonstrated some effort, and made some connections to the content. After discussing the task
with my peers or the teacher, I will need to re-attempt the task.
No Proficiency
I did not attempt the task. I do not understand the concepts or the directions of the task.
3
2
1
0
Comments:
(Student Notes)
Flexible Creativity, Inc.
(Teacher Notes)
©2015 All rights reserved
Page 17