This task was developed by high school and postsecondary mathematics and design/pre-construction
educators, and validated by content experts in the Common Core State Standards in mathematics and the
National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating
how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning –
and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.
TASK: MINIATURE GOLF
TARGET COMMON CORE STATE STANDARD(S) IN MATHEMATICS:
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy
physical constraints or minimize cost; working with typographic grid systems based on ratios).*
6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when
multiplying or dividing quantities.
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas
from a scale drawing and reproducing a scale drawing at a different scale.
7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to
write and solve simple equations for an unknown angle in a figure.
7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
7.RP.3 Use proportional relationships to solve multistep ratio and percent problems.
TARGET STANDARDS FOR MATHEMATICAL PRACTICES
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
TARGET COMMON CORE STATE STANDARD(S) IN ELA/LITERACY:
RST.9-10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the
precise details of explanations or descriptions.
RST.9-10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking
measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
RST.9-10.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a
table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
WHST.9-10.1 Write arguments focused on discipline-specific content.
WHST.9-10.4 Produce clear and coherent writing in which the development, organization, and style are
appropriate to task, purpose, and audience.
TARGET CAREER AND TECHNICAL EDUCATION (CTE) KNOWLEDGE & SKILLS STATEMENTS:
ACC01.01.03 Use appropriate formulas to determine percentages /decimals.
ACC03.01.01 Plan, organize, schedule and manage a project/job to optimize workflow and outcome.
ACC03.01.03 Estimate resources/materials required for a specific project or problem.
ACC03.01.05 Determine alternative solutions for a specific project/problem.
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ACC05.03.02 Understand the context of the projects.
ACC10.01.01 Interpret drawings used in project planning.
ACPA02.01.01 Deliver a presentation that explains a concept of design or preconstruction.
ACPA06.01.01 Identify client requirements.
ACPA06.02.02 Build models using referenced drawings and sketches.
ACPA06.02.03 Utilize computer technology when communicating concepts and designs.
RECOMMENDED COURSE:
Geometry; Integrated Math II; Applications in Design & Pre-Construction
ADDITIONAL INSTRUCTIONS:
This task should be completed over an extended period of time, including some time for research of designs and
general golf specifications and for writing the report. Some extensions might be completed with small groups or
partners.
* Modeling standards appear throughout the CCSS high school standards and are indicated by a star symbol (*).
About the Common Core State Standards in Mathematics
The Common Core State Standards (CCSS) for Mathematics are organized by grade level in grades K–8. At the high
school level, the standards are organized by conceptual category (number and quantity, algebra, functions,
geometry, and probability and statistics), showing the body of knowledge students should learn in each category to
be college and career ready, and to be prepared to study more advanced mathematics. The Standards for
Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics
increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise
throughout the elementary, middle and high school years. www.corestandards.org
About the Common Core State Standards in English Language Arts/Literacy
The Common Core State Standards (CCSS) for ELA/Literacy are organized by grade level in grades K–8. At the high
school level, the standards are organized by 9-10 and 11-12 grade bands. Across K-12 there are four major strands:
Reading, Writing, Speaking and Listening, and Language. The CCSS also include Standards for Literacy in
History/Social Studies, Science, and Technical Subjects, with content-specific (Reading and Writing) literacy
standards provided for grades 6-8, 9-10, and 11-12, to demonstrate that literacy needs to be taught and nurtured
across all subjects. www.corestandards.org
About the Career Cluster Knowledge and Skill Statements
As an organizing tool for curriculum design and instruction, Career Clusters™ provide the essential knowledge and
skills for the 16 Career Clusters™ and their Career Pathways. It also functions as a useful guide in developing
programs of study bridging secondary and postsecondary curriculum and for creating individual student plans of
study for a complete range of career options. As such, it helps students discover their interests and their passions,
and empowers them to choose the educational pathway that can lead to success in high school, college and career.
www.careertech.org/career-clusters/resources/clusters/architecture.html. Although not included in this template,
all Clusters and Pathways have Foundational Academic Expectations and Essential Knowledge & Skills Statements,
which, in some cases, overlap with the Common Core State Standards.
KEY TERMS


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Golf hole
Cup
Bank shot
Bank angle, angle of approach
Tee box
2
MINIATURE GOLF – The Task
The local miniature golf course would like to increase their profits by increasing the difficulty and number of
holes in the course. The owners believe players will like being able to play more holes for their money and
then may spend more at the concession stand.
In order to find designs for three new holes, they have decided to hold a design contest. Each design will be
judged on the most creative use of materials, the least likelihood that someone will score a hole-in-one, and
the best use of the available space.
The contest requires documentation of your design, including a scale drawing of the design with dimensions,
all of your calculations, and a report to the owners that explains your design.
Tasks:
1. Sketch a miniature golf hole design including any obstacles or general items required. The designed
hole must fit within a rectangle of no more than 128 square feet of area. Draw your design to scale,
using appropriate tools, and include all measurements. Make sure your dimensions will allow for a
player to comfortably approach the ball within the golf hole area. Identify the cup, the tee box,
obstacles, and all angles of approach. For purposes of computing area, your design should be
composed of two-dimensional shapes for which you can find the area.
2. Show that your design will fit within a rectangle of dimensions that meet the 128 sq ft specification. Be
sure to use as much of the area as possible, while still maintaining a creative design.
3. Calculate the total area of your golf hole design and the percentage of this total area you have used.
Show all your work. (Remember: You will be judged partially on the best use of space.)
4. Research and describe the regulation size for a golf cup for consideration and placement in your
design.
5. Identify and sketch two possible paths from tee to cup, with at least one path being a bank shot.
Explain the possible approaches and show and calculate all angles associated with your bank shot(s).
6. Write a report to submit with your design to explain why yours should be selected. Include information
regarding the creativity of your design, the level of difficulty, and the best use of available space.
3
MINIATURE GOLF – Possible Solution(s)
1. The design: (Scale: one unit = 6 inches)
2. The total design fits inside a rectangle that is 11’ x 11’ 6”, for a total of 126.5 square feet:
11’ x 11’ 6” = 11 x 11.5 = 126.5 square feet
This is less than the maximum by 1.5 square feet.
3. Calculate the area:
The total used area can be most easily calculated by subtracting the unused area from the total:
Total rectangle area: 126.5 square feet
4
The unused area includes three right triangles and one rectangle (shaded in this version of the design). The
rectangle is 2’ 6” by 5’, two triangles have legs of 3’ and 5’, and the third triangle has legs of 3’ and 6’.
Total unused area: 2.5’ x 5’ + 2[0.5(3’ x 5’)] + 0.5(3’ x 6’) = 12.5 + 15 + 9 = 36.5 square feet of unused space.
126.5 – 36.5 = 90 square feet of used space. 90 ÷ 126.5 = 0.711
This is approximately 71% of the total space.
4.
According to the USGA the regulation golf cup measures 4.25 inches in diameter. Since this design drawing
has one unit equal to 6 inches, the cup will fit easily into one square on the grid.
5.
There are two possible shots shown on this sample version of the design.
 In #1 (dark green line) the goal will be to hit the ball with the best possible speed to stop as close to
the center of point 1 as possible. This plan is not a bank shot and may be accomplished in as few as
two shots total.

In #2 (blue line) the ball will bank off the far wall of the hole and enter the hole. This shot is daring and
hopes for a hole-in-one. This can happen only if the bank angles are the same measure, ma = mb in
this version of the design. ma can be found by using the right triangle formed with the distance from
the bank point to the hole as the hypotenuse. Using the scale in the design of one unit = 6 inches, the
triangle legs will measure 36” (six full units) and 93” (15.5 units). The base angle, angle a, will have a
tangent of 93/36. So ma = 68.83…  or approximately 69.
Since both a and b have measures of 69, the angle at the bank point (2) would be 180 – 2(69)
= 42.
6.
Reports will vary based on the individual designs.
5
MINIATURE GOLF – Possible Extensions
The extensions below represent potential ways in which mathematics and/or CTE teachers can build on the
task above. All of the extensions are optional and can be used in the classroom, as homework assignments,
and/or as long-term interdisciplinary projects.
1. Consider possible placement options for the cup and propose two alternative locations, providing three
total cup sites. Discuss the implications that each cup position has on the level of difficulty and recommend
one cup site.
2. Focus Group Study: Select the favorite three designs of the class and present them to a random sample of
people to collect data on the preferred design. Compile, graph, analyze, and compare the data and
summary statistics based demographics, such as gender, age, and golf experience.
3. Create a project plan to complete the hole. Include local pricing for materials and total cost.
4. Create a three-dimensional sketch of the hole (e.g., using Google Sketchup). Create (and draw)
components of the hole that reflect its theme that you have determined with art students from your
school.
6
MINIATURE GOLF – Appendix: Alignment Ratings
The rating system used in the following charts is as follows:
3
EXCELLENT ALIGNMENT:
The content/performance of the task is clearly consistent with the content/performance of the Common Core State Standard.
2
GOOD ALIGNMENT:
The task is consistent with important elements of the content/performance of the CCSS statement, but part of the CCSS is not addressed.
1
WEAK ALIGNMENT:
There is a partial alignment between the task and the CCSS, however important elements of the CCSS are not addressed in the task.
N/A:
For Mathematical Practices a content rating does not apply.
In the charts C = Content Rating and P = Performance Rating


COLOR KEY
Black = Part of CCSS/K&S Statement
aligned to task
Gray = Part of CCSS/K&S Statement not
aligned to task
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Task-to-Mathematical Practice Alignment Recording Sheet
Task
Name
Aligned CCSS
Mathematical Practice
Standards
MINIATURE GOLF
MP.1 Make sense of
problems and persevere in
solving them.
Task Comments
C
N/A
P
Alignment Comments
3
For this task students analyze givens, constraints, relationships, and
goals. They must make conjectures about the form and meaning of the
solution and plan a solution pathway. They must check the
reasonableness of their solution, continually asking themselves, “Does
this make sense?”
MP.2 Reason abstractly and
quantitatively.
N/A
3
This task involves quantitative relationships. It requires that students
make sense of quantities and their relationships in the problem
situation. They must attend to the meaning of the quantities and pay
attention to units as they represent the quantities and measures in the
design, work, and their report.
MP.3 Construct viable
arguments and critique the
reasoning of others.
N/A
2
Students must present their design with a written report describing
their findings. There is no requirement to critique the reasoning of
others
MP.4 Model with
mathematics.
N/A
3
This task is an application from everyday life requiring that the student
create a geometric representation (model) that can replace the
situation described in the prompt. Students must identify important
quantities in the practical situation and use them to answer the
questions posed. Students are required to explain their decisions and
assumptions.
MP.5 Use appropriate tools
strategically.
N/A
3
Students are directed to use appropriate tools in their design. They
may use drafting tools, CAD programs, or other software.
3
This task requires that students communicate precisely, organizing
their information, as they perform their calculations and show their
mathematical thinking.
MP.6 Attend to precision.
N/A
(Strengths,
weaknesses, possible
improvements,
effectiveness, etc)
This is a multistage problem
with real life
applications and
considerations.
Students must
identify
measurements
and lengths to
make sure their
design meets the
specifications.
They must use
both abstract
reasoning and
quantitative
calculations.
8
Task-to-Common Core State Standards Alignment Recording Sheet
MINIATURE GOLF
Task
Name
Aligned CCSS
Content Standards
C
P
G.SRT.8 Use trigonometric ratios and the
Pythagorean Theorem to solve right triangles in
applied problems.*
3
3
Students must use trigonometric ratios to find the
angles associated with the bank shots.
G.MG.3 Apply geometric methods to solve design
problems (e.g., designing an object or structure to
satisfy physical constraints or minimize cost; working
with typographic grid systems based on ratios).*
3
3
This task is a design problem that involves
specifications and constraints.
Alignment Comments
6.RP.3d Use ratio reasoning to convert measurement
units; manipulate and transform units appropriately
when multiplying or dividing quantities.
3
3
As students form their design and calculate the area,
they will need to use and convert units of length and
area.
7.NS.3 Solve real-world and mathematical problems
involving the four operations with rational numbers.
3
3
Students must calculate the lengths and areas
associated with their design.
7.G.1 Solve problems involving scale drawings of
geometric figures, including computing actual
lengths and areas from a scale drawing and
reproducing a scale drawing at a different scale.
3
2
This task requires that students are able to create
their design to scale. They are not required to
reproduce a drawing at a different scale.
2
Students use facts about supplementary and adjacent
angles only. They must determine the measure of the
angle between the two congruent bank angles using
the sum of the three angles equals 180, which
involves an equation.
7.G.5 Use facts about supplementary,
complementary, vertical, and adjacent angles in a
multi-step problem to write and solve simple
equations for an unknown angle in a figure.
2
7.G.6 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.
2
3
This task focuses on 2-dimensional design composed
of polygons, for which the student must calculate area
only.
7.RP.3 Use proportional relationships to solve
multistep ratio and percent problems.
3
3
The task requires that students find the percent their
design uses of the total.
Task
Comments
This task
combines
planning,
design,
calculating,
comparing, and
presentation
with writing and
using
communication
skills.
* Modeling standards appear throughout the CCSS high school standards and are indicated by a star symbol (*).
9
Task-to-National Career Cluster Knowledge & Skills Statements Alignment Recording Sheet
MINIATURE GOLF
Task
Name
Aligned National Career Cluster Knowledge & Skills
Statements
C
P
ACC01.01.03 Use appropriate formulas to determine
percentages /decimals.
3
3
Task requires use of percentages and decimals.
ACC03.01.01 Plan, organize, schedule and manage a
project/job to optimize workflow and outcome.
1
1
Task requires design concepts not project management.
ACC03.01.03 Estimate resources/materials required for a
specific project or problem.
1
1
Task does not require pricing calculation.
ACC03.01.05 Determine alternative solutions for a specific
project/problem.
3
3
Task requires several solutions to determine best
outcome for the design of the project.
ACC05.03.02 Understand the context of the projects.
3
3
Task requires research for scale design.
ACC10.01.01 Interpret drawings used in project planning.
1
3
Task requires contest applicants to produce original
designs for the contest.
ACPA02.01.01 Deliver a presentation that explains a
concept of design or preconstruction.
3
2
Task requires a written report that fully explains the
design project.
ACPA06.01.01 Identify client requirements.
2
1
Task provides basic client requirements but requires
students to act as contest applicants not contractors.
ACPA06.02.02 Build models using referenced drawings
and sketches.
3
2
Task requires drawings to scale. Models are not built.
ACPA06.02.03 Utilize computer technology when
communicating concepts and designs.
2
1
Task does not identify use of specific computer
technology to be competitive in the competition.
Alignment Comments
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