Feature

Trig in Action: Build and Solve Mini-Golf Holes with Reflections and Right Triangles

Editor’s note: This is a curated classroom-resource guide that brings together teacher-made and education-publisher materials for using mini golf as a setting…

By Reid Callahan · 22 July 2026 · 19 min read

Editor’s note: This is a curated classroom-resource guide that brings together teacher-made and education-publisher materials for using mini golf as a setting for geometry and trigonometry.

A well-designed mini golf trigonometry project gives students a visible reason to use the math. A bank shot is not just a diagram on a worksheet. It is a path students can sketch, calculate, test, revise, and explain.

Across strong classroom examples, the mathematical core is consistent: students use the reflection rule for bank shots, turn a broken path into a straight construction, and then solve the resulting triangles with tools such as tangent, inverse tangent, and the Pythagorean theorem. Some projects stay mostly in geometry and angle measurement. Others extend into sine, cosine, and even the Laws of Sines and Cosines.

The best part for teachers is the flexibility. You can run this as a short paper-based modeling task, a digital construction activity, or a build-and-test project with real materials.

If you want the main source materials up front, these are the key references used throughout this guide:

Why Mini-Golf Makes Trigonometry Engaging

Mini golf works in class because the geometry is visible.

In Jennifer Lamb’s project handout, students meet the core idea directly: the angle of incidence equals the angle of reflection. Instead of treating that as an abstract rule, they use it to predict how a ball can rebound off a wall toward the cup.

That reflection idea leads naturally into right-triangle trigonometry. In Nat Banting’s Grade 10 project, students draw bounce paths, break them into triangles, and use a toolkit that includes:

tangent
inverse tangent
the Pythagorean theorem
triangle angle-sum reasoning

That is a strong instructional bridge. Students are not memorizing ratios in isolation; they are using them to answer questions that feel concrete:

Where should the ball hit the wall?
What angle should the player aim?
How far will the shot travel?
Is one route better than another?

The engagement case is real, but it should be stated carefully. The available evidence is mostly teacher-created and descriptive, not experimental. For example, Banting reports student reactions such as “Hey Mr. Banting, look how mathy this looks!” and “this is how I learn!” on his project page. Those quotes are anecdotal, not outcome data, but they do show why these tasks often feel more accessible than a page of disconnected exercises.

Mini golf also scales well across course levels:

A geometry-first class can emphasize reflections, angle measurement, and construction.
A trig-first class can emphasize tangent, inverse tangent, and distance.
An advanced class can compare routes, justify shortest paths, or move into non-right-triangle trig.

That flexibility is one reason WISELearn’s Geometry Mini Golf Project maps cleanly onto high school standards. The listed Wisconsin standards include:

HSG-SRT.C.6: understanding that side ratios in right triangles define trigonometric ratios for acute angles
HSG-SRT.C.8: using trigonometric ratios and the Pythagorean theorem to solve right triangles in applied problems

WISELearn also aligns the project to other geometry standards involving similarity, congruence, modeling, and construction. In practice, that means mini golf is not just a novelty context. It is a workable way to teach reflection, right triangles, and applied trigonometry in one task.

Core Materials and Setup for Any Classroom

One reason this project is so adaptable is that the materials can stay simple.

Here is a source-based overview of the main classroom setups.

Setup style	Core materials	Best-supported source
Paper/transparency	Hole photocopies, transparency cover, wet-erase marker, blank protractor tool, ruler, napkin/tissue	Nat Banting
Geometry desk tools	Protractors, rulers, graph paper, calculators	Jennifer Lamb PDF, TeachEngineering
Digital	GeoGebra, TI-Nspire or Geometer’s Sketchpad, optional GoodNotes for final presentation	GeoGebra project, Jennifer Lamb PDF
Build-and-test	2x4 wood, steel corners, golf balls, putters, graph paper, protractors, measuring tape	TeachEngineering

Low-cost classroom essentials

The most teacher-friendly low-prep version comes from Nat Banting’s project. Students worked with:

a golf-hole outline photocopied under a transparency
a wet-erase marker
a blank protractor tool
a ruler
a napkin or tissue for erasing

The blank protractor is an especially useful scaffold. Banting designed it so students could create congruent reflection angles without using a standard protractor first. In his workflow, regular protractors were held back until after the trigonometry was done, so measurement served as a check rather than a shortcut.

If you want a more conventional setup, Jennifer Lamb’s handout and TeachEngineering support adding:

standard protractors
graph paper
calculators
measuring tape

Digital options

If you want cleaner constructions or easier revision, the digital route is well supported too.

In Elizabeth Johnson’s GeoGebra mini golf project, students use:

the segment tool to draw the path
the angle tool to measure bounce angles with three points
the length or distance tool to show segment lengths

The tasks include one-wall, two-wall, three-wall, and even four-wall challenges, then ask students to create their own hole with multiple solutions.

Jennifer Lamb’s handout also suggests TI-Nspire or Geometer’s Sketchpad if you want more precise angle work. And Johnson’s GeoGebra project has students assemble a themed brochure in GoodNotes, which is useful if you want a polished final artifact.

Interactive practice tools

A full project asks students to design and justify. Before that, some classes benefit from skill practice.

Mr L’s Trigonometry Golf is a separate interactive practice game with modes for:

bearings
Pythagoras
trig side lengths
trig angles
challenge
unit circle

It is best used as fluency practice, not as a replacement for the full project. Its value is that students can rehearse distance and angle calculations in a golf-themed setting before they tackle reflection constructions and written justification.

Physical build materials

For a build-and-test version, TeachEngineering’s mini-golf activity lists:

about 16 feet of 2x4 wood
about 4 steel corners
putters
golf balls
protractors
graph paper
calculators
measuring tape

TeachEngineering gives an expendable cost of about $22 per group and notes lower-cost alternatives in its materials list, including reused materials and simpler barriers.

A practical teacher prep checklist

Before launching, it helps to decide which version you are actually running. A workable prep list, drawn from the sources above, is:

Choose the format: transparency, desk-tool, digital, or build-based.
Prepare the hole layouts: Banting’s printed holes, Lamb-style diagrams, or a GeoGebra file.
Decide your protractor policy: Banting’s “calculate first, measure second” approach is useful if you want trig to stay central.
Select the final product: diagrams only, guide + model, or digital brochure.
If building, gather the TeachEngineering materials and be ready for testing plus revision.

That keeps the project manageable and avoids the common problem of making the build more important than the math.

Step-by-Step: Solving Holes with Reflections and Tangent

The central move in a mini golf trigonometry project is simple:

Reflect first, then solve.

1. Choose the wall or walls

Start by deciding which wall the ball will bank off. For two-bank or three-bank shots, decide the order of the bounces first.

This matters because the order controls the reflection construction.

2. Reflect the hole across the wall

In both Jennifer Lamb’s handout and Nat Banting’s project, the reflection principle is the key idea. For a one-bank shot, reflect the hole across the chosen wall. That turns a rebound problem into a straight-path problem.

For multiple banks, work backward:

reflect the hole across the last wall
reflect that image across the previous wall
continue until each planned bounce has been built into the image

3. Draw the straight path to the reflected target

Connect the starting point to the reflected cup with a straight segment.

Where that line crosses the wall boundaries gives the bounce point or bounce points. When you map those crossings back to the original hole, you have the actual bank-shot route.

This is the moment when the reflection rule stops feeling like a rule to memorize and starts looking like a geometric necessity.

4. Decompose the path into right triangles

Once the route is drawn, label the horizontal and vertical distances and split the shot into right triangles.

Now the standard trig tools apply:

[ \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} ]

[ \theta=\tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right) ]

[ c=\sqrt{a^2+b^2} ]

These are the same tools Banting describes using after students had already learned tangent and inverse tangent.

5. Find the aiming angle

If the legs of the triangle are known, use inverse tangent to recover the angle. If an angle and one side are known, use tangent to find a missing leg.

Jennifer Lamb’s example diagrams include measured angles such as 48°, 58°, and 21°, which makes her project useful for the geometry side of the topic even when you want to extend it into trig afterward.

6. Find the segment lengths

For each straight portion of the route, calculate the distance.

Depending on what your students know, they can use:

the Pythagorean theorem if both legs are known
trig ratios if one side and an angle are known

7. Add the segments for total travel distance

After students find each segment, they add them to get total ball travel distance.

That lets them do more than find a single angle. They can compare paths and defend choices.

8. Check with a protractor after the math

Banting explicitly delayed regular protractors until after the trig work. That sequencing is worth borrowing:

construct the route
calculate the angle
measure to verify

It keeps the trigonometry from being replaced by direct measurement.

A clean classroom demonstration

If you want a quick verified example on the board, use a simple right triangle rather than a garbled scanned worksheet.

For instance, suppose the reflected straight path creates a right triangle with:

horizontal leg = 8 units
vertical leg = 6 units

Then the aiming angle relative to the horizontal is:

[ \theta=\tan^{-1}\left(\frac{6}{8}\right)\approx 36.87^\circ ]

And the path length is:

[ c=\sqrt{6^2+8^2}=10 ]

That gives students a clean model for the workflow:

identify opposite and adjacent
use inverse tangent for the angle
use the Pythagorean theorem for the distance

A note on a commonly shared trigonometry handout

A previewed Scribd assignment called Mini Golf Trigonometry Project Guide is often useful for seeing the overall structure of a trig-heavy version: divide the hole into triangles, show the trig used, and find total distance. But the preview text contains OCR errors, so it should not be quoted numerically as a worked example unless you have the clean original file.

What is safe to take from that preview is the assignment structure, not the exact printed calculations.

A teacher-ready sequence

A concise lesson flow that stays faithful to the source materials looks like this:

Give students a printed or digital hole.
Ask them to choose a one-bank path.
Reflect the cup across the wall.
Draw the straight route to the reflected image.
Mark the bounce point.
Create right triangles from horizontal and vertical distances.
Solve for angle and distance.
Verify with a protractor or digital angle tool.
Repeat with two-bank or three-bank paths.

That sequence preserves the big idea: the reflection construction is what makes the trigonometry possible.

Project Deliverables: Diagrams, Models, and Designs

The strongest projects ask students to show reasoning, not just give an answer.

Across the available sources, the most common deliverables fall into three groups: diagrams, models or constructions, and student-designed holes.

1. Labeled diagrams for bank shots

In Jennifer Lamb’s project, students create diagrams for:

1-wall
2-wall
3-wall

hole-in-one paths.

Those diagrams typically label:

bounce points
angle measures
path segments
relevant distances

If you are teaching a trig-heavy version, add the triangle decomposition and the equations used.

2. Physical models or scale drawings

Lamb’s project also asks students to design a hole and build a physical model from about 6 × 6 inches to 12 × 12 inches. The model is supposed to resemble the student’s diagrams and show the intended path structure.

That size range is manageable for display and grading. If a physical build is not practical, a scale drawing serves the same representational purpose.

3. A student-designed hole with trig calculations

A recurring capstone move is to have students design their own hole after analyzing provided ones.

That is where the task becomes more than guided practice. Students have to decide:

where the start and cup should go
which walls create interesting bank options
whether the hole supports one-, two-, or three-bank solutions
how to divide the design into triangles

The Scribd previewed trigonometry assignment also includes a student-designed hole requirement, along with showing trig work and total distance. Because that preview has OCR issues, it is better used as an example of project scope than as a ready-to-print class handout.

4. Brochures, guides, and screenshots

Elizabeth Johnson’s GeoGebra project adds a polished communication piece: students create their own hole, draw different bounce paths, measure angles and distances, then assemble screenshots into a themed brochure in GoodNotes.

That format works well because it naturally combines:

accurate construction
visible measurement
written explanation
design choices

A workable deliverables package

If you want a manageable set of final products, a strong package based on the sources is:

Three labeled routes: one-bank, two-bank, and three-bank
One student-designed hole
A calculations page showing triangles, equations, and total distances
One final artifact: a scale drawing, physical model, or digital brochure

That keeps creativity in the project without letting presentation replace mathematics.

Grading Rubrics and Assessment Strategies

The grading challenge in a mini golf trigonometry project is balance. If you grade only the final artifact, polished presentation can overshadow math. If you grade only calculations, you lose the design-and-communication element that makes the project engaging.

The sources suggest separating those pieces.

What to assess in the math

The Scribd trigonometry assignment preview describes a 50-point project with expectations such as:

divide holes into triangles
find sides and angles
show which trig was used
calculate total distance
meet all project requirements

Because the preview text is OCR-corrupted, teachers should verify any copied wording before classroom use. Still, the structure is useful.

A clean math rubric modeled on those expectations might be:

Category	Points
Correct reflection or bank-shot construction	10
Triangles labeled accurately	10
Trig equations shown and appropriate	10
Angle and side calculations correct	10
Total distance and completion of requirements	10

Total: 50 points

What to assess in the design or presentation

Jennifer Lamb’s project separates the representational work clearly:

Model: 30 points
Guide: 20 points

Her criteria include:

neatness
creativity
accuracy
resemblance to the diagrams

That separation is useful. It means the design score is real, but it does not hide the math score.

Why “resemblance to the diagrams” matters

In a mini golf project, resemblance is not just cosmetic. If the model does not match the diagram the student solved, then the build is not functioning as a mathematical representation.

So “looks like the diagram” is really a geometry criterion, not just a craft criterion.

Add error analysis for builds

TeachEngineering’s activity is especially helpful here because it asks students to compare calculated results with real-world results. That opens a valuable assessment layer.

Students can record:

predicted bounce points
predicted angles
predicted path distances
actual tested outcomes
observed differences

TeachEngineering frames that as part of engineering iteration: prototype, test, compare, revise.

Extensions and extra credit

Jennifer Lamb’s handout suggests optional extensions such as:

slope
equations
costs

Those can work well as extra credit or enrichment, especially if your class has already covered those topics.

A balanced rubric

For many high school classes, a balanced overall weighting looks like this:

Category	Weight
Mathematical accuracy and completeness	50%
Diagrams or construction quality	20%
Written explanation or justification	15%
Design creativity or model execution	10%
Reflection or error analysis	5%

That keeps the math first while still honoring the project format.

Digital Tools and Practice Games

Digital tools are most useful when each one has a specific job: construct, measure, practice, or present.

GeoGebra for construction and measurement

The clearest digital build is Elizabeth Johnson’s GeoGebra Mini Golf Project. Students can:

construct 1-, 2-, 3-, and 4-bounce paths
draw routes with the segment tool
measure angles with the angle tool using three points
display segment lengths with the length or distance tool
create their own hole layouts

That makes GeoGebra especially good for revision. Students do not have to redraw an entire hole every time they adjust a bounce path.

Interactive games for fluency

Mr L’s Trigonometry Golf works well for targeted practice before the larger project. Its modes cover:

bearings
Pythagoras
trig side lengths
trig angles
challenge
unit circle

The unit-circle mode is especially useful because it explicitly ties:

(\sin\theta) to the y-coordinate
(\cos\theta) to the x-coordinate

That is a nice extension if you want the mini golf theme to connect beyond right triangles.

TI-Nspire and Geometer’s Sketchpad

Jennifer Lamb’s handout suggests TI-Nspire and Geometer’s Sketchpad as tools for more precise angle work. If your department already uses those platforms, they can fill the same role as GeoGebra: cleaner measurement and easier verification.

GoodNotes and other presentation tools

Johnson’s GeoGebra project uses GoodNotes for the final brochure. The value is not the app itself; it is the workflow:

screenshot the construction
label paths and angles
add calculations
explain the design

Any annotation-friendly platform can serve that purpose if it helps students present the mathematics clearly.

A source-based digital workflow

A simple digital sequence built from the linked resources is:

Practice a few shots in Trigonometry Golf.
Construct bank-shot paths in GeoGebra.
Measure angles and distances in the applet.
Complete the trig calculations separately.
Assemble the final explanation as a brochure or slide-style guide.

That keeps the software purposeful instead of decorative.

Extensions: Advanced Trig and Physical Builds

Mini golf scales upward very well. The same reflection idea that supports tangent and inverse tangent can also support richer geometry, modeling, and design work.

Extend beyond tangent

In Nat Banting’s project, the basic toolkit begins with tangent and inverse tangent, then expands through extensions such as:

sine
cosine
distances
shortest paths
similar triangles

A separate student-facing trigonometry assignment preview goes even further and requires students to use:

sine
cosine
tangent
inverse trig
Law of Sines
Law of Cosines

That preview should again be treated cautiously because of OCR problems, but it does show that mini golf can work beyond introductory right-triangle trig.

Challenge students with shortest paths and similar triangles

Banting specifically mentions extensions such as shortest paths and similar triangles. Those are strong because they move students from calculation into reasoning.

Good extension questions include:

Is a one-bank route always shorter than a two-bank route?
When do reflected triangles become similar?
Can two legal bank-shot routes be compared and defended mathematically?

Expand into course design

WISELearn’s Geometry Mini Golf Project takes the idea beyond a single hole. The project has students design an individual scale-model hole and then combine work into a collaborative 18-hole course.

The listed mathematical scope includes:

area
perimeter
angles
trigonometry
dilations
cost calculations

That makes mini golf useful as a unit capstone, not just a one-off activity.

Build, test, and iterate

TeachEngineering offers the clearest build-and-test model. In that activity, students solve one-, two-, and three-bank shots on paper, then test them with real putters and golf balls, and finally design and build their own holes from wood frames and steel corners.

TeachEngineering gives a concrete planning benchmark:

Time required: about 3 hours 15 minutes
Format: four 50-minute periods

That is the strongest time estimate in the source set because it is explicitly published, not inferred.

Add multi-wall challenges

If students master the basics quickly, Johnson’s GeoGebra project already provides extension structure:

2-wall challenge
3-wall challenge
4-wall challenge

That makes it easy to differentiate without inventing a new task from scratch.

Keep extensions optional

Not every class needs Laws of Cosines, course budgeting, and physical construction in the same assignment. A good differentiation structure is:

keep the core on reflection + right-triangle trig
offer one or two extension paths for students ready to go further

That preserves rigor without turning the project into an all-or-nothing marathon.

FAQ

What prior knowledge do students need for a mini-golf trig project?

That depends on the version.

In Nat Banting’s project, students had already learned tangent and inverse tangent before starting. That suggests a trig-focused version should come after students can already set up and solve right triangles.

For a geometry-first version, TeachEngineering lists a prior lesson on angles and reflections as the activity dependency, and Jennifer Lamb’s handout assumes students can use a protractor and ruler.

So the minimum background is usually:

angle measurement
basic reflection reasoning
right-triangle setup

And for a trig-centered version:

tangent
inverse tangent
the Pythagorean theorem

How long does a typical mini-golf trig project take in class?

The clearest published benchmark is from TeachEngineering: about 3 hours 15 minutes, or four 50-minute periods, for a design-and-build version.

Shorter versions are possible, but the evidence pack gives that four-period build activity as the explicit time reference. If you omit physical construction and keep the work on paper or in GeoGebra, the project becomes easier to compress.

Are there downloadable files or templates available?

Yes.

The most direct classroom file set is Nat Banting’s Google Drive folder, which includes project files, blank protractors, and student examples.

Other useful starting points are:

Jennifer Lamb’s project PDF
WISELearn’s Geometry Mini Golf Project, which includes downloadable documents
Elizabeth Johnson’s GeoGebra Mini Golf Project

How do real ball paths differ from trig predictions?

On paper, these projects usually assume an ideal reflection model. Jennifer Lamb’s handout explains the reflection rule in the no-spin case: the ball rebounds at the same angle it struck the wall.

In a real build, TeachEngineering explicitly notes that actual results may vary from calculated results. In classroom terms, that difference can come from:

imperfect measurements
slight construction misalignment
inconsistent testing conditions

That is not a failure of the math. It is a useful modeling lesson: calculations describe an idealized system, and physical testing reveals how close the build comes to that system.

What math standards do these projects align to?

A documented standards-aligned example appears in WISELearn’s Geometry Mini Golf Project.

Two especially relevant Wisconsin standards are:

HSG-SRT.C.6: side ratios in right triangles define trigonometric ratios for acute angles
HSG-SRT.C.8: use trigonometric ratios and the Pythagorean theorem to solve right triangles in applied problems

WISELearn also lists related geometry standards involving similarity, congruence, modeling, and construction, which fits the way many mini golf projects blend reflection, triangle reasoning, and design.

Mini golf is a strong math-project context because its core idea is simple but expandable: reflect the target, draw the path, solve the triangle. From there, teachers can choose the version that fits their class: Banting’s transparency-based trig task, Lamb’s geometry guide and model project, Johnson’s GeoGebra brochure workflow, TeachEngineering’s build-and-test activity, or WISELearn’s standards-aligned course design project. Start with reflection and right triangles, add measurement and justification, and extend only as far as your students and schedule support.