Miniature Golf Course Design: A Similar Triangles Project
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we design a miniature golf course that uses similar triangles to optimize the playability and challenge of each hole while adhering to the principles of similarity transformations and criteria?Essential Questions
Supporting questions that break down major concepts.- How can similar triangles be used to accurately calculate distances and angles in miniature golf course design?
- What criteria define similar triangles, and how do these criteria apply to the design of a miniature golf course?
- In what ways can the principles of similarity transformations ensure the accurate scaling and construction of miniature golf course features?
- How can you apply the similarity criteria for triangles to solve real-world problems related to miniature golf course design, such as determining the optimal angle for a challenging shot?
- How can the properties of similar triangles be used to optimize the design and playability of a miniature golf course?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Apply properties of similar triangles to design a miniature golf course.
- Use similarity transformations to determine triangle similarity.
- Solve problems and prove relationships in geometric figures using similarity criteria.
math
Entry Events
Events that will be used to introduce the project to studentsMini-Golf SOS
A local miniature golf course owner presents a problem: their course is outdated and not challenging enough. Students, acting as design consultants, analyze an existing hole using similar triangles, identify its flaws, and pitch redesign ideas, emphasizing mathematical accuracy and playability.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Triangle Similarity Basics
Students will learn the basics of similarity transformations and how they apply to triangles. They will practice identifying similar triangles based on given criteria (AA, SAS, SSS).Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA worksheet with various triangle pairs where students determine if they are similar and explain why.Alignment
How this activity aligns with the learning objectives & standardsHSG-SRT.B.5 (Use the properties of similarity transformations to establish criterion for two triangles to be similar.)Mini-Golf Hole Scaling
Students will apply their knowledge of similar triangles to a scaled-down version of a miniature golf hole. They will calculate the lengths of sides and measures of angles using similarity transformations.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA scaled drawing of a miniature golf hole with all side lengths and angle measures labeled, demonstrating the use of similarity.Alignment
How this activity aligns with the learning objectives & standardsHSG-SRT.B.5 (Use the properties of similarity transformations to establish criterion for two triangles to be similar.) HSG-SRT.B.4 (Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.)Design Your Own Hole
Students will design their own miniature golf hole, incorporating at least two similar triangles. They need to calculate distances, angles, and obstacles to ensure playability and challenge.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA detailed design plan for a miniature golf hole, including a scale drawing, calculations of distances and angles using similar triangles, and a written justification for the design choices.Alignment
How this activity aligns with the learning objectives & standardsHSG-SRT.B.4 (Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.)Refine and Finalize Design
Students will refine their miniature golf hole designs based on peer feedback and mathematical accuracy checks.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA revised and finalized miniature golf hole design, incorporating feedback and demonstrating accurate calculations and justifications.Alignment
How this activity aligns with the learning objectives & standardsHSG-SRT.B.4 (Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.)Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioMiniature Golf Course Design Rubric
Understanding of Triangle Similarity
Demonstrates understanding of similarity transformations and triangle similarity criteria (AA, SAS, SSS).Triangle Identification and Justification
Accuracy in identifying and explaining similar triangles based on AA, SAS, and SSS criteria.
Exemplary
4 PointsAccurately identifies and explains all similar triangles, providing thorough and insightful justifications using AA, SAS, and SSS criteria.
Proficient
3 PointsAccurately identifies and explains most similar triangles, providing clear justifications using AA, SAS, and SSS criteria.
Developing
2 PointsIdentifies some similar triangles with difficulty, providing basic justifications using AA, SAS, and SSS criteria but with some errors or omissions.
Beginning
1 PointsStruggles to identify similar triangles and provides incomplete or inaccurate justifications using AA, SAS, and SSS criteria.
Worksheet Accuracy and Completion
Completeness and correctness of the worksheet.
Exemplary
4 PointsWorksheet is complete with all answers correct and explanations clear, concise, and mathematically sound.
Proficient
3 PointsWorksheet is mostly complete with only minor errors. Explanations are generally clear and mathematically sound.
Developing
2 PointsWorksheet is partially complete with several errors. Explanations are present but may lack clarity or mathematical accuracy.
Beginning
1 PointsWorksheet is incomplete with numerous errors. Explanations are missing or demonstrate a lack of understanding.
Application to Mini-Golf Hole
Applies knowledge of similar triangles to create a scaled-down version of a miniature golf hole.Scaling and Calculation Accuracy
Accuracy of scale factor application and calculations of side lengths and angle measures.
Exemplary
4 PointsApplies the scale factor flawlessly and accurately calculates all side lengths and angle measures with detailed precision.
Proficient
3 PointsApplies the scale factor accurately and calculates most side lengths and angle measures correctly with only minor errors.
Developing
2 PointsApplies the scale factor with some inconsistencies and makes several errors in calculating side lengths and angle measures.
Beginning
1 PointsStruggles to apply the scale factor and makes significant errors in calculating side lengths and angle measures.
Drawing Clarity and Accuracy
Clarity and accuracy of the scaled drawing, including labeling of all side lengths and angle measures.
Exemplary
4 PointsScaled drawing is exceptionally clear, accurate, and well-labeled, providing a professional-quality representation of the miniature golf hole.
Proficient
3 PointsScaled drawing is clear, accurate, and well-labeled, providing a good representation of the miniature golf hole.
Developing
2 PointsScaled drawing is somewhat unclear and contains a few inaccuracies or omissions in labeling.
Beginning
1 PointsScaled drawing is unclear, inaccurate, and poorly labeled, making it difficult to understand the miniature golf hole design.
Original Design and Application
Designs a miniature golf hole, incorporating similar triangles to enhance playability and challenge.Design Creativity and Feasibility
Creativity and feasibility of the miniature golf hole design, incorporating at least two similar triangles.
Exemplary
4 PointsDesign is highly creative, innovative, and feasible, seamlessly incorporating two or more similar triangles in a way that enhances playability and challenge.
Proficient
3 PointsDesign is creative and feasible, incorporating two or more similar triangles effectively.
Developing
2 PointsDesign shows some creativity but may lack feasibility or effective integration of similar triangles.
Beginning
1 PointsDesign lacks creativity and feasibility, with minimal or ineffective use of similar triangles.
Calculation Accuracy for Shots
Accuracy of calculations for distances and angles needed for successful shots, using similar triangles.
Exemplary
4 PointsCalculations are flawlessly accurate and demonstrate a deep understanding of how similar triangles affect shot trajectories and difficulty.
Proficient
3 PointsCalculations are mostly accurate and demonstrate a good understanding of the relationship between similar triangles and shot planning.
Developing
2 PointsCalculations contain some errors but show a basic understanding of the principles involved.
Beginning
1 PointsCalculations are largely inaccurate and demonstrate a limited understanding of how similar triangles influence shot planning.
Design Justification
Quality and clarity of the written justification for the design choices, explaining how similar triangles enhance playability and challenge.
Exemplary
4 PointsJustification is exceptionally clear, insightful, and persuasive, providing a compelling rationale for all design choices and demonstrating a sophisticated understanding of the mathematical principles involved.
Proficient
3 PointsJustification is clear, thorough, and well-reasoned, explaining the design choices effectively and demonstrating a solid grasp of the mathematical concepts.
Developing
2 PointsJustification is somewhat unclear or incomplete, lacking detail or demonstrating a limited understanding of the mathematical principles.
Beginning
1 PointsJustification is unclear, poorly reasoned, or missing key information, demonstrating a weak understanding of the mathematical concepts and design choices.
Design Refinement and Accuracy
Refines the miniature golf hole design based on feedback, ensuring mathematical accuracy and playability.Use of Peer Feedback
Incorporation of peer feedback to improve design, correct errors, and enhance playability and mathematical accuracy.
Exemplary
4 PointsDemonstrates exceptional responsiveness to peer feedback, making significant improvements to the design that greatly enhance playability, mathematical accuracy, and overall quality.
Proficient
3 PointsDemonstrates a strong ability to incorporate peer feedback, making noticeable improvements to the design in terms of playability and mathematical accuracy.
Developing
2 PointsIncorporates some peer feedback, but the changes may be superficial or not fully address the concerns raised.
Beginning
1 PointsShows limited evidence of incorporating peer feedback, with minimal changes made to the original design.
Final Design Accuracy and Justification
Final design demonstrates accurate calculations and well-supported justifications.
Exemplary
4 PointsFinal design exhibits flawless calculations and a compelling, well-supported justification that demonstrates a deep understanding of the mathematical principles and design considerations.
Proficient
3 PointsFinal design demonstrates accurate calculations and a clear, well-supported justification that shows a solid understanding of the mathematical concepts and design choices.
Developing
2 PointsFinal design contains a few minor errors in calculations or lacks sufficient justification in some areas.
Beginning
1 PointsFinal design exhibits significant errors in calculations or lacks a clear and well-supported justification, demonstrating a weak understanding of the mathematical concepts and design choices.