Pythagorean Mini Golf: Design Your Dream Course
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we apply the Pythagorean Theorem and geometric principles to design a challenging and engaging miniature golf course that demonstrates the relationship between math and recreational fun?Essential Questions
Supporting questions that break down major concepts.- How can the Pythagorean Theorem be used to design right triangles?
- How can angles and geometric shapes add challenges to the mini golf course?
- What is the relationship between the Pythagorean Theorem and the distance between two points on a coordinate plane?
- How can we use mathematical concepts to create a fun and engaging mini golf game?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Apply the Pythagorean Theorem to design right triangles in a mini golf course.
- Incorporate angles and geometric shapes to add challenges to the mini golf course.
- Relate the Pythagorean Theorem to the distance between two points on a coordinate plane.
- Use mathematical concepts to create a fun and engaging mini golf game.
Common Core Standards
Entry Events
Events that will be used to introduce the project to studentsImpossible Mini-Golf Holes Analysis
Present students with images of bizarre and seemingly impossible mini-golf holes from around the world. Challenge them to analyze these designs using the Pythagorean Theorem to understand how they work, inspiring them to create equally innovative (but mathematically sound) holes.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Pythagorean Theorem Primer
Students will review the Pythagorean Theorem and its proof. They will then apply this understanding to simple right triangles.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 showing different right triangles with calculated side lengths.Alignment
How this activity aligns with the learning objectives & standardsCovers 8.G.B.6 (Explain a proof of the Pythagorean Theorem).Right Triangle Hole Design
Students will design a mini golf hole using only right triangles. They must calculate the distances accurately and explain how the theorem is applied in their design.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 mini golf hole design with calculations for the side lengths of the right triangles.Alignment
How this activity aligns with the learning objectives & standardsCovers 8.G.B.6 (Apply the Pythagorean Theorem).Converse Confirmation Challenge
Students will explore the converse of the Pythagorean Theorem to determine if certain triangle configurations are right triangles, which is essential for the angles in their mini golf course design.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 report detailing different triangle configurations and whether they satisfy the converse of the Pythagorean Theorem, justifying why certain angles are right angles.Alignment
How this activity aligns with the learning objectives & standardsCovers 8.G.B.6 (Apply converse of the Pythagorean Theorem).Coordinate Course Creation
Students will plot their mini golf hole design on a coordinate plane and calculate distances between key points using the Pythagorean Theorem.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 mini golf hole design plotted on a coordinate plane with calculated distances between key points, demonstrating the application of the Pythagorean Theorem in a coordinate system.Alignment
How this activity aligns with the learning objectives & standardsCovers 8.G.B.6 (Application in coordinate plane).Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioMini Golf Design Challenge Rubric
Application of Pythagorean Theorem
Focuses on the accuracy of Pythagorean Theorem calculations, the clarity and precision of the design, and the effectiveness of the written explanation.Pythagorean Theorem Accuracy
Accuracy of calculations using the Pythagorean Theorem to determine side lengths of right triangles in the mini golf hole design.
Exemplary
4 PointsCalculations are precise and error-free, demonstrating a comprehensive understanding of the Pythagorean Theorem.
Proficient
3 PointsCalculations are mostly accurate with only minor errors, showing a good understanding of the Pythagorean Theorem.
Developing
2 PointsCalculations contain some errors, indicating a partial understanding of the Pythagorean Theorem.
Beginning
1 PointsCalculations are largely inaccurate or missing, suggesting a limited understanding of the Pythagorean Theorem.
Design Clarity and Precision
Clarity and precision of the scaled drawing of the mini golf hole design, including labeling and accurate representation of right triangles.
Exemplary
4 PointsThe scaled drawing is exceptionally clear, detailed, and accurately represents the mini golf hole design with precise labeling.
Proficient
3 PointsThe scaled drawing is clear, detailed, and accurately represents the mini golf hole design with appropriate labeling.
Developing
2 PointsThe scaled drawing is somewhat clear and represents the mini golf hole design, but may lack detail or accurate labeling.
Beginning
1 PointsThe scaled drawing is unclear, lacks detail, and does not accurately represent the mini golf hole design.
Explanation of Pythagorean Theorem Application
Effectiveness of the paragraph explaining how the Pythagorean Theorem is applied in the mini golf hole design, demonstrating understanding and application.
Exemplary
4 PointsThe paragraph provides a clear, insightful, and comprehensive explanation of how the Pythagorean Theorem is applied in the mini golf hole design.
Proficient
3 PointsThe paragraph provides a clear and thorough explanation of how the Pythagorean Theorem is applied in the mini golf hole design.
Developing
2 PointsThe paragraph provides a basic explanation of how the Pythagorean Theorem is applied in the mini golf hole design, but may lack detail.
Beginning
1 PointsThe paragraph fails to adequately explain how the Pythagorean Theorem is applied in the mini golf hole design.
Design Innovation
Assesses the creativity and originality of the mini golf hole design and how well it leverages the converse of the Pythagorean Theorem.Design Creativity and Originality
Creativity and originality in the mini golf hole design, demonstrating innovative use of right triangles to create a challenging and engaging experience.
Exemplary
4 PointsThe design demonstrates exceptional creativity and originality, using right triangles in an innovative way to create a uniquely challenging and engaging mini golf experience.
Proficient
3 PointsThe design demonstrates creativity and originality, using right triangles to create a challenging and engaging mini golf experience.
Developing
2 PointsThe design shows some creativity, but the use of right triangles is not particularly innovative or engaging.
Beginning
1 PointsThe design lacks creativity and originality, with a limited or ineffective use of right triangles.
Use of Converse of Pythagorean Theorem
Consideration of the converse of the Pythagorean Theorem in creating right angles within the design, confirming accuracy and geometric correctness.
Exemplary
4 PointsDemonstrates a deep understanding of the converse of the Pythagorean Theorem, using it effectively to create precise right angles and ensure geometric correctness in the design.
Proficient
3 PointsDemonstrates a good understanding of the converse of the Pythagorean Theorem, using it accurately to create right angles and ensure geometric correctness in the design.
Developing
2 PointsShows some understanding of the converse of the Pythagorean Theorem, but may have minor inaccuracies in creating right angles or ensuring geometric correctness.
Beginning
1 PointsLacks understanding of the converse of the Pythagorean Theorem, resulting in inaccurate right angles and geometric errors in the design.
Presentation and Coordinate Application
Evaluates the application of the Pythagorean Theorem within a coordinate plane and the overall quality of the presentation.Coordinate Plane Calculations
Application of the Pythagorean Theorem to calculate distances on a coordinate plane accurately, demonstrating a strong connection between geometric and algebraic concepts.
Exemplary
4 PointsDemonstrates a sophisticated ability to apply the Pythagorean Theorem to calculate distances on a coordinate plane accurately and efficiently.
Proficient
3 PointsAccurately applies the Pythagorean Theorem to calculate distances on a coordinate plane.
Developing
2 PointsShows some ability to apply the Pythagorean Theorem to calculate distances on a coordinate plane, but calculations contain some errors.
Beginning
1 PointsStruggles to apply the Pythagorean Theorem to calculate distances on a coordinate plane.
Presentation Quality
Quality of the presentation, including clarity, organization, and visual appeal of the final product (scaled drawing and calculations).
Exemplary
4 PointsThe presentation is exceptionally clear, well-organized, and visually appealing, enhancing the understanding of the design and calculations.
Proficient
3 PointsThe presentation is clear, well-organized, and visually appealing.
Developing
2 PointsThe presentation is somewhat clear and organized, but may lack visual appeal.
Beginning
1 PointsThe presentation is unclear, disorganized, and lacks visual appeal.