Mini Golf Congruence Challenge: Design and Build!

Created bySteve Morris

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Mini Golf Congruence Challenge: Design and Build!

Grade 10Math3 days

In this project, students apply triangle congruence theorems (ASA, SAS, SSS) to design a fair and challenging miniature golf course. They use rigid motions to explain congruence criteria and optimize the course's design for playability. The project connects mathematical concepts to a recreational activity, enhancing both understanding and engagement.

Triangle CongruenceMini-Golf DesignGeometric PrinciplesASASASSSSRigid Motions

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we design a fair and challenging miniature golf course using triangle congruence to ensure optimal playability and engagement?

Essential Questions

Supporting questions that break down major concepts.

How can triangle congruence be used in real-world applications?
How do ASA, SAS, and SSS criteria ensure triangle congruence through rigid motions?
What makes a miniature golf course hole fair and challenging?
How can geometric principles enhance the design and playability of a game?
In what ways can mathematical concepts be applied to create and improve recreational activities?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:

Apply triangle congruence theorems (ASA, SAS, SSS) to design fair and challenging miniature golf holes.
Use rigid motions to explain the criteria for triangle congruence.
Design a miniature golf course that is both playable and engaging.
Utilize geometric principles to optimize the design and playability of the golf course.
Apply mathematical concepts to create a recreational activity.

Common Core State Standards

HSG-CO.B.7

Primary

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.Reason: Directly addresses the core mathematical concept of the project.

Entry Events

Events that will be used to introduce the project to students

The Impossible Shot Challenge

A video surfaces online of a 'mini-golf impossible shot' that seems to defy the laws of physics and geometry. Students must use their knowledge of triangle congruence to debunk the trick and then design a hole where a seemingly impossible shot is actually achievable through precise geometric construction.

Mini-Golf Forensics

The teacher brings in a 'broken' mini-golf hole from a local course, with warped angles and mismatched segments. Students act as forensic mathematicians, using congruence theorems to diagnose the errors and propose reconstruction plans, leading into their own course design.

Design a Hole

A local mini-golf course owner presents a challenge: design a brand new hole that incorporates a specific theme (e.g., historical landmarks, famous movie scenes) while adhering to strict congruence rules for fairness and playability. The winning design will be built and featured at the course.

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Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.

Activity 1

SSS Congruence Challenge: Obstacle Design

Students begin by understanding the SSS congruence criterion. They will then apply this understanding to design a simple mini-golf obstacle, ensuring all triangles used are congruent by SSS.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Research and define the Side-Side-Side (SSS) congruence criterion.

2. Sketch three different triangles, ensuring that all three sides of each triangle have the same measurements as the corresponding sides of the other two.

3. Design a mini-golf obstacle incorporating these congruent triangles. The design should be functional and integrate the triangles seamlessly.

4. Write a short paragraph explaining how the SSS criterion is applied in the design to ensure congruence and fairness.

Final Product

What students will submit as the final product of the activityA detailed sketch of a mini-golf obstacle that uses SSS congruence, with measurements and a written explanation of how SSS is applied.

Alignment

How this activity aligns with the learning objectives & standardsAddresses HSG-CO.B.7 by focusing on understanding and applying the SSS congruence criterion in a practical design context.

Activity 2

SAS Congruence in Hole Design

Students will explore the SAS congruence criterion and design a mini-golf hole incorporating this principle to ensure a specific angle and the adjacent sides create predictable play.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Research and define the Side-Angle-Side (SAS) congruence criterion.

2. Design a mini-golf hole that includes at least one instance of SAS congruence. Specify the side lengths and angle measures that demonstrate SAS.

3. Create a scale drawing or digital model of the hole, labeling all relevant measurements.

4. Write a justification explaining how the SAS criterion is essential to the hole's design and playability.

Final Product

What students will submit as the final product of the activityA blueprint of a mini-golf hole design using SAS congruence, including angle measurements, side lengths, and a rationale for its use.

Alignment

How this activity aligns with the learning objectives & standardsAddresses HSG-CO.B.7 by focusing on understanding and applying the SAS congruence criterion in a practical design context.

Activity 3

ASA: Engineering Predictable Play

This activity requires students to use the ASA congruence criterion to design a more complex mini-golf feature, focusing on how angles between sides affect the path of the ball.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Research and define the Angle-Side-Angle (ASA) congruence criterion.

2. Design a feature of the mini-golf course where ASA congruence is critical. This could be a ramp, a curved section, or a series of obstacles.

3. Provide precise measurements and angle specifications in your design to clearly demonstrate ASA congruence.

4. Explain how the ASA criterion affects the ball's path and ensures a predictable outcome in the game.

Final Product

What students will submit as the final product of the activityA fully detailed plan for a mini-golf feature using ASA congruence, including diagrams, measurements, and a detailed explanation of how ASA ensures predictable outcomes.

Alignment

How this activity aligns with the learning objectives & standardsAddresses HSG-CO.B.7 by focusing on understanding and applying the ASA congruence criterion in a practical design context.

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Mini-Golf Congruence Challenge Rubric

Category 1

Application and Design

Focuses on the correct application of congruence theorems, clarity of explanations, and the design's overall effectiveness.

Criterion 1

Accuracy of Congruence Application

Accuracy of triangle measurements and congruence demonstrations.

Exemplary

4 Points

Measurements and angles are accurate and demonstrate exemplary understanding of congruence.

Proficient

3 Points

Measurements and angles are mostly accurate, demonstrating proficiency in congruence.

Developing

2 Points

Measurements and angles are somewhat accurate, showing developing understanding of congruence.

Beginning

1 Points

Measurements and angles are inaccurate, and congruence is not effectively demonstrated.

Criterion 2

Clarity of Explanation

Clarity and effectiveness of the written explanation of congruence criteria.

Exemplary

4 Points

Explanation is exceptionally clear, insightful, and demonstrates a deep understanding of congruence criteria with precise reasoning.

Proficient

3 Points

Explanation is clear, thorough, and demonstrates a good understanding of congruence criteria.

Developing

2 Points

Explanation is somewhat clear and demonstrates a basic understanding of congruence criteria.

Beginning

1 Points

Explanation is unclear, incomplete, and demonstrates a limited understanding of congruence criteria.

Criterion 3

Design Creativity and Practicality

Creativity and practicality of the mini-golf hole or obstacle design.

Exemplary

4 Points

Design is exceptionally creative, highly practical, and demonstrates an innovative application of geometric principles.

Proficient

3 Points

Design is creative, practical, and demonstrates a good application of geometric principles.

Developing

2 Points

Design shows some creativity and practicality, with a basic application of geometric principles.

Beginning

1 Points

Design lacks creativity, practicality, and demonstrates minimal application of geometric principles.

Category 2

Mathematical Understanding and Communication

Assesses the depth of research, ability to link math concepts to real-world situations, and precision in using mathematical language.

Criterion 1

Research Quality

Completeness and quality of research on congruence theorems (SSS, ASA, SAS).

Exemplary

4 Points

Research is comprehensive, insightful, and demonstrates an advanced understanding of congruence theorems.

Proficient

3 Points

Research is thorough, accurate, and demonstrates a strong understanding of congruence theorems.

Developing

2 Points

Research is adequate, with some understanding of congruence theorems.

Beginning

1 Points

Research is incomplete and shows limited understanding of congruence theorems.

Criterion 2

Real-World Connection

Ability to connect mathematical concepts to real-world applications (mini-golf design).

Exemplary

4 Points

Demonstrates an exceptional ability to connect mathematical concepts to real-world applications with innovative solutions.

Proficient

3 Points

Demonstrates a strong ability to connect mathematical concepts to real-world applications effectively.

Developing

2 Points

Demonstrates a basic ability to connect mathematical concepts to real-world applications.

Beginning

1 Points

Struggles to connect mathematical concepts to real-world applications.

Criterion 3

Mathematical Communication

Use of precise mathematical language and accurate geometric terms.

Exemplary

4 Points

Uses precise mathematical language and geometric terms with consistent accuracy and sophistication.

Proficient

3 Points

Uses precise mathematical language and geometric terms accurately and effectively.

Developing

2 Points

Uses mathematical language and geometric terms with some accuracy.

Beginning

1 Points

Uses imprecise or inaccurate mathematical language and geometric terms.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning

Question 1

How did your understanding of triangle congruence evolve as you designed and built your mini-golf course?

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Question 2

Which of the congruence criteria (SSS, SAS, ASA) did you find most challenging to apply in your designs, and why?

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Question 3

To what extent do you agree with the statement: 'Triangle congruence is essential for creating a fair and predictable mini-golf game'?

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Question 4

How did you ensure that your mini-golf hole designs were both challenging and fair, using the principles of triangle congruence? Provide specific examples from your design.

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Question 5

If you were to redesign your mini-golf course, what aspects would you change to better utilize triangle congruence and improve the overall playability?

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