Geometry, Trigonometry, and Forces: Visual Math in the Body

Created byAnge Evans

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Geometry, Trigonometry, and Forces: Visual Math in the Body

Grade 12ScienceMath12 days

This project integrates geometry, trigonometry, and the concept of forces to explore real-world applications in orthopedics, acupuncture, search and rescue, and emergency medical services. Students will apply mathematical models to predict forces on bones, use trigonometry for accuracy in medical procedures, and utilize vector decomposition to optimize patient safety. Through hands-on activities and simulations, students will solve problems related to bone traction, locating lost hikers, and optimizing stretcher ramp angles, culminating in a portfolio showcasing their understanding and application of these concepts.

GeometryTrigonometryForcesOrthopedicsSearch and RescueVector DecompositionMedical Procedures

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we use geometry, trigonometry, and forces to solve real-world problems in orthopedics, acupuncture, search and rescue, and emergency medical services while ensuring safety and accuracy?

Essential Questions

Supporting questions that break down major concepts.

How can mathematical models predict the forces on bones during traction?
How does trigonometry ensure accuracy and safety in medical procedures like acupuncture?
In what ways can trigonometry and the law of sines be applied to real-world search and rescue operations?
How can vector decomposition optimize patient safety when lifting and moving stretchers?

Standards & Learning Goals

Learning Goals

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

Apply the concept of bone levers and torque to calculate the force needed to keep leg bones in alignment during traction.
Use right triangle trigonometry to select the correct needle and angle for safe acupuncture depth.
Apply the law of sines to estimate the location of a lost hiker using triangulation and radio bearings.
Use vector decomposition to calculate strap tensions at different angles when lifting patients on a stretcher ramp.

Entry Events

Events that will be used to introduce the project to students

The Broken Leg Challenge: An Orthopedic Simulation

Students are presented with a simulated orthopedic case where a patient requires leg traction. They must use a model leg and weights to experiment with different force and distance combinations, aiming to realign a fractured bone visible via X-ray (provided). This hands-on activity sparks curiosity about bone levers and the role of torque in orthopedic treatment.

Distress Signal Decoded: A Search and Rescue Mission

Students receive a coded distress call from a 'lost hiker' including directional bearings. They are tasked with using a map, protractors, and the law of sines to determine the hiker's estimated location. This activity simulates a real search and rescue scenario, highlighting the practical application of trigonometry in emergency situations.

The Stretcher Ramp Dilemma: Optimizing Lifting Forces

An engaging video shows an EMS team struggling to lift a patient on a stretcher ramp, emphasizing the physical strain and challenges involved. Students are then presented with a similar scenario on a smaller scale (e.g., using weights and a model ramp) and challenged to find the optimal lifting angle and strap configuration to minimize the force required. This directly relates to their experiences of lifting objects and introduces the relevance of vector decomposition.

The Body's Mathematical Mysteries: An Image-Based Inquiry

Students are shown a series of images depicting various injuries and medical procedures related to the skeletal system. They are then challenged to connect the images to mathematical concepts like levers, angles, and force vectors, prompting them to brainstorm how math plays a role in understanding and treating these conditions. This open-ended approach encourages inquiry and challenges preconceived notions about the relevance of math and science in healthcare.

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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

Lever Basics & Bone Traction

Students will start with basic lever problems and gradually apply them to bone structures.

Steps

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

1. Research basic lever mechanics and torque.

2. Identify the fulcrum, force, and load in a leg traction scenario.

3. Calculate the force needed for alignment using the torque formula.

4. Write a report with diagrams and calculations.

Final Product

What students will submit as the final product of the activityA detailed report on force calculations for leg traction, including diagrams.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal 1: Apply the concept of bone levers and torque to calculate the force needed to keep leg bones in alignment during traction.

Activity 2

Lost Hiker Locator

Students will work on triangulation techniques to locate a lost hiker.

Steps

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

1. Understand triangulation and radio bearings.

2. Learn and apply the law of sines.

3. Calculate the hiker's location using bearings from two teams.

4. Create a map and report.

Final Product

What students will submit as the final product of the activityA map indicating the estimated location of the hiker, along with a report detailing the calculations.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal 3: Apply the law of sines to estimate the location of a lost hiker using triangulation and radio bearings.

Activity 3

Stretcher Ramp Optimization

Students will decompose force vectors to optimize lifting techniques.

Steps

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

1. Learn vector decomposition of forces.

2. Analyze forces on a stretcher ramp.

3. Calculate strap tensions at different angles.

4. Write a strategy proposal.

Final Product

What students will submit as the final product of the activityA strategy proposal for optimizing stretcher ramp angles and strap tensions, supported by vector calculations.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal 4: Use vector decomposition to calculate strap tensions at different angles when lifting patients on a stretcher ramp.

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Geometry, Trigonometry & Forces Portfolio Rubric

Category 1

Lever Mechanics and Bone Traction

Assessment of student's understanding of lever mechanics and its application to bone traction

Criterion 1

Calculation Accuracy

Accuracy of lever mechanics and torque calculations

Exemplary

4 Points

Calculations are precise, accurate, and demonstrate a deep understanding of lever mechanics and torque.

Proficient

3 Points

Calculations are mostly accurate with a good understanding of lever mechanics and torque.

Developing

2 Points

Calculations contain some errors, demonstrating a basic understanding of lever mechanics and torque.

Beginning

1 Points

Calculations are inaccurate or incomplete, demonstrating a limited understanding of lever mechanics and torque.

Criterion 2

Report Quality

Clarity and completeness of the report, including diagrams

Exemplary

4 Points

Report is exceptionally clear, well-organized, and includes detailed, accurate diagrams that enhance understanding.

Proficient

3 Points

Report is clear, well-organized, and includes accurate diagrams.

Developing

2 Points

Report is somewhat organized, but clarity is lacking in places, and diagrams may be incomplete or have minor inaccuracies.

Beginning

1 Points

Report is disorganized, unclear, and lacks diagrams or includes inaccurate/irrelevant diagrams.

Criterion 3

Application of Concepts

Application of lever concepts to the bone traction scenario

Exemplary

4 Points

Demonstrates sophisticated application of lever concepts to the bone traction scenario, with innovative insights.

Proficient

3 Points

Applies lever concepts effectively to the bone traction scenario.

Developing

2 Points

Applies lever concepts to the bone traction scenario inconsistently.

Beginning

1 Points

Struggles to apply lever concepts to the bone traction scenario.

Category 2

Triangulation and Search & Rescue

Assessment of student's understanding of triangulation and the law of sines in a search and rescue context

Criterion 1

Calculation Accuracy

Accuracy of triangulation and law of sines calculations

Exemplary

4 Points

Calculations are precise, accurate, and demonstrate a deep understanding of triangulation and the law of sines.

Proficient

3 Points

Calculations are mostly accurate with a good understanding of triangulation and the law of sines.

Developing

2 Points

Calculations contain some errors, demonstrating a basic understanding of triangulation and the law of sines.

Beginning

1 Points

Calculations are inaccurate or incomplete, demonstrating a limited understanding of triangulation and the law of sines.

Criterion 2

Map Quality

Quality and accuracy of the map indicating the hiker's location

Exemplary

4 Points

Map is exceptionally clear, accurate, and effectively indicates the estimated location of the hiker with detailed labeling and scale.

Proficient

3 Points

Map is clear, accurate, and indicates the estimated location of the hiker.

Developing

2 Points

Map is somewhat accurate but lacks clarity or detail in indicating the hiker's location.

Beginning

1 Points

Map is inaccurate, unclear, or does not effectively indicate the hiker's location.

Criterion 3

Application of Concepts

Application of triangulation and law of sines to the search and rescue scenario

Exemplary

4 Points

Demonstrates sophisticated application of triangulation and law of sines to the search and rescue scenario, with innovative problem-solving.

Proficient

3 Points

Applies triangulation and law of sines effectively to the search and rescue scenario.

Developing

2 Points

Applies triangulation and law of sines to the search and rescue scenario inconsistently.

Beginning

1 Points

Struggles to apply triangulation and law of sines to the search and rescue scenario.

Category 3

Vector Decomposition and Patient Safety

Assessment of student's understanding of vector decomposition and its application to optimizing patient safety on a stretcher ramp

Criterion 1

Calculation Accuracy

Accuracy of vector decomposition and strap tension calculations

Exemplary

4 Points

Calculations are precise, accurate, and demonstrate a deep understanding of vector decomposition and its application to strap tension.

Proficient

3 Points

Calculations are mostly accurate with a good understanding of vector decomposition and its application to strap tension.

Developing

2 Points

Calculations contain some errors, demonstrating a basic understanding of vector decomposition and its application to strap tension.

Beginning

1 Points

Calculations are inaccurate or incomplete, demonstrating a limited understanding of vector decomposition.

Criterion 2

Strategy Proposal Quality

Feasibility and optimality of the strategy proposal for stretcher ramp angles and strap tensions

Exemplary

4 Points

Strategy proposal is highly feasible, optimized for safety and efficiency, and demonstrates a deep understanding of force dynamics.

Proficient

3 Points

Strategy proposal is feasible, optimized for safety and efficiency.

Developing

2 Points

Strategy proposal is somewhat feasible but may not be fully optimized.

Beginning

1 Points

Strategy proposal is not feasible or shows little understanding of force dynamics.

Criterion 3

Application of Concepts

Application of vector decomposition to optimize patient safety when lifting and moving stretchers

Exemplary

4 Points

Demonstrates sophisticated application of vector decomposition to optimize patient safety, with innovative solutions and a deep understanding of biomechanics.

Proficient

3 Points

Applies vector decomposition effectively to optimize patient safety.

Developing

2 Points

Applies vector decomposition to patient safety inconsistently.

Beginning

1 Points

Struggles to apply vector decomposition to patient safety.

Reflection Prompts

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

Question 1

How did this unit change your perspective on the interconnectedness of math and science in real-world applications?

Text

Required

Question 2

To what extent do you agree that the models in this unit accurately represent real-world scenarios in orthopedics, acupuncture, search and rescue, and EMS?

Scale

Required

Question 3

Which project (Lever Basics & Bone Traction, Lost Hiker Locator, or Stretcher Ramp Optimization) provided the most significant learning experience for you, and why?

Multiple choice

Required

Options

Lever Basics & Bone Traction

Lost Hiker Locator

Stretcher Ramp Optimization