City Skate Park Design: Equations in Motion

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City Skate Park Design: Equations in Motion

Grade 9Math12 days

In this project, students design a city skate park, applying mathematical concepts such as slope-intercept, point-slope, and standard forms of linear equations to ensure safety and accessibility. They address a real-world problem by modeling ramps and pathways, incorporating safety standards, and optimizing the design for diverse users. The project culminates in a comprehensive skate park design plan and presentation, demonstrating the practical application of mathematical principles.

Skate Park DesignLinear EquationsAccessibility StandardsMathematical ModelingSlope-Intercept FormPoint-Slope FormStandard Form

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we design a city skate park so that every ramp and pathway meets safety and accessibility standards, using equations to model and adjust the slopes and heights of the ramps?

Essential Questions

Supporting questions that break down major concepts.

How do slope-intercept, point-slope, and standard forms help us represent linear relationships in the real world?
What are the safety and accessibility standards for skate park design, and how can we ensure our design meets them?
How can we use mathematical equations to model the slopes, heights, and pathways of ramps in a skate park?
How do parallel and perpendicular lines affect the design and flow of a skate park?
In what ways can we optimize the design of our skate park to accommodate diverse users and skill levels?

Standards & Learning Goals

Learning Goals

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

Apply slope-intercept, point-slope, and standard forms to design skate park ramps and pathways.
Incorporate safety and accessibility standards into the skate park design.
Use mathematical equations to model the slopes, heights, and pathways of ramps in a skate park.
Analyze the effect of parallel and perpendicular lines on the design and flow of a skate park.
Optimize the skate park design to accommodate diverse users and skill levels.

Common Core Standards

HSA.CED.A.2

Primary

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Reason: The project requires students to create equations to model the ramps and pathways of the skate park.

HSN.Q.A.1

Primary

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.Reason: Students will need to use units to define the dimensions and slopes of the ramps.

HSA.CED.A.3

Primary

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.Reason: Constraints such as safety and accessibility standards will be represented by equations or inequalities.

HSA.REI.D.10

Primary

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).Reason: Students will graph equations to visualize the ramps and pathways.

Unknown

GPE.5

Primary

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).Reason: The project involves designing parallel and perpendicular lines for the skate park.

Entry Events

Events that will be used to introduce the project to students

'Skate Park Crisis: The Case of the Unsafe Slopes!'

A local skate park is shut down due to safety concerns after a series of accidents. Students are hired as consultants to redesign the park, ensuring all ramps and pathways meet updated safety and accessibility standards, using their math skills to analyze and correct the dangerous slopes.

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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

Slope Exploration Station

Students investigate different slopes in real-world contexts, such as stairs, hills, and ramps, and then calculate and categorize them based on steepness and accessibility standards. They will also explore how slope is represented graphically and algebraically.

Steps

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

1. Measure the rise and run of various real-world examples of slopes (e.g., stairs, ramps, hills).

2. Calculate the slope of each example using the formula: slope = rise / run.

3. Categorize the slopes as steep, moderate, or gentle based on their numerical value.

4. Discuss the accessibility of each slope based on ADA (Americans with Disabilities Act) standards for ramps.

5. Represent the slopes graphically on a coordinate plane and algebraically using the slope-intercept form (y = mx + b).

Final Product

What students will submit as the final product of the activityA presentation or report summarizing their findings, including calculations, categorizations, graphical representations, and discussion of accessibility standards.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSN.Q.A.1 (using units to understand problems), HSA.REI.D.10 (graphing equations), and introduces slope-intercept form.

Activity 2

Ramp Design Challenge: Slope-Intercept Edition

Students will design a ramp using slope-intercept form to meet specific height and length requirements. They will create equations to represent their ramps and justify their design choices based on mathematical principles.

Steps

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

1. Define the desired height and horizontal length (run) for the ramp.

2. Calculate the required slope for the ramp based on the height and length requirements.

3. Write the equation of the ramp in slope-intercept form (y = mx + b), where m is the calculated slope and b is the starting height (y-intercept).

4. Graph the equation to visualize the ramp design.

5. Write a justification explaining how the equation meets the design requirements and mathematical principles.

Final Product

What students will submit as the final product of the activityA detailed ramp design plan including the slope-intercept equation, a graph of the ramp, and a written justification of the design.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSA.CED.A.2 (creating equations to represent relationships), HSA.REI.D.10 (graphing equations), and focuses on slope-intercept form.

Activity 3

Point-Slope Adjustment Lab

Students will learn to adjust a ramp design using point-slope form when given a fixed point and a desired slope. This activity emphasizes problem-solving and adapting designs to meet new constraints.

Steps

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

1. Start with an existing ramp design defined by two points on a coordinate plane.

2. Identify a fixed point on the ramp that must remain unchanged.

3. Determine a new desired slope for the ramp to meet specific safety or design criteria.

4. Use the point-slope form (y - y1 = m(x - x1)) to find the equation of the new ramp, using the fixed point (x1, y1) and the new slope m.

5. Graph both the original and adjusted ramp equations to compare the changes.

Final Product

What students will submit as the final product of the activityA report detailing the original ramp design, the adjusted ramp design (equation and graph), and an explanation of how the point-slope form was used to meet the new design constraints.

Alignment

Activity 4

Constraints and Pathways: Standard Form Challenges

Students will use standard form to define constraints for the skate park pathways and intersections. They will model pathways as linear equations in standard form and determine how these pathways intersect or remain parallel, ensuring smooth transitions and safe distances.

Steps

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

1. Represent different skate park pathways as linear equations in standard form (Ax + By = C).

2. Define constraints for the pathways, such as minimum distances between paths or maximum steepness.

3. Analyze the equations to determine the slopes and intercepts of the pathways.

4. Solve systems of equations to find the intersection points of pathways.

5. Adjust the equations to ensure pathways meet the defined constraints and provide smooth transitions.

Final Product

What students will submit as the final product of the activityA comprehensive plan of skate park pathways, represented by equations in standard form, with a detailed analysis of intersection points and adherence to design constraints.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSA.CED.A.3 (representing constraints by equations), HSA.REI.D.10 (graphing equations), and focuses on standard form.

Activity 5

Parallel and Perpendicular Park

Students design a section of the skate park using parallel and perpendicular lines to create specific features (e.g., parallel rails, perpendicular ramps). They must demonstrate an understanding of the relationships between the slopes of these lines and apply this knowledge to ensure their designs meet safety and aesthetic requirements.

Steps

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

1. Design a section of the skate park incorporating parallel and perpendicular lines for features like rails and ramps.

2. Determine the slopes of the parallel and perpendicular lines, ensuring they meet the required mathematical relationships (equal slopes for parallel lines, negative reciprocal slopes for perpendicular lines).

3. Write the equations for these lines in slope-intercept form or point-slope form.

4. Graph the lines to visualize the design and verify the parallel and perpendicular relationships.

5. Justify the design choices based on mathematical principles and aesthetic considerations.

Final Product

What students will submit as the final product of the activityA detailed design plan for a section of the skate park, including equations and graphs of parallel and perpendicular lines, and a written justification of the design choices.

Alignment

How this activity aligns with the learning objectives & standardsAligns with GPE.5 (parallel and perpendicular lines), HSA.CED.A.2 (creating equations), and HSA.REI.D.10 (graphing equations).

Activity 6

The Accessible Skate Park: Final Design and Presentation

Students synthesize all their learning to create a final skate park design that meets all safety and accessibility standards. They will present their design, explaining how they used equations and mathematical principles to address the driving question.

Steps

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

1. Combine all previous design elements (ramps, pathways, constraints, parallel and perpendicular lines) into a comprehensive skate park design.

2. Ensure the design meets all safety and accessibility standards, including ADA guidelines for ramps and pathways.

3. Create a detailed plan of the skate park, including equations, graphs, and dimensions of all features.

4. Prepare a presentation explaining the design choices and how mathematical principles were used to address the driving question.

5. Present the final design to the class, answering questions and justifying design decisions.

Final Product

What students will submit as the final product of the activityA comprehensive skate park design plan and presentation, demonstrating a clear understanding of mathematical principles and their application to real-world design problems.

Alignment

How this activity aligns with the learning objectives & standardsAligns with all standards (HSA.CED.A.2, HSN.Q.A.1, HSA.CED.A.3, HSA.REI.D.10, GPE.5) and learning goals, synthesizing all the skills and knowledge acquired throughout the project.

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Skate Park Design Project Rubric

Category 1

Mathematical Understanding and Application

Assessment of students' grasp of mathematical forms (slope-intercept, point-slope, and standard form) used in skate park design and their ability to apply these concepts.

Criterion 1

Slope-Intercept Form Application

Evaluation of students' ability to use slope-intercept form in ramp design calculations and representations.

Exemplary

4 Points

Demonstrates sophisticated understanding of slope-intercept form, applying it innovatively in ramp designs with thorough justification of design choices.

Proficient

3 Points

Demonstrates thorough understanding and correct application of slope-intercept form in ramp designs with clear justifications.

Developing

2 Points

Shows emerging understanding, with some errors in application of slope-intercept form in ramp designs and partial justifications.

Beginning

1 Points

Shows initial understanding with significant errors in application of slope-intercept form and insufficient justifications.

Criterion 2

Point-Slope Form Adjustment

Assessment of students' ability to adjust ramp designs using point-slope form, incorporating fixed points and desired slopes.

Exemplary

4 Points

Successfully adjusts ramp designs using point-slope form, demonstrating exceptional problem-solving skills with comprehensive explanations.

Proficient

3 Points

Accurately adjusts ramp designs using point-slope form with effective problem-solving and clear explanations.

Developing

2 Points

Applies point-slope form with some success in adjustments, but with missteps and limited explanations.

Beginning

1 Points

Struggles with adjusting designs using point-slope form, showing minimal problem-solving and explanations.

Criterion 3

Standard Form and Constraints

Evaluation of students' ability to define constraints and use standard form for pathways, ensuring safe and accessible designs.

Exemplary

4 Points

Demonstrates deep understanding of standard form and constraints, creating innovative solutions for pathways meeting all safety standards.

Proficient

3 Points

Shows solid understanding and application of standard form and constraints, ensuring pathways meet safety standards.

Developing

2 Points

Uses standard form with partial success, missing some constraints or designing pathways with minor safety oversights.

Beginning

1 Points

Limited ability to apply standard form and constraints, failing to ensure pathway safety.

Category 2

Design and Presentation

Assessment of students' ability to integrate mathematical concepts into a comprehensive skate park design and effectively communicate their ideas.

Criterion 1

Integration of Mathematical Concepts

Evaluation of how effectively students integrate mathematical equations and reasoning into their final skate park design.

Exemplary

4 Points

Seamlessly integrates mathematical concepts into design, showcasing exceptional critical thinking and innovative problem-solving.

Proficient

3 Points

Effectively integrates mathematical concepts into design, demonstrating thorough critical thinking and problem-solving.

Developing

2 Points

Integrates mathematical concepts with basic critical thinking, resulting in a design that fulfills some requirements.

Beginning

1 Points

Integrates mathematical concepts minimally, showing limited critical thinking and incomplete design implementation.

Criterion 2

Communication and Justification

Assessment of the ability to communicate design choices and mathematical principles effectively in presentations and reports.

Exemplary

4 Points

Presents design with clarity and depth, providing detailed justifications and engaging visual aids, demonstrating leadership in communication.

Proficient

3 Points

Communicates design effectively with clear explanations and adequate justifications, supported by visual aids.

Developing

2 Points

Presents design with basic clarity, but lacks depth in explanations and justifications; visual aids are underutilized.

Beginning

1 Points

Struggles to communicate design choices, providing minimal justifications with insufficient use of visual aids.

Reflection Prompts

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

Question 1

How did you incorporate the different forms of linear equations (slope-intercept, point-slope, standard) into your skate park design, and why did you choose each form for specific features?

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Question 2

In what ways did you ensure your skate park design meets safety and accessibility standards, and how did you use mathematical equations to model and adjust slopes and heights to comply with these standards?

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Question 3

How did you optimize your skate park design to accommodate diverse users and skill levels, and what mathematical considerations did you take into account to achieve this?

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Question 4

To what extent do you agree with the statement: 'Mathematical modeling is essential for creating functional and safe real-world designs'? (1-Strongly Disagree, 5-Strongly Agree)

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Question 5

Which aspect of the skate park design process did you find most challenging, and how did you overcome that challenge using mathematical concepts?

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Question 6

If you could redesign one aspect of your skate park based on what you've learned, what would it be and why?

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