Cardboard Mini Home Construction and Math Application
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Cardboard Mini Home Construction and Math Application

Grade 10Math10 days
The 'Cardboard Mini Home Construction and Math Application' project for 10th-grade math students involves creating an accurate scale model of a home using cardboard. Students apply geometric methods to accurately calculate volume and surface area, translating these measurements into estimations of real-world construction materials. Key activities include blueprint analysis, 3D model construction, and material estimation, all designed to connect theoretical math concepts with practical applications in architecture and construction.
Scale ModelMathematical ConceptsGeometryConstructionVolume and Surface AreaReal-World ApplicationArchitecture
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we apply mathematical concepts to create an accurate scale model of a home, and use it to determine the real-world materials needed for its construction?

Essential Questions

Supporting questions that break down major concepts.
  • How do scale models help in understanding and planning real-world constructions?
  • What mathematical concepts are necessary to accurately calculate volume and surface area?
  • How do we apply mathematical calculations to determine materials needed for construction projects?
  • In what ways does geometry influence the design and construction of buildings?
  • How can mathematical accuracy affect decision-making in real-world scenarios such as architecture and construction?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Students will apply geometric methods to design and construct a scale model of a mini home using cardboard, enhancing spatial reasoning and practical geometry skills.
  • Students will calculate the volume and surface area of the scale model accurately to determine the materials needed, illustrating the use of mathematics in solving real-world architectural problems.
  • Students will develop an understanding of how scale models function in the planning and execution of construction projects, bridging theoretical concepts with practical application.
  • Students will strengthen their ability to use geometric formulas to solve complex problems involving dimensions, volume, and surface area calculations.

Common Core Math Standards

HSG-MG.A.3
Primary
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).Reason: This standard aligns with the project's requirement to use geometric calculations (volume and surface area) to design and estimate materials for a mini-home model.
HSG-GMD.A.1
Primary
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.Reason: Students will need to understand and apply these formulas to calculate the volume and surface area necessary for determining building materials.
HSG-GMD.A.3
Primary
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.Reason: The project involves calculating the volume of various parts of the model home to estimate required materials.
HSG-GMD.B.4
Secondary
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.Reason: Understanding 3D objects and their 2D cross-sections will assist in visualizing and constructing the mini home model.

Entry Events

Events that will be used to introduce the project to students

Blueprint Analysis Challenge

Students are introduced to a set of diverse blueprints representing various mini home designs. Their task is to analyze these blueprints to identify potential materials required, calculate volume and surface area, and suggest enhancements based on mathematical calculations, fostering skills in architectural analysis and practical math application.
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Portfolio Activities

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.
Activity 1

3D Construction Exploration

Students translate their scaled blueprints into a 3D model using cardboard cutouts, fostering spatial reasoning and practical skills in construction.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Teach techniques for cutting precise measurements from cardboard, guided by the scale blueprint.
2. Assemble the cardboard pieces to construct the walls, roof, and other structures of the mini home.
3. Ensure each component aligns correctly, making adjustments as necessary to the assembled model.
4. Students present their finished 3D models to peers for feedback and refinement guidance.

Final Product

What students will submit as the final product of the activityA completed 3D cardboard scale model of the mini home based on individual blueprints.

Alignment

How this activity aligns with the learning objectives & standardsThis activity is aligned with standards HSG-MG.A.3 and HSG-GMD.B.4 as students apply geometric reasoning in constructing 3D shapes from 2D designs.
Activity 2

Mathematical Calculations Laboratory

Here, students calculate the volume and surface area of different sections of their cardboard mini home, preparing them for determining real-world needs like materials and energy efficiency.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Review necessary geometric formulas for calculating volume and surface area.
2. Apply these formulas to each section of the cardboard model.
3. Calculate total volume and surface area to use in estimating materials like shingles and drywall.
4. Discuss findings with peers and explore possible errors in calculation and assumptions.

Final Product

What students will submit as the final product of the activityA comprehensive calculation summary detailing volume and surface area for each segment of the mini home, justifying material estimates.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSG-GMD.A.1 and HSG-GMD.A.3, focusing on application of volume and area formulas to solve problems.
Activity 3

Material Estimation Strategy Session

Using the calculations from the previous activity, students will estimate the quantity of building materials needed for the mini home, including discussions on cost and sustainability.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Identify common materials needed for construction (e.g., shingles, drywall).
2. Using the surface area and volume data, determine quantities needed for each material type.
3. Research costs and sustainability factors for each material, incorporating environmental considerations.
4. Present a material requirement strategy with cost analysis to the class.

Final Product

What students will submit as the final product of the activityA detailed report or presentation that outlines material requirements, costs, and sustainability considerations for the mini home.

Alignment

How this activity aligns with the learning objectives & standardsThis step relates to HSG-MG.A.3, encouraging students to consider real-world constraints and design optimization in their planning.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Mathematical and Constructive Modeling Rubric

Category 1

Geometric Construction

Assessment of the students' ability to construct a scale model accurately using cardboard and blueprints.
Criterion 1

Construction Accuracy

Measures the precision in translating blueprints into a 3D model with accurate dimensions and alignment.

Exemplary
4 Points

The 3D model is constructed with perfect alignment and dimensional accuracy, exactly reflecting the blueprint and requiring no adjustments.

Proficient
3 Points

The 3D model is mostly accurate with minor alignment issues that do not significantly affect the model's integrity.

Developing
2 Points

The 3D model has noticeable alignment and dimensional inconsistencies but maintains overall structure.

Beginning
1 Points

The 3D model is poorly aligned with significant dimensional errors, failing to represent the blueprint effectively.

Criterion 2

Use of Construction Techniques

Evaluates the use of techniques for accurate measurement and assembly during model construction.

Exemplary
4 Points

Advanced techniques are employed, resulting in a flawless and precise model construction.

Proficient
3 Points

Adequate techniques are used with some room for refinement, resulting in a well-constructed model.

Developing
2 Points

Basic techniques are applied with noticeable errors affecting the construction quality.

Beginning
1 Points

Limited techniques applied, causing significant issues with model integrity.

Category 2

Mathematical Application

Evaluation of the application of geometric formulas and calculations used in the modeling project.
Criterion 1

Calculation Accuracy

Assesses the precision of calculations for volume and surface area as applied to the model construction.

Exemplary
4 Points

All calculations are accurate, well-documented, and applied correctly to determine material needs.

Proficient
3 Points

Most calculations are accurate and correctly documented, with minor errors that do not impact overall results.

Developing
2 Points

Several calculation errors exist, revealing gaps in understanding or application of formulas.

Beginning
1 Points

Calculations are mostly incorrect, lacking coherence and understanding of geometric principles.

Criterion 2

Justification of Calculations

Examines the students' ability to justify their calculations and reasoning in determining material quantities.

Exemplary
4 Points

Comprehensive and logical justification of calculations is provided, showing superior reasoning and understanding.

Proficient
3 Points

Reasonable justification is evident with minor gaps in logic, demonstrating good understanding and reasoning.

Developing
2 Points

Justification is limited and partially coherent, indicating areas for growth in reasoning skills.

Beginning
1 Points

Justifications lack clarity and logical structure, reflecting minimal reasoning.

Category 3

Real-World Integration

Assessment of students’ ability to correlate the model and calculations to real-world contexts and implications.
Criterion 1

Material Estimation and Analysis

Evaluates the students' capacity to estimate and analyze material needs, costs, and sustainability factors based on their calculations.

Exemplary
4 Points

Material estimates are precise, with comprehensive analysis of costs and sustainability thoroughly integrated into the report.

Proficient
3 Points

Material estimates are mostly accurate with good analysis but lack comprehensive integration of all factors.

Developing
2 Points

Material estimates show inaccuracies and limited analysis, with sustainability concerns minimally addressed.

Beginning
1 Points

Material estimates are significantly flawed, with little to no analysis of costs or sustainability considerations.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning
Question 1

How did creating a scale model of a mini home help you understand the application of mathematical concepts in real-world construction scenarios?

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Question 2

Reflect on the discussions with your peers during this project. How did peer feedback contribute to your learning and the final outcomes of your project?

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