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Deeper Learning Competencies
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Critical Thinking & Problem Solving
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- I can identify a possible paper pattern for covering a sphere and name some places where the design wastes paper, overlaps, or leaves gaps
- I can use simple observations from a first mock-up to say whether my idea might work better or worse than another shape’s net.
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- I can test a paper design on a sphere, measure or estimate surface area ideas from familiar shapes, and explain at least one change that could reduce waste or improve fit
- I can use what I notice about gaps, overlap, and bending to revise part of my plan.
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- I can compare two or more design options using measurements, surface-area reasoning, and evidence from repeated tests to justify which plan covers the sphere more efficiently
- I can explain how my revisions improved the model and how the shape relates to a matching map projection or other flat pattern.
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- I can independently design, test, and refine a sphere-covering paper model that uses the sheet efficiently with minimal waste, no overlap, and clear evidence-based reasoning
- I can defend my final choice by connecting geometric measurements, surface area, and map-projection distortion, showing how my solution responds to the problem and improves through critique and revision.
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Deeper Learning Competencies
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Effective Communication
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- I can share a basic update about my paper-sphere design, listen to my team’s ideas, and answer simple questions about what we tried and what we noticed
- I can use a few geometry words, measurements, or sketches to show my thinking, even if my explanation is still partial or needs support.
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- I can explain my design choices with some clear details, including how our paper shape uses surface area, where we saw gaps or overlaps, and one revision we made after testing
- I can speak and write so others can follow my reasoning, and I can connect my model to a matching map projection with some guidance.
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- I can present my final paper sphere cover clearly, using measurements, revision notes, and geometry vocabulary to explain how my team reduced waste and improved fit
- I can compare my model to a map projection, describe where flattening the sphere creates distortion, and respond to questions with relevant evidence.
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- I can communicate a well-organized, evidence-based explanation of how our one-piece paper design efficiently covers a sphere, why our revisions improved the result, and which map projection most closely matches our cut pattern
- I can adapt my presentation for the audience, use precise geometric reasoning and measurements, and thoughtfully respond to feedback and questions during the showcase.
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Deeper Learning Competencies
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Content Expertise
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- I can use given formulas and measurements to identify basic surface area parts of familiar solids and make a simple paper plan for covering a sphere
- I can name where my design fits, gaps, or overlaps, and I can share one fact about how my paper shape matches the sphere or map projection.
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- I can calculate and compare surface area for my paper design and use measurements from a test wrap to explain how much paper is used efficiently or wasted
- I can describe, with evidence, how my flat design changes when I revise it and how it begins to resemble a matching map projection.
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- I can independently apply surface area formulas and geometric properties to design, test, and revise a one-piece paper cover that uses paper efficiently with minimal gaps, overlap, and waste
- I can justify my choices with clear measurements and explain how my design compares to a map projection by pointing out specific distortions and shape changes.
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- I can strategically combine surface area reasoning, geometric modeling, and revision evidence to create and defend a highly efficient sphere-covering design that closely matches an appropriate map projection
- I can explain why my model works best, analyze distortion in precise mathematical language, and use my calculations and test results to support my conclusions with confidence.
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Deeper Learning Competencies
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Collaboration
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- I can participate in a team task by sharing ideas, listening to teammates, and helping build a first paper sphere-cover plan
- I can follow group roles or agreed steps and contribute at least one observation about what fits, overlaps, or wastes paper during our first test.
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- I can work with my team to revise our paper model after feedback by explaining what we noticed, suggesting changes, and helping compare options for reducing gaps, overlap, and waste
- I can take part in shared decisions and help record how our teamwork supported or slowed our progress.
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- I can collaborate with my team to test, measure, and improve a paper design using evidence from our trials and surface-area reasoning
- I can respectfully give and receive feedback, divide tasks fairly, and help my group make revisions that improve the fit of the sphere cover and our explanation of design choices.
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- I can lead and sustain collaborative design work by helping my team use evidence, geometry, and revision logs to create an efficient sphere-cover model and a clear display board
- I can build on teammates’ ideas, resolve problems productively, and help our group present a strong explanation of how our design choices and teamwork supported the final result.
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