How is "Math-Kitecture" mathematically sound?

New York City Department of Education Performance Standards Addressed (Middle School): M2a: Is familiar with assorted two- and three-dimensional objects (to recognize different shapes within the basic structures of architecture). M2c: Identifies three-dimensional shapes from two-dimensional perspectives, can draw two-dimensional sketches of three-dimensional objects (to recognize different shapes within the basic structures of architecture). M2d: Determines and understands length, area and volume (to measure length, area, and volume of classrooms and/or bedrooms, as well as floor plans/elevations of famous buildings). M2f: Analyzes and generalizes geometric patterns, such as tessellations (to recognize tessellations in architecture, as well as learn to create their own). M2j: Reasons proportionally with measurements to interpret maps and makes smaller and larger scale drawing (to convert the measurements from bedroom at home into a scale drawing). M6c: Estimates numerically and spatially (to estimate the length and area of classrooms and/or bedrooms). M6d: Measures length and area correctly (to draw a floor plan of classrooms). M6h: Uses pencil and paper, measuring devices, and computers to achieve solutions (to draft floor plans to scale).

Common Core State Standards: Geometry (Grade 7) Draw construct, and describe geometrical figures and describe the relationships between them. 1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

New York State Education Department Core Curriculum (Grades 7-8) Key Idea 4: Modeling/Multiple Representation 4A Visualize represent, and transform 2- and three-dimensional shapes 4B. Use maps and scale drawings to represent real objects or places 4I. Use appropriate tools to construct and verify geometric relationships 4J. Develop procedures for basic geometric constructions. Key Idea 5: Measurement 5A. Estimate make and use measurement in real world situations 5B. Select appropriate standard and non-standard measurement units and tools to measure to a desired degree of accuracy Key Idea 7: Patterns/Functions 7A. Recognize, describe, and generalize a wide variety of patterns 7G. Use properties of polygons to classify them. 7H. Explore relationships involving points, lines, angles, and planes