How Do Architects Use Geometry in Design?

Group Members:

Jennifer Cray

Susanne Hansen

Thelma Herrera

Kirstie Mackay

Janie Martinez

Shara Turner

Background: 

As we look to the rebuilding of structures in storm ravaged areas of our world such as Haiti, China, and Somoa we begin to wonder how architects use math in their designs and build in an eco-friendly and economical way.  This 3^rd-4^th grade unit is centered around a culminating project requiring students to use their knowledge of geometry in an architectural design.  All content areas are integrated throughout a four week period as students explore the architectural designs of Frank Lloyd Wright, learn ways to use renewable building materials, study architecture throughout history and the impacts that climate and resources can have on architecture, and investigate geometry in the world around them. Throughout all lessons technology will be integrated to further enhance understanding.

Mini-lessons will guide students as they step into the shoes of an architect and produce their own design consisting of a floorplan using at least 5 polygons.  They will design with pattern blocks and virtual manipulatives, and will be required to determine the lines, angles, perimeter, area, and polygons within their design.  They will then create a 3-D digital image of their design using Google Sketchup.  Multiple assessments will be conducted throughout the unit in all areas and the culminating project will be evaluated with specific criteria.

Rationale: 

Our goal for this unit is for students to apply their understanding of the geometrical components needed in architectural design, being sure to utilize renewable building materials within their structure.

TEKS:

§111.15. Mathematics, Grade 3.

(8)  Geometry and spatial reasoning. The student uses formal geometric vocabulary. The student is expected to name, describe, and compare shapes and solids using formal geometric vocabulary.

(9)  Geometry and spatial reasoning. The student recognizes congruence and symmetry. The student is expected to:

(A)  identify congruent shapes;

(B)  create shapes with lines of symmetry using concrete models and technology; and

(C)  identify lines of symmetry in shapes.

(11)  Measurement. The student selects and uses appropriate units and procedures to measure length and area. The student is expected to:

(A)  estimate and measure lengths using standard units such as inch, foot, yard,

centimeter, decimeter, and meter;

(B)  use linear measure to find the perimeter of a shape; and

(C)  use concrete models of square units to determine the area of shapes.

§111.16. Mathematics, Grade 4.

(4.8) Geometry and spatial reasoning. The student identifies and describes attributes of geometric figures using formal geometric language.

The student is expected to:

(A) identify and describe right, acute, and obtuse angles;

(B) identify and describe parallel and intersecting (including perpendicular) lines using concrete objects and pictorial models; and

(C) use essential attributes to define two- and three-dimensional geometric figures.

(4.9) Geometry and spatial reasoning. The student connects transformations to congruence and symmetry. The student is expected to:

(A) demonstrate translations, reflections, and rotations using concrete models;

(B) use translations, reflections, and rotations to verify that two shapes are congruent; and

(C) use reflections to verify that a shape has symmetry.

(4.11) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass.  The student is expected to:

(A) estimate and use measurement tools to determine length (including perimeter), area, capacity and weight/mass using standard units SI (metric) and customary;

(B) perform simple conversions between different units of length, between different units of capacity, and between different units of weight within the customary measurement system;