1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
5. Use appropriate tools strategically.
7. Look for and make use of structure.
Visualize relationships between two-dimensional and three dimensional objects
Identify the shapes of two-dimensional cross-sections of three dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Apply geometric concepts in modeling situations
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).
Common Core State Standards: ELA
Comprehension and Collaboration
Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9-10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively.
b. Work with peers to set rules for collegial discussions and decision-making
(e.g., informal consensus, taking votes on key issues, presentation of
alternate views), clear goals and deadlines, and individual roles as needed.
Arizona Educational Technology Standards (2009)
- Creativity and Innovation
- Concept 1: Knowledge and Ideas
- PO 1: Analyze, evaluate, and synthesize information to generate new ideas, processes, or products.
- Concept 4:
- PO 1: Create innovative products or projects using digital tools to express original ideas.
- Communication and Collaboration
- Concept 2: Digital Solutions
- PO 1: Communicate and collaborate for the purpose of producing original works or solving problems.
- Research and Information Literacy
- Concept 2: Processing
- PO 4: Synthesize research information to create new understanding and innovative solutions.
- Students will demonstrate geometric vocabulary required within real-life professions.
- Students will present and contrast group designs and interpretations of buildings with different purposes and within different geographical regions.
- Students will use the language of mathematics to explain which geometric two- and three-dimensional figures were used in the design and how they were used.
- Students will explain how the chosen shapes and design met the requirements of the “client.”
- Appropriate mathematics vocabulary relating to geometry.
- Knowledge of simple two- and three-dimensional figures and their properties.
- Have students view Math at Work: “John Paul Jones: Architect” segment at Discovery Education Streaming (or alternate video) and record (digitally or hard copy) key components required of an architect to complete a project.
- Introduce yourself as a prospective client interested in having an architect design a building based on specific requirements such as space constraints, its purpose, and the relationship to its environment, including other buildings. (Alternative: Enlist architects or architecture students from a local university to be the “prospective clients.”)
- You may invite a guest speaker with enough expertise to discuss the craft of architecture.
Present New Content
- In small groups, have students learn the basics of using Google SketchUp to design a three-dimensional representation of a building.
- Modification: Please note that you may use any building design software to complete the task.
Independent Learning Experience
- Divide students into collaborative groups to interview a prospective client (the teacher or someone of teacher’s designation) and discuss the ideas and constraints of the building’s design.
- Have students use Google Earth to determine a site for a building.
- Have students use SketchUp to complete an initial design of a building. Ensure that they observe aspects highlighted by architects in the video: collaboration, geometry in the design process, and the physical environment, such as the sun’s angle on the building’s face at different times of day. (Use the SketchUp shadow tool.)
- Have groups choose how they wish to share their project building with prospective client and other student groups.
- Presentation software such as Microsoft PowerPoint, Apple Keynote, Prezi, Google Presentations, or other presentation tool may be used to accompany building design.
- Students might also want to design a web page or wiki to accompany their proposal.
- Use Google SketchUp to present the MyBuilding.skp file of a three-dimensional representation of their project in relation to its environment.
- Students highlight geometrical features of the building, and how the client’s demands were accommodated.
- Use the language of mathematics to explain which geometric two- and three-dimensional figures were used in the design and how they were used.
Cross-Curricular Lesson Extension
- Add a social studies component by having groups research the effect of buildings in different types of locations and the purposes of zoning laws.
- In the role of prospective client, circulate around the room to provide ongoing feedback to
groups. Provide comments and guidance on next steps to each group.
- During collaborative planning, students should identify the three-dimensional geometric shapes considered and their properties. Groups should submit a final draft of the building,
demonstrating how they accommodated the client’s needs.
Alternate video: Ameller & Dubois : architects at work
- Demonstrate geometric vocabulary required within real-life professions.
- Create rubric for design and mathematical components of the standards and project. (May use Rubistar or another rubric tool to create.)
Discovery Channel School. Math at Work. 2006. Retrieved October 16, 2006, unitedstreaming.