Target Audience

            The intended audience of this project is High School Geometry students. These students should already be familiar with the concepts of area, perimeter, volume, and surface area. Students will have a chance to revisit some basic types of angles such as supplementary, complimentary, acute, and obtuse angles. In this project students will construct new geometry and architecture knowledge upon their prior knowledge. It is recommended that these students also be in a position to learn a new technology such as software called CADD.

Project Description

In teams of three, students will design a building of their choice.  They will begin by researching the architecture of a culture of their interest using the Internet, architecture journals, and other available resources in the library. Students will identify the geometric contributions to their respective architectural genre. We will start the six-week project using an anchor video displaying the most renowned world architecture. A discussion regarding the different geometrical figures present in the video will follow. With this introductory knowledge, students will be introduced to definitions, theorems, and examples of different angles and triangles.  After this lesson, students will return to their research and see where these different types of angles occur.  As a result, they will begin to realize the importance of geometry in architecture as they continue exploring these designs.  After a short lesson on blueprints, students will begin to design their buildings.  They will meet with a local architect and, with a series questions and answers and suggestions, students will proceed to transfer their designs onto the computer through the use of CADD.  By putting their designs into a 3-D model, students will learn how to conceptualize and visualize 3-D shapes, which is paramount in understanding other concepts in mathematics and other disciplines such as physics or chemistry.  After completion and approval of their computer model designs, students will proceed to build a model of their building with foam board. Students will be compiling a portfolio of their project along the way, with all their research, designs, and analyses of the mathematical concepts they have learned. At the end of the project, they will be asked to present their final design to the rest of the class, discussing the geometric concepts they used, difficulties they encountered, and how they would go about this project if they had the opportunity to do it again.

Driving Question:

What role does Geometry play in Architecture?

Rationale

Low class attendance, discipline problems and lack of engagement have resulted in low student performance in AISD. NCTM recommends improving math instruction by using technology, more collaborative work, more emphasis on conceptual rather than procedural teaching, and more real-world based activities that serve as an anchor to studentsÕ overall understanding. Teachers rarely implement the NCTM recommendations because they are too busy drilling students for standardized testing. As a result, students will view mathematics as a disjointed set of procedures instead of meaningful and useful set of problem solving techniques. (Boaler, 1999)

            The goal of this project is to move students beyond procedural mathematics. In this project students will have the chance to practice architecture as professionals, by using technology such as CADD, Sketch Pad and simulations. Student will broaden their world-view on different architectures that include very different specific geometrical figures, such as triangles, arches spheres, circles and many others. They will also use context of architecture to explore angles, lines, and all the required geometry standards. Austin is a diverse urban district and therefore, it is important to find projects that appeal to everyone in the classroom. Here, students are free to explore any world architecture they choose and investigate it. This will allow students to connect math concepts to their direct personal interests. Through collaborative work, students will learn to listen to each other, respect each other, and eventually find out that a higher quality work can be achieved through teamwork. Research supports that giving students the opportunity to chose will yield a higher level of responsibility, a higher level of engagement, and consequently a more solid level of understanding of math concepts.

Evaluation Plan

Formative Assessment

       Students will be given a pre-test assessment, so we, as teachers are aware of the misconceptions students carry, as well as finding efficient pedagogical means to fix or completely eradicate those misconceptions. It is crucial that students build new knowledge on correct conceptions, so they have strong mathematical foundations. Students will be given periodic quizzes over relevant material encountered in both class discussions and benchmark lessons. They will also be asked to sign up for at least one conference a week with the teacher, so progress can be regularly monitored.  Students will turn in assignments throughout the project as benchmarks. Students will also be keeping a portfolio as they go. All work will be kept in it, and students will write short explanations about what they learned or found valuable on certain days. As a teacher, we would be able to keep track of progress, understanding, and interest, so improvements and modifications can be made for the following year.

Summative assessment

At the end of the project, for a final grade, students will turn in a written paper describing all the geometry concepts they used, and why did they use them in addition to their final portfolio. Moreover, they will be asked to present their final design to the rest of the class, discussing the geometry concepts they used, difficulties they encountered, and how they would go about this project if they had the opportunity to do it again. A post-assessment will be given to students, so we can evaluate the overall success of not only studentsÕ performance, but also our own performance. Few days after the post-assessment, we will use the empty outlines assessment technique, as well as the concept map technique to make students think about all concepts they learned during the six-week. Such techniques will give the students an opportunity to connect all the concepts they learned. It is important for students to not only connect different mathematics concepts, but also to get the big picture, which will solidify their understanding.

The overall project will be graded against the following rubric. Looking for any improvements in the standardized test scores at the end of the year can also be used in evaluating the success of this project.

Final Rubric:

Written Paper: 1- Turned in, but NOT complete

2- Completed but lacks many points, many grammar errors

3- Completed, has many good points, but a few grammar errors

4- Completed, all points covered, no grammar errors

Presentation: 1- Missing parts of project, didnÕt convey information well

2- Conveyed some main points, but missed a lot of them

3- Conveyed information effectively, but missed a few points

4- Conveyed all main points clearly and professionally.

Group participation: (group evaluations to be done partly by peers)

1-    Contributed very little to group,

2-    Contributed some to group

3-    Contributed his/her share to group

4-    Contributed more than expected to group

Individual Accountability:

1-    Turned in no assignments throughout project

2-    Turned in under half of the assignments

3-    Turned in over half of the assignments

4-    Turned in all of the assignments given during project

Rubric:

                                                                        FINAL GRADE: __________

Overall Goals

- To show students the importance of Geometry in the real world

- To demonstrate the connections between different aspects of Geometry

- To have students understand how to conceptualize objects in 3-D

- To introduce students to the concept of Design

- To inspire students to experience the fun in Mathematics

Project Objectives

- To have student complete a 3-D model of a geometric building

- To have students complete a project portfolio outlining the topics they found both

interesting and important throughout the project.

- For students to understand the design process of an Architect

- For students to enhance their collaborative skills by working together in groups

Content specific Background

As our contribution to the community, a web-based written report on the most significant challenges that were faced by both students and teachers, along with suggestions on how to improve this project will be provided to our fellow teachers that are planning to use this very project in the future. We will include in the written report, a step-by-step tutorial of CADD software, which will help students and teachers in learning how to use such software.

The project focuses on the math concepts that are introduced during the second six weeks in Austin ISD geometry classrooms. Specifically this project targets the many types of angles, triangles, and their properties. The students will be exploring different types of angles, such as complimentary, supplementary, vertical, alternate interior, corresponding, and linear pairs of angles. The combination of different type of angles may result in different shapes, such as rectangles, triangles, or even circles. Students will be trained to visualize and conceptualize all these different type of angles, to eventually use them in their final building model. Architecture visibly expresses the principles of harmony, order and similarity. Therefore, the activities will incorporate mathematical principles such as symmetry, similarity, Pythagorean theorem, congruence, ratio, proportion and measurement. These basic elements of geometry reinforce the concepts of order and continuity. To design or build a structure, we must use simple geometry. To create order or patterns we much use symmetry. The four basic forms of symmetry used in architecture to reinforce the concepts of grouping, order and patterning are translation, rotation, reflection glide reflection. These principles are demonstrated in various ways in architectural designs and buildings. Congruency is also a large part of our lesson, and is seen and applied everywhere in Architecture. Congruency can be used to compare shapes and understand how they are related. Another important aspect of the project is designing blue prints, which are one-dimensional viewings of an object, which students will learn to draw in order to enhance their understanding of 3-D figures.

TEKS addressed

7.08 (B) Make a net (two dimensional model) of the surface area of a solid.
7.08 (C) Using geometric concepts and properties to solve problems in
fields such as art and architecture.
7.04.(A) generate formulas involving conversions, perimeter, area,
circumference, volume, and scaling
7.04.(B) graph data to demonstrate relationships in familiar concepts such as
conversions, perimeter, area, circumference, volume, and scaling
7.06.(C) use properties to classify solids, including pyramids,
cones, prisms, and cylinders
7.08.(B) make a net (two-dimensional model) of the surface area of a solid
7.09. The student is expected to estimate measurements and solve
application problems involving length (including perimeter and
circumference), area, and volume

NCTM Standards.

3) Geometric figures and their properties. Geometry consists of the study of geometric figures of zero, one, two, and three dimensions and the relationships among them. Students study properties and relationships having to do with size, shape, location, direction, and orientation of these figures

2) The student analyzes geometric relationships in order to make and verify conjectures. Following are performance descriptions.

(A) The student uses constructions to explore attributes of geometric figures and to make conjectures about geometric relationships.

(B) The student makes and verifies conjectures about angles, lines, polygons, circles, and three-dimensional figures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

(3) The student understands the importance of logical reasoning, justification, and proof in mathematics. Following are performance descriptions

(B) The student constructs and justifies statements about geometric figures and their properties.

National Technology Standards

TF-III.A

Facilitate technology-enhanced experiences that address content standards and student technology standards. Candidates:

1.         Use methods and strategies for teaching concepts and skills that support integration of technology productivity tools (refer to NETS for Students).

4.      Use methods and strategies for teaching concepts and skills that support integration of problem solving/ decision-making tools (refer to NETS for Students).

TF-III.C

Apply technology to demonstrate students' higher order skills and creativity. Candidates:

1.         Use methods and facilitate strategies for teaching problem solving principles and skills using technology resources.

TF-III.D

Manage student learning activities in a technology-enhanced environment. Candidates:

1.         Use methods and classroom management strategies for teaching technology concepts and skills in individual, small group, classroom, and/or lab settings.