Introduction |
| Anchor Video |
| Concept Map |
| Project Calendar |
| Lesson Plans |
Letter to Parents |
| Assessments |
| Resources |
Modifications |
| Grant |
The target audience of this Description is for any educator interested in helping students learn geometry in a hands-on manner. This includes all high school math teachers and those administrators who make decisions of mathematics curricula.
Project Description
When will we ever need to know this stuff? This is an all too familiar question found in mathematics classrooms here in Austin. Due to the continuous Olympic hype we decided to ask the students to design Olympic venues as if the next Olympics would be in here in Austin. The Olympics offers every student something that they can be interested in. The project itself has three main parts. In the first phase (week one) we engage the students. The second phase (approximately four weeks) of the project is the design of three Olympic structures: the Olympic village houses, an indoor swim facility, and the main Olympic stadium. Finally the students will be ready to begin with the construction portion of the project. All three parts come together in the end when the students give a presentation of their Olympic venue to a panel of architects. The students will benefit greatly because during the unit they apply and learn new geometric concepts such as surface area and volume in a real world context thus allowing them to become interested and engaged.
Driving Question
What is the best design for an Olympic venue?
Overall Goals of Project
We hope that students become engaged in mathematics through this Olympic venue design process. Students should also begin to see all of the mathematics that can be found in the real world. Students will gain communication skills by working in groups and presenting to a panel of professional architects.
Project Objectives
Students will be able to:
-use blueprints and find the total area of seating for a stadium (the area of a larger circle with a smaller circle of area taken out in the center.)
-use circumference and area to find the exact number of seats for any stadium within their project.
-determine whether a particular number of seats for a stadium is reasonable.
- create a blueprint of stadium.
- draw a similar figure of an object (especially a circle).
- determine the actual size of a building by looking at a blueprint.
- analyzes the relationship between three-dimensional objects and related two-dimensional representations and uses these representations to solve problems.
-relate volume to real world situations like cost effectiveness of air conditioning various Olympic structures.
-re-evaluate their own designs to see if they can still maintain factors such as building capacity while minimizing a/c cost.
- work basic trigonometric problems involving missing parts of right triangles. -use this knowledge to aid them in finding appropriate roof angles for the structures they will design in the future for the project
Rationale
From experience in the Austin area, my colleagues and I have found that students have a difficult time retaining knowledge they believe will not be used in their future; in particular connecting geometry to read world applications. We propose a project that will give students a reason to care about geometry. Not only is Geometry a requirement for graduation in Austin Independent School District, but on the 11th grade exit TAKS Test, a quarter of the questions ask cover geometry concepts. Giving the students a reason to care about geometry and connecting it to the real world, will enable them to retain the information and correctly answer the questions on the TAKS test. Not only will the project help the students pass the test, but they gain a respect for math and will possibly choose a math-related career. NCTM states that Òbecause students' interests and aspirations may change during and after high school, their mathematics education should guarantee access to a broad spectrum of career and educational options.Ó Do to the continuous Olympic hype we decided to ask the students to design Olympic venues as if the next Olympics would be in here in Austin. The Olympics offers every student something that they can be interested in. Whether it is the next Michael Johnson, Carly Patterson, or Michael Phelps, every student in your class can be interested in some sport or athlete in the Olympics. Students find geometry difficult to relate to because we often do not get to show off its useful features. Teaching the students the geometry concepts through a project like designing the future Olympic venue, will allow the students to see the real world applications and allow them a broader spectrum of career choices in mathematics.
Background
When will we ever need to know this stuff? This is an all too familiar question found in mathematics classrooms here in Austin. To address this problem, my colleagues and I have designed a project-based unit that bridges this gap between necessary geometric concepts and their real world applications. During this six week unit, the students will be designing several Olympic structures, constructing scale models, and fitting the structures onto a proposed Olympic venue site near their hometown. Designing the Olympic Stadium allows all students to be engaged since the Olympics are exciting to all, no matter age or gender. The project itself has three main parts. In the first phase (week one) we engage the students with an anchor video, investigate background information concerning Olympic structures, and divide students into groups as we familiarize them with the computer program Smart-Draw that they will be using in the coming weeks to assist in designing their structures. The second phase (approximately four weeks) of the project is the design of three Olympic structures: the Olympic village houses, an indoor swim facility, and the main Olympic stadium. Here the students will, first design the stadium layout using the computer program SimCity3000, then structure by structure, use Smart-Draw to complete the overall design and the creation of blueprints. During these lessons students are given real world constraints such as local building codes, material costs, and need for air conditioning efficiency and then encouraged to work around these predetermined constraints in a group setting. During this time they will be introduced to all of the ÒtoolsÓ necessary to complete the tasks. Trigonometry, surface area, volume, and perimeter are geometry concepts seamlessly integrated into this part of the project. By the time the final part of the project arrives, the students have already designed three main structures and will be ready to begin with the construction portion of the project. Here they will take their blueprints from Smart-Draw and cover yet another geometric concept of similarity as they construct their three main structures on a smaller scale. Over the next week they continue to scale down their designs and fit the three structures on their proposed site in a reasonable way. As the six weeks wind to a close the students are required to present their projects in a professional manner, leading us to the successful culmination of a project based unit that covered the necessary geometric concepts while engaging the students the whole way. One problem that we must over come is time limitations. However, if students are engaged they will be more willing to work on the project at home. Building an Olympic Stadium is attractive to all students; they will find it more exciting than working on a geometric proof, and therefore more willing to work outside the classroom.
Standards Addressed
TEKS addressed:
111.34.a.2-Geometric thinking and spatial reasoning. Spatial reasoning plays a critical role in geometry; shapes and figures provide powerful ways to represent mathematical situations and to express generalizations about space and spatial relationships. Students use geometric thinking to understand mathematical concepts and the relationships among them.
111.34.a.4-The relationship between geometry, other mathematics, and other disciplines. Geometry can be used to model and represent many mathematical and real-world situations. Students perceive the connection between geometry and the real and mathematical worlds and use geometric ideas, relationships, and properties to solve problems.
111.34.d.1-The student analyzes the relationship between three-dimensional objects and related two-dimensional representations and uses these representations to solve problems.
111.34.c.4The relationship between geometry, other mathematics, and other disciplines. Geometry can be used to model and represent many mathematical and real-world situations. Students perceive the connection between geometry and the real and mathematical worlds and use geometric ideas, relationships, and properties to solve problems.
111.34.f.2The student uses ratios to solve problems involving similar figures.
The student analyzes geometric relationships in order to make and verify conjectures. Following are performance descriptions. The student uses constructions to explore attributes of geometric figures and to make conjectures about geometric relationships. Dimensionality and the geometry of location: knowledge and skills and performance descriptions. The student analyzes the relationship between three-dimensional objects and related two-dimensional representations and uses these representations to solve problems.
(a) Basic understandings
(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling, and justification and proof.
(f) Similarity and the geometry of shape: knowledge and skills and performance descriptions. The student applies the concepts of similarity to justify properties of figures and solve problems. Following are performance descriptions.
(4) The student describes the effect on perimeter, area, and volume when length, width, or height of a three-dimensional solid is changed and applies this idea in solving problems.
(d) Dimensionality and the geometry of location: knowledge and skills and performance descriptions.
(1) The student analyzes the relationship between three-dimensional objects and related two-dimensional representations and uses these representations to solve problems. Following are performance descriptions.
(A) The student describes, and draws cross sections and other slices of three-dimensional objects.
(B) The student uses nets to represent and construct three-dimensional objects.
(C) The student uses top, front, side, and corner views of three-dimensional objects to create accurate and complete representations and solve problems.
¤111.35. Precalculus
(3) The student uses functions and their properties to model and solve real-life problems. The student is expected to:
(A) use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;
National Technology Standards addressed:
- Students demonstrate a sound understanding of the nature and operation of technology systems.
- Students are proficient in the use of technology.
- Students develop positive attitudes toward technology uses that support lifelong learning, collaboration, personal pursuits, and productivity.
- Students use technology tools to enhance learning, increase productivity, and promote creativity.
- Students use productivity tools to collaborate in constructing technology-enhanced models, prepare publications, and produce other creative works.
- Students use a variety of media and formats to communicate information and ideas effectively to multiple audiences.
- Students use technology resources for solving problems and making informed decisions.
- Students employ technology in the development of strategies for solving problems in the real world.
Formative and Summative Assessments
Throughout the six weeks students will be keeping a lab book or journal. In this book each student will keep record of decisions the group has made toward the final project. Each group will be making different decisions for their stadiums. It is important that the students keep track of all the decisions they make in one place. Also, each group will be designing blueprints for each stadium and the overall layout of the Olympic venue. These blueprints are working models for the entire six weeks. These blueprints will be checked periodically to make sure students are progressing both in a timely manner and in an appropriate content manner. For the final project assessment, the students will present their Olympic Venue model to a panel of architects. These presentations will require posters of different stadiums with blueprints and pictures as well as a portfolio detailing each stadium in the venue and a 3-D model of the main Olympic Stadium.