How Does Math Build a House?
by Jeannette Babiak, Lou Peterson,
Bill Schiesler
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Target Audience: 9th grade regular Geometry Project Description: How Math Builds a House is a project designed to give students autonomy in creativity while maintaining a structure that moves students to the goals of the project. The students will be introduced to the community via guest speakers and a field trip. Students will also be using architectural software to create their own designs. Problem solving will be strengthened, by having students make decisions about the project due to constraints imposed by the project. Students will have an increased sense of responsibility from being part of a group. Finally students will see math as something that is part of their everyday lives, rather than a school based experience only. Driving Question: How Does Math Build a House? Project Goals: The project will incorporate real world activities into the regular mathematics curriculum so that students are able to connect mathematical concepts to the real world they see around them. Students will develop technology skills by using various computer programs. Students will interact with computer leaders such as architects, who will show them that mathematics can be applied to the real world with real world job opportunities. Students will integrate multiple disciplines, such as math, science and art.
Project Objectives: Students will be able to:
Rationale: Students lack interest in learning mathematics because they don’t believe math affects them. Our project will show students how math is important in everyday life. Students will improve their interpersonal, mathematical and problem solving skills, while working in groups and with professional members of the community to learn “How math builds a house.” One of the primary needs for sustaining life is shelter. Everyone has a place they call home. Students will engage in discovering how math was used to build their home. They will calculate perimeter and area in order to find the amount of material needed for different aspects of construction (paint, flooring, etc). Students will find different volumes and surface areas to make decisions about materials, appliances fixtures and the basic design and how things will fit into designated spaces. Students will also engage in scaling and proportion while drawing their floor plan and building the model of their house. Students will interact with professionals from their community by inviting architects, contractors, and engineers to visit the classroom and share their expertise. This exposes students to different professions that use higher levels of mathematics that might encourage students to learn more. Students will also be involved in a daylong field trip in which they will visit and work on a local Habitat for Humanity site. This will give the students an opportunity to use the skills they have learned while also giving back to their community. This experience is a real world application that includes a chance to volunteer and learn about service. Through this project, students will develop an increased belief in their ability to do math, improve their proficiency with group interactions and communications skills. As students become more confident in their mathematical abilities, they may be more likely to be open to continuing their math education, which will benefit us all. Background: How Math Builds a House will introduce students to geometry by having students integrate volume, surface area, and the Pythagorean theorem. Surface area will be implemented when students will need to find areas needed for carpets walls and windows. Volume will be necessary when students must find the amount of paint needed to cover various surfaces and when students are choosing the kind of heating ant air conditioning equipment that they will need. The Pythagorean theorem will be needed as students are trying to find the dimensions of roof surfaces and types of triangular windows. Trigonometric identities ma be incorporated as well as circumference circular surface area for more complex creations. Other geometric ideas involving transformations will be needed in this project as well. Students will be learning how to do translations, rotations, and reflections. The students will be able to do these transformations by processes that function on the coordinate grid. The coordinate grid will transfer to the three dimensions of the house that the students are working on. Tessellations will also be introduced when students begin to decorate the interior of their houses. This will be in the form of tiling and wallpaper. Students will become proficient when dealing with proportions, through the use of a computer aided design program called Sketchup. This program will be used to create blueprints for their house and students will also become familiar with using a computer, for professional type of program. Students will also have to verify, using formulas, that thee dimensions of their physical constructions are proportional to their blueprints. Students will became familiar with using excel software as well, when examining project costs and maximizing their purchases. Standards addressed: TEKS: 7.08 (B) Make a net (two dimensional model) of the surface
area of a solid. 7.04.(B) Graph data to demonstrate relationships in
familiar concepts such as 7.09. The student is expected to estimate measurements and
solve NCTM: 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. Evaluation and Assessment Plan: Each student will have a project journal in which they keep most of their assignments. This will be kept in the room and checked at the end of each week for and assignment check. It will be turned in for a final grade at the end of the project. This will account for 25% of the project grade. Interest Checklist: Due on Day 1. At the beginning of the project "How
does math build a house?" I will pass out a list with the different
components we will be working on and the projects that each group will be
involved in. After each element I will have a checklist asking the students
about their interest, knowledge, and skill pertaining to each section. This
will give the students an overview of the project and help them to prepare
for the sections that they may have no knowledge or interest in and also make
them excited about the sections that they do. Project Prospectus: Due on Day 6. After each group is formed, they will be
given a several working days to decide which portion of the project they
would like to work on and then work as a group to come up with a project
prospectus, which will be an overview of their project and how they will
accomplish their goals. The Minute Paper: Due at the end of each Monday. All of the students are going to be working in different groups, each with their own set tasks. I think that having the students quickly reflect on how they have been working toward their goals is a good way to assess what they are getting from their project. It will highlight where there may be problems or which teams may need more responsibility or direction. Categorizing Grid: Due at the end
of week three and six. Students
will be given a list of the different component of their project and then a
list of the different mathematical skills that will be used to complete them.
They will then use a categorizing grid
to place each component with a corresponding math concept that they used
while working on it. This exercise will help me to assess whether or not the
students understand when to use math in their project. It will also remind
the students of all the different math skills they have been utilizing while
working on their houses. This will be
an on going grid that they keep in their project journal. There will be one grid check in the middle of the project and one at
the end when they turn their journal
in with their project. This will account
for 10% of the final project grade. One-page summaries: Due at the end of the speaker days. For my project "How does math build a house?" I plan to have local professionals come into the classroom and speak to the students about the areas of the project that they work on in their jobs. At the end of the discussions, I will have the students write a one page summary of Who the speaker is, What they do, For Who or What do they do this to, When, Where, How, and Why and then also how this pertains to math and the project. It will be very short but it will hopefully keep them paying attention and asking questions while our guests are visiting. What is the principal: At the beginning of each work day, we will take 5 minutes of quiet time while students write in their project journal. They will date their page and at the top write, what is the principal? They will then briefly describe their problem for the day and how they are going to go about solving it. What is their working strategy for the day? It can pertain to the project as a whole, their group dynamic or a math concept that they are unsure of. They can then evaluate at the end of the class day how well they met this goal when they are writing their process analysis. Evaluation Sheet: Due at the end of the second day. Near the beginning of the project I will pass out a list of the specific duties of each group and the different tasks that each group must complete. Each student must fill out and evaluation sheet on themselves that will relate their confidence level for each of the items. This will help me to assess if the students have anxiety or low confidence for any area of the project. As a class we can help each other through these areas by working slowly and more diligently to make sure that every student has confidence in the understanding of the project. This will also help students to voice to themselves any concerns that they may be having in their work. Work Evaluation: Two minutes at the
end of each workday. While working on "How does Math build a
house", each student will keep a log in which they write what they
worked on that day. They will describe how they are going about solving their
problems and assignments that are associated with their house. CADD blueprint of house: Preliminary due at the end of week 1, Revised due in week six before presentation. Students will be using a computer aided design (CADD) program to create a blueprint of their house, with appropriate labeling (lengths, areas, and units). After students have made adjustments to their house due to budgetary constraints, the students will create a revised CADD blueprint, which will be their final design. Fieldtrip reflection: Due at the end of week 4. The students will write a one-page reflection on their experiences during the field trip. Students will comment on what they found interesting, what they were surprised to find, and what aspects they liked and disliked about the fieldtrip. Final Evaluations: Students will be evaluated using the project Rubric. 70% of the grade will be based on completion of the project and 30% of the grade will be determined by the presentation of the project. Students will be able to choose from three final project (assessment) options. All options include these: 1) A summary of all areas of the home, materials and costs on Microsoft Excel. 2) A written report supporting the decisions made regarding the choices in the home. 3) A copy of the floor plan with appropriate areas. 4) Dependent on student choice of one of the following: a.) Student serves as the architect – Student creates a scaled version of house b.) Student serves as the real estate agent – Student creates a brochure of the house to use as a sales tool c.) Student
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