Cafeteria Mayhem

By J.P. McCaskey High School, September 26, 2008

Grade Level

High School

Subject Area

Mathematics

Lesson Time

five fifty-minute class periods

Introduction

This lesson is designed to get students to really think about how volume and area have practical applications. The idea is to help the kids start to see the answer to the age old question: When am I going to use this in the real world? The lesson introduces the concepts of perimeter, volume, circumference, angles, area, and surface area in a way that gets the kids working hands on. The students must redesign the cafeteria in a way that allows the cafeteria to operate more smoothly and the student flow to be more efficient. The students must design a cafeteria which serves 450 students. The cafeteria must include seating for all students, lunch lines, an entrance, and an exit. All of these elements must be laid out in manner which promotes easy flow and minimizes congestion in the cafeteria. This assignment achieves the same end result as the more traditional worksheets but allows the students to see the practical application and hopefully have a little more fun while they are doing it.

National Standards

NM-GEO.9-12.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships NM-GEO.9-12.4: Use visualization, spatial reasoning, and geometric modeling to solve problems NM-MEA.9-12.1: Understand measurable attributes of objects and the units, systems, and processes of measurement NM-MEA.9-12.2: Apply appropriate techniques, tools, and formulas to determine measurements NM-DATA.9-12.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer. NM-DATA.9-12.3: Develop and evaluate inferences and predictions that are based on data NM-PROB.PK-12.1: Build new mathematical knowledge through problem solving; NM-PROB.PK-12.2: Solve problems that arise in mathematics and in other contexts; NM-PROB.PK-12.3: Apply and adapt a variety of appropriate strategies to solve problems;

Common Core State Standards:

Anchor Standards for Writing

Text Types and Purposes:

CCSS.ELA-LITERACY.CCRA.W.1 Write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and sufficient evidence.

CCSS.ELA-LITERACY.CCRA.W.2 Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.

CCSS.ELA-LITERACY.CCRA.W.3 Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details and well-structured event sequences.

Production and Distribution of Writing:

CCSS.ELA-LITERACY.CCRA.W.4Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

CCSS.ELA-LITERACY.CCRA.W.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.

Research to Build and Present Knowledge:

CCSS.ELA-LITERACY.CCRA.W.7 Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding of the subject under investigation.

Range of Writing:

CCSS.ELA-LITERACY.CCRA.W.10

Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.

Anchor standards for Speaking and Listening

Comprehension and Collaboration:

CCSS.ELA-LITERACY.CCRA.SL.1 Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others' ideas and expressing their own clearly and persuasively.

CCSS.ELA-LITERACY.CCRA.SL.2 Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

CCSS.ELA-LITERACY.CCRA.SL.4 Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

CCSS.ELA-LITERACY.CCRA.SL.6 Adapt speech to a variety of contexts and communicative tasks, demonstrating command of formal English when indicated or appropriate.

 Anchor standards for Language:

Conventions of Standard English:

CCSS.ELA-LITERACY.CCRA.L.1Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

CCSS.ELA-LITERACY.CCRA.L.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Knowledge of Language:

CCSS.ELA-LITERACY.CCRA.L.3 Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.

Vocabulary Acquisition and Use:

CCSS.ELA-LITERACY.CCRA.L.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing meaningful word parts, and consulting general and specialized reference materials, as appropriate.

CCSS.ELA-LITERACY.CCRA.L.5 Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

CCSS.ELA-LITERACY.CCRA.L.6 Acquire and use accurately a range of general academic and domain-specific words and phrases sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when encountering an unknown term important to comprehension or expression.

Objectives

Students will be able to formulate and solve problems of area, perimeter, circumference, and volume.
Students will be able to design a floor plan for a cafeteria which seats 450 students.

Materials

paper (for notes and design)
assorted shapes (paper) to represent tables and counters
poster board for blueprint

Vocabulary

surface area: the measure of how much exposed area an object has
measurement: the act or process of measuring; a figure, extent, or amount obtained by measuring
length: the longest dimension of an object
area: the surface included within a set of lines
perimeter: the boundary of a closed plane figure
volume: the amount of space occupied by a three-dimensional object
circumference: the perimeter of a circle
angle: the figure formed by two lines extending from the same point

Procedures

1. Introduce the actual cafeteria measurements to the students. Show the students the blue print as it currently exists. 2. Review the formulas for area, volume, circumference, perimeter, etc. 3. Explain that the purpose is that they must use the data given to identify a more practical and efficient floor plan for the current cafeteria. 4. Arrange students in groups of no more than four students. 5. Provide the students with the measurements and paper to begin designing. 6. Students analyze the efficiency of the current floor plan so that they can identify the problem. The students should then discuss the problem with the teacher in a mini conference. 7. Once the problem has been identified students work together to design a new layout. They should be exploring new shapes, sketching the shapes out, and trying to identify any problems before they arise. 8. Teacher pulls the students back together as a group once most students seem to have a new design idea. Teacher redirects students to think about the original problem and then explains that students must now actually implement their design using the poster board and blueprints. Students are only to be given one piece of poster board. 9. Students create design. 10. Students demonstrate design for the teacher. 11. Students write a one to two paragraph short essay which discusses the successes and failures of their own design. Students should address what they would have done differently in their new design.

Assessment

The success of the unit is going to be seen in the demonstration of the design and the short essay that the students must write in response to the design process. A design can fail but the student can still reflect learning and understanding of the process through the short essay.